Publicly Available Report - Volant Products · Evaluation Protocol (TWCCEP) ISO Publicly Available...

Noetic Engineering 2008 Inc. 4120 – 56th Avenue NW Edmonton, AB T6B 3R8 Canada

Phone: 780.414.6241 Fax: 780.469.1250 Web: www.noetic.ca

Noetic.PubliclyAvailableReport.FEABenchmarkingGuidelines.Edition1.2019-06-19

Publicly Available Report

Date: 2019-06-19 E-mail Address

To:

Cc: Participants of Noetic TWCCEP Maintenance Multi-Client

Project (MCP)

From: Garret Meijer, Dan Dall’Acqua, Jarek Nowinka, Noetic Engineering 2008 Inc.

[email protected] [email protected]

[email protected]

File: 40.108.214 Pages: 91

Re: TWCCEP FEA Benchmarking Tool – Publicly Available Report Edition 1 -

2019-06-19

Urgent For review Original to follow by mail Please reply

Dear Recipient,

This Publicly Available Report Edition 1 of 2019-06-19 (PAR) contains guidelines for validating (benchmarking) finite-element analysis (FEA) conducted according to Thermal Well Casing Connection

Evaluation Protocol (TWCCEP) ISO Publicly Available Specification (PAS) 12835 Edition of 2013-12-15. This FEA validation methodology is referenced as TWCCEP FEA Benchmarking Tool. In a general sense,

the guidelines contained in this document are also referenced as FEA benchmarking guidelines (FEA

BGs).

The TWCCEP FEA Benchmarking Tool was originally developed in a multi-client project (MCP) on

TWCCEP Maintenance and Upgrades (TWCCEP Maintenance MCP) coordinated by Noetic Engineering 2008 Inc. (Noetic). The TWCCEP Maintenance MCP was funded by eight companies referenced as MCP

Participants: Cenovus, ConocoPhillips, Evraz, Nexen (subsequently CNOOC), Shell, Statoil (subsequently

Equinor), Suncor, and Tenaris. Following completion of the TWCCEP Maintenance MCP, the MCP

Participants agreed to make the TWCCEP FEA Benchmarking Tool publicly available.

This PAR is substantially based on the MCP final report that was provided to the MCP Participants, with modifications of the introductory sections resulting from the change of the document format from the

project final report to the publicly available report, and with (minor) modifications of some numerical

results based on modelling enhancements that became available after the MCP final report issuance.

The TWCCEP FEA Benchmarking Tool consists of two steps referenced as Step 1 and Step 2. Step 1

specifies analytical (qualitative) checks for pipe-connection modeling carried out in a TWCCEP-compliant analysis. Step 2 consists of quantitative comparisons of results for a generic premium connection with

pre-determined reference results. In general, a benchmarking process can consist of only Step 1 or both steps. Executing both steps is recommended as it is more technically rigorous and increases confidence

in the benchmarking outcomes.

Use of the TWCCEP FEA Benchmarking Tool requires familiarity with advanced numerical modelling techniques and post-yield material behaviour. Furthermore, the benchmarking techniques described

herein have specifically been created to provide a higher level of confidence in the FEA scope described in TWCCEP/ISO PAS 12835, and might not be appropriate for other connection FEA applications without

mailto:[email protected]



TWCCEP FEA Benchmarking Tool – Publicly Available Report Edition 1 – 2019-06-19

2 of 91

further consideration. Users of this document should thus exercise caution in applying this methodology

to other modelling scopes without further consideration of appropriate benchmarking components1.

The authors of this PAR and the MCP Participants will welcome feedback from all recipients of this PAR; and in particular, comments that will allow further improvement of the TWCCEP FEA Benchmarking

Tool. We will be glad to consider such feedback and might periodically issue enhanced versions of this

PAR with incremented edition numbers. Users of this PAR should contact Noetic to confirm they are

using the most current PAR edition.

If you have any questions or comments regarding this PAR, please contact Garret Meijer, Dan Dall’Acqua, or Jarek Nowinka via return email or by phone at the addresses and phone numbers provided

below.

Regards,

Garret Meijer, Ph.D., P.Eng. Dan Dall’Acqua, M.Sc., P.Eng. Jarek Nowinka, Ph.D., P.Eng. Lead Engineer General Manager Senior Consultant

+1.780.784.3523 +1.780.784.3505 +1.780.784.3522

[email protected] [email protected] [email protected]

1 Verification of FEA Used in OCTG Connection Evaluations. Meijer, G., Dall’Acqua, D., Nowinka, J.

SPE Thermal Well Integrity and Design Symposium 2017, 28-30 November 2017, Banff, Alberta. SPE-188158-MS




TWCCEP FEA Benchmarking Tool Prepared by Noetic Engineering 2008 Inc.

Publicly Available Report Edition 1

2019-06-19

ii

TWCCEP FEA Benchmarking Tool Prepared by Noetic Engineering 2008 Inc.

Publicly Available Report Edition 1

2019-06-19

Prepared by: Reviewed by:

Garret Meijer, Ph.D., P.Eng. Dan Dall’Acqua, M.Sc., P.Eng.

Lead Engineer Senior Consultant

Prepared under APEGA Permit Number P10167

iii

NOTICES

This Publicly Available Report Edition 1 of 2019-06-19 (PAR) is based on engineering work performed

in a multi-client project (MCP) on TWCCEP Maintenance and Upgrades (TWCCEP Maintenance MCP). The TWCCEP Maintenance MCP was coordinated by Noetic Engineering 2008 Inc. (Noetic) and executed

by Noetic and its subcontractor Marion Oilfield Engineering Inc. The TWCCEP Maintenance MCP was

funded by eight companies referenced as MCP Participants: Cenovus, ConocoPhillips, Evraz, Nexen

(subsequently CNOOC), Shell, Statoil (subsequently Equinor), Suncor, and Tenaris.

Copyright - Restriction on use and distribution

This Publicly Available Report Edition 1 of 2019-06-19 is available from Noetic upon request.

All analytical and experimental procedures and related “know-how” described or contained in this

document constitute a contribution from Noetic and the MCP Participants to recipients of this PAR.

Copyright in this PAR is owned by Noetic. Each recipient of this PAR is entitled to make copies of this

document for its own internal purposes, and to provide copies of this document in its entirety to other

parties with an acknowledgement of Noetic being the original document author.

Disclaimer

The TWCCEP FEA Benchmarking Tool has been developed to facilitate verification of connection modelling strategy and correctness of finite element analysis (FEA) performed in accordance with

Thermal Well Casing Connection Evaluation Protocol (TWCCEP). The TWCCEP FEA Benchmarking Tool is not intended to endorse or recommend any particular connection model, but rather to facilitate

assessment of compliance of a given model with TWCCEP modelling guidelines.

Nothing contained in this document is to be construed as granting any right, by implication or otherwise, to manufacture, sell, or use any method, apparatus, or product covered by patents or other forms of

intellectual property protection, or as indemnifying or protecting anyone against liability for infringement

of patents or other forms of intellectual property protection.

Users of the TWCCEP FEA Benchmarking Tool are responsible for making technical judgments on

suitability of benchmarked connection models and for determining applicability of results generated from their use. The TWCCEP FEA Benchmarking Tool might not address all potential issues related to

modelling connections for thermal well applications. Circumstances might negate the usefulness of the TWCCEP FEA Benchmarking Tool in specific instances. Users of the TWCCEP FEA Benchmarking Tool

are responsible to ensure compliance with any existing applicable regulatory requirements.

MCP Participants and Noetic make no representation or warranty with respect to the reliability, accuracy, fitness, validity, nature or content of the TWCCEP FEA Benchmarking Tool or the information contained

in the PAR. Under no circumstances shall MCP Participants or Noetic be liable to a PAR recipient for any loss, damages or expenses which the recipient may suffer, sustain, pay or incur by reason of any use

or reliance upon the TWCCEP FEA Benchmarking Tool or the information contained in the PAR.

Copyright © 2019 Noetic Engineering 2008 Inc. All rights reserved.

iv

Table of Contents

NOTICES ...................................................................................................................................... iii Copyright - Restriction on use and distribution ................................................................................ iii Disclaimer ..................................................................................................................................... iii Table of Contents .......................................................................................................................... iv Table of Figures ............................................................................................................................ vi List of Tables .................................................................................................................................. i 1 Introduction ............................................................................................................................ 2 2 Terms and definitions .............................................................................................................. 3 3 TWCCEP FEA Benchmarking Tool ............................................................................................. 4

3.1 Scope ............................................................................................................................... 4 3.2 TWCCEP FEA Benchmarking Tool Step 1 ............................................................................ 4 3.3 TWCCEP FEA Benchmarking Tool Step 2 ............................................................................ 4

4 Benchmarking guidelines use ................................................................................................... 4 4.1 Scope and documentation ................................................................................................. 4 4.2 Guideline use by an analyst ............................................................................................... 4 4.3 Guideline use by an operator ............................................................................................. 5

5 Step 1: Analytical checks .......................................................................................................... 5 5.1 Scope ............................................................................................................................... 5 5.2 Pipe and connection model considerations .......................................................................... 5

5.2.1 Review of connection geometry and tolerances ............................................................ 5 5.2.2 Geometry represented by axisymmetric model ............................................................. 5 5.2.3 Circumferential and axial symmetry conditions ............................................................. 6 5.2.4 Make-up procedure .................................................................................................... 6 5.2.5 Internal pressure application ....................................................................................... 7 5.2.6 Temperature application ............................................................................................. 7 5.2.7 Boundary conditions ................................................................................................... 7 5.2.8 Mesh ......................................................................................................................... 7 5.2.9 Material model ........................................................................................................... 8 5.2.10 Analysis parameters ................................................................................................... 9 5.2.11 Seal contact stress intensity ........................................................................................ 9 5.2.12 Maximum seal contact stress .................................................................................... 10 5.2.13 Maximum thread contact stress ................................................................................. 10 5.2.14 Effective high-stiffness and low-stiffness lengths ........................................................ 11

5.3 Pipe-body modeling checks ............................................................................................. 11 5.3.1 Scope ...................................................................................................................... 11 5.3.2 Pipe-body model ...................................................................................................... 12 5.3.3 Pipe-body parameters for comparison ....................................................................... 13 5.3.4 Isothermal uniaxial loading ....................................................................................... 14 5.3.5 Isothermal multiaxial loading .................................................................................... 17 5.3.6 Thermal loading ....................................................................................................... 27

5.4 Connection modeling checks ............................................................................................ 33 5.4.1 Scope ...................................................................................................................... 33 5.4.2 Model geometry checks ............................................................................................ 34 5.4.3 Thread backlash check ............................................................................................. 36 5.4.4 Contact force and displacement verification ............................................................... 41 5.4.5 Mesh density and contact surface resolution .............................................................. 46

6 Step 2: Quantitative comparison ............................................................................................. 50 6.1 Scope ............................................................................................................................. 50 6.2 Generic connection specifications ..................................................................................... 50

6.2.1 Generic connection geometry .................................................................................... 50 6.2.2 Mesh ....................................................................................................................... 51 6.2.3 Material properties ................................................................................................... 52

v

6.2.4 Load path ................................................................................................................ 52 6.2.5 Connection make-up ................................................................................................ 54

6.3 Make-up torque, seal contact stress intensity and equivalent high-stiffness length calculations 55

6.3.1 Make-up torque calculation ....................................................................................... 55 6.3.2 Seal intensity calculation ........................................................................................... 56 6.3.3 Equivalent low-stiffness length calculation ................................................................. 56

6.4 Generic Connection reference results ............................................................................... 57 Appendix A: Detailed description of benchmarking process......................................................... 63 Appendix B: Generic connection drawing ................................................................................... 74 Appendix C: Temperature-dependent material true stress-true strain curves ............................... 75 Appendix D: von Mises stress and accumulated effective plastic strain contour plots .................... 77

vi

Table of Figures

Figure 1. Comparison of connection model geometries on cutting planes at intervals of 90° around the

circumference. ........................................................................................................................ 6

Figure 2. Contact stress distribution and calculation of seal contact stress intensity. ......................... 10

Figure 3. 3D visualization of the 2-D mesh in an axisymmetric pipe body model. .............................. 13

Figure 4. Simple pipe model geometry for axisymmetric modeling. .................................................. 13

Figure 5. Material stress - strain curves at ASL temperatures. ......................................................... 14

Figure 6. Loads and boundary conditions for axisymmetric pipe-body model in isothermal uniaxial

loading case. ......................................................................................................................... 15

Figure 7. Load path for isothermal uniaxial loading case. ................................................................ 15

Figure 8. Pipe body FEA results obtained using isotropic hardening plasticity model compared to input

material stress strain curves. .................................................................................................. 17

Figure 9. Loads and boundary conditions for axisymmetric pipe-body model in isothermal multiaxial

loading case. ......................................................................................................................... 18

Figure 10. Load path for isothermal multiaxial loading case. ........................................................... 19

Figure 11. Axial constraint check P2.1 showing original (grey) and deformed (black) meshes.

Deformations are magnified. .................................................................................................. 20

Figure 12. Incorrect end constraints resulting in non-uniform radial displacements. Displacements are

magnified. ............................................................................................................................. 21

Figure 13. Example comparison of FEA (5°C material properties) and theoretical elastic axial reaction

force and radial displacement. ................................................................................................ 22

Figure 14. Reaction forces (over one radian of axisymmetric model) under uniaxial loading. ............. 23

Figure 15. Comparison of von Mises stress on the pipe ID from elastic theory and pipe-body FEA model

at 180C. ................................................................................................................................ 25

Figure 16. Post-yield material input and resultant stress-strain curves. ............................................ 26

Figure 17. Loads and boundary conditions for axisymmetric pipe-body model in thermal loading case.

............................................................................................................................................ 28

Figure 18. Load path for thermal loading case................................................................................ 28

Figure 19. Radial deformation consistency check using a radial strain band plot. Displacements are

magnified. ............................................................................................................................. 29

Figure 20. FEA-predicted total, mechanical and thermal strain. ....................................................... 31

Figure 21. FEA axial stress from axially constrained thermal cycle and analytical elastic prediction. ... 32

Figure 22. Initial heating response compared to temperature-dependent stress-strain curves. .......... 33

Figure 23. Change in stress distribution in models from different circumferential positions. ............... 35

Figure 24. Applied make-up and internal pressure and temperature cycle. ....................................... 37

Figure 25. Locations for backlash check (connection in made-up position). ...................................... 38

Figure 26. Axial location of matching points on pin and box load flank. ............................................ 39

Figure 27. Contact forces at matching points on pin and box load flank. .......................................... 39

Figure 28. Axial location of matching points on pin and box stab flank. ............................................ 40

vii

Figure 29. Contact forces at matching points on pin and box stab flank. .......................................... 40

Figure 30. Balanced contact forces in the seal and torque shoulder. ................................................ 41

Figure 31. Balanced contact forces in an incomplete thread. ........................................................... 42

Figure 32. Plastic deformation at shoulder at the end of thermal cycle. ............................................ 42

Figure 33. Correctly defined contact surfaces with radial contact biased to left thread. ..................... 43

Figure 34. Incorrectly specified contact surfaces resulting in no contact force and pin/box overlap at left

thread................................................................................................................................... 43

Figure 35. Schematic and nomenclature for Hertzian contact in a casing connection metal-to-metal seal.

............................................................................................................................................ 44

Figure 36. Example Hertzian contact stress distribution on curved seal contact surfaces of 72 mm and

292 mm diameter. ................................................................................................................. 46

Figure 37. Seal contact stress intensity mesh sensitivity check. ....................................................... 48

Figure 38. Maximum seal contact stress mesh sensitivity check. ...................................................... 49

Figure 39. Location of reference plane for connection dimensions and definition of make-up interference.

............................................................................................................................................ 51

Figure 40. Generic Connection load path........................................................................................ 53

Figure 41. Pressure application regions on pin and box seal regions. ............................................... 54

Figure 43. Stiffness length calculation procedure schematic and nomenclature................................. 57

Figure 44. Seal contact stress distributions during applied internal pressure and temperature loads. Pin

tip is towards the left. ............................................................................................................ 60

Figure 45. Seal contact stress intensity during thermal and pressure cycle. ...................................... 61

Figure 46. Shoulder axial force during temperature and pressure cycle. ........................................... 62

Figure 47. von Mises stress distributions upon completion of make-up............................................. 77

Figure 48. von Mises stress at elevated temperature. ..................................................................... 78

Figure 49. von Mises stress distribution at end of cycle. .................................................................. 79

Figure 50. Accumulated effective plastic strain after make-up. ........................................................ 80

Figure 51. Accumulated effective plastic strain at elevated temperature. ......................................... 81

Figure 52. Accumulated effective plastic strain at end of cycle. ....................................................... 82

List of Tables

Table 1. List of benchmarking pipe body checks. ............................................................................ 12

Table 2. Pipe body geometry. ....................................................................................................... 13

Table 3. Material properties assumed constant with temperature. ................................................... 14

Table 4. Example results from check P1.1 to verify true stresses and strains in pipe body obtained with

isotropic hardening plastic material. ........................................................................................ 17

Table 5. Pipe body multiaxial loading results. ................................................................................. 27

Table 6. Pipe body thermal cycle results. ....................................................................................... 33

Table 7. List of benchmarking connection checks. .......................................................................... 34

Table 8. Dimensions for nominal generic connection configuration and two geometry-tolerance

configurations. ...................................................................................................................... 51

Table 9. Material properties and modelling method used in the Generic Connection Model. ............... 52

Table 10. Applied load path. ......................................................................................................... 52

Table 11. Generic connection make-up specifications. .................................................................... 54

Table 12. Generic connection reference results. ............................................................................. 59

Table 13. Generic connection effective stiff length calculation. ........................................................ 59

2

1 Introduction The TWCCEP FEA Benchmarking Tool is a method for verification of connection modelling strategy and

correctness/accuracy of a TWCCEP-compliant finite element analysis (FEA). References to TWCCEP

tasks or clauses are per ISO PAS 12835:2013 (ISO 12835).

The TWCCEP FEA Benchmarking Tool focuses on axisymmetric analyses performed to select worst-case configurations of connection samples for full scale testing, in accordance with ISO 12835 Task 2.2

Specimen Configuration Analysis (Clause 12.3). The connection being evaluated is referenced as

Candidate Connection. The decision-instruction algorithm followed to perform the benchmarking is

referenced as the Benchmarking Process.

