What Is MSC Fatigue and What New About MSC …...Fatigue Seam Weld Fatigue Multiaxial Fatigue...
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1 RLD Ltd © 2012 Dr NWM Bishop 45 What Is MSC Fatigue and What New About MSC Fatigue and MSC Software’s Fatigue Business 45 RLD Ltd © 2012 Dr NWM Bishop 46 • Conceived in 1991 as joint venture between MSC and nCode • nCode provides the core solver for MSC Fatigue (and in versions 2011, 2012 and 2012.2 will provide new DTLIB fatigue solver algorithms) • MSC provides the integration and GUI (currently Patran). MSC Fatigue Background
Transcript of What Is MSC Fatigue and What New About MSC …...Fatigue Seam Weld Fatigue Multiaxial Fatigue...
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What Is MSC Fatigue
and
What New About MSC Fatigue and MSC Software’s Fatigue Business
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• Conceived in 1991 as joint venture between MSC and nCode
• nCode provides the core solver for MSC Fatigue (and in versions 2011, 2012 and 2012.2 will provide new DTLIB fatigue solver algorithms)
• MSC provides the integration and GUI (currently Patran).
MSC Fatigue Background
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Think of MSC Fatigue like a big old luxury car where,
• nCode provide the engine.
• MSC the gearbox, transmission, electrical system, chassis and exterior bodywork.
• The seamless integration of these 3 things (solver, ancillary components and GUI) make MSC Fatigue unique.
MSC Fatigue Background
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A reminder – What is MSC Fatigue
S-N
E-N
Crackpropagation
Vibration Fatigue
Shaker Table Fatigue Fatigue &
MBS
Fatigue of Wheels
Spot Weld Fatigue
Seam Weld Fatigue
Multiaxial Fatigue
Utilities
Fatigue Pre & Post
MSC Fatigue Modules
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Stress-Life & Strain-Life module (new features in 2011) • Updated GUI and environment • Repackaging of entry level product (with Stress-Life & Strain-Life modules). • New DTLIB based module in 2012
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Dynamics Response and MSC Fatigue
Options for analysis
Frequency Domain Time Domain
Static Dynamic (transient)
Dynamic (MPC)
PSD’s from solver
FRF’s (transfer functions)
from solver
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Frequency v Time Domain (What is a PSD?)
Random DISPLAY OF SIGNAL: Y27A.PSD
Deterministic Time domain Time domain
Frequency domain
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Key elements of a PSD type analysis
What is a PSD
How to build a PSD input from specified
details
How to do structural analysis using PSD’s
How to calculate RCC’s and fatigue life from the
response PSD’s
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Typical PSD loadings for a missile design
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Features�
– Multi input loads�
– Correlation effects using Cross PSD’s�
– Resolution of stresses onto Principal planes�
– Calculation of response PSD using TF’s and input PSD’s�
– Calculate fatigue life from PSDs�
Vibration Fatigue in the Frequency DomainTransfer Functions on
component axes�
Transfer Functions rotated on to Principal planes by MSC
Fatigue�
� Response PSD’s calculated by MSC Fatigue�
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Input PSD [A]�
Transfer Function [B]�
Response PSD [C]�
Rainflow histogram and fatigue life calculated by
MSC Fatigue�
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MSC Shaker (new in ver. 2012) • MSC Fatigue Shaker predicts the fatigue life of components subjected to a
single input random vibration load or sine sweep – a typical example of which would be a shaker table test. Shaker tables are routinely used to “proof test” components before sign-off. Typical input loads could be displacement, velocity or acceleration PSD’s.
• The module works for a single input loading only and the following methods are available,
• Dirlik• Narrow Band• Steinberg • Lalanne
Mode 1 Mode 3 Mode 2
11.2 Hz 17.6 Hz 8.8 Hz
Mode 5 Mode 4
26.9 Hz 121.4 Hz
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MSC Fatigue Spot Welds (new solver in ver. 2011)
FE Model of Car Body Component Location and Fatigue Life of Spot Welds
No attempt to directly calculate stresses in the spot weld, instead we use moments and forces in equivalent beams from which structural stresses are derived.
MSC Fatigue Spot Weld uses the Rupp, Storzel and Grubisic algorithms for computing stresses in each spot-weld nugget and in adjacent sheets.
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MSC Fatigue Seam Welds (new solver in ver. 2011)MSC Fatigue includes, as standard, the traditional weld classification approach (BS5400/BS7608 etc) for the fatigue design of weldment details. Using this type of approach there is no attempt to model the weld detail. Instead, “component” S-N curves are used which have the weld classification detail (loading and geometry) built in to the S-N detail. This approach can, however, be awkward and time consuming to implement for thin sheet steels commonly used for automotive manufacturing because the level of integration with FE is minimal.
More recent work has focused on calculating the equivalent structural stress in the weld detail. The method implemented in MSC fatigue is based on the method developed by Fermer et al. Ref: SAE 982311
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MSC Fracture Little known and under used crack growth tools embedded in MSC Fatigue which provide sophisticated crack growth modeling tools for estimating life to grow a crack through a structure. Features include:• Kitagawa minimum crack sizing• Fracture toughness failure criterion• Mean stress correction• User-defined life units• Rain flow cycle counting with cycle re-ordering• Initial and final crack length specifications• Plane stress correction• Notch effects modeling• Retardation and closure effects modeling• Modified Paris law modeling based on effective stress intensity range• Fracture mechanics triangle solutions (stress – stress intensity – crack length)• Graphical interface to NASA/FLAGRO 2.03 (via MSC Patran or MSC Fatigue Pre & Post)
Compliance Function (Y)LibraryStandard specimens
• Single edge crack in tension• Single edge crack in pure bending• Double edge crack in tension• Center cracked plate in tension• Center cracked square plate in tension• Three-point bend specimen• Compact tension specimen• Round compact tension specimen• Wedge opening load specimen• Quarter circular corner crack tension specimen
Cracks at holes•Single crack at a hole in tension•Double crack at a hole in tension•Surface crack at a hole in tension
Elliptical, semi-elliptical cracks in plates•Surface cracks in tension•Surface cracks in bending•Embedded cracks in tension•Embedded cracks in bending•Surface and embedded cracks in combined loading
Cracks at corners•Quarter elliptical corner crack in tension•Quarter elliptical corner crack at a hole in tension
Cracks in solid cylinders•Circumferential crack in tension•Straight crack in tension•Semi-circular crack in tension•Crack at thread in tension•Straight crack in bending•Semi-circular crack in bending
Cracks in hollow cylinders•Internal surface crack under a hoop stress•Circumferential crack in thin-walled tube in tension
Cracks in welded plate joints•Weld toe surface cracks in tension•Weld toe surface cracks in bending•Weld toe embedded cracks in tension•Weld toe embedded cracks in bending•Surface cracks in combined tension and bending
Cracks in welded tubular jointsCracks at spot welds in tensionUser parametric definitions
K = Yσσ((ππa)1/2
da/dN = C(ΔΔK) m (Paris Law)
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MSC Strain Gauge MSC Fatigue Strain Gauge allows the creation of virtual Software Strain Gauges within an MSC Nastran finite element (FE) model. These gauges can be used to produce analytical response time histories from the FE model under the effect of multiple time varying applied loads. Stress and strain time histories may be extracted at any point on the FE model surface, based on either standard or user-defined strain gauge definitions. The results obtained from the Software Strain Gauge may be based on static, transient, or quasi-static FE loading.
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MSC Fatigue Wheels
Aircraft wheels play a major role in the takeoffs and landings of an aircraft, whether it’s a 747 loaded with 568 passengers, the Space Shuttle, or an F-16 Fighting Falcon. Repetitive landings, takeoffs and associated taxi runs subject the wheels to a considerable spectrum of operational loads that the wheels must withstand time and again. Ensuring that a wheel meets stress and load criteria over time is an important part of the product development process and typically is accomplished by testing physical prototypes. However, building and testing a prototype is expensive and time consuming and wheel development programs often require several prototypes be evaluated before the production design is finalized.
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0 50 100 150-81.32
161.4 GAGE 1X( uS) GAGE103.DAC
0 50 100 150-274.6
559.5 GAGE 1Z( uS) GAGE102.DAC
0 50 100 150-651
716.2 GAGE 1Y( uS) GAGE101.DAC
MSC Fatigue Multiaxial
Some components have multiaxial loads inputs, and some of those have multiaxial stresses and strains in critical locations. In these situation uniaxial methods may give poor answers needing bigger safety factors. MSC Fatigue includes sophisticated stress state assessment tools to test for the presence of secondary stresses and non-stationary stresses. MSC Fatigue then has available several methods for multiaxial fatigue calculations which include,
• 6 Critical Plane Methods & 1 Total Life Factor of Safety Method • Wang-Brown method, with and without mean stress correction • Normal Strain, Shear Strain, SWT-Bannantine and Fatemi-Socie critical plane
methods.
