Sissala - FEA Simple Tension Test Progressive Failure

7/27/2019 Sissala - FEA Simple Tension Test Progressive Failure

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Stress Finite Element Analysis of a Simple HY-80 Steel Tension

Specimen Using Progressive Failure Feature in ABAQUS

by

Amy N. Sissala

An Engineering Project Submitted to the Graduate

Faculty of Rensselaer Polytechnic Institute

in Partial Fulfillment of the

Requirements for the degree of

MASTER OF ENGINEERING IN MECHANICAL ENGINEERING

Approved:

_________________________________________

Ernesto Gutierrez-Miravete, Engineering Project Adviser

Rensselaer Polytechnic Institute

Hartford, Connecticut

August, 2012

(For Graduation December 2012)


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Copyright 2012

by

Amy N. Sissala

All Rights Reserved


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CONTENTS

Finite Element Analysis of a Simple Tension Specimen Using Progressive Failure

Feature in ABAQUS ..................................................................................................... i

LIST OF SYMBOLS ........................................................................................................ iv

LIST OF TABLES ............................................................................................................. v

LIST OF FIGURES .......................................................................................................... vi

LIST OF KEYWORDS ................................................................................................... vii

ACKNOWLEDGMENT ................................................................................................ viii

ABSTRACT ..................................................................................................................... ix

1. Introduction and Literature Review ............................................................................. 1

2. Problem Statement ....................................................................................................... 3

3. Theory .......................................................................................................................... 4

4. Methodology ................................................................................................................ 5

4.1 Model Geometry and Material Properties .......................................................... 5

4.2 Analysis .............................................................................................................. 9

5. Results........................................................................................................................ 12

5.1

Model without Element Deletion (ABAQUS/Standard).................................. 12

5.2 Model with Element Deletion (ABAQUS/Explicit) ........................................ 13

6. Conclusion ................................................................................................................. 16

7. References .................................................................................................................. 17

8. Appendices ................................................................................................................ 18

8.1 ABAQUS Keyword File .................................................................................. 18


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LIST OF TABLES

Table 1: Type 1 Standard Tension Specimen Dimensions ................................................ 6

Table 2: HY-80 Material Properties .................................................................................. 7

Table 3: Stress-Strain Values for HY-80 Steel .................................................................. 8

Table 4: Finite Element Model Load Ramping ............................................................... 10


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LIST OF FIGURES

Figure 1: Type 1 Standard Tension Specimen ................................................................... 5

Figure 2: Tension Specimen Finite Element Model .......................................................... 6

Figure 3: Stress-Strain Curve for HY-80 Steel at Various Temperatures (7) .................... 7

Figure 4: Finite Element Model Boundary Conditions ..................................................... 9

Figure 5: Finite Element Loads ....................................................................................... 10

Figure 6: Finite Element Model without Element Deletion Option ................................ 12

Figure 7: Finite Element Model with Element Deletion Option Before Failure ............. 13

Figure 8: Finite Element Model with Element Deletion Immediately After Failure ...... 14

Figure 9: Final Finite Element Model with Element Deletion ........................................ 15


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LIST OF KEYWORDS

Finite Element Analysis

ABAQUS

Progressive FailureHY-80


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ACKNOWLEDGMENT

I would like to thank my advisor, Ernesto Gutierrez-Miravete, for his advice and

guidance of this project. Also I thank Kevin Black for helping edit the grammar and

readability of the paper.


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ABSTRACT

The focus of this project is finite element modeling using progressive failure of HY-80

steel in tension. A piece of steel will fail through plasticity and cracking under tension.

The finite element code ABAQUS calculates the stress for each integration point in eachelement. It also includes an addition feature to zero out the stresses at integration points

that pass a predefined limit. The ASTM A770/A770M-8 Standard Specification for

Through-Thickness Tension Testing of Steel Plates for Special Applications offers a

simple specimen and scenario to perform a study of how accurate the progressive failure

feature in ABAQUS is. Stress was tracked throughout each analysis. Failure stress is a

common variable reported for materials and can aid in designing structures. The areas of

highest stress occur near the failure point in the middle of the specimen. In the end the

ABAQUS progressive failure feature provides a more accurate view of the realistic

results of loading steel to failure by account for those elements that have failed and can

no longer carry any stress.