TWCCEP analyses can be performed by connection manufacturers, connection users or independent evaluators. The party that performs the analysis, or an independent party, might wish to verify the

connection modelling assumptions, method, and results, following the guidelines described in the

TWCCEP FEA Benchmarking Tool. Such verification of modelling assumptions and method might take

place prior to, in parallel with, or after the analysis being verified.

This Publicly Available Report Edition 1 of 2019-06-19 (PAR) describes the technical elements of the TWCCEP FEA Benchmarking Tool. Section 2 contains a list of terms and definitions. A general overview

of the two-step benchmarking process employed in the TWCCEP FEA Benchmarking Tool is given in Section 3. General guidelines for use of the TWCCEP FEA Benchmarking Tool are given in Section 4.

Specific guidelines for TWCCEP FEA Benchmarking Tool Step 1 are provided in Section 5, and for Step 2

in Section 6. Examples of flowcharts that can be followed in executing a benchmarking process according to the TWCCEP FEA Benchmarking Tool are described in Appendix A. Appendices B, C and D

provide technical data for completion of Step 2.

ISO 12835 specifies several analysis input values and output requirements, but leaves the details of the

modelling method to the analyst because those details depend on specific FEA software used for the

analysis. The guidelines contained in the TWCCEP FEA Benchmarking Tool are considered applicable to commercial FEA packages typically used for structural modelling. Use of the TWCCEP FEA Benchmarking

Tool requires familiarity with FEA principles and advanced modelling of thermo-mechanical behaviour of pipe-connection systems (e.g. post-yield material response, surface-to-surface contact, temperature

dependency, and others).

The benchmarking techniques described herein have specifically been created to provide a higher level

of confidence in the FEA scope described in ISO 12835, and might not be appropriate for other

connection FEA applications without further consideration. Users of this document should thus exercise caution in applying this methodology to other modelling scopes without further consideration of

appropriate benchmarking components.

TWCCEP FEA Benchmarking Tool – Publicly Available Report Edition 1 –2019-06-19

3

2 Terms and definitions The following definitions are adopted in this document:

ASL – TWCCEP application severity level

Benchmarked Candidate Connection Model – FEA model of the Candidate Connection after

completing the benchmarking process. The successfully benchmarked candidate connection model is

suitable for ISO 12835-Compliant FEA.

Benchmarking Analyst – party who executes a Benchmarking Process.

Benchmarking Process – decisions and instructions included in the TWCCEP FEA Benchmarking Tool

as described in Appendix A.

Benchmarking Step – level of complexity of the Benchmarking Process, either including only

qualitative checks or both qualitative and quantitative checks as defined in Section 1.

Candidate Connection – a connection product submitted for evaluation according to ISO 12835.

Candidate Connection Model – FEA model of the Candidate Connection that is the subject of the

benchmarking process (i.e., a “variable” model).

FEA – finite element analysis.

TWCCEP FEA Benchmarking Tool – a method for verification of connection modelling strategy and

correctness/accuracy of a TWCCEP-compliant FEA, as described in Section 1.

FEA Benchmarking Report - documentation of the Benchmarking Process, completed by the

Benchmarking Analyst.

Generic Connection Model – a connection model with “generic” geometry, i.e. not corresponding to a commercial product, prescribed in Step 2 and re-created by the Benchmarking Analyst for quantitative

comparisons with pre-determined reference results.

ID – pipe inner diameter.

ISO 12835 – the latest published edition of ISO 12835; i.e. ISO PAS 12835:2013 for PAR Edition 1.

ISO 12835-Compliant FEA – Connection FEA that meets all requirements and the level of rigour

specified in ISO 12835.

ISO 12835 FEA – a complete set of finite element analyses required by ISO 12835.

Nominal Reference Case – analysis case consistent with ISO 12835 Clause 12.3.3.

OD – pipe outer diameter.

PAR – Publicly Available Report.

Primary Seal – a metal-to-metal seal of a premium connection. The seal contact stress is typically in

a radial direction compared to the pipe axis.

Step 1 – Benchmarking Step in which only qualitative checks are performed.

Step 2 – Benchmarking Step in which both qualitative and quantitative checks are performed.

TWCCEP – Thermal Well Casing Connection Evaluation Protocol, published as ISO 12835.


4

3 TWCCEP FEA Benchmarking Tool 3.1 Scope

The TWCCEP FEA Benchmarking Tool consists of two parts:

1. Step 1. Analytical checks based on the comparison of numerical (FEA) results with analytical

expressions and force and displacement balances, and

2. Step 2. Quantitative check where results of analyses on a defined generic connection under

specified load is compared to precompiled connection results.

Step 1 and Step 2 of the TWCCEP FEA Benchmarking Tool are described in Sections 3.2 and 3.3,

respectively. The processes and task sequences in Step 1 and Step 2 are illustrated in Appendix A.

3.2 TWCCEP FEA Benchmarking Tool Step 1

Step 1 analytical checks are a compilation of simple analyses that one would complete to verify functionality and numerical accuracy of FEA software. Step 1 can also be used to ensure that model

loads, boundary conditions and material properties are properly applied. Step 1 checks can be completed when a connection model is built or on a previously completed connection model. Pipe-body checks can

be done using a separate pipe body model or within the pipe-body part of the connection model, but

proximity to the connection will influence the comparison between numerical and analytical results in the latter case. Individual Step 1 analytical checks generally evaluate a single item within the process

of building a connection model and simulating thermal service. The process for using Step 1 of the

TWCCEP FEA Benchmarking Tool is described in Appendix A.5.

3.3 TWCCEP FEA Benchmarking Tool Step 2

In contrast to Step 1, which is used to evaluate single components of an analysis, Step 2 quantitative check is a verification of the entire simulation process. If the results of simulation using the Generic

Connection Model agree, within an acceptable level of accuracy as jointly decided by the parties executing the TWCCEP analysis, with the results provided in the Step 2, then the connection model and

thermal service simulation are verified. If there is a disagreement then the source of difference must be found – for example, by using analytical checks provided in Step 1. The process for using Step 2 of the

TWCCEP FEA Benchmarking Tool is described in Appendix A.6.

4 Benchmarking guidelines use 4.1 Scope and documentation

The TWCCEP FEA Benchmarking Tool can be used by analysts designing and qualifying connections and

operators seeking detailed information on connection performance.

The employed benchmarking process and outcomes should be documented in a comprehensive report

(FEA Benchmarking Report), which can serve as a reference for the parties verifying the accuracy of

the performed analyses, and to facilitate future connection modelling.

4.2 Guideline use by an analyst

The TWCCEP FEA Benchmarking Tool has been developed to assist connection analysts troubleshoot

and verify their connection analyses. These guidelines are to be used in combination with the analyst’s

knowledge and experience to produce a connection model and load simulation suitable for TWCCEP connection qualification analyses. The described analysis checks can be implemented as a part of the

analysis process agreed to by the parties completing the TWCCEP qualification. A description of how these benchmarking guidelines can be implemented within the TWCCEP process is provided in

Appendix A.


5

4.3 Guideline use by an operator

An operator might use the TWCCEP FEA Benchmarking Tool as a resource for understanding how an

analyst may verify performance of a connection model. This should assist the operator in critically reviewing connection analyses processes performed in house or by third parties. The operator might

request that some, or all, of the checks be completed to provide high confidence in the analysis results.

An operator might request that a Step 2 comparison be completed to verify the applied connection

model construction and thermal loads simulation process.

5 Step 1: Analytical checks 5.1 Scope

Step 1 of the TWCCEP FEA Benchmarking Tool specifies analytical checks for pipe-connection modeling

carried out in compliance with ISO 12835. Applicable pipe-connection modelling techniques are described in Section 5.2. Specific pipe-body checks (labelled with a ‘P’), which are applied to verify

modeling assumptions independent from connection geometry, are described in Section 5.3. Connection checks (labelled with ‘C’), which verify connection-specific model inputs, are described in Section 5.4.

Guidance on the process for Step 1 execution is given in Appendix A.5.

Step 1 checks can be performed on the Candidate Connection Model, or a portion of that model appropriate for a given check (e.g., the pipe-body portion only), or a separate “working” model with all

relevant model parameters consistent with the Candidate Connection Model.

5.2 Pipe and connection model considerations

5.2.1 Review of connection geometry and tolerances

ISO 12835 requires an analysis of multiple connection geometries within manufacturing tolerances specified by the connection supplier (see Clause 12.3.4). As those dimensional tolerances might be

offset from, or non-symmetric about, the intended target value, ISO 12835 implies that a careful review

of the Candidate Connection geometry and all tolerance cases must be completed prior to the connection analyses. The connection supplier should be consulted if there is uncertainty regarding the connection

tolerances or nominal dimensions.

In some connection designs, combinations of tolerances for different dimensions are also specified,

leading to extra tolerance cases for consideration in an ISO 12835-Compliant FEA. An example of an

interdependent tolerance combination might be a specified allowable combination of thread interference and thread taper such that the thread profile does not deviate from its nominal position by more than

a set amount at any location along the thread length.

5.2.2 Geometry represented by axisymmetric model

ISO 12835 Task 2.2 Specimen Configuration Analysis (as defined in ISO 12835 Clause 10.1 Figure 6) is

most efficiently executed with an axisymmetric connection model. Only the axisymmetric model is

considered in this TWCCEP FEA Benchmarking Tool.

The axisymmetric model represents the thread geometry at a single location around the connection

circumference. Moving away from that circumferential position will move the thread profile up or down the thread taper relative to the fixed reference locations on the pin and box. This movement of the

threads is represented in Figure 1.

Changing the axisymmetric model to represent a different circumferential position may lead to modest

changes in contact stress distribution in the threads and at the seal, because of changes in thread

engagement and necessary changes in the finite element mesh. Therefore, the worst-case tolerance scenarios should be compared at the same circumferential position with the minimum required change

in finite element mesh.


6

Figure 1. Comparison of connection model geometries on cutting planes

at intervals of 90° around the circumference.

5.2.3 Circumferential and axial symmetry conditions

The pipe-connection model includes a section of the pipe-connection string from the centre of a pipe

joint to the centre of an adjacent coupling for a threaded and coupled connection (ISO 12835 Clause A.2.3). Modelling an integral connection requires a complete connection geometry, from the centre of

the pipe on one side of the connection to the pipe centre on the other side of the connection. The

cutting plane at the ends of a coupled connection model are planes of cyclic symmetry or periodicity,

which are assumed to be axially constrained but radially free during the applied thermal cycles.

5.2.4 Make-up procedure

Connection make-up is a crucial task in modelling a pipe-connection system because it simulates assembly of the connection pin and box components and resolves diametric interferences in the seal

and the threads and axial interference at the shoulder.

ISO 12835 requires connection make-up for all analyses in Task 2.2 (Clause 12.3). ISO 12835

Clause A.2.7 contains a general requirement for the numerical simulation of the make-up to be

reconciled with the supplier’s make-up procedures. The Benchmarking Analyst must select a method for make-up simulation, which will capture the physical behaviour of the connection during make-up and

generate numerical results representative of field make-up.

The method for modelling connection make-up should be agreed upon by the parties executing the

TWCCEP program, and reported as per ISO 12835 Appendix A.2.2, and documented in the FEA Benchmarking Report. The method should include reconciliation of make-up simulation with field make-

break data. While connection models shall be frictionless as per ISO 12835 (Clause A.2.3), friction

estimates can be used to calculate make-up torque from contact forces, as a post-processing calculation

to verify the make-up modelling accuracy.

A-A

B-B

C-C

D-D

Load Flank ofThird Pin Thread

Connection Section Views Connection End View

A

A

C

C

BB

D D


7

5.2.5 Internal pressure application

ISO 12835 specifies that internal pressure of magnitude equal to the steam saturation pressure at the upper-bound temperature be applied to the connection model (see Clause A.2.6). The Benchmarking

Analyst must select model surfaces to which the pressure must be applied.

Since the secondary seal at the pin-tip is disabled during full-scale testing, it is reasonable to apply

pressure on all surfaces “inside” the primary seal. In practice, the specific finite element model geometry (e.g., line or surface) to which the pressure is applied may lead to pressure application on a small region

“outside” the primary seal. This is not expected to be detrimental when the analysis results are used for

relative ranking. In cases where the seal contact patch is wide, variations in the pressure application area should be explored to determine if it is expected to change the results relevant for ISO 12835

Task 2.2.

5.2.6 Temperature application

ISO 12835 specifies (see Clause A.2.6) that temperature be applied as a body load to all components

(i.e., pipe body, pin and box). The lower-bound temperature is specified as 5°C for all ASL’s. The upper-

bound temperature results from the chosen ASL.

Finite element software typically requires specification of an initial body temperature. That initial

temperature must be set to the 5°C minimum cycle temperature to avoid erroneous additional thermal

strain in the first solution step.

5.2.7 Boundary conditions

Boundary conditions shall be applied in accordance with ISO 12835 Clause A.2.3. Axial constraint must be applied so that planes of symmetry remain plane but free to move radially. The make-up procedure

may include some axial movement of the pin and/or box. It is desirable that, during make-up, axial constraints are removed or specified to avoid introducing axial load in the pipe body during make-up.

Given that application of symmetry conditions is straightforward in commonly-used FEA packages, the

TWCCEP FEA Benchmarking Tool does not prescribe any additional guidelines for their application.

5.2.8 Mesh

ISO 12835 Task 2.2 requires accuracy and consistency in prediction of seal contact stress intensity (for

sealability) and contact stresses on the seal surfaces, in the threads, and at the torque shoulder and pin-tip (for galling), to enable comparison of results under various connection tolerances, material

strengths and make-up torques. Appropriate two-dimensional axisymmetric elements should be selected based on the recommendations of the FEA software being used. Considerations include element size

and shape, number of nodes representing the geometry, element formulation, and integration order.

Specification of these parameters should follow the software provider’s recommendations. The implication of these variables on simulation accuracy and performance is dependent on the element

formulations in the FEA software.

The mesh density should be chosen to provide an optimum balance between results accuracy and

numerical efficiency. A model with a mesh that is too coarse will not simulate local variations

(e.g., concentrations) of displacement or contact stress. A model with a very fine mesh will be computationally inefficient, and sometimes will also introduce convergence challenges. A standard

procedure for evaluating suitability of a finite element mesh is to monitor analysis output, i.e. a selected solution variable, as the mesh density is successively increased. When the output no longer changes

significantly with further mesh density increases, a satisfactory mesh density has been achieved. The

level of required mesh refinement will depend on the solution variable being monitored.

The implications of the selected element shape should be fully understood and the implications of

element choice must be understood within the context of the specific FEA software being used. Elements with extremely acute or obtuse corners should be avoided and changes in mesh density should occur

over reasonable length scales to avoid unacceptable element shapes. Regardless of the element shape

selected for the model, mesh sensitivity studies should be conducted to ensure results are accurate.


8

ISO 12835 Clause A.2.1 indicates that a large strain formulation is not required, although a large deformation formulation is recommended to model the effects of geometry change on applied loads. An

element type with large-strain formulation is not generally required unless large plastic strains in excess of the tensile uniform elongation limit are found within the connection model. Use of the large-

displacement formulation could change both the predicted behaviour of the structure and the reference

system compared to FEA completed using small displacements. When the large-displacement FEA formulation is used, the analyst should reconcile any differences between the FEA and analytical results

because the analytical methods are generally derived using a small-strain, small displacement basis.

Mixed-formulation (displacement/pressure) elements should be used to control undesirable element

deformations (e.g., hour-glassing), which can result with some element formulations in certain situations. Element integration order should be selected based on the analyst’s experience and the

advice of the finite element software vendor.

5.2.9 Material model

The material constitutive model must use temperature-dependent properties. The isotropic hardening elastic-plastic formulation is recommended in ISO 12835 Clause A.2.2. An alternative material

formulation may be used if material-specific information indicates that it is more suitable than the

isotropic hardening formulation.

Advanced material models, typically representing rate-dependent and/or cyclic material response, can be used in the connection analyses, but require appropriate calibration and performance verification.

Calibration of advanced models will typically require extensive material testing and data processing to

obtain adequate model input. It is important that the fundamental material model performance is verified under the loading modes found in the connection analyses. Material calibration and verification

efforts and results should be reported as per ISO 12835 Appendix A.2.2, and documented in the FEA

Benchmarking Report.

Material properties can have large impacts on modelling results such as stress and strain. Differences

in modelling results will relate to the number of temperatures at which material stress-strain curves are measured or estimated, bilinear versus multi-linear models, extrapolation of the input stress-strain data

beyond the ultimate tensile strength and material model formulation.

ISO 12835 Clause A.2.2 suggests using an elastic Poisson’s ratio of 0.3 unless otherwise justified, and

an elastic modulus consistent with results from ISO 12835 Task 2.1. Both elastic modulus and Poisson’s ratio will be dependent on the connection material and temperature. An estimate of temperature-

dependent elastic modulus should be available from required material characterization tests, but

measurement of Poisson’s ratio requires additional equipment and is not required by ISO 12835. Use of a Poisson’s ratio other than 0.3 based on connection material selection should be technically justified,

reported as per ISO 12835 Appendix A.2.2, and documented in the FEA Benchmarking Report.

Material stress-strain curves are to be measured from material characterization tests at multiple

temperatures over the ASL temperature range on a representative material sample (see ISO 12835

Clause 12.2). Connection analyses are to be performed based on materials having the specified minimum yield strength and the specified maximum yield strength (see ISO 12835 Clause 12.3.6). The

API yield point (stress at a specified extension under load) is used as a room-temperature basis to translate the measured temperature-dependent stress-strain curves to represent the minimum and

maximum allowable yield materials.

Care should be taken to ensure the appropriate stress-strain derivations, such as the differences between engineering and true stress and strain descriptions, are used for inputs to the FEA simulations.

Similarly, care should be taken when interpreting the stress and strain results from the simulations as

different programs may have different default outputs for true or engineering stress-strain units.


9

ISO 12835 Clause 12.2.2.2 suggests four alternatives for obtaining the coefficient of thermal expansion

(CTE) for the connection analyses:

1. Assume a 14×10-6 mm/mm/°C average CTE over the ASL temperature range;

2. Measure the average CTE over the ASL temperature range by testing;

3. Use existing representative data to determine the CTE;

4. Calculate CTE according to a temperature-dependent formula that is considered representative

over the temperature range corresponding to the selected ASL.