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MSC Fatigue UtilitiesMSC Fatigue Utilities contains advanced and practical applications to help the MSC Fatigue user who has a need to collect, analyze, and post process measured data, such as stress or strain time histories, or to process such data to prepare for a subsequent MSC Fatigue analysis.
Advanced Loading Manipulation Arithmetic Manipulation Multi-Channel Editor Rainflow Cycle Counter Formula Processor File Cut and Paste Multi-File Peak-Valley Extraction Simultaneous Values Analysis Amplitude Distribution Auto Spectral Density Fast Fourier & Butterworth Filter Frequency Response Analysis Statistical Analysis
Advanced Fatigue Utilities Single Location Stress-Life & Strain-Life Analysis Single Location Vibration Fatigue Cycle and Damage Analysis Time Correlated Damage Multi-Axial Life Crack Growth Data Analysis Kt/Kf Evaluation
Graphical Display & Conversion Utilities Graphical Editing Single & Multi-File Display Two & Three Parameter Display Binary/ASCII Convertor Signal Regeneration RPC to DAC - DAC to RPC & Cross-Platform Conversion Waterfall File Create
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MSC Fatigue Pre & Post (new in ver. 2011)
MSC Fatigue Pre&Post provides the required graphical interface to efficiently and easily set up, run and post process an MSC Fatigue analysis. It is intended for the user who doesn’t need the full processing power of Patran to run MSC Fatigue or perhaps has an alternative pre & post for routine day to day work.
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Development Process MSC Fatigue
Themes Key Features
Incorporate DTLIB
Refresh GUI
Spotweld, SeamweldDuty cycle, hybrid loadings
New ribbon plus updated forms
Themes Key Features
Rest of DTLIB
Ancillary comps
Virtual Shaker Table S-N and E-N update
Composites (layered results)
���������� ������������� ���
� An upgraded (nCode) solver, � Better ancillary components (eg welds, crack growth, etc) � A more modern user interface.
• This work is being implemented in a phased process over the next 2-3 releases. [2010.2.3 & 2011 already released]
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Topics For Future Releases
� Thermo Mechanical Fatigue
� Composite Fatigue Platform
� Fatigue of Rubbers
� Integration of SWAP3D weld modelling tools
?
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Nastran Embedded Fatigue
Its Not About The Stresses!
Put the fatigue solver at the same point as the stress solver
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In traditional approaches how do the stress solver and fatigue solver interface?
Identify materialparameters.
Build FE model and check global FE model quality. I d e n t i f y l o a d s ,
constraints
Apply unit loads to FE stress model to produce stress fields.
Calculatestress time historiesFatigue analysis
• plot results, identify critical (hot spot) locations
• FE modelling/meshing quality in critical locations?
• more sophisticated fatigue method required?
Perform sensitivity analysis
Stress solver
Fatigue solver
This is true for staticand dynamic problems
Move stress file
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FIN file FES file
Nastran SOL101
Patran DB file
Fatigue solver FEF results file
Read into Patran DB file
Other types of results produced
interactively
PFMAT(materials)
Duty cycle tool
An example with MSC Fatigue
OP2 file
The OP2, Patran DB and FES files are significant bottlenecks making the analysis of large models difficult or impossible
All major competitive products have the same bottlenecks
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Nastran File Flow
Preferred GUI
Optional output files
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Nastran Embedded Fatigue (Nastran 2013)
“The most important development in CAE Fatigue since the introduction of MSC Fatigue.”
• No large data files to transfer. • No complicated file management. • Significant reduction in CPU requirements. • Likely that whole fatigue calculation process can be done in memory. • Will open up opportunity to do full optimization for fatigue calculations. • Full Body Fatigue calculations, including dynamic behavior, will be
practical option.
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Define Elements for Fatigue Analysis:
SET4 (bulk data) - Defines unique set of elements by referring to their element properties
FTGDEF (bulk data) - FaTiGue DEFinition: Defines the part(s) of the model for fatigue analysis
Define Loading:
FTGLOAD (bulk data) - FaTiGue LOADing: Defines load variations with time (time histories) or frequency (Input PSDs)
FTGEVNT (bulk data) - FaTiGue EVeNT: Defines a loading event that is made up of a sequence of fatigue loads
FTGSEQ (bulk data) - FaTiGue load SEQuence: Specifies a time based loading sequence made up of loading events.
TABLFTG (bulk data) - TABLe FaTiGue: Defines actual tabular data of fatigue loading
Define Properties:
PFTG (bulk data) - Property FaTiGue: Defines properties for fatigue analysis (surface finish, surface treatment, etc.)
Define Materials:
MATFTG (bulk data) - MATerial FaTiGue: Defines materials for fatigue analysis (S-N & e-N curves)
Define General Parameters:
FTGPARM (bulk data) - FaTiGue PARaMeters: Defines fatigue parameters
Bulk Data Entries Overall Case Control
FATIGUE (case control) - Requests one or more fatigue analyses
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Integration of fatigue in SOL. 200
• Fatigue responses like LIFE, DAMAGE are integrated with other standard responses like stress, strain, displacement etc.
• Fatigue responses may be defined as objective function and/or as constraints
• The DRESP1 bulk data entry is utilized for defining Fatigue responses
• In release 1, fatigue responses will only be allowed for static analysis
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DRESP1 (Bulk Data)
This defines a design optimization response. This entry already exists in Nastran but needs to have a few more responses defined as shown here for doing optimization taking fatigue life/damage into account.
Format:
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Nastran Embedded Fatigue (Nastran 2013) (beta in Q4 2012)
Fatigue solutions Nastran solution routines
Stress-Life solver Strain-Life solvers Multi Thread Processing
SOL 101 SOL 103 SOL 112 SOL 200
���������������������
Fully embedded Bulk Data File driven fatigue analysis
Fatigue solutions Nastran solution routines
Spot Weld solver Seam Weld solver Vibration Fatigue solver Dang Van Temperature Loads
SOL 108 SOL 109 SOL 111 SOL 400
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R3 or later? Short Fibre Composites, Thermo Mechanical Fatigue,
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Pre & Post support
Fatigue solutions Nastran solution routines
Stress-Life solver Strain-Life solvers Multi Thread Processing
SOL 101 SOL 103 SOL 112 SOL 200
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ANSA Hypermesh
� ��������� ������� �������� �����
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Differentiating between a GUI Based Approach and Solver Embedded
MSC Fatigue (GUI driven)
When to use • Failure investigation. • Sensitivity studies (eg effect of load change). • Where stresses are from non Nastran solvers. • For highly interactive analysis. • Where a large amount of post processing is
anticipated.
Nastran Fatigue (Solver Embedded)
When to use • Well defined processes. • Large models. • Many load inputs. • For optimisation of parts or systems. • Simpler and more concise file management. • Extremely fast analysis. • BDF file auditable process.
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Fatigue Engineering Services
Promotion and support of FEA based fatigue activities worldwide.
High level technical backup.
BBeessppookkee ssooffttwwaarree ssoolluuttiioonnss
• Specialist or general training activities
[PAT318 & PAT319]. Conventional Eng Services
• Fatigue-Manager • Fatigue-Health-Check • Fatigue-Tech-Transfer [Quick-Start] • Fatigue Audit
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Materials Characterization and Fatigue Testing Service – including Strain-Life and Stress-life, for Metallic, Composite and Advanced Materials
• Fatigue life testing, stress-life and strain-life• Single and multi axis, static and dynamic specimen
and component testing.• Full specimen preparation from stock materials.• Extraction of specimens from real components.• Strain-life fatigue testing in tension/compression,
fully-reversed bending and torsion.• Load controlled fatigue testing for the derivation of
stress-life or load-life parameters.• Static and cyclic thermal loading from -40°C to
1050°C.• Tension/compression from 5kN to 150kN. Torsion up
to 5,000Nm.
Materials Testing Service
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MSC Fatigue is an excellent platform on which to build company processes – it can also be linked with SimManager
How can MSC Fatigue be used in a large company structure
Auditable and Repeatable Processes MSC Fatigue is configured to run in a similar way to Nastran using an editable text batch file (cf BDF file). This leaves a useful auditable trail as well as a convenient means to run in batch mode.
Incorporate More Reliable Material Properties Because reliable materials data is an essential part of any fatigue and durability process MSC Software is pleased to now offer a comprehensive materials testing service (see separate brochure).