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1. Introduction and Literature ReviewMaterial strength and failure govern engineering design of structures. The goal of design

is to optimize the strength while reducing weight and cost. This pushes materials to their

limits and makes it important to know their failure behavior. This helps the engineerschedule adequate inspections and assists the inspector recognizing the manifestations of

material failure.

Ductile materials, such as high strength steel, fail through two processes:

plasticity and damage mechanics. Plasticity is a non-reversible change in shape in

response to applied forces due to dislocations along the slip planes inside the materials

microscopic structure. Damage mechanics, on the other hand, is the nucleation, growth,

and coalescence of microdamages in regions of high stress (1).

Physical testing of every material in a load situation can be expensive and time

consuming. Therefore, many finite element software codes, such as ABAQUS/Explicit

6.11, offer a progressive failure element option. Chang-Sik Oh had success using

ABAQUS to create a stress-strain curve of a material loaded into deformation. The team

also performed various sensitivity tests on the element density of their model (2).

When loads are applied, deformation occurs in the component. As the component

deforms, it loses its ability to carry the applied stress. The load propagating through that

section is then applied elsewhere, possibly loading another microscopic section to

failure. As loading continues, the stress distribution and elastic modulus are decreased

(3). This process can continue until the specimen fractures and macro cracks appear.

In a standard finite element analysis, elements never lose their ability to carry

loads. However, the stress continues to climb until the loading reaches equilibrium, even

after reaching the materials limit. It is the engineers responsibility during post

processing job to identify the areas where the material would fail. This does not

accurately represent what occurs in realistic application.

In an explicit finite element analysis, when the stress at an elements integration

point reaches its defined maximum, the point is set equal to zero. In order to do this the

finite element code forces the particular value in the stress matrix to equal zero. This is

how progressive failure is modeled, which identifies more realistically the areas of the


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model that fail and become ineffective at carrying stresses. The progressive failure

option also identifies the time the integration point fails for an increasing load (4).

In order to study the progressive failure element option, a test with known and

verified results was chosen for analysis. ASTM A770/A770M-8, Standard Specification

for Through-Thickness Tension Testing of Steel Plates for Special Applications, is a

common test that has been performed on various types of materials. By using a known

test, the area and values of maximum stress and failure are known.


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2. Problem StatementEngineers study failure in order to understand when and how it occurs in a structure. If

the engineer knows when failure occurs for various materials, the appropriate material

can be chosen from the beginning and a schedule of inspections can be established. Bystudying how failure occurs, engineers and inspectors can prevent critical failure through

observation.

The two main techniques of studying failure are physical testing and computer

analysis. Traditional materials and structures have been tested in a lab, but this is time

consuming, costly, and subject to human error. With the increasing capacity of

computers and advanced finite element software, analytical testing has become more

popular. With computers, the same specimen or model can be run in various scenarios

multiple times with little time or effort. Also, more complex scenarios that are not

possible in a laboratory setting can be studied.

Basic finite element codes record the maximum stress, force, and other values in an

element with no regard for material limits. The codes have slowly advanced to allow for

progressive failures of elements. As the plastic stress is reached, the integration points

stress is set to zero and therefore they stop carrying load. This is more accurate of a

portion of the specimen failing. Once all integration points of an element fail, it can then

be removed from the model. This replicates the plasticity that actually occurs.


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3. TheoryThe stress-strain relationship for an elastic material is defined below where is

the stress, E is the elastic modulus, and is the strain.

= Equation 1The elastic modulus matrix is calculated as in Equation 2 where is Poissons

ratio.

= Equation 2

Stresses can be calculated where their value is the same regardless of the

coordinate system, such as von Mises stress, vm

. Von Mises stress is generally used to

predict the onset of yielding in ductile materials. Von Mises stresses uses the general

stress axial, , and shear, , components as calculated with Equation 3 (5).