The CTE material property units must be consistent with the analysis geometry and temperature units.

A constant CTE over the ASL temperature range is acceptable. A temperature-dependent CTE is more

accurate and thus preferred when testing of temperature dependency is inexpensive to obtain. Temperature-dependent CTEs are often formulated based on a reference temperature. This reference

temperature must be consistent between formulation and input CTE data. Consult the FEA software

documentation for a description of CTE implementation and proper CTE data preparation.

5.2.10 Analysis parameters

The Benchmarking Analyst should carefully consider specifications for the following analysis parameters

to best balance the solution speed and accuracy, numerical convergence, and result review purposes.

• Solution time step – the magnitude of the time step is relevant when a rate-dependent material model is being used. The number of solution steps is critical to producing accurate results. For

nonlinear (e.g., elastic-plastic) analysis a sufficient number of solution steps must be used to adequately predict the nonlinear behaviour. The correct number of solution steps can be found

by doing comparative analyses, but for the pipe body checks using a very simple FEA model a

large number of solution steps can be used with little execution time penalty.

• Saving results – it is suggested that results for as many solution steps as is practical are saved

for evaluation and comparison to analytical predictions. Each set of saved results should include:

o Component and von Mises stresses

o Component strains, component plastic strains and accumulated equivalent plastic strain

o Thermal strains and total strains

o Displacements, reactions and contact forces

• Solution convergence criteria – convergence criteria should be based on the analyst’s experience and the recommendations of the FEA software being used. If needed, testing of solution

convergence and accuracy, consisting of multiple analyses, can be done to determine most

appropriate convergence criteria.

5.2.11 Seal contact stress intensity

The seal contact stress intensity is the primary variable for evaluating relative seal performance in ISO 12835 FEA. In ISO 12835, the seal contact stress intensity is the integral of the contact stress between

the pin and the box over the axial length of the primary seal region as expressed in Figure 2 and

Equation 1.


10

Figure 2. Contact stress distribution and calculation of seal contact stress intensity.

𝑆𝑒𝑎𝑙 𝐶𝑜𝑛𝑡𝑎𝑐𝑡 𝑆𝑡𝑟𝑒𝑠𝑠 𝐼𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦 = ∫ 𝜎𝑐(𝑙)𝑑𝑙𝑙1

𝑙0

Equation 1

Where 𝜎𝑐 is the contact stress as a function of distance, 𝑙, along the seal contact surface.

The intent of the seal contact stress intensity calculation is to characterize contact in the primary seal

and omit secondary contact between the pin tip and box shoulder that is not part of the intended seal. In practice, it is common to eliminate secondary contact near the pin tip from the calculation by specifying the integration limit, 𝑙0, at a location between the pin tip/shoulder and the primary seal. In

physical testing, the secondary seal at the pin tip is disabled by notching the pin tip prior to final

connection make-up.

Seal contact stress intensity calculated from contact stress (or contact force), is influenced by pressure

load acting on the seal surfaces and the length of the pressure application. The pressure acting within the seal region reduce contact stress intensity by pushing the pin and box surfaces apart; and the length

of pressure application will affect the seal activation by changing the balance of load acting on the outside and inside surfaces of the pin. It is understood that pressure will reduce from its full magnitude

to zero through the length of the seal, but proper characterization of the pressure distribution is challenging in many FEA packages. The result is that the calculated seal contact stress intensity must

be considered with respect to how and where pressure is applied within the seal region.

The method of seal contact stress calculation and its verification should be agreed upon by the parties

executing the ISO 12835 FEA and documented in the FEA Benchmarking Report.

5.2.12 Maximum seal contact stress

Accuracy of contact stresses calculated from seal contact forces can be sensitive to the connection geometry and the finite element mesh. For this reason, changes in maximum seal contact stress for

different mesh densities are a good indicator for necessary mesh refinement. Given that seal surfaces

are generally smooth and regular, the contact stress distribution will typically stabilize at a mesh density that is somewhat finer than the one in the bulk connection volume (i.e., mesh density far from contact

locations). Care must be taken in interpreting contact force/stress results as a “jagged” contact force distribution might be predicted by FEA depending on the contact algorithm and finite element mesh

even if the true distribution is smooth.

5.2.13 Maximum thread contact stress

Thread contact stress is geometry- and finite element mesh-dependent. In threads with small radii and

small contact zones, a high mesh density is needed to produce consistent contact stress results.

The thread contact stresses can be influenced by the selection of axisymmetric plane selected for the analysis model. Each position around the circumference of the connection will produce different model

geometry due to the helix of the threads. This change in the assumed axisymmetric geometry changes

l1 l0

σc(l)

Box

Pin

Metal to metal seal


11

the contact force distribution among the threads and hence the magnitude and location of the maximum

contact stress in the threads.

5.2.14 Effective high-stiffness and low-stiffness lengths

ISO 12835 Task 2.2.1 connection effective high- and low-stiffness lengths (see Clause B.1.3) are determined using the Nominal Reference connection geometry. These lengths are used for calculating

strain adjustments applied in the full-scale thermal cycle test. Modelling requirements to produce sufficiently accurate seal contact stress intensities and seal and thread contact stresses, described

above, are also considered sufficient for determining effective high and low stiffness lengths in

Task 2.2.1.

5.3 Pipe-body modeling checks

5.3.1 Scope

The pipe-body model checks verify modeling assumptions independent from connection geometry. Specific loading conditions are applied so that numerical (FEA) predictions can be compared to closed-

form analytical results.

The Benchmarking Analyst can perform these checks on a pipe-body model that is either the pipe-body portion of the Candidate Connection Model (i.e., excluding the connection part of that model), or a

separate pipe-body model. If a separate (simple) pipe-body is used, then it must have a material definition consistent with the Candidate Connection Model being benchmarked. In either case, the

Benchmarking Analyst must ensure that the Candidate Connection Model being benchmarked satisfies

all pipe-body model checks.

These pipe-body modeling checks can also be used to verify results in the pipe-body portion of the

connection model away from the connection. This can be done with the understanding that as the verification location approaches the connection, the results will be increasingly affected by the structure

of the connection.

Four different aspects of the model are checked using pipe-body cross-checks:

1. Material response,

2. Pressure load response,

3. Thermally-induced load response, and

4. Boundary condition application.

To confirm that the above four aspects of the model are being accurately captured by the benchmarked

FEA, the axisymmetric pipe model should be subjected to three different load cases:

1) Isothermal uniaxial loading,

2) Isothermal multiaxial loading, and

3) Thermal loading.

Sections 5.3.2 and 5.3.3 describe, respectively, the pipe-body model geometry and its parameters, to

be used for comparative checks. Sections 5.3.4 to 5.3.6 present the comparative checks for the three

load cases listed above. Each of those three sections includes the following:

- load path and boundary conditions for the load case,

- description of case-specific comparisons, and

- examples of results, for possible comparison with the pipe-body model being benchmarked.

The pipe body benchmarking checks are listed in Table 1. The list includes the aspects of the model

that are checked and the load case for which the check is done.


12

Table 1. List of benchmarking pipe body checks.

Check Page Subject Model Description

P1.1 16 Material response Isothermal

uniaxial load Material stress-strain curve check

P2.1 19 Boundary conditions

Isothermal multiaxial

load

Check axial displacements at pipe end

P2.2 20 Load response Radial displacement and axial force check

P2.3 22 Loads &

Boundary

conditions

Reaction force balance

P2.4 24 Material & Load

response Triaxial elastic stress-state check

P2.5 25 Material response Post-yield stress-strain check

P3.1 28 Boundary conditions

Thermal load

Check for axial displacements at constraints

P3.2 29 Load response Check radial displacement and hoop strain.

P3.3 29

Loads &

Boundary conditions

Reaction force balance

P3.4.1 29 Material response Axial mechanical strain check

P3.4.2 31 Load response Axial stress check

P3.4.3 32 Material response Check temperature-dependent material behaviour

5.3.2 Pipe-body model

The pipe-body model consists of a short pipe body segment. A visualization of how the two-dimensional

mesh is used in an axisymmetric model is given in Figure 3. The pipe-body model should be extracted from the Candidate Connection Model or set up as illustrated in Figure 4. The illustrated example uses

quadrilateral two-dimensional axisymmetric elements.

The pipe-body model geometry is defined by three parameters: Outer Diameter (“OD”), Inner Diameter (“ID”), and Length (“L”). The pipe material should be prescribed as defined in the connection analysis

per ISO 12835 Clause A.2.2.


13

Figure 3. 3D visualization of the 2-D mesh in an axisymmetric pipe body model.

Figure 4. Simple pipe model geometry for axisymmetric modeling.

5.3.3 Pipe-body parameters for comparison

For comparison and verification of loading, constraints, and multi-linear material characteristics, the

following model properties, and corresponding results, are provided. The pipe body geometry used in

Step 1 examples is given in Table 2, and the stress-strain characteristics and material properties in Figure 5 and Table 3. The stress-strain curves in Figure 5 are representative of an L80-grade material

(per ISO 11960/API 5CT).

Table 2. Pipe body geometry.

OD ID Wall Thickness Length

177 mm 161 mm 8 mm 500 mm

L

OD/2ID/2

Pipe Center Line


14

Figure 5. Material stress - strain curves at ASL temperatures.

Table 3. Material properties assumed constant with temperature.

Elastic Modulus Poisson’s Ratio Coefficient of Thermal Expansion

200 GPa 0.3 14×10-6 mm/mm/°C

5.3.4 Isothermal uniaxial loading

5.3.4.1 Boundary conditions and load path

The isothermal uniaxial loading case involves application of an axial displacement to one end of the pipe while the other end is axially constrained. Among other aspects of the model results, the stresses and

strains predicted by the pipe-body model should be checked to verify that they match closed-form analytical values. Figure 6 illustrates the application of loads and boundary conditions used in this

loading scenario, and Figure 7 illustrates the order of load application.

The surface(s) at one end of the pipe-body model should be axially constrained to zero displacement and free to displace radially. A uniform axial displacement is applied on surface(s) at the end of the pipe

model which is not axially constrained, but those surfaces are free to radially displace. The magnitude of the uniform axial displacement should be large enough so that there is some plastic strain in the pipe

when the displacement is fully applied. For example, the full axial displacement should be at least 0.5% (and 1.0% is used in subsequent examples) of the pipe length for OCTG materials commonly used for

thermal service (i.e., K55 and L80-Type 1 grades). This displacement is then fully reversed to check

functionality of the selected strain hardening formulation. A sufficient number of solution steps should be used during each phase of displacement loading to allow proper representation of the input stress-

strain curve and the results at each solution step used to plot the resultant stress-strain curve for

comparison to the input.

0

100

200

300

400

500

600

700

800

900

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

True

Stress

(MPa)

True Strain (mm/mm)

5 °C

180 °C

240 °C

290 °C

325 °C

350 °C


15

The isothermal uniaxial loading case is to be administered on the pipe-body model at the two extreme thermal-cycle temperatures (5°C and the maximum ASL temperature), to confirm the pipe-body model

behaviour is consistent with the material curve input at these two temperatures.

Figure 6. Loads and boundary conditions for axisymmetric pipe-body model in isothermal

uniaxial loading case.

Figure 7. Load path for isothermal uniaxial loading case.

5.3.4.2 Checks and balances

The following check (P1.1) is to be administered on the pipe-body model at two thermal-cycle extreme

temperatures (5°C and the maximum ASL temperature) to confirm the pipe-body model behaviour is

consistent with the material curve input.

Boundary Condition:

Zero Axial Displacement

Free Radial Displacement

Pipe Center Line

Boundary Condition:

Applied Axial Displacement


0 1 2 3 4 5

Applied

Strain

(mm/mm)

Solution Time Step

0

Max.

Min.


16

P1.1 Material stress-strain curve check

During the tensile loading, the axial stress-strain response from the pipe-body model should closely

follow the uniaxial material input curve. The material yield and strain hardening must be properly represented. After peak tensile loading (and the displacement reverses direction), the axial stress-strain

response of the pipe-body model should unload initially along the slope of the elastic modulus of the

uniaxial material input curve and then change as the material begins to deform plastically under

compression.

Method

The axial stress-strain response from the pipe-body model should be compared with the uniaxial input

material curve for the two thermal cycle temperature extremes in the selected ASL. Care should be taken to ensure that consistent units are being used for comparison (i.e., engineering or true stress-

strain values). This check ensures that the material model follows the input stress-strain curves properly

in a simple uniaxial loading case at two different temperatures.

Example result

The stress and strain distributions within the pipe body should be uniform along the length of the pipe body model. In addition to the axial strain, there will be circumferential (hoop) and radial strain due to

Poisson’s ratio. The results should be uniform throughout the model. If there is variation in stress and

strain distribution immediately adjacent to the constrained end or displaced ends of the pipe, the

application of the boundary conditions should be checked.

Figure 8 presents an example of a close match that should be obtained between the pipe-body material input curve and its true stress-strain response to isothermal uniaxial loading, with an isotropic material

model. This example was obtained for the pipe body geometry described in Sections 5.3.2 and 5.3.3 and the load path illustrated in Figure 7, at constant temperatures of 5°C and 350°C. Example stresses

and strains are listed in Table 4.

The close match between the pipe-body material input curve and the true stress-strain response

indicates that the material model has been correctly applied.


17

Figure 8. Pipe body FEA results obtained using isotropic hardening plasticity model

compared to input material stress strain curves.

Table 4. Example results from check P1.1 to verify true stresses and strains in pipe body

obtained with isotropic hardening plastic material.

5°C 350°C

Solution

Step

True Stress

(MPa)

True Strain

(mm/mm)

True Stress

(MPa)

True Strain

(mm/mm)

0 0 0 0 0

1 586.90 0.01 460.24 0.01

2 -589.79 0 -476.81 0

3 -613.29 -0.01 -495.72 -0.01

4 620.38 0 502.57 0

5 634.97 0.01 513.36 0.01

5.3.5 Isothermal multiaxial loading

The isothermal multiaxial loading case involves application of internal pressure and axial displacement

loads to the pipe. Among other aspects of the model results, the stresses and strains predicted by the

FEA model are checked to verify that they match closed-form analytical values.

5.3.5.1 Boundary conditions and load path

Figure 9 illustrates the application of loads and boundary conditions used in this loading scenario, and

Figure 10 illustrates the order of load application.

The surface(s) at one end of the pipe model should be axially constrained to zero displacement and free to move radially. A uniform radial pressure load is applied to the inner surface of the casing to simulate

-800

-600

-400

-200

0

200

400

600

800

-0.015 -0.010 -0.005 0.000 0.005 0.010 0.015

Stress

(MPa)

Strain (mm/mm)

5°C Output

5°C Input

350°C Output

350°C Input


18

internal pressure, followed by a uniform axial displacement on the surface(s) at the unconstrained end of the pipe model. The magnitude of the internal pressure applied should be such that the pipe body

remains entirely elastic after full pressure application. The magnitude of the uniform axial displacement load should be high enough so that when fully applied there is plastic strain in the pipe. For example –

for K55 and L80 materials, the full axial displacement should be at least 0.5% of the pipe length to

induce plastic deformation. The direction of displacement can be either tensile or compressive. In the presence of internal pressure, the direction of axial displacement will influence the displacement at

which yielding will initiate, but the elastic and post-yield checks described in this section are still valid.

Examples shown are for compressive displacement.

The isothermal multiaxial loading simulation should be completed at two thermal-cycle extreme temperatures (5°C and the maximum ASL temperature) to confirm the pipe-body model behaviour is

consistent with the material curve input.

Figure 9. Loads and boundary conditions for axisymmetric pipe-body model in isothermal

multiaxial loading case.

Applied Internal Pressure

Boundary Condition:



Pipe Center Line

Boundary Condition:

Applied Axial Displacement



19

Figure 10. Load path for isothermal multiaxial loading case.

5.3.5.2 Checks and Balances

P2.1 Axial displacements at constrained pipe end

The axial displacements at the constrained end of the model should be confirmed to be zero through

the entire loading path. If the axial displacements at the constrained end of the model are not zero through the entire loading path, then the application of the boundary condition in the pipe-body model

input should be re-visited.

Method

Small axial-displacement differences can be obtained from detailed nodal displacement results and

visualized with magnified mesh displacements, which is useful in demonstrating the function of axial constraints. Also confirm that the nodes on the axially displaced end of the model all equally translate

axially and the nodes on the fixed end do not move axially.

Example result

As an example, the light-grey image in Figure 11 is the original mesh, while the black image shows the

deformed pipe body with magnified deformations. The right side is constrained only axially, while the left side is axially displaced, and the model is free to expand radially. This check ensures that axial

boundary conditions (at the pipe ends) function correctly.

Axial

DisplacementPressure

Analysis Time Step

Internal Pressure

Axial Displacement

0 1 2


20

Figure 11. Axial constraint check P2.1 showing original (grey) and deformed (black)

meshes. Deformations are magnified.

P2.2 Radial displacement and axial force: solution time steps 0 to 1

This check ensures that the pipe is free to expand radially, and that internal pressure and axisymmetric

conditions are applied correctly. The radial displacements should be uniform along the length of the model through the entire loading path. The radial displacements and axial forces up to analysis time

step 1 should be reconciled with the analytical predictions for the given applied internal pressure load.

Method

Uniform radial displacements can be verified by reviewing the results in a band plot of radial

displacements, a band plot of radial strains, or by extracting nodal displacement results at various points along the model length. If there is a discrepancy in the radial displacements at a given radial position

along the length of the model or the axial load, it is possible that the boundary conditions are incorrect

or that the loads are not being applied correctly.

Example analytical calculations

Elastic radial deformation and axial force can be calculated by closed-form solution and should be compared with numerical results. The thick-wall pressure vessel (Lamé) calculation in Equation 2

predicts the elastic radial displacement at the ID of the pipe model when the pipe end axial displacements are specified to be zero (i.e., axially constrained) in analysis solution step 1 and a 1 MPa

internal pressure is applied. Since these calculations are only valid for elastic response, the stresses

state should be checked to ensure that it remains below the yield strength.