Comprehensive Solution MSC Software now offer a complete solution including advanced fatigue software (MSC Fatigue), advance materials testing facilities and, new with this release, a comprehensive engineering analysis(for fatigue) consulting service.
#3.1ANALYSIS TYPE = VIBRATION FEA RESULTS LOCATION = NODE AVERAGING = GLOBAL TITLE = P3DATABASE = VS_FRA.dbS-N DATA SET 1 = 817M40 S-N TYPE = Material M_DIRECTORY = CENTRAL FINISH = No Finish TREATMENT = No Treatment KF = 1 REGION = skin MULTIPLIER = 1 OFFSET = 0 WELD = N/A TENSOR TYPE = STRESS STRESS UNITS = MPA STRESS COMBINATION = MAX ABS PRINCIPAL MEAN STRESS CORRECTION = NONE VIBRATION METHOD = DIRLIK DESIGN CRITERION = 50. FEA ANALYSIS TYPE = TRANSFER FUNCTION FEA RESULTS TYPE = DATABASE TRANSFORMATION = BASIC EQUIVALENT UNITS = 1. FEU UNITS = SECONDS DATABASE = nmatsmas.dbNUMBER FREQUENCY STEPS = 45 NUMBER PSD INPUT = 3 LOAD FILENAME = FSFDS.PMX PSD_DIRECTORY = INPUT ID = 1 FREQUENCY ID 1 = 2.1-1.1-1- FREQUENCY ID 2 = 2.2-1.1-1- FREQUENCY ID 3 = 2.3-1.1-1- FREQUENCY ID 4 = 2.4-1.1-1-
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Linking Fatigue, FE & Dynamics
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Dealing With Dynamics (For Fatigue Analysis) These methods can be applied to any type of full body system,
eg automotive, ground vehicle, aeronautical, space system etc.
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Simulating Operating Loads
Test track
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Dealing With Dynamics (For Fatigue Analysis)
Shaker table simulation of structures or components
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Mode 1
Mode 5
Mode 3 Mode 2
Mode 4
PASCAR type analysis
11.2 Hz 17.6 Hz 8.8 Hz
26.9 Hz 121.4 Hz
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Is it necessary to include dynamic response ? Is the highest possible frequency of loading greater than one third of the 1st natural frequency?
frequency
Transfer function
Fn1st natural frequency
FLHighest loading
frequency
FL < 1/3 FN
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Simple Problem description
What is the stress history and what is the fatigue life?
Local Stress Histories
P2(t)
P1(t) P1(t)
P2(t)
Fatigue
)(tijσ
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Pseudo Static
= Stress for unit load case k
P1,fea=1
P2,fea=1
x
+
=
x
Real Load P1(t)
Real Load P2(t)
Stress time signal at element ij in some predetermined direction
σ ij (t) = Pk (t)σ ij,k
1
⎛
⎝⎜
⎞
⎠⎟
k
∑
1,ijσ
2,ijσ
1,ijσ
2,ijσ
)(tijσ
kij ,σ
FL < 1/3 FN
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Transient
Stress for combined loads calculated by FE point by point.
Local Stress Histories Load Time
Histories
P2(t)
P1(t) P1(t)
P2(t)
For long time histories, there will be issues with solution time and disk space requirements
Fatigue
)(tijσ
FL > 1/3 FN
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Modal Participation Factor method
Stress time signal at element ij in some predetermined direction
∑=m
mijmij tt ,)()( σφσ
1,ijσ
)(tijσ
Modal stress results at element ij for modes
1,2,…m
Load time history at point k=1
Load time history at point k=2
1,2)( == mktφ2,2)( == mktφ
5,2)( == mktφ
3,2)( == mktφ4,2)( == mktφ
1,1)( == mktφ2,1)( == mktφ
5,1)( == mktφ
3,1)( == mktφ4,1)( == mktφ
Combine Participation Factors for each mode
FL > 1/3 FN
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Modal Participation Factors The basis of the Modal Participation Factor (MPF) method is that each loading input can be split up into the contribution factors associated with each mode shape for the structure. In Nastran both the modal stresses and modal participation factors can be extracted from a single sol 112 analysis. The modal superposition is then calculated as follows:
where σ(t) is the output stress tensor
σi is the stress tensor for mode i
φi(t) is the modal participation factor for mode i
∑=i
ii tt )()( φσσ
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PSD Approach
H(f) = Complex frequency transfer function for each load case Sab(f) = Auto & Cross-Power Spectra
P1(f) =1
P2(f)=1
H1(f)
H2(f)
FL > 1/3 FN
)(.)(.)()(2
1
2
1fSfHfHfS abba
ba∑∑==
=
Transfer Function [B]
Output PSD [C]
Input PSD [A]
A x B = C
Mass M
Stiffness K
Sinusoidal Stress with amplitude
Damping C
Sinusoidal Force
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Managing Durability
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Correlation
Durability Management
Data Prep & Analysis
Desired responses
Fatigue Editing
Critical Locations
FE Linked Fatigue
Loads Data Management
System
Edited responses
Calculated responses
Measured responses
RPC Iteration
Drive files Rig Test
Virtual Load Histories
Measured loads
Customer Usage
Measured strains
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The Role of Testing and Analysis
NO
NO
YESYES
CAE based fatigue analysis
Build it
Test it
BeginProduction
OK?� Out of �time?�
Generate idea
Fix it
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Fatigue Analysis vs. Fatigue Testing��
Distribution of FE results
Distribution of test results
Single test result Single FE result
Life results 300 hours 100 hours
Therefore, any fatigue life specified must also be linked to a particular confidence level
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How Testing Supports AnalysisProvision of material fatigue properties Verification of stress/strain analysis results Correlation of life predictions Provision of load data Final sign-off
How Analysis Supports TestingEliminating unnecessary tests Test acceleration Gauge type selection and positioning Test design
Fatigue Analysis vs. Fatigue Testing Testing is not a good way to optimise designs, but is always required for sign-off. Useful fatigue analysis requires verification and good test-based information. Neither Testing nor Analysis have exclusively the “right” fatigue answer; Best results are obtained when an integrated approach is adopted
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Stress-Life Fatigue (elements of)
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More About (Stress-Life) Fatigue Techniques
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Crane failures resulting from crack growth����
Railway accidents can be very destructive�
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What is Fatigue?
• Fatigue is:– “Failure” under a repeated or otherwise varying
load which never reaches a level sufficient to cause failure in a single application. (deformation based approach)
– The growth of an existing crack, or growth from a pre-existing material defect, until it reaches a critical size. (material behavior based approach)
MSC Fatigue offers both approaches
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What is Failure
Crack too big
Crack initiation
Glue joint breaking
Loss of stiffness delamination
Loss of functionality
Durability Fatigue
Damage Tolerance
MSC Fatigue is being extended to deal with non metallic's
Total seperation
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S-N curves
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Grandfather of Fatigue
Between 1852 and 1870, August Wöhler studied the progressive failure of railway axles. He plotted nominal stress Vs. cycles to failure on what has become known as the S-N diagram. Each curve is still referred to as a Wöhler line.
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Designing against Fatigue - Wöhler
Poor fatigue perfomance
• Extreme stress concentration at P • Severe fretting corrosion at P
Designing against fatigue
• Low stress concentration at A • Fretting at B is harmless at A
PB
A
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Example: Using Paper Clips to Generate an S-N Curve
Take 5 paper clips each
Group 1 - apply 45 degree repeated strains
Group 2 - apply 90 degree repeated strains
Plot results on S-N curve
Estimate scatter and discuss!
Load or displacement control?
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A Typical S-N Plot
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Fatigue Technology...�
� Is very old technology (40-160 years old);
� Is a collection of empirical rules that were induced to fit observed behaviour and are generally accepted to work;
� The designer, or engineer, wishing to exploit it should be familiar with the concepts but not necessarily all of the theories
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• S-N (Stress-Life) Relates nominal or local elastic stress to fatigue life
• εε-N (Strain-Life) Relates local strain to fatigue life
• LEFM (Crack propagation) Relates stress intensity to crack propagation rate
Fatigue Technology �The Three Basic Methods�
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Low Cycle v High Cycle (deformation based)�S
N
NSm=K LCF, say <10000
HCF, say >10000
Note that Strain-Life is OK for all N
Strain-Life OK
Stress-Life OK
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Example: Using different material specifications
The nSoft materials database uses the following S-N formulation:
where b and SRI1 are listed amongst the material properties (see Table 3).