= + + + + + /Equation 3In finite element theory, the results are calculated at every node or integration

point of an element. For example, for a C3D8R and C3D6R there are eight and six nodes

respectively. Each element may or may not be connected to another via the nodes. This

way each element is related to the next and the applied loads are carried through the

structure. Finite element codes represent every element and node in large matrices.

The progressive failure option sets an integration point to zero when a set stress

limit, the failure stress limit of the material, is reached. This places a zero into the

appropriate matrix in the finite element code. Physically, this means that this portion of

the element has failed and can no longer carry loads or stresses. Once all the integration

points of an element have been set to zero the element is deleted from the model.

Though, this option can be overridden. The loads and stresses must redistributethemselves to other areas. Essentially that integration point has failed.


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4. MethodologyEngineers rely on knowing the method of failure of materials in their design. Knowing

when and how a material will fail leads to a more efficient design and use of material.

ABAQUS/Explicit 11.0 helps analyze material failure by incorporating a progressivefailure element option into their software. In order to explore the progressive failure

feature, a simple test with accepted results was modeled. This model follows the ASTM

standard for a simple tension test.

The method of this study is the following:

CAD Model of Tension Specimen Verification in ABAQUS/Standard 11.0 in Section 5.1 Increasing Failure in ABAQUS/Explicit 11.0 in Section 5.2 Analysis of Stresses

4.1 Model Geometry and Material PropertiesThe model geometry follows the criteria in ASTM Standard A770/A770M-03, Standard

Specification for Through-Thickness Tension Testing of Steel Plates for Special

Applications (6). A type 1 specimen represents a one inch thick piece of steel, called

the reduced section. This is held in place in the testing machine by two thicker ends, or

caps. Figure 1 shows the shape of the type 1 standard tension specimen. The values for

the symbols are given in Table 1.

Figure 1: Type 1 Standard Tension Specimen


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Table 1: Type 1 Standard Tension Specimen Dimensions

Plate Thickness (t) 2.54 cm

Diameter (D) 0.889 cm

Radius (R) 0.635 cm

Length of Reduced Section (A) 4.445 cm

To simplify the model, only half of the specimen was modeled and symmetric

boundary conditions were applied to the edge. Figure 2 displays the modeled and

meshed specimen in ABAQUS CAE.

Figure 2: Tension Specimen Finite Element Model

The material of the model is HY-80, high strength steel. This is a commonmaterial used in pressure vessels, heavy equipment, and large steel structures. It has a

high tensile strength, high ductility, and is weldable. Table 2 describes the material

properties of HY-80 steel (7).


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Table 2: HY-80 Material Properties

Density 0.284 lb/in3

Elastic Modulus 30,000 ksiPoissons Ratio 0.3

Tensile Strength 80 ksi

The other material property in the model was the stress-strain curve. This curve

tracks how much a material deforms as it reaches its yield stress and failure stress.

Holmquist did a series of tests of HY-80 steel at various temperatures and created the

curve in Figure 3. A table of values taken from the curve is in Table 3.

Figure 3: Stress-Strain Curve for HY-80 Steel at Various Temperatures (8)


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Table 3: Stress-Strain Values for HY-80 Steel

Stress (ksi) Strain

100 0

102 0.007

109 0.02

116 0.039

123 0.05

131 0.065

138 0.09

144 0.138

138 0.18

133 0.20

In the test, the specimen was held at both ends and a force is applied in opposite

directions. In the model, the centers of the two caps are held in all six degrees of

freedom. The symmetric half of the model was also held to not allow displacement in the

x direction and rotation about the y direction. Doing this forced the elements to act as if

the rest of the specimen is adjacent to them, thereby simulating a complete specimen.


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Figure 4: Finite Element Model Boundary Conditions

In order for the elements to zero out their stresses once failure had been reached,two lines had to be added to the ABAQUS keyword file. The tension failure and shear

failure keywords can be seen in Appendix 8.1.