∆𝑟𝑑 =𝑑

2 ∙ 𝐸(𝐷2 − 𝑑2)[(1 − 𝑣 − 2 ∙ 𝑣2)(𝑃𝑖𝑑

2 − 𝑃𝑜𝐷2) + (1 + 𝑣)

𝑑2𝐷2

4 ∙ 𝑟2(𝑃𝑖 − 𝑃𝑜) −

𝜈𝐹

𝜋] Equation 2

where:

r = 80.5 mm, the radius at the pipe ID

d = 161 mm, the pipe ID,

D = 177 mm, the pipe OD,

Pi = 1 MPa, internal pressure,

Po = 0 MPa, external pressure,

F = 0 N, axial load at end of first time step,

E = 200,000 MPa, material elastic modulus, and

ν = 0.3, material Poisson’s ratio.

∆𝑟𝑑 =161

2 ∙ 200,000(1772 − 1612)

× [(1 − 0.3 − 2 ∙ 0.32)(1 ∙ 1612 − 0 ∙ 1772) + (1 + 0.3)1612 ∙ 1772

4 ∙ 80.52(1 − 0) −

0.3 ∙ 0

𝜋]

Pipe Centre Line


21

∆𝑟𝑑 = 4.034 × 10−3 mm

The total axial reaction force when 1 MPa internal pressure is applied and the pipe is axially constrained

is:

𝐹𝐴𝑥𝑖𝑎𝑙 =𝜋 ∙ 𝜈

2(𝑃𝑖 ∙ 𝑑

2 − 𝑃𝑜 ∙ 𝐷2) Equation 3

where all variables are previously defined.

𝐹𝐴𝑥𝑖𝑎𝑙 =𝜋

2∙ 0.3(1 ∙ 1612 − 0 ∙ 1772)

𝐹𝐴𝑥𝑖𝑎𝑙 = 12.215 kN

Note that the way axial forces are input and output for an axisymmetric model varies between FEA software. Some programs may report the total force on the whole pipe cross-section and other programs

may report the force over one radian of revolution. In the latter case, the total force is the output force

multiplied by 2π.

Example result

Figure 12 demonstrates a visual review of the radial displacements. In this case the radial displacement

is not uniform and there appears to be an error in the boundary conditions (radially constrained) on the

right side of the model.

Figure 12. Incorrect end constraints resulting in non-uniform radial displacements.

Displacements are magnified.

Subsequent example results in this section are for the correct boundary conditions.

The FEA radial displacement results on the inside of the pipe should be compared to the analytical result. Both methods predict a displacement of ∆𝑟 = 4.034x10-3 mm after 1 MPa internal pressure is

applied to the axially constrained pipe. Good agreement between the closed-form predictions and FEA results should be achieved as long as the material remains elastic. FEA pipe body check P2.2 was found

to produce the identical tensile axial reaction force. Example comparisons of FEA and analytical radial

displacement and axial force are shown in Figure 13.

Incorrect radial constraint


22

Figure 13. Example comparison of FEA (5°C material properties) and theoretical elastic

axial reaction force and radial displacement.

The radial displacement and reaction force are linear functions of internal pressure as long as the pipe material remains elastic. It is beneficial to check the stress state to ensure the von Mises stress has not

exceeded the temperature-dependent proportional limit specified for the material model. Linearity can

be verified by plotting the radial displacement and reaction force as a function of internal pressure.

P2.3 Force reaction balance for solution time steps 1 to 2

The sum of axial forces at each end of the model should be equal and opposite at each loading stage.

Method

To check this, the axial forces along each end of the model are summed independently and reviewed

for every step of the load path to confirm they are equal and opposite.

Example result:

A visual demonstration of this can be seen in Figure 14. The axial reaction forces at the ends of the pipes are equal and opposite. This should be checked at several analysis time steps. The reaction forces

should be zero at the beginning of the analysis (time step 0) and be equal, but in opposite directions,

for time steps 1 and 2.

0

0.002

0.004

0.006

0.008

0.01

0.012

0

2

4

6

8

10

12

14

0 0.2 0.4 0.6 0.8 1

Radial

Displacement

on ID(mm)

Axial

Reaction

Force(kN)

Internal Pressure (MPa)

FEA - Axial Reaction Force

Theory - Axial Reaction Force

FEA - Radial Displacement

Theory - Radial Displacement


23

Figure 14. Reaction forces (over one radian of axisymmetric model) under uniaxial

loading.


24

P2.4 Triaxial elastic stress-state check

The elastic stress-strain behaviour should be checked to confirm that the structural behaviour of the

pipe-body model under multi-axial loading is consistent with closed-form solutions. Agreement between the closed-form predictions of stress and FEA results in the elastic range should be very good. This

check ensures that the FEA correctly calculates stresses when compared to theory for a simplified

geometry.

Method

For this check, the axial, hoop, and radial stresses and strains at the OD and ID of the pipe, and the resultant von Mises (effective) stress, should be calculated analytically using appropriate formulae, such

as thin wall or thick wall (i.e., Lamé’s equations) pressure vessel relationships and Hooke’s Law. The analytical predictions should be compared with the numerical results up to the point at which yielding

occurs in the model.

Equations 4, 5, 6 and 7 are used to calculate the component stresses and the resultant von Mises stress.

Analytical elastic stress equations

Hoop Stress:

𝜎ℎ𝑜𝑜𝑝 = [(𝑃𝑖𝑑2 − 𝑃𝑜𝐷

2) +(𝑃𝑖 − 𝑃𝑜)𝑑

2𝐷2

4𝑟2] /(𝐷2 − 𝑑2)

Equation 4

Axial Stress:

𝜎𝑎𝑥𝑖𝑎𝑙 = 2 ∙ν (𝑃𝑖𝑑

2 − 𝑃𝑜𝐷2

𝐷2 − 𝑑2) + 휀𝑎𝑥𝑖𝑎𝑙 ∙ 𝐸

Equation 5

Radial Stress:

𝜎𝑟𝑎𝑑𝑖𝑎𝑙 = [(𝑃𝑖𝑑2 − 𝑃𝑜𝐷

2) −(𝑃𝑖 − 𝑃𝑜)𝑑

2𝐷2

4𝑟2] /(𝐷2 − 𝑑2)

Equation 6

Von Mises stress:

𝜎𝑒 = √(𝜎ℎ𝑜𝑜𝑝 − 𝜎𝑟𝑎𝑑𝑖𝑎𝑙)

2 + (𝜎𝑟𝑎𝑑𝑖𝑎𝑙 − 𝜎𝑎𝑥𝑖𝑎𝑙)2 + (𝜎𝑎𝑥𝑖𝑎𝑙 − 𝜎ℎ𝑜𝑜𝑝)

2

2

Equation 7

where all variables were defined previously and σhoop, σaxial and σradial are assumed to be the principal

stresses.

Example results

Figure 15 shows an example of a close match that should be obtained between the analytically-

calculated and FEA-determined von Mises (effective) stress when internal pressure is increased to 1 MPa

at solution time 1 while the axial strain is held at 0 and axial compressive strain is then increased to

0.02 mm/mm at solution time 2, using the 5°C material response curve shown in Figure 5.


25

Figure 15. Comparison of von Mises stress on the pipe ID from elastic theory and pipe-

body FEA model at 180C.

P2.5 Post-yield stress-strain check

The post-yield stress-strain response of the pipe-body model should be reconciled with the input material curve, to ensure that the model functions properly under multiaxial loading after yielding

occurs.

Method

For this check, the von Mises stress and equivalent plastic strain should be calculated based on the

model stress-strain results at the pipe OD and ID through the load path. The calculated von Mises stress and equivalent plastic strain values should be plotted and compared against the specified stress-strain

material curve (accounting for its temperature-dependency). The von Mises stress and equivalent plastic strain points will form a curve that closely overlaps the post-yield part of the material stress-strain curve

if the material response is being accurately captured in the pipe-body model. Care should be taken to

ensure that consistent units and stress-strain formulations are used for comparison (i.e., engineering or true stress-strain values). This check indicates correct implementation of loading, boundary conditions,

and material model under multi-axial loading.

0

100

200

300

400

500

600

700

0 0.5 1 1.5 2

von

Mises

Stress(MPa)

Solution Time Step

FEA

Elastic Theory

Internal Pressure Applied Axial Compression Applied

Yielding


26

Strain calculation

Equivalent plastic strain:

휀𝑒𝑞𝑣𝑝𝑙𝑎𝑠𝑡𝑖𝑐

=√2

3√(휀ℎ𝑜𝑜𝑝

𝑝𝑙𝑎𝑠𝑡𝑖𝑐− 휀𝑟𝑎𝑑𝑖𝑎𝑙

𝑝𝑙𝑎𝑠𝑡𝑖𝑐)2 + (휀𝑟𝑎𝑑𝑖𝑎𝑙

𝑝𝑙𝑎𝑠𝑡𝑖𝑐− 휀𝑎𝑥𝑖𝑎𝑙

𝑝𝑙𝑎𝑠𝑡𝑖𝑐)2 + (휀𝑎𝑥𝑖𝑎𝑙

𝑝𝑙𝑎𝑠𝑡𝑖𝑐− 휀ℎ𝑜𝑜𝑝

𝑝𝑙𝑎𝑠𝑡𝑖𝑐)2 Equation 8

where:

휀ℎ𝑜𝑜𝑝𝑝𝑙𝑎𝑠𝑡𝑖𝑐

is the hoop plastic strain in the pipe body under multiaxial loading, from

the FEA;

휀𝑟𝑎𝑑𝑖𝑎𝑙𝑝𝑙𝑎𝑠𝑡𝑖𝑐

is the radial plastic strain in the pipe body under multiaxial loading, from

the FEA; and

휀𝑎𝑥𝑖𝑎𝑙𝑝𝑙𝑎𝑠𝑡𝑖𝑐

is the axial plastic strain in the pipe body under multiaxial loading, from

the FEA;

This formulation assumes that the hoop, radial and axial directions correspond are the principal strain axes as is the case under the specified internal pressure and axial loading. All strain components must

correspond to the same radial location in the pipe wall. Unlike the von Mises stress that is valid for all stresses, the equivalent strain calculation in Equation 8 is valid for plastic strains only since the

formulation assumes conserved material volume, which is similar to assuming a Poisson’s ratio of 0.5.

The von Mises stress is calculated by Equation 7.

Example result

Figure 16 presents an example of a close match that should be obtained between the input material stress-strain curve (at a temperature of 5°C) and the von Mises stress-equivalent strain curve obtained

with the pipe-body model.

Figure 16. Post-yield material input and resultant stress-strain curves.

580

585

590

595

600

605

610

0 0.005 0.01 0.015 0.02

von

Mises

Stress(MPa)

Equivalent Plastic Strain (mm/mm)

Multiaxial FEA Results

Material Model Input


27

5.3.5.3 Example results for comparison

Table 5 provides examples of results obtained for a pipe-body model under isothermal multiaxial loading. The pipe-body model was defined with geometry and material inputs as described in

Sections 5.3.2 and 5.3.3 and subjected to loading illustrated in Figure 10 (with both displacement and

internal pressure applied).

Note that the magnitudes of the sequentially applied internal pressure and axial displacement may be

adjusted to suit the analyst, but for results similar to those shown in this section the pipe must remain elastic under full internal pressure and must become plastic during the subsequent application of axial

displacement.

Table 5. Pipe body multiaxial loading results.

Analysis

Temperature (°C)

Solution

Time Step

Applied Internal

Pressure

(MPa)

Applied Axial

Strain

(mm/mm)

von Mises

Stress

(MPa)

Equivalent Plastic

Strain

(mm/mm)

5

0 0 0 0 0

1 1.0 0 10.27 0

2 1.0 0.02 604.29 0.0170

350

0 0 0 0 0

1 16.5 0 169.42 0

2 16.5 0.02 488.97 0.0188

Note: Pressure and displacement loads, as functions of solution time, are shown in

Figure 10. Internal pressures are applied (1 MPa at 5°C and 16.5 MPa at 350°C) followed by 0.02 mm/mm axial strain.

5.3.6 Thermal loading

5.3.6.1 Load path and boundary conditions

The thermal loading case involves heating and subsequent cooling of a pipe axially constrained at both

ends to simulate constrained thermal expansion and contraction of a cemented casing string subjected to temperature variations. Boundary conditions, and the stresses and strains predicted by the FEA model

being benchmarked, are checked to verify that they match closed-form analytical values.

In this loading case, each end of the model should be axially constrained through the thickness of the pipe. The pipe’s initial temperature is 5°C, then it increases to the maximum ASL temperature, and then

it decreases back to 5°C. No internal pressure or other loads are applied in this case. Figure 17 illustrates the model geometry and loading scenario with boundary conditions, and Figure 18 illustrates the load

path.


28

Figure 17. Loads and boundary conditions for axisymmetric pipe-body model in thermal

loading case.

Figure 18. Load path for thermal loading case.

5.3.6.2 Checks and balances

The following five pipe-body model checks named P3.1 to P3.4 should be completed to ensure the

model behaviour is consistent with closed-form results.

P3.1 Axial displacements at constraints

The axial displacements at both ends of the model shall be confirmed to be zero through the entire

loading path. If the axial displacements at the ends of the model are not zero through the entire loading path, then the application of the boundary conditions should be re-visited in the FEA model input. This

is done following the method described in Check P2.1.

Boundary Condition:



Applied Temperature to Full Pipe Body

Pipe Center Line

Boundary Condition:



0 0.5 1 1.5 2

Temperature

(°C)

Solution Time Step

5°C

ASL


29

P3.2 Radial displacement and hoop strain consistency

The radial displacements at a given radial location should be uniform along the length of the model

through the entire loading path. If there is a discrepancy in the radial displacements along the length of the model, then it is possible that the boundary conditions are incorrect or that the loads are not

being applied correctly.

Method

Radial displacements and hoop strains are checked following the method described in Check P2.2.

Example result

Figure 19 shows a radial strain plot near the end of the load path application (i.e. at an elevated

temperature). The radial strain is uniform through the pipe, which means that the radial displacements are also uniform along the length of the pipe, and that boundary conditions affecting radial location are

applied correctly.

Figure 19. Radial deformation consistency check using a radial strain band plot.

Displacements are magnified.

P3.3 Force reaction balance

The sum of axial forces at each end of the model should be the equal and opposite at each stage during

the loading. Radial reactions should be zero on each end.

Method

To check this, the nodal axial reaction forces along each end of the model can be summed independently

and reviewed through the load path to confirm axial forces are equal and opposite and radial forces are

zero. This is done using the same method as Check P2.3.

P3.4 Material stress-strain checks

The stresses and strains in the model should be checked to confirm that the model results are consistent

with expectations from the FEA input. Three individual checks are recommended for this, as described

below. Check P3.4 ensures that the material model behaves correctly under thermal loading.

Check P3.4.1 Axial mechanical strain

Axial mechanical strain in the pipe-body model should be consistent with that expected for constrained thermal expansion and contraction through the loading path. This check ensures that the material

expands as analytically predicted under applied temperature, and ensures that the pipe-body model is

appropriately thermally constrained.

Method

FEA software typically reports the total strain and thermal strain where the thermal strain is calculated from the coefficient of thermal expansion and the temperature change. In this check of axial mechanical

strain, the total strain will be reported as zero and the mechanical strain is calculated by Equation 9. The axial mechanical strain is then compared with an analytical prediction based on the thermal

expansion coefficient and temperature change.

Pipe Centre Line


30

Strain calculations

The following equations describe the axial strain in the modeled scenario:

𝜺𝒕𝒐𝒕𝒂𝒍 = 𝜺𝒕𝒉 + 𝜺𝒎𝒆𝒄𝒉 = 0 Equation 9

where:

𝜺𝒕𝒐𝒕𝒂𝒍 is the total axial strain in the pipe (equal to 0 because the pipe ends are axially

constrained)

𝜺𝒕𝒉 is the thermal strain in the pipe (expansion or contraction)

𝜺𝒎𝒆𝒄𝒉 is the axial mechanical strain in the pipe.

From Equation 9 and knowing the total strain is zero, the mechanical strain must be equal and opposite

in sign to the thermal strain:

𝜺𝒎𝒆𝒄𝒉 = −𝜺𝒕𝒉 = −𝜶 ∙ ∆𝑻 Equation 10

where:

𝛼 is the coefficient of thermal expansion, and

∆𝑻 is the temperature change from the initial pipe temperature.

Example result

Figure 20 presents an example of a close match that should be obtained between the absolute value of

the mechanical strain from the pipe-body model and the analytically-predicted thermal strain. The FEA example used to demonstrate thermal loading checks below has a coefficient of thermal expansion of

14×10-6 mm/mm/°C, and a maximum temperature of 350°C. If a variable coefficient of thermal

expansion is used, Equation 10 must be adjusted accordingly.


31

Figure 20. FEA-predicted total, mechanical and thermal strain.

Check P3.4.2 Axial stress

Axial stress in the pipe-body model during elastic constrained thermal expansion should be predicted analytically and reconciled with the results from the FEA model. This check ensures that the material

model appropriately transitions from elastic to plastic behaviour (and back) under thermal loading.

Method

The calculated mechanical strain and Hooke’s Law can be employed to predict the elastic stress for a

given axial mechanical strain.

Example result

A comparison of the FEA-predicted axial stress to calculated elastic axial stress is shown in Figure 21, where negative stress is compressive and positive stress is tensile. The model results diverge from the

elastic prediction when yield occurs in the FEA model. The model is further affected by the temperature-dependent material properties used. When the FEA model is cooled, it elastically unloads along the

same slope as the elastic prediction as seen in Figure 21.

0

100

200

300

400

500

600

-0.006

-0.004

-0.002

0

0.002

0.004

0.006

0 0.5 1 1.5 2

Temperature

(°C)

True

Strain

(mm/mm)

Solution Time Step

Total Strain

Thermal Strain

Mechanical Strain

Temperature

εThermal = 0.00483 mm/mm

εMechanical= 0.00483 mm/mm


32

Figure 21. FEA axial stress from axially constrained thermal cycle and analytical elastic

prediction.

If the elastic modulus varies with temperature, the slopes in Figure 21 would no longer be constant,

and the equations used to predict stress from applied strains should be adjusted accordingly.

Check P3.4.3 Temperature-dependent stress-strain behaviour

The FEA-predicted axial stress-strain response during axially constrained thermal expansion can be reconciled with the temperature-dependent material stress-strain curves provided as FEA material model

input. The resultant stress-strain curve should intersect each of the material curves at the mechanical strain level associated with constrained thermal expansion for the corresponding temperature of the

material curve. The FEA stress-strain results should transition between material stress-strain curves according to the temperature during heating (moving from the 5°C curve, to the 180°C curve, to the

240°C curve, etc.).