N S SRIb− =. 1 log log logNb
Sb
SRI− = −1 1
1
Material Type: Copper Alloy Copper Alloy Copper Alloy
ultimate tensile strength (UTS) 206 MPa 435 MPa 531 MPa
stress range intercept (SRI1) 1037.9 MPa 3254 MPa 3646 MPa
first slope (b1) -0.143 -0.19 -0.19
transition life point (NC1) 1E8 1E8 1E8
Material Name: BS 1861 CU-2.2AL CU-4.2AL
second slope (b2) -0.077006 -0.10497 -0.092896
SAE1008_91_HR
plain car wr st<0.2% c
363 MPa
2289.7 MPa
-0.18
1E8
-0.098901
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Example: Using different material specifications (cont)
However, many companies use the S-N formulation given below:
N S km. = log log logN m S k+ =
mb
= −1
{ }k SRI b= −11
Therefore,
Material Type: OFHC Copper Copper Alloy Copper Alloyultimate tensile strength (UTS) 206 MPa 435 MPa 531 MPa
first slope (m1) 6.99 5.26 5.26second slope (m2) 12.97 9.53 10.76k1 1.24e21 MPa 3.06e18 MPa 5.58e18 MPa
Material Name: BS 1861 CU-2.2AL CU-4.2AL
k2 1.47e39 MPa 2.89e33 MPa 2.20e38 MPa
SAE1008_91_HR
plain car wr st<0.2% c
363 MPa
5.56
10.11
4.63E18 MPa
9.36E33 MPa
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Summary of “variations on a simple approach”
Constant amplitude fully reversed cycles in to S-N diagram
Log S
Log N
1
3 Mean stresses = 1
2
2
1
4 3 2 Palmgren Miner
1
5 Notches, etc, etc, etc..
Rainflow Cycle Counting
Block loading
Irregular sequences
Palmgren Miner
Eg, Goodman
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Block Loading – Palmgren Miner Hypothesis
Palmgren Miner states failure when,
Or when,
nN∑ = 1 0.
0.1...3
3
2
2
1
1 =+++Nn
Nn
Nn
time
1aS 2aS 3aS
1n 2n
3n cycles
Log S
Log N2N
1S
1N3N
2S
3S
Linear Non-interactive
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S
N
100 MPa
60000
Material Life Curve�
Life�Accumulated damage� %�5�.�0�60000�
300� ==�==�∴∴�
Range�
300 Cycles�
100
MPa
�
∑∑�==�i� f�
i�N�N�Damage�
DAMAGE COUNTING WITH MINER
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1.45 x 10-3 300 5001.21 x 10-3 250 25000.98 x 10-3 203 150000.76 x 10-3 157 1203000.68 x 10-3 140 4000000.60 x 10-3 124 10000000.54 x 10-3 112 30000000.45 x 10-3 93 5000000
Strain range recorded Derived stress range (MPa) Number of occurrences
Part of a steel structure, located permanently in the sea, is known to be susceptible to fatigue damage. Strain gauges attached to this part were monitored continuously during the first year of service producing the following information.
Specimen tests on the same material showed that the fatigue limit in air was 156 MPa and that in seawater (no corrosion protection) it was 110 N/mm2. In addition it was found that stresses above either of these levels produced failure according to the following relationship.
3333.825.10196.2 −= SxNAfter 7 years the corrosion protection fails. Determine the expected fatigue life of this structure after failure of the corrosion protection.
Would the original total life of 20 years be achieved?
Example: Stress-Life Fatigue Life Calculation
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During first seven years, damage occurs only at a strain range of 0.76 x 10-3 (157MPa) and above.
Total damage during this period = 0.0437 x 7 = 0.3059.
Therefore, remaining damage to be accumulated = 1 – 0.3059 = 0.6941.
n N n/N with CP
n/N without CP
1.45 x 10-3 300 500 49,700 0.01 0.01
1.21 250 2,500 225,000 0.0111 0.0111
0.98 203 15,000 103 x 106 0.0115 0.0115
0.76 157 120,300 10.8 x 106 0.0111 0.0111
0.68 140 400,000 27.4 x 106 0.0 0.0146
0.60 124 1,000,000 77.7 x 106 0.0 0.0129
0.54 112 3,000,000 187 x 106 0.0 0.0160
0.45 93 5,000,000 854 x 106 0.0 0.0
SΔεΔ
Example: Stress-Life Fatigue Life Calculation (cont)
0.0437 0.0872
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0 ⋅6941
0 ⋅ 0872= 7⋅ 96 years
If corrosion fatigue occurs, amount of damage/annum = 0.0872.Therefore, remaining life after breakdown of protection is
NB. Life = remaining damage factor / damage per year
With corrosion protection the life would be 22.9 years.
Without corrosion protection the life would drop to 14.96 years.
The above example demonstrates the reduction due to subsequent corrosion.
Example: Stress-Life Fatigue Life Calculation (cont)
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Effect of Mean Stress
Ultimate strength, σσult
Alternating Fatigue Strength (endurance limit σσe)
Mean Stress. σσm
Alte
rnat
ing
Stre
ss, σσ
a
Goodman Law
1==++ult
m
e
aσσσσ
σσσσ
Gerber Parabola 12
==⎟⎟⎟⎟⎠⎠
⎞⎞⎜⎜⎜⎜⎝⎝
⎛⎛++
ult
m
e
aσσσσ
σσσσ
[Index is material dependant]
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Correcting for the Effect of Mean Stress (Stress-Life Method)
• Goodman method σσa/Se + σσm/Su = 1 • Gerber method σσa/Se + (σσm/Su)2 = 1
Goodman and Gerber are approximately upper and lower bounds
σσa = stress amplitude σσm = mean stress Su = ultimate tensile stress Se = equivalent stress for σσm = 0
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Mean Stress Correction – Multiple S-N Curves
104 105 106 107 108 1090
100
200
300
Cycles to failure
Stre
ss A
mpl
itude
, Sa (
Mpa
) R = - 1
Sm = -138 (R = - 4)
Sm = 414 (R = 0.53)
7075-T6 Al
Some software products allows fatigue analysis with multi-mean stress curves. These curves (S-N curves for different R-Ratios) which account for mean stress effects in S-N method by Goodman, Gerber or other empirical methods.
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A component undergoes an operating cyclic stress with a maximum value of 759 MPa and a minimum value of 69 MPa. The component is made from a steel with an ultimate strength Su of 1035 MPa, an endurance limit Se (at 106) of 414 MPa and a fully reversed stress at 1000 cycles, S1000 of 759 MPa.
Plot a Goodman diagram with 2 constant life lines on it corresponding to 103 and 106
cycles. These must both go through Su on the zero mean stress amplitude (x) axis and the appropriate points on the stress amplitude (y) stress axis which are the endurance limit, Se, and S1000 values (see Figure below).
Example: Correcting For Mean Stress Effects
Sa=345Sm=414
103
106
759
573
414
Su=1035
Altern
ating S
tress
S a (M
Pa)
Mean Stress Sm (MPa)
.
S a=0 =
S 0
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= 345MPa�
= 414MPa
When the stress conditions for the component (Sa = 345 MPa, Sm = 414 MPa) are plotted on the Goodman diagram, the point falls between the 103 and 106 life lines. This indicates that the component will have a finite life, but the life is greater than 1000 cycles. This 3rd line intersects the fully reversed alternating stress axis at a value of 573 MPa.
By taking one vertical (zero mean stress) slice through this diagram the equivalent (zero mean stress) S-N diagram can be envisaged.
A 3rd line can be drawn through Su (on the x axis) and another point defined by the operating stress.
269759
2SSS minmax
a−
=−
=
269759
2SSS minmax
m+
=+
=
Example: Correcting For Mean Stress (cont)
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The value for Sn can now be entered on the S-N diagram to determine the life of the component Nf. (Recall that the S-N diagram represents fully reversed loading). When a value of 573 MPa is entered on the S-N diagram for the material used for the component, the resulting life to failure can be obtained graphically as Nf = 2.4 x 104 cycles. Alternatively, this figure can be obtained using the S-N equation stated earlier.
106310 410 510
Alte
rnat
ing
Stre
ss, S
(MPa
)
Life to Failure, N (cycles)
S = 7591000
S = 573nS = 414e
N = 2.4 x 10 cycles4
Example: Correcting For Mean Stress (cont)
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An example of R ratio - R=Smin/Smax
-200
-100
0
100
200
300
400
500
600
-2
-1.5
-1
-0.5
0
0.5
1
Typical stress signal
Rratio R
=inf
R=
-1
R=
0
R=
0.5
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FKM Method The FKM method uses 4 factors M1-4 which define the sensitivity to mean stress in 4 regimes:
I R>1II –infinity <= R < 0III 0<= R < 0.5IV 0.5 <= R < 1
The values of M1-4 can be determined from material tests or estimated from material specific empirical coefficients.