4.2 AnalysisThe goal of this explicit finite element analysis was to stress the elements such that they

reach their failure stress and are subsequently deleted from the model. Since a well-

known test and material was used, a tensile strength of 80 ksi is given (7). Therefore, the

stress was monitored throughout the analysis to validate the model and the process.

The specimen was loaded in two ways: by forcing an opposing deflection at the caps

and by placing two opposing loads at the caps. The deflection load was used in

ABAQUS/Standard and the force was used in ABAQUS/Explicit in order to aid

convergence. The load was applied to induce failure throughout the reduction area. In


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order to ensure that the model did not crash due to excessive deformation, the load was

applied with an increasing amplitude. The steps can be seen in Table 4.

Figure 5: Finite Element Loads

Table 4: Finite Element Model Load Ramping

Time Amplitude

0.0 0

0.01 0.2

0.02 0.4

0.03 0.6

0.04 0.8

0.05 1.0


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Several iterations of the model were performed to examine how failure spread

across the specimen. Initially, the model was run without the element failure feature

turned on to examine the necking phenomenon often seen in testing. To apply the load in

this case, a forced deflection was applied to the caps.

After the model was verified, the load was continually increased until all

elements in the reduction area were observed to fail. Once the analysis was complete, the

model was post processed in order to find the maximum von Mises stresses. This value

was compared to the known tensile strength of HY-80 steel to confirm the accuracy of

the model.


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5. ResultsThe model consisted of 2548 elements using a combination of C3D8R and C3D6R. The

elements were chosen because the reduced integration option would shorten the

computing time.

5.1 Model without Element Deletion (ABAQUS/Standard)A total deflection of 0.21 inches was applied to the top and bottom of the specimen. As

shown in Figure 6, the specimen starts to neck in the center of the reduction area. This is

the same result that is seen in physical testing. This verifies that the model produces

realistic results. The maximum von Mises stress seen by the model was 179 ksi. The

fracture stress from Table 3 is 144 ksi. Since the stress in the model is above the fracture

stress the model is accurately representing the physical application.

Figure 6: Finite Element Model without Element Deletion Option


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5.2 Model with Element Deletion (ABAQUS/Explicit)For the analysis including the element deletion the load was ramped over the total

analysis time of 0.05 seconds. This avoided any errors in the analysis code due to

excessive failure in the specimen. It also enabled the program to save results showinghow the specimen was slowly loaded and then failed.

Figure 7 shows the specimen just before failure where the load applied is 425 kips.

The red in the fringe shows the high stress through out the reduction area while the end

caps are less stressed. The maximum von Mises stress is 133 ksi, just below the element

deletion threshold of 144 ksi.

Figure 7: Finite Element Model with Element Deletion Option Before Failure

Figure 8 is the specimen after the maximum von Mises stress has reached 144

ksi. As shown, the elements in the middle of the reduction area have started to fail at

their integration points. As that happens, the load must be carried by other elements.


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Figure 8: Finite Element Model with Element Deletion Immediately After Failure

Figure 9 shows the specimen at the end of the 0.05 second explicit analysis. The

final maximum von Mises stress is 126 ksi. There are some indications of trouble with

the finite element solver in the lower portion of the model as seen by the dissentious

fringe. This could be resolved through adjusting the ramping and time limit of the

analysis.

This value is lower than the final von Mises stress for the ABAQUS/Standard

analysis without element deletion. Yet this analysis is more accurate to the physical

limitations of the material. It cannot carry load beyond the failure limit.


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Figure 9: Final Finite Element Model with Element Deletion


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6. ConclusionMaterial strength and failure govern engineering design of structures. The goal of design

is to optimize the strength while reducing weight and cost. This pushes materials to their

limits and makes it important to know their failure behavior. This helps the engineerschedule adequate inspections and the inspector recognize the manifestations of material

failure.