Method

The FEA-predicted axial compressive stress during initial heating is plotted as a function of the thermally-

induced mechanical strain. In this case of uniaxial loading the axial stresses and strains can be used. Under multiaxial loading the von Mises effective stress and equivalent strain must be used. This check

is only valid for monotonic loading (i.e., no unloading or cyclic loading).

Example result

This comparison is shown in Figure 22, where the FEA results are shown as diamonds on a plot

comparing compressive stress and thermally-induced mechanical strain. The figure contains stress-strain curves representing the isothermal FEA input data and the resultant stress-strain behaviour under

constrained thermal expansion during heating. The upper horizontal axis shows the pipe-body temperature, which is proportional to strain in the thermal loading case with a constant coefficient of

thermal expansion. Under this monotonic thermally induced stress and strain, the pipe body stress-

strain curve should intersect each isothermal FEA input stress-strain curve at the mechanical strain corresponding to the applied temperature. Figure 22 shows a very good match between the

0

100

200

300

400

500

600

-1200

-900

-600

-300

0

300

600

0 0.5 1 1.5 2

Temperature

(°C)

True

Stress

(MPa)

Solution Time Step

Predicted Stress

Elastic Solution

Temperature

Yielding

Elastic Unloading


33

temperature-dependent material input stress-strain curves and results from initial heating of the

constrained pipe-body.

Figure 22. Initial heating response compared to temperature-dependent stress-strain

curves.

5.3.6.3 Example results for comparison

Numerical results for the FEA example (ASL = 350°C) used to demonstrate the thermal loading checks

are included in Table 6. The mechanical strains reported in Table 6 correspond to those shown in

Figure 20 and the axial stresses correspond to those shown in Figure 21.

Table 6. Pipe body thermal cycle results.

Solution Time Step

Temperature (°C)

Stress (MPa)

Mechanical

Strain (mm/mm)

Accumulated Effective

Plastic Strain (mm/mm)

0 5 0 0 0

1 350 -429.915 -0.004830 0.002680

2 5 536.085 0 0.002680

5.4 Connection modeling checks

5.4.1 Scope

The connection model checks verify that specific features of connection geometry, loading and contact

surfaces are simulated correctly.

The Benchmarking Analyst can perform these checks on either their Candidate Connection Model or the

Generic Connection Model (described in Section 6). In either case, the Benchmarking Analyst must

ensure that the model being benchmarked satisfies all connection model checks.

0

100

200

300

400

500

600

700

0 0.001 0.002 0.003 0.004 0.005

Compressive

True

Stress(MPa)

Compressive True Strain (mm/mm)

5°C

180 °C

240 °C

290 °C

325 °C

350 °C

MaterialStress-Strain

Curves

180°C 240°C 290°C 325°C 350°C

Axial stress in axially constrained pipeheated from 5°C to 350°C

(thermal strain vs. compressive stress)

5°C

Pipe Body Temperature


34

The connection checks focus on four aspects of the model:

1. Geometry,

2. Make-up,

3. Contact surface, and

4. Mesh density on contact surfaces.

All of these checks are performed on the subject connection model be that the Candidate Connection

Model or the Generic Connection Model.

The connection checks, and the page on which each is described, are listed in Table 7.

Table 7. List of benchmarking connection checks.

Check Page Subject Model Description

C1.1 34 Geometry

Generic

Connection

Model or

Candidate Connection

Model

Incorporation of geometric tolerances

C1.2 35 Helical thread geometry

C1.3 35 Make-up Make-up interference basis

C2.1 36

Contact surfaces

Thread backlash traversal

C3.1 41 Seal /shoulder contact force balance

C3.2 41 Thread contact force balance

C3.3 42 Contact resolution and structure overlap

C3.4 43 Seal contact width and contact stress

C.4.1 47

Mesh density

Seal contact surface mesh

C4.2 47 Thread contact surface mesh

C4.3 47 Pin-tip/shoulder contact surface mesh

5.4.2 Model geometry checks

The model geometry checks C1.1-C1.3 are intended to verify that significant characteristics in the connection design drawings and makeup specifications are properly represented by the finite element

model. The checks in this section are also intended to ensure that the applied boundary conditions correctly reflect geometric symmetries. Regardless of the strategy used to promote reliable contact

resolution and solution convergence, the individual geometries of the pin and box components must be consistent with the respective facets of the connection drawing, and their relative position must be

selected to result in appropriate axial and radial interferences and associated makeup torque.

C1.1 Incorporation of geometric tolerances

All dimensions and tolerances should be reviewed. If dimensions are unclear to the Benchmarking

Analyst, questions should be resolved with the connection supplier.

It is recommended that the Benchmarking Analyst assembles a table of geometries to evaluate the

effects of combined tolerance requirements on connection geometry. Each possible tolerance

combination becomes a case in the analysis matrix to evaluate key geometry features such as thread

and seal tapers and reference diameters.

The pin tip, box shoulder and seal surfaces, together with the thread dimensions (diameters and tapers) and contact points, should receive special attention as they are primary to connection performance. The

Benchmarking Analyst should compare the provided dimensions from the connection supplier to the

corresponding model features, and resolve any discrepancies found.


35

C1.2 Helical thread geometry treatment in axisymmetric model

The effects of axisymmetric cutting-plane selection and the resulting position of first thread and last

scratch on worst-case geometry selection should be reviewed by evaluating results of axisymmetric models produced from cutting the connection geometry model at various circumferential positions. To

illustrate the effect of circumferential position, consider that a rotation of 180°, or half of a full revolution,

advances the thread by half of the thread pitch. The change in the representation of the thread geometry also changes the incomplete thread geometry, thread contact stress for galling assessment, and load

distribution along the thread form.

Figure 23 demonstrates differences in von Mises effective stress plots from two connection geometry

models at taken at two different circumferential cutting positions of the example connection. While effective stresses near the seal remain nearly identical, the stress distribution in the threads changes.

Because results may vary with circumferential position, all ISO 12835 FEA cases should use the same

circumferential position, or thread advance.

Figure 23. Change in stress distribution in models from different circumferential positions.

C1.3 Connection make-up interference basis

The Benchmarking Analyst should confirm that initial interferences at pin tip, seal, and threads result in

the intended make-up torque for the model geometry and make-up torque combination, and that interferences are fully resolved with no overlapping contact geometry remaining by the end of make-

up.

For a given pin-box configuration and the relative position of the pin with respect to the box during the make-up process, the torque is estimated from resultant normal contact forces and applicable friction

factors, as explained in Section 6.3.1. This torque can be compared with the “target” torque, which the Benchmarking Analyst selects based on connection supplier specifications and an iterative process used

to adjust torque by changing the relative position of the pin. Iterations should be repeated until the

calculated numerical torque is within the required tolerance of the target torque. The required tolerance should be agreed upon by the parties executing the TWCCEP prior to performing the analyses, and

documented in the FEA Benchmarking Report. Linear interpolation can be used to refine selection of

the initial axial interference to arrive at the targeted make-up torque.

The starting value (first assumption) for the initial axial pin-box shoulder interference can be selected

based on connection torque-turns data.


36

5.4.3 Thread backlash check

Check C2.1 verifies that the relative pin-box axial movement in the threads is properly simulated under changing axial compression/tension during the connection’s heating and cooling in a thermal cycle.

Common buttress-style thread geometries will typically traverse connection backlash, if any exists in the thread profile design, during a thermal cycle. Some thread types, such as wedge threads, are designed

to minimize or eliminate thread backlash. A review of relative pin and box movements and thread flank movements should be completed to confirm backlash traverse behaviour is properly captured in the

analysis.

C2.1 Thread backlash traversal during thermal cycling

The Benchmarking Analyst shall confirm that the traverse of thread backlash in the FEA, if backlash

exists, occurs as expected for given operational conditions. In typical connections, this will occur as the

pin tip and/or torque shoulder yield during heating.

Thread backlash traversal can be verified by plotting contact forces and axial displacements versus

temperature through the thermal cycle for two pairs of nodes that contact each other. Those pairs of

nodes should be selected using engineering judgement, according to the following criteria:

• The first pair of nodes should consist of two neighbouring nodes on opposing pin and box load

flanks.

• The second pair of nodes should consist of two neighbouring nodes on opposing pin and box

stab flanks.

• The specific node pairs used should be located away from thread roots and corners.

When in contact, the contact surface stress distributions on the pin and the box should be equal in magnitude and opposite in direction to maintain force balance. Contact forces in a pair of nodes, one

on the pin and one on the box, will only be equal only if the nodes are directly in contact with each

other. Interpolation within the contact stress distribution can be used to estimate contact stress at

coincident points on the pin and box.

Thread contact during make-up and a thermal cycle usually follow the sequence:

1. As the connection is made up, and before radial clearance of the tapered thread is eliminated,

threads will be in contact on the stab flanks.

2. As the radial interference is introduced, the contact will transfer to the load flanks due to the

thread taper.

3. As the specimen is heated leading to axial compression in the connection, the thread contact

will move from the load flanks to the stabbing flanks.

4. As the specimen is cooled back down to the minimum temperature, the thread contact will

transfer back to the load flanks as tensile axial load builds.

The above steps are generally true along the length of threads, but not all threads will travel through

the backlash at the same time, due to compliance or yielding of the pin and box and thread geometry.

Axial displacement can also be used to confirm that backlash is properly simulated, especially if contact

does not transfer from one load flank to the other (i.e., the backlash is not fully traversed during the

thermal cycle).

Backlash behavior should be checked using contact forces and displacements for at least two different

axial positions, preferably on both stab and load flanks.

Demonstration

The load path shown in Figure 24 was applied to the connection model to simulate:

• make-up (solution times 0 to 2),


37

• application of internal pressure (solution times 2 to 3),

• connection heating (solution times 3 to 5),

• removal of internal pressure (solution times 5 to 6), and

• removal of elevated temperature (solution times 6 to 8).

The light red chart background region represents the period when the connection is at elevated temperature. This temperature scheme is used in subsequent charts showing how the threads travel

through their backlash during a thermal cycle.

To demonstrate how the threads travel through the backlash during a thermal cycle, the axial locations

and contact stresses on the pin and box stab and load flanks are compared. For this example, the points on the pin and box stab flanks have one radial position, and the points on the pin and box load flanks

have a different radial position. The connection schematic in Figure 25 shows the example point

locations.

Figure 24. Applied make-up and internal pressure and temperature cycle.


38

Figure 25. Locations for backlash check (connection in made-up position).

Figure 26 and Figure 27 show the axial location and contact forces, respectively for the pin and box

points on the load flank. When the pin and box are in contact the axial locations are equal and the contact forces are non-zero and of equal magnitude. These figures show that initially there is no contact

in the load flank (i.e., zero contact force), but that contact is made by the end of make-up. As the

connection is heated, load flank contact is quickly lost and not regained until near the end of cooling. Contact forces shown are not exactly equal and this is due to differences in the box and pin finite

element size and results interpolation.

Figure 28 and Figure 29 how the axial location and contact forces, respectively for the pin and box

points on the stab flank. Stab flank contact is not modelled during make-up, but then stabbing forces

are expected to be relatively small. The stab flanks contact when the connection is hot and the thermal

expansion of the long pipe body pushes the pin into the box.

LoadFlank

StabFlank

Box

8th Pin Thread


39

Figure 26. Axial location of matching points on pin and box load flank.

Figure 27. Contact forces at matching points on pin and box load flank.

-29.75

-29.7

-29.65

-29.6

-29.55

-29.5

-29.45

-29.4

-29.35

0 1 2 3 4 5 6 7 8

Axial

Location

(mm)

Solution Time Step

Pin

Box

Load Flank

During make-up prior to radial interference

0

5

10

15

20

25

30

35

40

0 1 2 3 4 5 6 7 8

Contact

Force

(kN)

Solution Time Step

Pin

Box

Load Flank

During make-up prior to radial interference


40

Figure 28. Axial location of matching points on pin and box stab flank.

Figure 29. Contact forces at matching points on pin and box stab flank.

-33.1

-33.05

-33

-32.95

-32.9

-32.85

0 1 2 3 4 5 6 7 8

Axial

Location

(mm)

Solution Time Step

Pin

Box

Stab Flank

0

2

4

6

8

10

12

14

16

18

0 1 2 3 4 5 6 7 8

Contact

Force

(kN)

Solution Time Step

Pin

Box

Stab Flank


41

5.4.4 Contact force and displacement verification

The procedures outlined in check C3.1-C3.3 are intended to check contact forces and displacements in the thread, seal and pin-tip/shoulder regions of the connection. The net sum of contact forces between

pin and box in the entire connection should be equal to zero at any point in the connection analysis, and pin and box surfaces should never overlap beyond the contact tolerance limit specified by the

analyst in the FEA software.

It is typically useful to separately consider axial and radial contact force components. Evaluation of the

separate components allows for understanding of the stress distributions in the pin and box that will be

useful for results interpretation.

C3.1 Radial and axial force balances at seal and pin-tip/shoulder region

The axial and radial forces at the seal and pin-tip/shoulder are summed separately, for the pin and box, at three simulation steps: after make-up, at peak ASL temperature, and at the end of the thermal cycle.

In each of those steps:

• Sum of axial contact forces on pin should be equal to sum of axial contact forces on box.

• Sum of radial contact forces on pin should be equal to sum of radial contact forces on box.

A demonstration of balanced forces can be visually seen in Figure 30, which shows shoulder and primary seal contact forces on both pin and box. The simulation step shown for Figure 30 is at peak ASL

conditions.

Figure 30. Balanced contact forces in the seal and torque shoulder.

C3.2 Radial and axial force balances in threads

The axial and radial forces at the contact surfaces in the pin and box threads should be summed

separately at three simulation steps: after make-up, at peak ASL temperature, and at the end of the

thermal cycle. In each of those steps:

• Sum of axial contact forces on pin should be equal to sum of axial contact forces on box.

• Sum of radial contact forces on pin should be equal to sum of radial contact forces on box.

An example of balanced forces in an individual thread can be seen in Figure 31 for one of the incomplete

threads. The simulation step shown for Figure 31 is after at peak ASL temperature. Force summations should be over the entire threaded region. If the contact forces on the pin and box do not balance, each

thread should be checked individually.


42

Figure 31. Balanced contact forces in an incomplete thread.

C3.3 Contact resolution and structure overlap

Overlap of pin and box contact surfaces shall be within the contact surface overlap tolerance specified for the FEA solver, and there should be no structural overlap between the pin and box in areas without

contact surface pairs, for example within the dope relief groove. Nodes on surfaces that are in contact

should show compatible deformation. Displaced node locations on pin and box contact surfaces should be checked for solutions at the completion of make-up and at multiple solution times during the thermal

cycle.

Demonstration

Figure 32 shows the outline of a deformed pin tip and box shoulder following make-up and a thermal cycle. Deformation on the surface of the shoulder is consistent with the deformed shape of the pin. The

pin tip and shoulder are separated because the connection is cooled and is now in tension, reflecting

traversal of thread backlash and tensile load carried by the load flanks.

Figure 32. Plastic deformation at shoulder at the end of thermal cycle.

Figure 33 and Figure 34 show the same set of threads with two different contact surface specifications:

• Figure 33 shows contact forces in a few of the threads with the contact surfaces correctly

located oriented and paired.

• Figure 34 shows what happens when the contact surfaces of a thread, identified by the label “Incorrectly specified contact forces”, do not interact; there are no contact forces in that area,

and structural overlap occurs after make-up. Additionally, forces to the right of the figure (away from the faulty contact surfaces) are significantly changed, as seen on the right side of the

figure.


43

Figure 33. Correctly defined contact surfaces with radial contact biased to left thread.

Figure 34. Incorrectly specified contact surfaces resulting in no contact force and pin/box

overlap at left thread.

C3.4 Seal contact width and contact stress verification

While it can be difficult to confirm the numerical results of contact analysis in FEA, Hertzian contact

calculations can sometimes be effectively used to estimate the contact stress distribution in the metal-

to-metal seal, provided the geometry is favourable and the stresses remain in the elastic range.

5.4.4.1 Method

Total contact force, contact stress magnitude and contact patch width at connection FEA solution times when the contact is elastic can be compared to analytical Hertzian contact calculations. In most cases,

the total contact force from the FEA results will be used as input to the Hertzian contact calculations

and the resulting calculated contact stress and contact patch width will be compared to FEA results.

5.4.4.2 Contact width and stress calculation

Primary assumptions in the use of the following Hertzian contact calculations are:

• The stress state is elastic, and

• The connection diameter is sufficiently large that axisymmetric seal contact can be represented

by contact between two infinitely long cylinders (for approximating two curved seal surfaces in

contact) or a cylinder and a plane (for approximating a conical seal surface in contact with a

curved seal surface).


44

Figure 35 shows a schematic of two cylinders in contact and the nomenclature used in Equation 11 to

Equation 12 for calculating maximum contact stress and contact width.

Figure 35. Schematic and nomenclature for Hertzian contact in a casing connection metal-

to-metal seal.

The contact width is calculated by Equation 112

𝑏 = 2√2

𝜋𝐹𝐶𝑜𝑛𝑡𝑎𝑐𝑡 ∙ 𝐾𝐷 ∙ 𝐶𝐸 Equation 11

where:

𝐹𝑐𝑜𝑛𝑡𝑎𝑐𝑡 is the total contact force per unit seal length around the

connection circumference,

𝐾𝐷 =𝐷1 ∙ 𝐷2𝐷1 + 𝐷2

where D1 and D2 are shown in Figure 35, and

𝐶𝐸 =1 − 𝜈1

2

𝐸1+1 − 𝜈2

2

𝐸2

where the subscripts indicate elastic modulus and Poisson’s

ratio of the pin and box.

If one of the contact surfaces is conical (i.e., has no curvature) then its diameter is infinite, and that term drops out of the equation for 𝐾𝐷 . 𝐾𝐷 is then equal to the radius of the other contact surface.