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Multiple S-N Mean Stress Curves
• Some software products allows fatigue analysis with multi-mean stress curves. These curves (S-N curves for different R-Ratios) which account for mean stress effects in S-N method by Goodman, Gerber or other empirical methods.
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Mean Stresses
mean stress
stress range
stre
ss
2minmax
mσσ
σ+
=
σσmax
σσmin
max
minRσσ
= mean stress ratio
mean stress
R ratio Loading condition R>1 σσmax and σσmin are negative,
negative mean stress R=1 Static loading 0<R<1 σσmax and σσmin are positive,
positive mean stress R=0 Zero to tension loading, σσmin = 0 R=-1 Fully reversed, zero mean stress R<0 abs(σσmax) < abs(σσmin),
σσmax approaching zero R infinite σσmax = 0
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R-ratio = -0.5
R-ratio = +0.5
Mean Stress Using Multiple S-N Curves
● Damage is calculated from appropriate S-N Curve, or by interpolating between curves
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Rainflow Cycle Counting
• How do we identify cycles in a random variable amplitude loading sequence?
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Rainflow Cycle Counting – Original definition
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[1]. Extract peaks and troughs from the time signal so that all points between adjacent peaks and troughs are discarded.
[2]. Make the beginning, and end, of the sequence have the same level. This can be done in a number of ways but the simplest is to add an additional point at the end of the signal to match the beginning.
[3]. Find the highest peak and reorder the signal so that this becomes the beginning and the end. The beginning and end of the original signal have to be joined together.
[4]. Start at the beginning of the sequence and pick consecutive sets of 4 peaks and troughs. Apply a rule that states,
Rainflow Cycle Counting – Practical definition Long-short-long rule
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If the second segment is shorter (vertically) than the first, and the third is longer then the second, the middle segment can be extracted and recorded as a Rainflow cycle. In this case, B and C are completely enclosed by A and D.
[5]. If no cycle is counted then a check is made on the next set of 4 peaks, ie peaks 2 to 5, and so on until a Rainflow cycle is counted. Every time a Rainflow cycle is counted the procedure is started from the beginning of the sequence again.
Eventually all segments will be counted as cycles and so for every peak in the original sequence there should be a corresponding Rainflow cycle counted. There will be 5 cycles obtained from 10 peaks and troughs.
Rainflow Cycle Counting – Practical definition (cont)
A
BC
D
or
A
B C
D
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Peak 1 2 3 4 5 6 7 8 9
Value 0 135 67.5 112.5 22.5 112.5 45 90 0
Example: Rainflow Cycle Counting
Cycles
Range 45 90 135
Mean = 67.5 1 1 1
Mean = 90 1
0
22.5
45
67.5
90112.5
135
As an example of this let us extract Rainflow cycles from the following sequence.
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Variable Amplitude Loading • SN tests are conducted under constant
amplitude sinusoidal loading
• Real loading is usually fairly random
• The question is how do we break down real loads into equivalent cycle ranges so we can use the same SN curves?
• The is done using Rainflow Cycle Counting
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The importance of the S-N relationship
mSKN =
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Strain-Life Fatigue (differences from Stress-Life)
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The Strain-Life (Local Strain, ε-N, or “Crack Initiation”) Method
• Relates local strain to fatigue damage at that point • Useful when cycles have some plastic strain component • Suitable for predicting life in components which are supposed to be
defect free, i.e., not structural joints, sharp features, etc.
(Low Cycle Fatigue – LCF)
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• MSC Fatigue Features – Based on Local Strain Concepts – Mean Stress Correction – Elastic-Plastic Conversion – Statistical Confidence Parameters – Palmgren-Miner Linear Damage – User Defined Life – Cyclic Stress-Strain Modeling – Surface Conditions – Factor of Safety Analysis – Biaxiality Indicators – Multiple Loads
Strain-Life (ε-N):
σσ��1/2cycle�
1cycle�
1/2cycle�
1cycle�1cycle�
1/2cycle�
Strain�
εε�
Time�
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Cyclic Testing - Hysteresis Loops and End Point Definition
2Nf
Stabilized Hysteresis Loop
Stre
ss
Stra
in
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Stress-Strain Relationships
Monotonic:
Cyclic:
εε = σσ��E
+1/n
[ ] σσ��K
εεa = σσa σσa
E K’
1/n’ + [ ]
a = amplitude!
Ramberg-Osgood Relationships
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EN Fatigue Tests
• Specimens are subjected to constant amplitude strain using an extensometer in the servo loop
• EN test controls plastic strain, the parameter that governs fatigue
• The number of cycles to crack initiation is plotted against the total strain on a log-log plot and the best fit curve computed
( ) ( )cffb
ff
a NNE
22 `` ⋅+⋅= ε
σε
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Elastic & Plastic Components (Due to Basquin, Coffin and Manson)
(2Nf)b + εεf’(2Nf)cσσf
’
EΔΔεε��22��
=
Elastic (Basquin)
Plastic (Coffin-Manson)
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Neuber’s Rule
The strain concentration factor,
and the stress concentration factor,after plastic yielding.
Neither are known but Neuber suggested that the square root of the product of the stress and strain concentration factors was equal to Kt .Hence Neuber’s Rule is simply:
Re-arrangement of this Rule gives a useful equation:
eKe
ε=
SK σ
σ =
( )2. Te KKK =σ
( ) σε=SeKT2
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Another re-arrangement gives:
in which the LHS is known. This can be solved with the cyclic stress strain curve equation simultaneously to derive σσ and εε ��
Topper simply replaced Kt by Kf to make Neuber’s Rule applicable in fatigue analysis for local stress strain tracking.
Use of Kf in Neuber’s Rule
( ) σε=EeKT2
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1
23
Kf
σσ��
e
s
εε��
Cyclic Stress Strain Curve
NeuberEquation
Solution point
Graphical Solution for Local and εσ
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Morrow Life Plot
Stra
in A
mpl
itude
(M/M
)
Life (Reversals) nCode nSoft
STW Life Plot
STW
Par
amet
er (M
Pa)
Life (Reversals) nCode nSoft
Morrow Smith-Topper-Watson
( ) ( )Δ
ΕΝ Ν
ε σ σε
22 2= + f m
fb
f fc'
' ( ) ( ) c+bfff
2bf
2f
max 2''2'2
Ν+ΝΕ
=Δ
σεσ
σε
Correcting for Mean Stress
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Post Processing Results
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to:– Estimate Life of Initial Design – Define Fatigue Critical Regions – Determine Factors of Safety – Evaluate Multi-axial Conditions – Plot “quality”, eg stress mobility or
2nd principal value
Log of Life or Damage�
Global Multi-Location Analysis
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Post-processing: Results
• Tabular Results of: – Individual Nodes/Elements – Most Damaged Nodes/Elements – Statistical Summary of Damage Distribution – Interactive Results Interrogation of All Life and
Damage Estimates – Factor-or-Safety – Multiaxiality Indicators
• Red / Yellow / Green Indicators
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Post-processing: Histogram Plots
Cycles vs. Damage�
Range magnitude
Mean stress level
Number of cycles
+ve
-ve
Range magnitude
Mean stress level
Damage
+ve
-ve
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Post-processing: Design Optimization • Localized Analysis for Evaluation of
Alternative: – Surface Conditions – Material Types / Parameters – Statistical Confidence – Loading Conditions – Residual Stresses and Stress
Concentrations – Mean Stress
• Search for Better/Worse Material • Calibration to Test Results • Sensitivity Calculations
An Traditional FE Based Fatigue Design (eg MSC Fatigue)
14/10/2012 152
Sensitivity Analysis and Optimization
Geometry & FEA (Stress/strain) Results
Loading and/or Test (Lab) Results
Materials Information
Damage Distributions
Fatigue Life Contours
Tabular Results
Analysis Options
• Stress (total) Life
• Strain (initiation) Life
• Crack Propagation
• Vibration Fatigue
• Multiaxial Fatigue
• Spot & Seam Weld
• Wheels Fatigue
• Software Strain Gauge
• Utilities
Everything else is post processing
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Intro to Crack Growth Methods (Fracture & Damage Tolerance)
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Fracture & Damage Tolerance
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Background to Fracture Mechanics
• Relatively new field of engineering developed since start of 20th century. • 1913, Inglis, ‘Stresses in a Plate Due to the Presence of Cracks and Sharp
Corners’ introduction of infinite stress concentration. – Study of plate with circular hole & elliptical hole.
• 1921, Griffith elastic energy balance approach. (Tests on glass rods). – Crack propagation will occur if energy released on crack growth is sufficient
to provide all energy required for crack growth, i.e. energy cannot be created or destroyed.