Physical testing of every material in a load situation is expensive and time

consuming. Therefore, many finite element software codes, such as ABAQUS/Explicit

6.11, offer a progressive failure element option. In an explicit finite element analysis,

when the stress at an elements integration point reaches its defined maximum, the point

is set equal to zero. This is how progressive failure is modeled, which identifies more

realistically the areas of the model that fail and become ineffective at carrying stresses.

The progressive failure option also identifies the time the integration point fails for an

increasing load (4).

In order to study the progressive failure element option, a test with known and

verified results was chosen for analysis. ASTM A770/A770M-8, Standard Specification

for Through-Thickness Tension Testing of Steel Plates for Special Applications, is a

common test that has been performed on various types of materials. After establishing

that the model behaved as expected in ABAQUS/Standard, i.e. necking and high stress

in the reduction area, the model was put under tension with the tension failure defined as

the failure stresses.

The progressive failure option performed as expected. It accurately loaded the

specimen, indicating material failure in the reduction area. It accurate predicted that after

the tension failure limit was reached in the reduction area, that area would fail and the

load would be carried by the smaller sections at either end. The next step after this study

is to explore some of the other codes available that specifically model cracks and

calculate their stresses. Instead of removing the elements from the model, elements are

disconnected along the crack and then the stresses recalculated.


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7. References1. Rashid K. Abu Al-Rub, George Z. Voyiadjis. On the coupling of anisotropic

damage and plasitcity models for ductile materials. 2003, International Journal of Solids

and Structures 40, pp. 2611-2643.2. Chang-Sik Oh, Nak-Hyun Kim, Yun-Jae Kim, Jong-Hyun Baek, Young-Pyo

Kim, Woo-Sik Kim.A finite element ductile failure simulation method using stress-

modified fracture strain model. 2011, Engineering Fracture Mechanics 78, pp. 124-137.

3. Ellingwood, Baidurya Bhattacharya and Bruce. Continuum damage mechanics

analysis of fatigue crack initiation. 1998, International Journal of Fatigue 9, pp. 631-639.

4. DCS Simulia. ABAQUS 6.11 Analysis User's Manual.Abaqus 6.11 Documentation.

Providence : s.n., 2011, p. 22.2.8.

5. Robert Cook, David Malkus, Michael Pelsha, and Robert Witt. Concepts and

Applications of Finite Element Analysis. New York City : John Wiley & Sons, INC,

2002. ISBN: 0-471-35605-0.

6. ASTM International. Standard Specification for Through-Thickness Tension Testing

of Steel Plates for Special Applications. 2012, pp. A770/A770M-03.

7. Matweb. HY-80 Material Properties. [Online] [Cited: July 16, 2012.]

8. T.J., Holmquist.Strength and Fracture Characteristics of HY-80, HY-100, and HY-

130 Steels Subjected to Various Strains, Strain Rates, Temperatures, and Pressures.

Dahigren, VA and Silver Spring, MA : Naval Surface Warfare Center, Research and

Technology Department, 1987.

9. Robert Cook, David Malkus, Michael Pelsha, and Robert Witt. Concepts and

Applications of Finite Element Analysis. New York City : John Wiley & Sons, INC,

2002. ISBN: 0-471-35605-0.


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**

** STEP: Explicit Load

**

*Step, name="Explicit Load"

*Dynamic, Explicit

, 0.05

*Bulk Viscosity

0.06, 1.2

**

** BOUNDARY CONDITIONS

**

** Name: BC-1 Type: Symmetry/Antisymmetry/Encastre

*Boundary

_PickedSet19, XSYMM

**

** LOADS

**

** Name: Load-2 Type: Body force

*Dload, amplitude=Amp-1

_PickedSet26, BY, -300000.

** Name: Positive Type: Body force

*Dload, amplitude=Amp-1

_PickedSet27, BY, 300000.

**

** OUTPUT REQUESTS

**

*Restart, write, number interval=1, time marks=NO

**

** FIELD OUTPUT: F-Output-1

**

*Output, field, variable=PRESELECT


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** HISTORY OUTPUT: H-Output-1

**

*Output, history, variable=PRESELECT

*End Step

Sissala - FEA Simple Tension Test Progressive Failure

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