The maximum contact stress is then calculated by Equation 12

𝜎𝑐𝑜𝑛𝑡𝑎𝑐𝑡,𝑚𝑎𝑥 = √2 ∙ 𝐹𝑐𝑜𝑛𝑡𝑎𝑐𝑡𝜋 ∙ 𝐾𝐷 ∙ 𝐶𝐸

Equation 12

2Young, W.C. and Budynas, R.G. Roark’s Formulas for Stress and Strain 7th Ed. 2002, McGraw-Hill, New York

𝒄𝒐 𝒕𝒂𝒄𝒕,𝒎𝒂

Pin Box

D2

b

D1


45

5.4.4.3 Example results

Maximum contact stress and contact patch width can be compared to a solution step at which the contact surfaces and adjacent regions of the model are elastic. This will generally occur during make-

up. As an example of the contact stress calculation, consider a connection where the box and pin seals

touch at a diameter of 292 mm with a total contact force around the circumference of 200 kN, representing a 218 N/mm seal contact stress intensity. The Pin seal surface has curvature with radius

of 146 mm and the box seal surface has a radius of 36 mm. Both the pin and box have elastic modulus

equal to 200 GPa and Poisson’s ratio equal to 0.3.

The contact patch width, for Hertzian contact, is calculated by Equation 11 where

= 𝐾𝐷 =𝐷1 ∙ 𝐷2𝐷1 + 𝐷2

= 72 𝑚𝑚 ∙ 292 𝑚𝑚

72 𝑚𝑚 + 292 𝑚𝑚= 57.8 𝑚𝑚

and

𝐶𝐸 =1 − 𝜈1

2

𝐸1+1 − 𝜈2

2

𝐸2=

1 − 0.32

200,000 𝑀𝑃𝑎+

1 − 0.32

200,000 𝑀𝑃𝑎= 9.10 × 10−6 1 𝑀𝑃𝑎⁄

then

𝑏 = 2√2

𝜋𝐹𝐶𝑜𝑛𝑡𝑎𝑐𝑡 ∙ 𝐾𝐷 ∙ 𝐶𝐸 = 2√

2

𝜋218.0 𝑁 𝑚𝑚⁄ ∙ 57.8 𝑚𝑚 ∙ 9.10 × 10−6 1 𝑀𝑃𝑎⁄ = 0.542 𝑚𝑚

The maximum contact stress is calculated by Equation 12,

𝜎𝑐𝑜𝑛𝑡𝑎𝑐𝑡,𝑚𝑎𝑥 = √2 ∙ 𝐹𝑐𝑜𝑛𝑡𝑎𝑐𝑡𝜋 ∙ 𝐾𝐷 ∙ 𝐶𝐸

= √2 ∙ 218.0 𝑁/𝑚𝑚

𝜋 ∙ 57.8 𝑚𝑚 ∙ 9.10 × 10−6 1 𝑀𝑃𝑎⁄= 514 𝑀𝑃𝑎

The resulting example contact stress distribution is shown in Figure 36.


46

Figure 36. Example Hertzian contact stress distribution on curved seal contact surfaces of

72 mm and 292 mm diameter.

5.4.5 Mesh density and contact surface resolution

The checks outlined in this section are intended to verify that the overall mesh density is adequate to provide physically accurate load transfer and stress-strain distribution, and enough contact stress

resolution in the seal, threads, pin-tip and shoulder. The seal contact stress intensity, seal galling and thread galling criteria in ISO 12835 Annex A are based on contact stress at the seal and threads,

respectively, so it is important to ensure that the predicted contact stresses are reliable. This procedure

involves resizing finite elements throughout the connection model, but particularly along the contact

surfaces, in successive analyses.

The Benchmarking Process suggests a mesh convergence study or a mesh sensitivity study be completed to evaluate mesh density. The Benchmarking Analyst should use a combination of localized

mesh refinement and global refinement to adequately model important model features. Areas located

away from contact surfaces, or that exhibit low effective stress gradients (for example in the pipe body, away from the connection) can use a coarser mesh, while other areas (such as threads flanks, roots

and corners and contact surfaces in the primary seal) require a finer mesh. After initial meshing, the Benchmarking Analyst should run several analyses, with different refined mesh sizes (a minimum of

three) and observe how the solutions approach an asymptotic value as the mesh density is increased. Mesh dimensions are typically reduced by half for each successive analysis, while all other modelling

conditions (e.g., loads, boundary conditions, geometry and materials) are held constant.

When key results are plotted as functions of a parameter defining mesh density (e.g., an element dimension or number of elements), the curve will typically approach an asymptote representing the

physically accurate solution as the mesh density is increased. For TWCCEP comparative analyses, the mesh is acceptable when the calculated results from check C4.1 are within 5% of the asymptotic value.

Once the refined mesh is created, the same mesh sizes should be used for all TWCCEP analysis cases,

as the geometry changes between cases are typically minimal. Satisfying such a mesh convergence criterion may be acceptable for comparative analyses, but for analyses to determine absolute values of

performance indicators, such as fatigue, a more stringent criterion is likely required.

0

100

200

300

400

500

600

-0.3 -0.2 -0.1 0 0.1 0.2 0.3

Contact

Stress

(MPa)

Contact Width (mm)


47

Sometimes this asymptotic trend is interrupted by the influence of geometric singularities or other non-physical finite-element mesh effects. Discrepancies in element sizes between contacting surfaces or

poorly aligned contacting nodes can have a large impact on contact results making it difficult to produce successful convergence on contact related criterion. It is frequently difficult to successfully define an

accurate convergence trend on thread contact stress at a specific location because of the geometry

features (e.g., small radii at thread roots) and discrete contact regions. These difficulties make the use

of engineering judgement essential.

The nature of the selected element type may also influence convergence of results with increasing mesh density. The method of convergence analysis is independent of element type, but characteristics such

as element order (e.g., linear or quadratic) will influence how quickly results converge with a change in

mesh density.

Separate mesh sensitivity studies are described in checks C4.1-C4.3 for the seal region, threaded region

and pin-tip/shoulder region. C4.1-C4.3 can be conducted in separate analyses to get refined mesh for each region, which would require a minimum of nine analyses. Alternatively, the Benchmarking Analyst

may refine mesh in all three regions at the same time, which would have a minimum of three analyses and reduce model execution time. Even if all regions are refined in the same three analyses, all the

solutions used in C4.1-C4.3 must converge.

C4.1 Seal contact surface mesh

The initial mesh density may be based on the recommendations in ISO 12835 Clause A2.5, or the

discretion of the Benchmarking Analyst. From the initial mesh density in the seal region, the contact stresses in the seal region on the pin and box should be retrieved from the model results and the seal

contact stress intensity calculated at three simulation steps during the analysis: after make-up,

maximum temperature, and cycle end.

Successively finer mesh in the seal region should be used for subsequent analyses, where the element

lengths are halved in each iteration. The solutions that should be compared for the seal region are the maximum contact stress and the seal contact stress intensity. Mesh in the sealing region is deemed

sufficiently fine if the solutions are within 5% of the apparent asymptote. If the solutions do not meet convergence requirements within three analyses, further mesh refinement and analyses may be

conducted to determine the measure density needed to satisfy the convergence criterion.

Greater understanding of the mesh influence on seal performance can be gained by evaluating the seal

contact stress distributions and resulting seal contact stress intensity from each analysis.

C4.2 Thread contact surface mesh

In ISO 12835, the worst-case geometry for thread galling is based on the maximum contact stress in

the threads. Calculation of the maximum thread contact stress is very sensitive to mesh geometry,

density and alignment between contact surfaces so care in evaluating thread mesh density is advised. Refinement of thread mesh should be supported by engineering judgment and must be of sufficient

quality to appropriately simulate contact and accurately report structural response.

After the mesh has been selected, the same mesh size must be used for all ISO 12835 analysis cases

to provide valid comparisons.

C4.3 Pin-tip/shoulder contact surface mesh

Evaluation of the pin-tip/shoulder contact surface resolution follows the same procedure as for the seal

surfaces, except that mesh in the pin-tip/shoulder region is being modified and the total pin-tip/shoulder contact force is being compared with successive mesh refinements. In this region, the mesh need only

be sufficient to appropriately simulate the contact conditions and provide reasonably accurate structural response. The pin-tip/shoulder contact stresses or deformations are not included in the selection of

worst-case-geometry full-scale test connections, sufficient element density is still required to capture

plastic deformation in the pin tip and shoulder.


48

Demonstration of mesh sensitivity

Results from check C4.1 are shown in Figure 37 and Figure 38. The figures show five successive element

size refinements, where element size reduces as refinement ratio is increased. All five mesh sizes meet the convergence requirement for seal intensity, while the convergence requirement for maximum

contact stress is only met in the two cases with the finest mesh.

Figure 37. Seal contact stress intensity mesh sensitivity check.

SealContactStress

Intensity(%Final)

Mesh Refinement Ratio


49

Figure 38. Maximum seal contact stress mesh sensitivity check.

SealContactStress

(%Final)

Mesh Refinement Ratio


50

6 Step 2: Quantitative comparison 6.1 Scope

Step 2 of the TWCCEP FEA Benchmarking Tool provides guidelines for an analysis of a generic connection model including a specific geometry (created especially for Step 2 of this TWCCEP FEA

Benchmarking Tool), material properties, load path, and make-up procedures. This connection model is

referenced as the Generic Connection Model.

The Generic Connection Model was created using an arbitrary geometry with features commonly

encountered in threaded and coupled premium connections with a metal-to-metal cone-on-cone primary seal and buttress-style thread. The primary seal pin and box tapers were intentionally chosen to be

close-to-cylindrical, to avoid confusion with any existing commercial connection products. While a connection with such close-to-cylindrical seal tapers could not be assembled in practice, this

configuration is suitable for benchmarking of the Generic Connection Model. The Generic Connection

Model was not subject to an in-depth design process and is meant for use only in this TWCCEP FEA

Benchmarking Tool to quantitatively compare numerical results.

Step 2 guidelines provide input parameters, specifics used for output calculations, and reference results for the Generic Connection Model. The Benchmarking Analyst can complete the Step 2 analysis of the

Generic Connection Model using his or her FEA program, and compare the obtained results to the

reference results provided in this TWCCEP FEA Benchmarking Tool. Step 1 analytical checks described

in Section 5 can also be a useful aid to match results on the Generic Connection Model.

When the Benchmarking Analyst’s results from his or her Generic Connection Model match the reference results sufficiently closely, the Generic Connection Model is assumed to be correctly constructed and

the Benchmarking Analyst’s analysis methods correctly applied. The Generic Connection Model can then be modified to represent the Candidate Connection geometry, load path and material properties, while

using the same (“verified”) modelling methodology.

Appendix A.6 provides guidance on the execution of Step 2. Upon completion of Step 2 checks, the Benchmarking Analyst should prepare a comparison of the Generic Connection Model results to the

reference results, and include that in the FEA Benchmarking Report.

6.2 Generic connection specifications

6.2.1 Generic connection geometry

Connection drawings adopted for the Generic Connection Model are shown in Appendix B. The adopted

configuration of the Generic Connection is based on a 245 mm 54.5 kg/m (9.625 inch 40 lb/ft) size-weight combination, with a close-to-cylindrical cone-on-cone primary seal (also see comments in the

second paragraph of Section 6.1).

Three connection geometry-tolerance combinations are used in Step 2, as listed below and described in

Table 8:

1. Nominal geometry

(Configuration 1)

2. Geometry with fast pin and slow box thread tapers and minimum thread and seal diametral interferences (PF/BS, minimum thread interference, minimum seal interference). (Configuration 2)

3. Geometry with slow pin and fast box thread tapers and maximum thread and seal diametral interferences (PS/BF, maximum thread interference, maximum seal interference). (Configuration 3)


51

Dimensions are shown on the drawing in millimetres (mm), and diametral tapers are in mm/mm. The Benchmarking Process described in this document is focused on Geometry 1 of Table 8, while

Geometries 2 and 3 are recommended for optional additional comparisons.

Table 8. Dimensions for nominal generic connection configuration and two geometry-

tolerance configurations.

Dimension

Connection configuration

Nominal Geometry

Pin Fast Box Slow Minimum Thread Int.

Minimum Seal Int.

Pin Slow Box Fast Maximum Thread Int.

Maximum Seal Int.

Configuration 1 2 3

Pin seal gauge diameter (mm)

235.50 235.45 235.55

Box seal gauge diameter (mm)

235.00 235.05 234.95

Pin thread gauge pitch diameter (mm)

241.07 241.02 241.12

Box thread gauge pitch diameter (mm)

241.02 241.07 240.97

Pin thread taper (mm/mm)

0.10 0.1005 0.0995

Box thread taper (mm/mm)

0.095 0.0945 0.0955

The connection is drawn with most axial dimensions referenced to a plane containing the vertices created by the seal and shoulder on the box and the seal and pin tip on the pin. This reference plane is

shown in Figure 39, and is labeled Base Plane in the connection drawing in Appendix B. The axial

distances to the seal gauge plane and the thread gauge plane are with respect to this reference passing

through both pin and box vertices.

Figure 39. Location of reference plane for connection dimensions and definition of make-

up interference.

6.2.2 Mesh

Finite element mesh design is left to the discretion of the Benchmarking Analyst, in both the FEA

Benchmarking Process, and the ISO 12835 FEA process as a whole. Mesh sensitivity tests (described in Section 5.4.5) should ensure acceptable mesh quality, regardless of element type. If the Benchmarking

Pin

Box

Axial Dimensions Reference Plane

Pin as on Drawing

Initial Radial InterferencePin Vertex (original)

Box Vertex (original)


52

Analyst is following the procedure described in Appendix A6.2, it is recommended that the same general mesh sizes and element types be used for the Candidate Connection Model and the Generic Connection

Model constructed by the Benchmarking Analyst.

6.2.3 Material properties

The Generic Connection Model uses ISO/API L80 Type 1 steel, characterized by the temperature-

dependent true stress-strain curves shown in Figure 5. The corresponding data is tabulated in Appendix C. Other material properties and model features are listed in Table 9. Elastic modulus, Poisson’s ratio

and coefficient of thermal expansion are assumed temperature-independent for the Generic Connection

Model. Note that the elastic modulus, Poisson’s ratio and coefficient of thermal expansion are assumed

to be temperature independent.

Table 9. Material properties and modelling method used in the Generic Connection Model.

Material Characteristic Value

Elastic modulus 200 GPa

Poisson’s ratio 0.3

Coefficient of thermal expansion 14.0x10-6 mm/mm/°C

Material model Multi-linear thermal elastic-plastic

Strain hardening model Isotropic

6.2.4 Load path

The evaluation of the Generic Connection Model is conducted to ASL 350 (see ISO 12835 Clause 9.3

and A.2.6) and the load path is shown in Table 10, and Figure 40.

Table 10. Applied load path.

Load Condition Solution

Time Step Temperature

(°C) Pressure

(MPa)

Unloaded 0 5 0

Radial make-up 1 5 0

Axial & radial make-up complete 2 5 0

Internal pressure complete 3 5 16.5

Heating – intermediate step 4 192 16.5

Heating complete 5 350 16.5

Depressurization complete 6 350 0

Cooling – intermediate step 7 50 0

Cooling complete 8 5 0


53

Figure 40. Generic Connection load path.

6.2.4.1 Boundary conditions application

The Generic Connection Model has a length of 7,352.72 mm from the centre of the connection to the

centre of the pipe. For the axisymmetric model, the planes of symmetry at the center of the pipe joint and center of the connection were constrained to each remain plane but free to expand radially. In

addition, constraint on the coupling symmetry plane prevent axial displacement for all solution steps

while the plane of symmetry at the centre of the pipe body was free to move axially during make-up and then, after experiencing a small displacement associated with make-up, axially constrained to

prevent further displacement through the thermal cycle. Further information on connection modelling

techniques and model construction methodology is found in Section 5.2.

6.2.4.2 Pressure load application

Internal pressure is increased linearly from zero to 16.5 MPa from solution time 2 to time 3. The pressure

is held at its maximum value while temperature is increased (time steps 3 to 5) and then decreased to zero at solution time 6. The pressure is applied to all surfaces “inside” the primary seal including the

pipe and connection inside diameters, the pin tip and shoulder and part of the seal surfaces. The internal-pressure end locations on the pin and box shown by the heavy outlines in Figure 41. The point

of termination is at approximately the middle of the primary seal, and this position influences the

calculated seal contact stress intensity as described in Section 6.3.2.

0

2

4

6

8

10

12

14

16

18

20

0

50

100

150

200

250

300

350

400

450

500

0 1 2 3 4 5 6 7 8

Internal

Pressure

(MPa)

Connection

Temperature

(°C)

Make-up(%)

Solution Time Step

Make up Temperature Pressure

ConnectionTemperature

(°C)

Make-Up(%)

InternalPressure

(MPa)


54

Figure 41. Pressure application regions on pin and box seal regions.

6.2.4.3 Temperature load application

Temperature is applied to the entire connection and pipe body as a body load. To obtain the benchmarking data the temperature was increased from 5°C to 350°C over time steps 3 to 5 while

internal pressure was held at its maximum. The temperature was then decreased back to 5°C after

internal pressure was removed (time steps 6 to 8).

6.2.5 Connection make-up

ISO 12835 requires connection make-up for all analyses and the evaluation of minimum and maximum

torques within the range specified by the supplier to determine the torque required for sealability tests (see ISO 12835, Clause 12.3.7), but the specification does not describe how make-up is applied to the

axisymmetric FEA model. In general, make-up is simulated by first resolving initial radial interference between the pin and box thread and seal surfaces and then resolving initial axial interference between

the pin tip and box shoulder. The make-up torque, however, is a result of contact forces associated with

both thread, seal, and torque shoulder interference, so an iterative procedure is typically used to determine the relative position of the pin and box necessary to produce the desired make-up torque.

This allows the thread positions to be set in optimal positions for ease of contact convergence during the initial solution time steps. The make-up torque is calculated by the procedure described in

Section 6.3.1.

Torque targets and friction coefficients used in the generic connection analyses are listed in Table 11.

Note that the torque targets are not consistent for the three geometry tolerance cases.

Table 11. Generic connection make-up specifications.

Variable

Connection configuration

Nominal Geometry

Pin Fast Box Slow Minimum Thread Int.

Minimum Seal Int.

Pin Slow Box Fast Maximum Thread Int.

Maximum Seal Int.

Configuration 1 2 3

Make-up torque (Nˑm) 18,085 15,995 20,495

Assumed coefficient of friction in threads*

0.05

Assumed coefficient of

friction in seal and

shoulder

0.10

* While threads at either end of the thread engagement interval will typically have a higher friction coefficient than in the middle of that interval, because the thread compound is unconfined at those

ends; a single friction coefficient was used for all threads for these analyses for simplicity.