• 1957, Irwin developed stress intensity factor approach. – Introduction of the term ‘fracture toughness, Kc’– Fracture process at crack tip cannot be related to local stress due to
singularity (see later notes). – SIF is used based on stress remote from crack tip.
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Will a crack grow?
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Ductility~Brittleness
• Increasing the yield strength of a metal by processes such as cold work, precipitation strengthening and solution strengthening generally decreases the ductility.
• Reducing temperature reduces toughness and ductility.
Ductility is the ability to deform irreversibly without fracture.
Stress
Strain
Toughness
Temperature
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Ductility~Brittleness, cont’d
• Rupture is the void nucleation around inclusions. (The fracture surface shows the halves of the holes, hence appears dull).
• Cleavage is the splitting apart of atomic planes. Each plane or facet is flat and causes the surface to sparkle when fresh.
• Both modes are fast, though brittle failure occurs at 3 times that of ductile. (1600m/s ~ 500m/s).
There are only two mechanisms by which fracture can occur, namely:
Ductile (or dimple) Rupture Cleavage
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Trade-off, strength~toughness
Material Yield Strength KIC MPa ksi MPa√√m ksi√√in
Aluminum alloy (7075-T651)
495 72 24 22
Aluminum alloy (2024-T3)
345 50 44 40
Titanium alloy (Ti-6Al-4V)
910 132 55 50
Alloy steel (4340 temp @ 260°°C)
1640 238 50 46
Alloy steel (4340 temp @ 425°°C)
1420 206 87 80
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Crack Initiation and Growth
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Formation of a crack causes local stress concentration at the crack tip. The area ahead of the crack is now undergoing cyclic plastic deformation.
Crack
Stress concentration
Initiation and Propagation
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Slip and Stage I Growth
Alternating Stress
Crystal surface
Slip bands formalong planes ofmaximum sheargiving rise tosurface extrusionsand intrusions
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Fast brittle fracture Beachmarks due to
crack propagation
Striations
Stage II Growth
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Two surface cracks in plates subjected to tension and bending - experimental observation
Verification of Crack Shape Development
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Micro-structural Short Cracks
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Concept of Damage Tolerance
Definition: A structure is said to be damage tolerant when in a damaged state it can still sustain acceptably high loads. This term was introduced after numerous unexpected incidents involving military aircraft.
Note: The civil (commercial) aircraft manufacturers can seldom justify the enormous costs required to pursue an innovative research program. The military usually can.
[The accepted worldwide certification standards for aircraft civil certification are JAR/FAA Chapter 25.571.]
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Damage Tolerance – U.S. background
In 1969, a wing pivot fitting of an F-111aircraft failed under a steady 4g manoeuvre after 105FH. The failure resulted in loss of aircraft. The fitting was designed for 11g!
In 1970, the USAF started to develop a Damage Tolerance Philosophy in order to eliminate the type of structural failures and cracking problems encountered on many aircraft.
In 1974 a document entitled ‘Airplane Damage Tolerance Requirements’ MIL-A-83444 was issued.
In 1996, ‘Aircraft Structural Integrity Program’ MIL-HDBK-1530 – Approved for public release.
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Specification requirements
Satisfaction of the design guidelines can be achieved by consideration of what are now standard philosophy.
• Proper material selection and control. • Control of stress level. • Use of fracture resistant design concepts. • Manufacturing process control. • Use of qualified inspection procedures.
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Approach to certification
• Define aircraft utilisation. • Develop CG load factor spectrum. • Select critical locations for evaluation (SSI’s). • Develop stress spectra for each SSI. • Establish basic crack growth analysis method. • Obtain material properties (da/dN, KIc etc).• Determine residual strength under limit load conditions. • Produce crack growth curve for each feature. • Liaise between manufacturer, operator & certification authority. • Collectively decide on inspection methods, intervals.
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Crack growth curve.
Total Life
Inspection Period
CrackLength
Time ai
ac
ad
Threshold
Inspection Period Repeat Inspection Period
ac = Critical crack length ad = Detectable crack length ai = Initial crack length
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Crack lengths.
• ac This is the ‘critical’ or permissible length at which the structure is considered failed. (Kcexceedence or NSY).
• ad This is the ‘detectable’ crack length at which the chosen method of inspection is likely to identify.
• ai This is the ‘initial’ crack length as is a function of several factors including inspection technique employed, quality of access, available lighting etc.
As the majority of crack growth occurs during the early stages of propagation, the choice of aihas a profound effect on life and inspection interval.
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Inspection techniques.
• Visual. Feature must be easily accessible. Inspectable size is large (>50mm) resulting short (and expensive) intervals.
• Penetrant. Coloured, fluorescent liquid is sprayed onto surface, which penerates crack. Surface then washed carefully and a developer applied. UV light is then shone onto component to reveal any surface cracking.
• Magnetic particle. Similar to above except the liquid contains magnetic particles which when placed in a magnetic field and observed under a UV indicate any cracking. Component must be removed from structure and inspected in a special cabin. Components must be magnetic!
• X-Ray. X-rays pass through structure and are caught on film. Sensitive but not reliable for surface flaws. Component must be examined in laboratory.
• Ultrasonic. Probe transmits high frequency wave into material. The wave is reflected by the crack. The time taken between pulse and reflection indicates position of crack.
• Eddy current. Coil induces eddy current in the metal, which induces a current in the coil. Under the presence of a crack, the induction changes. Ideal for bores and holes. Cheap but sensitive technique.
• None! This ‘method’ assumes total failure, hence, adjacent structure must withstand redistributed loads. Results in a severe weight penalty in order to achieve a multi-load path ‘Fail Safe’ design. No inspection cost. Consider safe life approach.
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Inspection intervals. Two types of inspection interval require calculating;
• Threshold
• Repeat
Generally the inspection requirement is governed by the end user. The engineering must comply…
The threshold inspection is the first time an aircraft has to be inspected. Usually this is taken as the fatigue life divided by 5. Or, what is more likely, the operator will determine when the first inspection will take place, eg 5 yrs, 15000 FH. This then sets the required fatigue life. i.e. Fatigue life = 15000 x 5 = 75000 Flying Hours.
The repeat inspection interval is the time from detectable to critical divided by a suitable factor, between 2 & 4 (dependant on confidence of data, test backup etc.) This then allows the inspector more than ‘1 bite of the cherry’ to detect the pre-critical defect.
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Linear Elastic Fracture Mechanics
Most Aerospace materials exhibit some ductility, but are brittle (or semi-brittle) from an engineering point of view.
• Overall behaviour to failure is elastic.
• Hence behaviour is termed linear elastic.
• Analysis using linear elastic fracture mechanics (LEFM).
LEFM assumes that the body deforms as a linear elastic material except in a small region near the crack tip. This requires that the global stresses are below the yield stress, typically σσapplied < 0.8σσyield for LEFM to be valid.
Not valid when macroscopic yielding occurs prior to fracture, this is covered by Elastic Plastic Fracture Mechanics, EPFM. (Beyond the scope of this course!)
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The Concept of Stress Intensity
σσ TK=max 3=TK )21(baKT +=
∞=TK
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Stress Intensity Factor (SIF)
• Primary Equation: K = ββσσ((ππa)1/2
ββ is a dimensionless factor dependent on geometry which is sometimes called a Compliance Function (Y). The factor includes crack length and crack geometry amongst other things
σσ is the stress which occurs remote from crack tip. MPa
a is the crack length. m – do not forget this!
If two cracked components exist each of same material, but differing crack lengths, they will respond in the same manner if they have the same SIF (K).
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Stress Intensity Factor Coefficient (ββ)
• Sometimes referred to as ‘dimensionless stress intensity factor’. • Independent of material properties & loading magnitude. • Accounts for geometric effects (boundaries). • SIFC solutions are generally plotted in a non-dimensional form, by dividing
through by a suitable parameter. • Can be considered analogous to the stress concentration used in fatigue
analysis, Kt.
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Example :Edge crack in a finite width sheet
SIFC (ββ)
ββ��
a/b1.12
0 0.1 0.2 0.3 0.4
β = 1.12-0.23(a/b)+10.6(a/b)2-21.7(a/b)3+30.4(a/b)4
Reference Brown & Strawley STP 410 ASTM (1966).
a
b
σσ��
σσ��
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Mode I crack Growth through a solid
2c
a
t
Modes of Crack Growth • When considering stresses at crack tip, it is important to understand loading
mechanism present. Though in reality modes II & III are seldom experienced.
Mode I (Opening)
Mode II (Sliding)
Mode III (Tearing)
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When the SIF at a crack reaches a certain value, rapid unstable crack growth occurs.