Pin

Box

6.001 mm

6.081 mm


55

6.3 Make-up torque, seal contact stress intensity and equivalent high-stiffness length calculations

Successful Step 2 benchmarking is based on the primary connection analysis input values and results

used by the ISO 12835 evaluation. In general, the values and results are calculated from the FEA output stresses, strains and displacements. The following are described in sub-Sections 6.3.1 to 6.3.3,

respectively:

1. The calculation of make-up torque from resultant contact forces using the connection geometry

and parameters specified in Table 11,

2. Seal contact stress intensity from resultant seal contact stresses using the seal geometry, and

3. The equivalent high-stiffness length from the resultant pipe body force under a specified applied

axial displacement using pipe body geometry specified in Appendix B and material properties

listed in Table 9.

6.3.1 Make-up torque calculation

The degree to which a connection is made up is typically related to the target make-up torque, which can be calculated from FEA contact forces and appropriate friction coefficients. Torque is calculated by

summing (for all nodes) the contact force multiplied by the moment arm length (radial location in

axisymmetric model) and friction coefficient at each node on a contact surface in the shoulder, seal, and threads using Equation 13. The summation is over all contact nodes on either the pin or the box

(thread contact, primary seal contact, and shoulder contact):

𝑇 = ∫ 𝐶𝑓 ∙ 𝜎(𝑙) ∙ 𝑟(𝑙) ∙ 𝑑𝑙 ≈ ∑𝐶𝑓𝐹𝑛𝑜𝑑𝑒 ∙ 𝑟𝑛𝑜𝑑𝑒𝑙1𝑙0

Equation 13

where:

𝑇 is the total make-up torque,

𝐶𝑓 is the friction coefficient for a given contact surface,

𝜎(𝑙) is the local contact stress as a function of distance along the contact surface,

𝑙 is the distance along the contact surface,

𝑟(𝑙) is the local contact radius as a function of distance along the contact surface,

𝐹𝑛𝑜𝑑𝑒 is the contact force at the node, and

𝑟𝑛𝑜𝑑𝑒 is the radius at the node.

The nodal contact force used should account for the full circumference at a given nodal position and

may need to be adjusted depending on the FEA program used.


56

6.3.2 Seal intensity calculation

Seal intensity can be calculated from element contact stresses using the following formula, where the

sum occurs over all the elements in the seal:

𝐼 = ∫ 𝜎𝑐(𝑙)𝑑𝑙 ≈1

𝐿∑𝜎𝑐−𝑒𝑙𝑒𝑚𝑒𝑛𝑡 ∙ ∆𝑙

𝑙1

𝑙0

Equation 14

where:

𝜎𝑐 is the contact stress as a function distance along the seal contact surface,

𝑙 is the distance along the seal contact surface.

𝜎𝑐−𝑒𝑙𝑒𝑚𝑒𝑛𝑡 is the average seal contact stress on a finite element,

∆𝑙 is the element length, and

𝐿 = 𝑙1 − 𝑙0 is the total length over which the seal contact stress intensity, 𝐼, is

calculated.

Equation 14 extends the original definition of seal contact stress intensity in Equation 1 by reducing the

integral to an easily applied summation of discrete contact stresses on axisymmetric element edges of

known length.

For calculation of the seal contact stress intensity, the contact stress integral is over the primary seal

and does not include any secondary radial sealing stress near the torque shoulder. The Generic Connection Model does not have secondary radial sealing stress and the summation in Equation 14

included all nodes on the entire conical seal surface of the pin. Other connections can have a secondary radial seal and the length over which the integral is taken should be adjusted to omit the secondary

seal from the seal contact stress calculation.

The seal contact stress intensity can also be calculated from the nodal contact forces in the primary seal. The seal contact stress intensity is the total contact force in the primary seal divided by a

representative seal circumference.

For most connection architectures, the calculated seal contact stress intensity will be somewhat

dependent on the pressure application strategy on the seal surfaces (also see Section 5.2.11). Pressure

applied through the seal will reduce the contact stress intensity by pushing the seal surfaces apart and might also influence the contact stress intensity by changing the balance of pressure acting on the inside

and outside of the pin tip. In operation, pressure is likely to decline across the primary seal, and some FEA packages might approximate this behaviour, but for simplicity full pressure has been applied to the

points on the pin and box of the generic connection indicated in Figure 41. The Generic Connection

Model used for Step 2 is relatively insensitive to pressure application location, but this might not be the

case for all connection architectures.

6.3.3 Equivalent low-stiffness length calculation

In accordance with Clause 12.3.3 of ISO 12835, the Benchmarking Analyst must determine the connection’s equivalent high- and low-stiffness lengths by applying a small axial load to the pipe end of

the FEA model after the completion of a thermal cycle, visualised in Figure 42.


57

Figure 42. Stiffness length calculation procedure schematic and nomenclature.

Upon completion of make-up and a thermal cycle (as specified in ISO 12835 Clause 12.3.3), apply a small compressive elastic displacement (Δδ) to the end of the model and the measured compressive

reaction force increment is ΔF. It will generally be easier to apply a known displacement following the

thermal cycle than to apply a force since the applied displacement is consistent with the displacement boundary condition applied during thermal cycle loading. Alternatively, a known force can be applied,

but this will require changing from a zero-displacement boundary condition applied during the thermal

cycle to an applied force boundary condition for calculation of effective stiff length.

The calculation is based on the assumption that the model consists of a length with stiffness equal to pipe body (½Ljoint) and an equivalent high-stiffness length that is rigid (½Lstiff). These definitions of Ljoint

and Lstiff are consistent with ISO 12835 Clause B.1.3. The equivalent high-stiffness length is calculated

from connection FEA axial reaction force result using Equation 15.

𝐿𝑠𝑡𝑖𝑓𝑓 = 2 ∙ [𝐿𝑚𝑜𝑑𝑒𝑙 − 𝐸 ∙ 𝛿 ∙ ∆𝜎𝑝𝑖𝑝𝑒] Equation 15

where:

Lmodel is the length of the connection model prior to the unload,

E is the elastic modulus,

δ is the applied axial displacement, and

Δσpipe is the change in pipe body axial stress during the unload.

Given the method described by Equation 15 is founded in a globally elastic pipe/connection system response, it is important that the system responds generally elastically (i.e. with no global plasticity and

only with localized plastic deformations) as possible) over the range of FEA timesteps used to determine

the high-stiffness length. Depending on the thermal cycle maximum temperature, the pipe may be in a tensile global yielding condition upon completion of the thermal cycle. A compressive displacement is

then necessary to produce an elastic unload.

6.4 Generic Connection reference results

Table 12 shows the results of the three cases of Generic Connection Model specified in Section 6.2.1.

The calculated high-stiffness and low-stiffness lengths are given in Table 13. Consistent with the result of Equation 15, the high- and low-stiffness lengths are for a full joint equal to twice the length of the

connection model. Resulting contact stress at the radial seal at key points in the load path are shown

Lmodel

½Ljoint½Lstiff

δ

ΔF ΔF


58

in Figure 43. Seal contact stress intensity and shoulder axial load are shown as functions of connection temperature in Figure 44 and Figure 45, respectively. Contour plots of von Mises stress and accumulated

effective plastic strain are given in Appendix D.

It is recognized that connection models created by different analysts and with different software – even

if according to the same “prescribed” geometry, material properties, boundary conditions and loading –

will inevitably contain subtle differences. Due to those inherent differences, it is not practical to expect a perfect match of results obtained from the Generic Connection Model created by Noetic and the

Generic Connection Model re-created by the Benchmarking Analyst.

As general guidance, we recommend that modelling results such as those listed in Table 12 and Table

13, and the seal contact stress distributions, contact stress variations during the thermal cycle, and von Mises stress and accumulated equivalent plastic strain distributions obtained by the Benchmarking

Analyst during Step 2 Benchmarking be reviewed and compared with those provided in the tables below

and in Appendix D.

The following process and criteria could be used for considering the results obtained by the

Benchmarking Analyst to be in sufficient agreement with the reference results contained in Appendix D. This process is not intended to be a specification for pass/fail criteria; instead, it is provided as an

example of the approach that will enable analysts to detect issues in their modelling strategy with a

higher level of confidence.

• Based on general engineering practice and some criteria used in international standards (including ISO 12835), consider three arbitrary levels of acceptable relative difference between

a set of comparative results: 5%, 10%, and 15%.

• For pipe body axial stress, seal intensity, maximum seal contact stress, total thread contact force, and total shoulder contact force, select acceptable relative differences for each numerical

result obtained by the Benchmarking Analyst. As a starting suggestion, all results should reasonably be within at least 15% of the corresponding result given in Table 12, and certain

results compared per Table 12 should be within at least 5% or 10% of the corresponding result

given in Table 12.

o For the high-stiffness length, the numerical result obtained by the Benchmarking

Analyst should be within 5% of the results given in Table 13. A close agreement is

expected, as this calculation should be insensitive to fine modelling details.

o For pipe body axial stresses, results should be within 5% given the significance of

appropriate axial stress, axial strain, and thermal loads on the overall mechanical

response of typical connections.

o As seal contact intensity is a primary variable in determining geometric tolerances for subsequent ISO PAS 12835 physical testing, seal contact intensity results should be

within 5%.

o Total thread and shoulder contact forces should be within 10%.

o Local contact stresses in threads and seal may vary due to meshing artefacts, but

should be within 15%.

• Distributions of stresses and strains should be compared qualitatively based on engineering judgement, with particular attention given to locations of maximum stress or strain values and

changes observed for different interference/taper combinations.

Further to the starting suggestions above, the Benchmarking Analyst and other parties developing

confidence in the analysis process and outcomes should use the above levels of results agreement as

guidelines, and must ultimately retain responsibility for completing a sound analysis and deciding on its

acceptability.


59

Table 12. Generic connection reference results.

Connection

Configuration

Solution Time Step1

Pipe Body Axial

Stress (MPa)

Seal Intensity (N/mm)

Maximum Seal

Contact Stress (MPa)

Total Seal

Contact Force2

(kN)

Total Thread Contact Force2

(kN)

Total Shoulder Contact Force2

(kN)

1

Nominal Geometry

2 - 457 1,573 337 1,088 653

3 53 560 1,654 413 1,856 510

4 -386 606 1,620 449 2,179 1,651

5 -313 558 1,384 414 1,933 1,390

6 -366 423 1,123 314 1,679 1,503

7 477 264 1,006 195 3,594 0

8 584 246 983 182 4,361 0

2

Pin Fast Box Slow

Min. Seal Int. Min Thread

Int.

2 - 375 1,463 277 937 613

3 53 486 1,530 359 1,641 460

4 -386 552 1,543 409 2,024 1,631

5 -313 510 1,350 378 1,778 1,370

6 -366 372 1,022 276 1,564 1,516

7 477 204 786 151 3,569 0

8 584 187 704 138 4,349 0

3

Pin Slow Box Fast

Max. Seal Int. Max Thread

Int.

2 - 534 1,659 394 1,280 702

3 53 629 1,680 465 2,087 560

4 -386 653 1,652 484 2,337 1,673

5 -313 596 1,405 443 2,101 1,408

6 -366 463 1,156 344 1,832 1,507

7 477 315 1,119 233 3,658 0

8 584 299 1,141 221 4,383 0

Note 1. See Table 10 and Figure 40 for load path details.

Note 2. Contact force around full circumference of connection.

Table 13. Generic connection effective stiff length calculation.

Axial Displacement,

Δδ (mm)

Reduction in Pipe Body Axial Stress,

Δσ (MPa)

High-stiffness length*,

Lstiff (mm)

Model Length**,

Lmodel (mm)

1.0 2.73 69.6 7352.72

* **

High-stiffness length is for a full coupling and casing joint. Periodicity of casing string used to reduce model to the half pipe joint (with one pin) plus half

coupling with one box represented in Figure 42.


60

Figure 43. Seal contact stress distributions during applied internal pressure and

temperature loads. Pin tip is towards the left.

0

200

400

600

800

1000

1200

1400

1600

1800

5.255.55.7566.256.5

Pin

Contact

Stress

(MPa)

Axial Position from Pin Tip Apex (mm)

2. Make-Up Complete

3. Pressure Applied

5. Heated

6. Pressure Removed

8. Cooled

Nominal Geometry

0

200

400

600

800

1000

1200

1400

1600

1800

5.255.55.7566.256.5

Pin

Contact

Stress

(MPa)


2. Make-Up Complete

3. Pressure Applied

5. Heated

6. Pressure Removed

8. Cooled

Pin Fast Box SlowMin. Seal Int.Min. Thread Int.

0

200

400

600

800

1000

1200

1400

1600

1800

5.255.55.7566.256.5

Pin

Contact

Stress

(MPa)


2. Make-Up Complete

3. Pressure Applied

5. Heated

6. Pressure Removed

8. Cooled

Pin Slow Box FastMax. Seal Int.Max. Thread Int.


61

Figure 44. Seal contact stress intensity during thermal and pressure cycle.

0

100

200

300

400

500

600

700

800

0 50 100 150 200 250 300 350 400

Seal

Contact

Stress

Intensity

(N/mm)

Temperature (°C)

Nominal Geometry

0

100

200

300

400

500

600

700

800

0 50 100 150 200 250 300 350 400

Seal

Contact

Stress

Intensity

(N/mm)

Temperature (°C)


0

100

200

300

400

500

600

700

800

0 50 100 150 200 250 300 350 400

Seal

Contact

Stress

Intensity

(N/mm)

Temperature (°C)



62

Figure 45. Shoulder axial force during temperature and pressure cycle.

0

200

400

600

800

1000

1200

1400

1600

1800

0 50 100 150 200 250 300 350 400

Shoulder

Axial

Force

(kN)

Temperature (°C)

Nominal Geometry

0

200

400

600

800

1000

1200

1400

1600

1800

0 50 100 150 200 250 300 350 400

Shoulder

Axial

Force

(kN)

Temperature (°C)


0

200

400

600

800

1000

1200

1400

1600

1800

0 50 100 150 200 250 300 350 400

Shoulder

Axial

Force

(kN)

Temperature (°C)


63

Appendix A: Detailed description of benchmarking process This section describes the structure of the Benchmarking Process.

Elements of the Benchmarking Process are described in Section A.2. A flowchart of the overall Benchmarking Process is provided in Section A.3. Basis for selecting the benchmarking mode and

complexity level is provided in Section A.4.

Flowcharts and task descriptions for Step 1 and Step 2 are provided in, respectively, Section A.5 and

Section A.6.

A.1 Additional Definitions Benchmarking Mode – type of the Benchmarking Process, either validating a previous analysis or

assisting an ongoing analysis.

Original Candidate Connection Model – connection model used in Original ISO 12835 FEA where

the benchmarking mode is that of validating a previous analysis (validation mode).

Original ISO 12835 FEA – an ISO 12835 FEA previously completed by a party, and subject to

verification.

Parallel Mode – a Benchmarking Mode aimed at assisting an ongoing ISO 12835-Compliant analysis.

Reference Load Cases – loading, material and geometry cases applied to the Generic Connection

Model in Step 2 of the Benchmarking Process.

Validation Mode – a Benchmarking Mode in which a previous ISO 12835-Compliant analysis is

validated.

A.2 Process elements

A.2.1 Benchmarking modes The Benchmarking Process may be conducted in one of the following modes:

• “Validation Mode” - validation of a previously completed analysis;

• “Parallel Mode” – in support of an ongoing ISO 12835-Compliant analysis.

The basis for selecting the Benchmarking Mode is explained in Section A.4.1.

A.2.2 Benchmarking steps The TWCCEP FEA Benchmarking Tool can be used with the following complexity levels (Benchmarking

Steps):

• Step 1 – qualitative checks and possible revisions of modelling strategy of a Candidate

Connection model submitted for benchmarking.

• Step 2 – quantitative checks and possible revisions of the connection model being benchmarked,

with comparisons against numerical results of reference models.

The basis for selecting the Benchmarking Steps is explained in Section A.4.2.

A.2.3 Tasks Each Benchmarking Step (Step 1 and Step 2) contains two tasks; i.e. there is Step 1 Task 1, Step 1

Task 2, Step 2 Task 1, and Step 2 Task 2. In a general sense, Step 1 Task 1 and Step 2 Task 1 are

“what-to-do” tasks; and Step 1 Task 2 and Step 2 Task 2 are “what-to-conclude” tasks.


64

The tasks are structured so that instructions common to various benchmarking modes (see Section A.2.1) are grouped in one task; for example, Step 1 Task 1 is the same for both modes, and

Step 2 Task 1 is also the same for both modes. Instructions different for various modes are grouped in

another task; e.g. Step 1 Task 2 Validation Mode is different from Step 1 Task 2 Parallel Mode.

A.3 Process flowchart

A.3.1 Major decisions and resultant task sequence The overall Benchmarking Process is presented in the flowchart in Fig. A-1, showing the major

benchmarking decisions and the resultant task sequence. The flowchart format is described in

Section A.3.2.

The Benchmarking Process includes two major decisions:

• Selection of Benchmarking Mode; i.e. either Validation Mode or Parallel Mode;

• Selection of benchmarking complexity; i.e. either Step 1 only, or both Step 1 and Step 2.

Each combination of the selected mode and complexity results in a specific task sequence to be followed

in the Benchmarking Process. These task sequences are listed below, together with references to

subsequent sections and figures in this document, where the tasks are described in detail.

Task sequence for Validation Mode if only Step 1 is completed:

1. Step 1 Task 1 – per Section A.5.2 and Fig. A-2.

2. Step 1 Task 2 Validation Mode – per Section A.5.3 and Fig. A-3.

Task sequence for Parallel Mode if only Step 1 is completed:


2. Step 1 Task 2 Parallel Mode – per Section A.5.4 and Fig. A-4.

Task sequence for Validation Mode if Step 1 and Step 2 are completed:



3. Step 2 Task 2 Validation Mode – per Section A.6.3 and Fig. A-6.

Task sequence for Parallel Mode if Step 1 and Step 2 are completed:



3. Step 2 Task 2 Parallel Mode – per Section A.6.4 and Fig. A-7.


65

Fig. A-1. Benchmarking mode/step selection and resultant task sequences.

A.3.2 Process flowchart format Figures Fig. A-1 to Fig. A-7 are formatted as follows:

Green oval: start-point or end-point of a Benchmarking Process step.

Blue square rectangle: task instruction.

Blue diamond: decision point.

Orange rounded rectangle: conclusion.

Orange oval: go-to instruction.