This value is known as the Fracture Toughness Kc, or
KIC to indicate which mode.
The critical crack size (ac) occurs when SIF (K) = Kc.
This material property significantly varies with component thickness.
Fracture Toughness
Kc = ββσσ((ππac)1/2
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Stress field ahead of crack.
Crack
σσ
r
σσ
σσfield
σσK2ππ r
:=
Consider a small crack in a large body subjected to a remote stress, σfield. The crack acts as a stress concentration – infact, theoretically, the stress tends to infinity as we get close to the crack tip and for an elastic material the stress distribution is given by the ‘square root singularity’. (A singularity stress field is a stress field that tends to infinity at some point in the body).
Note: ‘r’ is distance from crack tip. σσfield
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B
Crack Tip Plastic Zones
ry
Crack
σσy
LocalStress
Crack Length
ry
Crack Length rp ~ 2ry
Crack
A
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Load Interaction effects.
• A single overload retards crack growth ( for a limited time)
• A –ve load following the overload reduces the benefit but does not eliminate it.
• A heavy compressive overload can have the effect of accelerating crack growth.
• Unless accurate spectra is available, it is considered prudent to ignore load interaction.
The above sketch shows how three single overloads increase the crack growth life by almost 5.
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Fracture Toughness
Thickness, t (mm)
Frac
ture
To
ughn
ess
KIC
KCmax
Plane Stress
Transitional Behaviour
Plane Strain
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Plane Stress ~ Plane Strain.
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Thickness effects • Thin material does not permit a state of tri-axial tension to
exist, i.e. there is no through-the-thickness stress, σz = 0. This is the definition of ‘bi-axial’ stress.
• For plane stress, yielding takes place when the maximum principal is equal to the yield stress. For plane strain, much higher stresses are required.
• Yielding is plastic deformation which takes place by slip, it is therefore caused by shear stresses.
• Thick materials (> 6mm approx) plane strain, prohibit the ‘thinning’ of the plate local to the crack and if the stresses in all three planes are equal, ‘tri-axial’, then there is NO SHEAR.
No shear = no deformation = low toughness
This is the definition of brittle.
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Fatigue and Cracks
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Crack Growth Data
Smax
SminR=Smin/Smax=0.5
Stre
ss
Time
Kmax
Kmin
K
Time
ΔΔK increase as crack extends
dN
da
Cra
ck L
engt
h
N
a
Kmin = ββσσmin((ππa)1/2
ΔΔK = Kmax - Kmin
Kmax = ββσσmax((ππa)1/2
Growth Rate = da/dN
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Propagation Rates
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Representation of Data
Log ΔΔK
da/d
N
X
X
X
XXX X
XX
X
X XXX X XX
XXXXXXX
XXXX
XX
XX
Log ΔΔK
da/d
N
X
XX
X
XXX X
XX X XXX X XX
XXXXXXX
XXXX
XX
XX
Paris Equation. Forman Equation.
(( ))nKCdNda
ΔΔ==(( ))
⎟⎟⎠⎠
⎞⎞⎜⎜⎝⎝
⎛⎛−−−−
ΔΔ==
RKKKC
dNda
c
n
11
max
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Calculating Lifetimes
Need:
• Initial crack size
• Final crack size
• Stress IF range
• ββ coefficient
• Material growth law
da/dN = C(ΔΔK) m (Paris Law)
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Crack Growth Calculation Process
(v) Integrate this equation between a = ai and a = af to give the number of cycles needed to grow a crack from ai to af. This is the predicted life of the component. A classical integration is adequate if the Compliance Function is constant. Other Compliance Functions will require a numerical integration, as will any non-constant amplitude signal. Check if ai is critical (Kmax vs Fracture Toughness).
dNda
dNda
dNda 21 ××==
(i) Estimate the size of crack likely to be present in the component when it is first put into service, ai.
(ii) From a measured value of KIc, estimate the maximum crack length, ac, which the component will tolerate when the applied stress reaches maximum tension. An expression for the crack-tip stress intensity factor will be needed.
(iii) Using the same expression for crack-tip stress intensity factor and a value for ββ, then calculate Kmax & Kmin at ai, and hence ΔΔK.
(iv) Substitute ΔK into the Paris equation to obtain a crack propagation rate. This will put da/dN in terms of crack length a.Calculate geometric mean if necessary,
dNdaaNi
ΔΔ==ΔΔ
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Example: Crack Growth calculation using the PARIS equation.
Problem: A plate of width 200mm contains an edge crack of initial length 12mm. The plate is subject to a cyclic uniaxial stress of 50MPa +/- 25MPa.
• Calculate the no. of cycles to grow the crack to 42mm.
• What is the critical crack length?
Data
ββ = 1.12-0.23(a/b)+10.6(a/b)2-21.7(a/b)3+30.4(a/b)4.
Assume Paris equation, where C = 1.14x10-10, n = 3.75.
Fracture Toughness = 33.3MPa m0.5.
Suggest use steps of 6mm.
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Worked Example
0.012 0.06 1.14 16.6 5.5 11.1 9.377E-071.440E-06 4167
0.018 0.09 1.17 20.9 7.0 13.9 2.211E-063.083E-06 1946
0.024 0.12 1.21 24.9 8.3 16.6 4.301E-065.805E-06 1034
0.030 0.15 1.27 29.2 9.7 19.5 7.835E-061.014E-05 592
0.036 0.18 1.33 33.5 11.2 22.4 1.311E-051.668E-05 360
0.042 0.21 1.4 38.1 12.7 25.4 2.122E-058099
a a/b ββ Kmax ΔΔNKmin ΔΔK da/dN Geometric Mean
Crack critical at 36mm hence total growth time to critical = 8099 - 360 = 7739 cycles.
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Notches and Joints
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Stress Concentrations
• Discontinuities introduce ‘stress concentrations’.
• Kt is the theoretical stress concentration factor – Kt is geometry dependant – Value of Kt is seldom reached in ductile materials – Material yields and the loading (stress) redistributes
• Kf is the fatigue stress concentration factor – Kf is dependant on both geometry and material – Kf also known as fatigue notch factor
specimennotchedofstrength Fatiguespecimenunnotchedofstrength FatigueKf =
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Notch Sensitivity Factor, q
• The value ‘q’ for a specific material remains fairly constant, independent of notch geometry
q1
1α
r+
:=
• Most common equation for estimating q;
q =K f −1
Kt −1
Ref. Peterson. Page 11.
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Notch Sensitivity Factor, q
• Typical values of α are: – Ref. Peterson
α = 0.51mm aluminium alloys
α =0.254mm low strength steels (quenched & tempered)
α = 0.063mm high strength steels(σu > 800 MPa) (annealed or normalised)
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Use of Kt with Material Data
Kt=1 Kt=2 Kt=3
Reduced qEffect
Full Kt Effect
Alte
rnat
ing
Stre
ss
Cycles to Failure
1 10 100 1000 104 105 106 107
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Use of Kt with Material Data
• Fatigue calculations for notched location
– Performed using plain (unnotched) S-N data – Theoretical stress concentration factor, Kt used – Fatigue calculation will be pessimistic
• IMPORTANT NOTE – Kt is always related to a reference stress. Some data sheets use net stress
and others gross stress. Care must be exercised in applying the Kt to the appropriate reference stress. American methodology often relate Kt to bearing stress.
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Notches Kt = Stress Concentration Factor (geometry based)
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1E3 1E4 1E5 1E6 1E7 1E8
200
400
600
8001000
SMOOTH
Kt=3, Kf=2.67
NOTCHED UNNOTCHED
Life(Cycles)
Nom
inal
Str
ess
Am
plitu
de(M
Pa)
The Effect of Kt and Kf on Fatigue Life
Smooth/2.67
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Notches
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Joints
• The prime function of a joint is to transmit load from one part to another. They include: – Lugs – Rivets– Assemblies of bolts and rivets – Bolts – Bondings– Welds
• Fatigue problems often occur within joints. • The concept of similitude is doubtful for this structure.
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Lugs
• A lug is a simple joint with a single pin or bolt. Often single load path. • Kt for lugs are generally high. • Fatigue limits can be very low due to secondary effects such as fretting and
pin-bending. • Size effect significantly influences fatigue life. • Life prediction excludes methods based on basic material fatigue properties. • Lugs are rarely critical statically.
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Riveted Joints
• Well designed riveted joints can possess good endurance characteristics, if loaded in shear only.
• Rivets ‘swell’ on installation causing plastic hole expansion and providing support to the hole wall.
• Rivet squeeze improves clamping. Additional loadpath created at interface due to friction.
• The friction developed can promote fretting.