A.4 Mode and step selections

A.4.1 Selection of benchmarking mode Selection of the Benchmarking Mode is the first major decision in the Benchmarking Process.

If the benchmarking is done in the Validation Mode, then the previously completed analysis is referenced as the Original ISO 12835 FEA. The pipe-connection model used in that previous analysis is referenced


66

as the Original Candidate Connection Model. Upon benchmarking commencement, that original model

is assumed as the “starting version” of the Candidate Connection Model, to be validated.

If the FEA benchmarking is conducted in the Parallel Mode supporting an ongoing ISO 12835-Compliant analysis the specified connection geometry and material properties (obtained following ISO 12835

requirements) are used to construct the Candidate Connection Model.

Once the Benchmarking Mode is selected, and a “starting version” of the Candidate Connection Model is assumed accordingly, the Benchmarking Analyst decides on the benchmarking complexity (see

Section A.4.2).

A.4.2 Selection of benchmarking complexity Selection of the Benchmarking Step is the second major decision in the Benchmarking Process. At the

discretion of the Benchmarking Analyst, he or she may execute a Benchmarking Process with only Step 1 or with both steps. In general, executing both steps provides a more rigorous verification, and is thus

recommended to increase the level of confidence in the benchmarking results.

If only Step 1 is executed, then the Benchmarking Process includes checks of the modelling strategy

and assumptions but not numerical results. At the end of this process, the Benchmarking Analyst arrives

at a qualitatively-correct Benchmarked Candidate Connection Model.

If both steps are executed, then the process commences with Step 1 and then continues with Step 2,

and includes checks of the modelling strategy and comparisons of numerical results. At the end of the Benchmarking Process, the Benchmarking Analyst arrives at a quantitatively-correct Benchmarked

Candidate Connection Model.

Note, the Benchmarked Candidate Connection Model achieved when both Step 1 and Step 2 are

performed might be different from the one achieved when only Step 1 is executed. The model achieved

with both steps is considered meet ISO 12835 FEA requirements.

ISO 12835 FEA requirements are based on the need for consistent comparisons of analysis results from

models having small changes in geometry, changes in material yield strength and changes in initial interference. The FEA requirements are not based on a need for high numerical accuracy such as needed

for fatigue life prediction. TWCCEP FEA need not have as refined finite element mesh or precisely defined

load surfaces as other FEA applications may require, but FEA conditions must be similar for all analyses

completed within a TWCCEP evaluation.

A.5 Step 1

A.5.1 General description Step 1 of the TWCCEP FEA Benchmarking Tool specifies qualitative checks for pipe-connection modeling carried out in compliance with ISO 12835. These checks verify correctness of assumptions for boundary

conditions, material model, contact conditions, meshing, load application and output calculations. Step 1

describes how those modelling assumptions are verified (Section 5). Upon completion of Step 1, the Benchmarking Analyst can proceed to Step 2, which provides a reference model to check results

quantitatively (Section 6).

Step 1 checks can be used for model verification in either the Validation Mode or the Parallel Mode, and

as a guide for constructing new models in either Step 1 or Step 2.

Step 1 contains two tasks:

• Step 1 Task 1 – qualitative checks of model assumptions.

• Step 1 Task 2 – completion of ISO 12835 FEA, either by adopting previously-obtained results from the Original ISO 12835 FEA (Step 1 Task 2 Validation Mode), or running a full-scope “new”

FEA according to ISO 12835 (Step 1 Task 2 Parallel Mode).


67

Verification checks in Step 1 Task 1 are the same for either the Validation Mode or the Parallel Mode,

so Step 1 Task 1, described in Section A.5.2, is the same for both benchmarking modes.

Instructions in Step 1 Task 2 are different for each mode. Step 1 Task 2 Validation Mode is described in

Section A.5.3, and Step 1 Task 2 Parallel Mode is described in Section A.5.4.

A.5.2 Step 1 Task 1 Step 1 Task 1 is the same for the Validation Mode and the Parallel Mode, with the Candidate Connection Model having been selected/generated for each mode as described in Section A.4.1. The Step 1 Task 1

process is illustrated in Fig. A-2.

Per the initial instructions, Step 1 pipe body and connection checks are performed according to Step 1

guidelines (Section 5). These checks ensure that the material model behaves correctly (with load

reversal and temperature changes), and that the methods used to apply boundary conditions and loadings are applied are correct. In each check, the Benchmarking Analyst compares the modelling

assumptions used for the Candidate Connection Model with relevant aspects of the Step 1 guidelines. If the Candidate Connection Model does not meet Step 1 model requirements, the Candidate Connection

Model is revised until sufficient agreement is reached. This model revision process is illustrated with the first decision point and corresponding modelling revision instructions in Fig. A-3. After all checks-and-

balances are successfully completed, the Candidate Connection Model is presumed qualitatively correct.

The next decision point determines the process continuation path according to the applicable task sequence (see Section A.3.1 and Fig. A-1), and depending on if Step 2 is performed. If Step 2 is

performed, then the Candidate Connection Model is saved, and the process moves to Step 2.

If Step 2 is not performed, then the Candidate Connection Model becomes the Benchmarked Candidate

Connection Model. Process completion instructions are then executed in Step 1 Task 2 Validation Mode

or in Step 1 Task 2 Parallel Mode, whichever applies.


68

Fig. A-2. Step 1 Task 1.

A.5.3 Step 1 Task 2 Validation Mode Step 1 Task 2 Validation Mode is illustrated in Fig. A-3. Note, this task is executed only if Step 2 is not

performed.

Step 1 Task 2 Validation Mode commences with a decision point, at which the Benchmarking Analysts

checks if the Benchmarked Candidate Connection Model is different from Original Candidate Connection Model; i.e. if any model revisions of the Candidate Connection Model took place during the Step 1 Task 1

checks. If no model revisions occurred in Step 1 Task 1, the Original ISO 12835 FEA is presumed correct

(“qualitatively validated”) and the Benchmarking Process is complete.

If model revisions did occur in Step 1 Task 1, then the Original Candidate Connection Model is not valid

and the Original ISO 12835 FEA cannot be considered as validated. All analyses of the ISO 12835 FEA are re-done using the Benchmarked Candidate Connection Model, and then the Benchmarking Process

is complete.


69

Fig. A-3. Step 1 Task 2 Validation Mode.

A.5.4 Step1 Task 2 Parallel Mode Step 1 Task 2 Parallel Mode is illustrated in Fig. A-4. Note, this task is executed only if Step 2 is not

performed.

In the Parallel Mode, there are no previous results available for comparison. The Benchmarking Analysts uses the Benchmarked Candidate Connection Model to execute the full scope of the ISO 12835 FEA.

The Benchmarking Process is then complete.

Fig. A-4. Step 1 Task 2 in Parallel mode.


70

A.6 Step 2

A.6.1 General description Step 2 of the TWCCEP FEA Benchmarking Tool provides instructions for a quantitative comparison of analysis results for a generic connection model constructed by the Benchmarking Analyst (Generic

Reference Model) with a set of reference results “pre-defined” by Noetic for the same (also “pre-

defined”) model. Step 2 guidelines (Section 6) provide the information needed by the Benchmarking Analyst to duplicate Noetic’s “pre-defined” generic model, including geometry, material properties, load

path, and make-up torques.

Step 2 of the TWCCEP FEA Benchmarking Tool (Section 6) provides three sets of geometries which can

be compared to verify correctness of the Benchmarking Analyst’s Generic Reference Model. These geometries have varying thread tapers and interferences in a similar manner to those specified in ISO

12835. While the first geometry case (Case 1, or “Nominal”) is required for the Benchmarking Process;

the other geometry cases (Cases 2 and 3) are provided for optional further comparison. Results for the

“pre-defined” generic models are provided in Section 6.3.

Step 2 contains two tasks:

• Step 2 Task 1 – quantitative checks based on a reference model.

• Step 2 Task 2 – completion of ISO 12835 FEA, either by adopting previously-obtained results from the Original ISO 12835 FEA (Step 2 Task 2 Validation Mode) or running a full-scope “new”

FEA according to ISO 12835 (Step 2 Task 2 Parallel Mode).

Comparative checks in Step 2 Task 1 are the same for either the Validation Mode or the Parallel Mode,

so Step 2 Task 1, described in Section A.5.2, is the same for both benchmarking modes.

Instructions in Step 2 Task 2 are different for each mode. Step 2 Task 2 Validation Mode is described in

Section A.5.3, and Step 2 Task 2 Parallel Mode is described in Section A.5.4.

A.6.2 Step 2 Task 1 Step 2 Task 1 is the same for the Validation Mode and the Parallel Mode. The Step 2 Task 1 process is

illustrated in Fig. A-5.

The first instruction in Step 2 Task 1 is for the Benchmarking Analyst to construct a Generic Reference Model. The assumptions for this model are consistent with Step 1. The model geometry and material

properties are pre-defined and “generic”, i.e. representative of a premium connection but not

corresponding to any specific commercial product. Section 6 provides specific instructions needed to construct the Generic Reference Model. The objective for this modelling task is for the Benchmarking

Analyst to arrive at a model that will produce numerical results consistent with Noetic’s model defined for the same geometry, tolerances and make-up torques. Optionally, the Benchmarking Analyst may

modify the Candidate Connection Model achieved in Step 1 so that its geometry and material model are

consistent with Step 2 specifications for the Generic Connection Model.

The second instruction in Step 2 Task 1 is for the Benchmarking Analyst to subject the constructed

Generic Reference Model to the Reference Load Cases (contained in Section 6.2.4). The results from the Benchmarking Analyst’s Generic Reference Model are then compared to the pre-determined Step 2

reference results (contained in Section 6.4). If the results do not agree, the Benchmarking Analyst revises their Generic Reference Model and subjects it to the Reference Load Cases again, until enough

agreement of numerical results is reached. Once the results from the Benchmarking Analyst’s Generic

Connection Model agree with the pre-determined reference results, the Benchmarking Analyst’s Generic

Reference Model is presumed sufficiently accurate.

The next instruction is for the Benchmarking Analyst to modify geometry, material properties (material model) and make-up interferences of their Generic Reference Model to those consistent with the


71

Candidate Connection Model developed in Step 1 Task 1. The resultant (modified) model now becomes

the Candidate Connection Model.

The model revisions associated with modifications of the Generic Connection Model to the resultant Candidate Connection Model are subjected to (repeat) Step 1 Task 1 checks to verify that the resultant

model remains error-free. If errors are found, the Candidate Connection Model is revised. Once the

verification is completed, the resultant Candidate Connection Model becomes the Benchmarked Candidate Connection Model. At this point, the Benchmarking Process proceeds to Step 2 Task 2

Validation Mode or Step 2 Task 2 Parallel Mode, whichever applies.

Note, the above-mentioned Benchmarked Candidate Connection Model was subjected to both qualitative

and quantitative checks applied in Step 1 Task 1 and Step 2 Task 1. In general, this model might be different from the Benchmarked Candidate Connection Model achieved when only Step 1 checks are

performed (see Section A.4.2).

Fig. A-5. Step 2 Task 1.


72

A.6.3 Step 2 Task 2 Validation Mode Step 2 Task 2 Validation Mode is illustrated in Fig. A-6.

The Benchmarking Analyst first uses the Benchmarked Candidate Connection Model for a load case consistent with ISO 12835 Nominal Reference Case per Clause 12.3.3, and compares the obtained

results with the results obtained for that load case in the Original ISO 12835 FEA.

The Original ISO 12835 FEA is considered valid if the above comparison satisfies the following two

conditions:

1. No revisions of the Candidate Connection Model occurred in Step 1 Task 1; and

2. Results obtained with the Benchmarked Candidate Connection Model for the Nominal Reference

Case in Step 2 Task 2 (as described above) agree with the results from the Original Candidate

Connection Model.

If both these conditions are satisfied, then the Original ISO 12835 FEA is validated, and the

Benchmarking Process is complete.

If either of the above conditions is not satisfied, then the Original ISO 12835 FEA is not valid. All analyses

of ISO 12835 FEA are re-done using the Benchmarked Candidate Connection Model, and then the

Benchmarking Process is complete.

Fig. A-6. Step 2 Task 2 Validation Mode.


73

A.6.4 Step 2 Task 2 in Parallel Mode Step 2 Task 2 Parallel Mode is illustrated in Fig. A-7. Instructions for Step 2 Task 2 Parallel Mode are

the same as those for Step 1 Task 2 Parallel Mode, but the Benchmarked Candidate Connection Model used in Step 2 Task 2 might be different from the one used in Step 1 Task 2, for the reasons explained

in Section A.4.2.

The Benchmarking Analysts uses the Benchmarked Candidate Connection Model to execute the full

scope of the ISO 12835 FEA. The Benchmarking Process is then complete.

Fig. A-7. Step 2 Task 2 Parallel Mode.

74

Appendix B: Generic connection drawing

75

Appendix C: Temperature-dependent material true stress-true strain curves

5°C 180°C 240°C

Strain (%) Stress (MPa) Strain (%) Stress (MPa) Strain (%) Stress (MPa)

0.00291 582.00 0.002575 515.00 0.002 400.00

0.004 582.70 0.004 515.78 0.003 464.05

0.0055 583.75 0.0055 520.92 0.0045 492.69

0.007 584.80 0.007 534.13 0.006 508.76

0.0085 585.85 0.0085 544.11 0.0075 520.12

0.01 586.90 0.01 552.15 0.009 528.95

0.0115 587.95 0.0115 558.92 0.0105 536.20

0.013 589.00 0.013 564.76 0.012 542.37

0.0145 590.05 0.0145 569.90 0.0135 547.74

0.016 593.56 0.016 574.51 0.015 552.50

0.0175 597.89 0.0175 578.68 0.0165 556.78

0.019 601.85 0.019 582.50 0.018 560.67

0.0205 605.49 0.0205 586.01 0.0195 564.24

0.022 608.87 0.022 589.27 0.021 567.54

0.0235 612.02 0.0235 592.31 0.0225 570.61

0.025 614.98 0.025 595.16 0.024 573.47

0.0265 617.76 0.0265 597.85 0.0255 576.16

0.028 620.39 0.028 600.38 0.027 578.70

0.0295 622.88 0.0295 602.78 0.0285 581.10

0.031 625.24 0.031 605.07 0.03 583.38

0.0325 627.50 0.0325 607.25 0.0315 585.55

0.034 629.66 0.034 609.33 0.033 587.61

0.0355 631.72 0.0355 611.32 0.0345 589.59

0.037 633.70 0.037 613.23 0.036 591.49

0.0385 635.60 0.0385 615.07 0.0375 593.31

0.04 637.43 0.04 616.84 0.039 595.06

0.0415 639.20 0.0415 618.54 0.0405 596.74

0.043 640.90 0.043 620.19 0.042 598.37

0.0445 642.55 0.0445 621.78 0.0435 599.94

0.046 644.14 0.046 623.32 0.045 601.46

0.0475 645.69 0.0475 624.81 0.0465 602.93

0.049 647.18 0.049 626.26 0.048 604.35

0.06 656.98 0.06 635.72 0.0495 605.73

0.09 676.83 0.09 654.92 0.07 621.42

0.3 738.45 0.3 714.51 0.1 637.82

0.6 776.11 0.6 750.95 0.4 704.92

0.9 798.98 0.9 773.07 0.7 733.78

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290°C 325°C 350°C

Strain (%) Stress (MPa) Strain (%) Stress (MPa) Strain (%) Stress (MPa)

0.0019 380.00 0.0018 360.00 0.0017 340.00

0.0025 428.76 0.0025 411.25 0.0025 392.96

0.004 464.19 0.004 442.75 0.004 421.04

0.0055 481.53 0.0055 458.75 0.0055 435.79

0.007 493.28 0.007 469.72 0.007 445.99

0.0085 502.24 0.0085 478.11 0.0085 453.84

0.01 509.50 0.01 484.94 0.01 460.24

0.0115 515.63 0.0115 490.71 0.0115 465.66

0.013 520.93 0.013 495.72 0.013 470.37

0.0145 525.62 0.0145 500.14 0.0145 474.53

0.016 529.81 0.016 504.10 0.016 478.27

0.0175 533.62 0.0175 507.70 0.0175 481.66

0.019 537.10 0.019 511.00 0.019 484.77

0.0205 540.31 0.0205 514.04 0.0205 487.64

0.022 543.29 0.022 516.86 0.022 490.30

0.0235 546.07 0.0235 519.49 0.0235 492.79

0.025 548.68 0.025 521.96 0.025 495.12

0.0265 551.14 0.0265 524.29 0.0265 497.32

0.028 553.46 0.028 526.49 0.028 499.40

0.0295 555.67 0.0295 528.58 0.0295 501.38

0.031 557.76 0.031 530.57 0.031 503.26

0.0325 559.76 0.0325 532.46 0.0325 505.05

0.034 561.66 0.034 534.27 0.034 506.76

0.0355 563.49 0.0355 536.01 0.0355 508.40

0.037 565.25 0.037 537.67 0.037 509.97

0.0385 566.93 0.0385 539.27 0.0385 511.49

0.04 568.55 0.04 540.81 0.04 512.94

0.0415 570.12 0.0415 542.29 0.0415 514.35

0.043 571.63 0.043 543.73 0.043 515.70

0.0445 573.09 0.0445 545.11 0.0445 517.02

0.046 574.51 0.046 546.46 0.046 518.29

0.0475 575.88 0.0475 547.76 0.0475 519.52

0.049 577.20 0.049 549.02 0.049 520.71

0.06 585.90 0.06 557.27 0.06 528.53

0.09 603.55 0.09 574.04 0.09 544.41

0.3 658.41 0.3 626.18 0.3 593.82

0.6 691.97 0.6 658.09 0.6 624.08

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Appendix D: von Mises stress and accumulated effective plastic strain contour plots

Figure 46. von Mises stress distributions upon completion of make-up.

Nominal

Pin Slow Box Fast Max. Seal Int. Max. Thread Int.

Pin Fast Box Slow Min. Seal Int. Min. Thread Int.

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Figure 47. von Mises stress at elevated temperature.

Nominal



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Figure 48. von Mises stress distribution at end of cycle.

Nominal



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Figure 49. Accumulated effective plastic strain after make-up.

Nominal



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Figure 50. Accumulated effective plastic strain at elevated temperature.

Nominal



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Figure 51. Accumulated effective plastic strain at end of cycle.

Nominal



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