• Static analysis assumes equal load transfer for each rivet – NOT SO IN FATIGUE.
• Joint failure usually occurs at the first (row) fastener – unless engineered otherwise.
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Derivation of Fastener Loads
– Elastic distribution of fastener loads in a simple joint
P P
Kf=fastener spring constantK = AE/l (plate)
l
0.4P
0.3P
0.2P
0.1P
0
Kf=K
Kf=0.4K
Kf=0.1K
Fastener load distribution of five rows of fasteners
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Derivation of Fastener Loads
• Long continuous joints (typically > 10 fasteners). – Central fasteners - equal load distribution assumed.
• Short joints – Load distribution determined by:
• Modelled using MSC NASTRAN • Derived using data sheets (i.e. Niu).
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Bolted Joints
• Bolts can be loaded in either shear or tension or both.
• If the ‘fit’ of the bolt is tight, then fatigue benefits can be gained. With an interference fit bush, the benefit is greater
• Significant ‘clamp-up’ can be generated, improving life, (friction load-path). In the railway industry this is often the only loadpath in many applications. Tight fit is expensive.
• Tensile fatigue spectra can be very damaging to under-head and to the threads. High Kt’s exist here.
• Threads and under head radii must be rolled in fatigue critical areas if subject to tension.
• Tension bolts can be pre-loaded to significantly improve life.
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Bonded Joints
• Bonding – no holes! High quality and durable joints are possible.
• The major cause of premature failure of riveted or bolted joints is eliminated. FRETTING. A major advantage.
• Overlap greater for bonded joint. Lower secondary bending effects.
• Two failure modes can arise; • Adhesion or cohesion failure. Not so common due to improvements in surface
treatment & adhesive quality. • Plate failure due to kt effect and secondary bending.
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Welded Joints
The term ‘welded joints’ relates many to techniques;
• Arc welding • Gas welding • Electron beam welding • Laser welding • Resistance spot welding • Friction welding and more…
Analysis of welded structure can be very complex and can be considered a discipline on its own.
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Welded Joints
• Welding is known for its own characteristic failure modes.
• These modes have initiated the development of many NDI techniques.
• Welding is unsuitable for materials with high static strength obtained by heat treatment. The welding process will destroy this treatment.
• Thin sheets can suffer distortion due to the heat flux, however, spot welding can be an attractive welding process for such a case.
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Welded Joints
Some terms and defects of a butt welded joint.
Excess weld material
Heat affected zone (HAZ)
Weld Toe
Base metal
Slag Inclusions
Porosity Lack of
penetration
Lack of fusion
Undercut
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Welded Joints
• General aspects of butt joint example (Welded one side only). – Major defect is the root failure (lack of penetration). Produces surface crack
characteristics. – Undercuts can have a sharp profile ~ high Kt. – Slag inclusions act as initial flaws and are more serious than porosity due to the
shape of these defects.
• The fatigue strength of a weld is a direct function of the quality of the weld. NDI is implicit in the quality.
• The fatigue strength of welded aluminium structure is low.
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Welded Joints
• Welding introduces residual tensile stresses due to thermal effects – the cool down from melting temperature to room temperature.
• Impractical to re-heat treat the structure.
• Fatigue is improved significantly by; – Grinding the excess weld material and the weld toe. This reduces Kt – increases
life. – If possible introduce ‘backing bars’ to permit ‘full penetration’ weld. Cost! – Stringent quality control. Use of NDI. Cost!
• Life obtained using traditional S~N approach with curves appropriate for each ‘class’ of weld. F.E. analysis now also possible.
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EFFECT OF WELDING ON DURABILITY
Parent material Fusion zone Heat affected zone
Weld toe
Seam weld in a tube, showing grain structure
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EFFECT OF WELDING ON DURABILITY (CONT.)
• The fatigue properties of a welded joint are completely different from those of the parent plate because of: – Fairly sharp and ill-controlled geometric features – Defects such as slag inclusions – Residual stresses (usually unknown) – Heat affected zone
• Fatigue properties of welds in a range of steels have much less variation than in the parent plate
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• Welds generally coincide with geometric features, changes in section, etc
• The fatigue strength of welded joints is in general much less than that of the “parent plate”
• Even in well-designed welded structures, the welds are the most likely failure locations
S-N Data PlotclassFSRI1: 1.201E4 b1: -0.3333 b2: -0.2 E: 2.07E5 UTS: 500 BS4360-50DSRI1: 1903 b1: -0.123 b2: 0 E: 1.914E5 UTS: 480
1E1
1E2
1E3
Stre
ss R
an
ge
(M
Pa
)
1E3 1E4 1E5 1E6 1E7 1E8Life (Cycles)
EFFECT OF WELDING ON DURABILITY (CONT.)
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SPOT WELD FATIGUE
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MOTIVATION FOR SPOT WELD ANALYSIS
• About 50% of automotive structural durability problems are associated with spot-welds
• About 80% of automotive body durability problems are associated with spot-welds
• The tooling cost for one spot weld on an automated production line is about $30,000
• Late additions may cost twice this amount • Besides any structural importance, the durability of spot welds can have an
important effect on perceived quality, ie, squeaking and rattling
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STRUCTURAL STRESS-BASED (LBF) METHOD
• Coarse mesh, with spot welds modeled as stiff beam elements
• Beams are used as force transducers to obtain forces and moments transmitted through the spot welds
• Forces and moments in the beams are used to calculate structural stresses , around the edge of the weld spot
• Life is calculated using Miner's rule • Method is generally applicable and can handle
multiaxial loads
( Rupp - Storzel - Grubisic )
Spotweld Nugget
d
Beam Element
d
ShellElements
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AUTOMOTIVE PART WITH SPOT WELDS
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FATIGUE ANALYSIS WITH SPOT WELDS
Optimization & Testing
Loading (Time History)
Material (Weld S-N Data)
Geometry (Beam Elements)
Fatigue Analysis (Spot Weld Analyzer)
Post Processing
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EXAMPLE LOAD HISTORY ON A DAMPER
Vertical Loads on Damper Mounting
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STRUCTURAL STRESS CALCULATIONS
The structural stresses are calculated from the forces and moments on each beam element :
Sheet 2 Weld Nugget
Sheet 1
Fz
Mx
Fx
Fy
My
My
Fy
Fx Mx
Fz
Fz
Mx
Fx
Fy
My
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Stresses in sheet :
STRUCTURAL STRESS CALCULATIONS (CONT.)
• Stresses vary as a function of angle • Similar equations for stresses in nugget • Corrections made for size effect
Fz
Mx
My
Fy
Fx
s�
d�
σ�π�r�
x�y�F�
ds�,�max�,�=�
σ� r�z�F�
s�=�1�744� 2�.�
σ� r�x� y�M�
ds�,�max�,�.�=�1�872� 2�
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S-N CURVE DETERMINATION
• Specimens tested include H-shear (shown), H-peel, hat-profile, etc.
• Specimens must be modelled and analysed to determine structural stress for S-N curves
• S-N data falls in single scatter band for sheet failure
• Nugget failure is rare (under-dimensioned welds)
• 3 sheet welds handled by treating as 2 welds and ignoring middle sheet failure
S-N Data Plotspot_nugget_genericSRI1: 2100 b1: -0.1667 b2: -0.09091 E: 2.1E5 UTS: 500 spot_sheet_genericSRI1: 2900 b1: -0.1667 b2: -0.09091 E: 2.1E5 UTS: 500
1E2
1E3
1E4
Str
ess R
an
ge
(M
Pa
)
1E2 1E3 1E4 1E5 1E6 1E7 1E8Life (Cycles)
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EFFECT OF WELDING ON MATERIAL PROPERTIES
● When steels of widely differing grades are welded, the resulting S-N curves tend to fall within a single scatter band
● Therefore generic curves are suitable for most purposes
Spot Weld Load-Life Curves
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LIFE PREDICTION OF SPOT WELDED STRUCTURES
FE - Model
nugget sheet metal
R = 0
Fz
MxMy
Fx
FyF(t), M(t)
Analytical model
σσ(θθ,t)
δδx(t)
MBD model
Damage calculation
Post-processing
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GENERAL PROBLEMS WITH MODELLING SPOT WELDS
● Inconvenient meshing (node-to-node matching)
● Model stiffness is a little too low
● Requires different models for durability, NVH, etc.
● Method rather pessimistic for high loads (when plastic deformation is significant)
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MODELLING SPOT WELDS WITH CWELD
• Spot welds can also be modelled using:
– Nastran CWELD elements – HEX elements linked by MPC
equations
Both give improved stiffness and do not require congruent mesh on flanges
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• Stresses and fatigue damage are calculated at 10 intervals around the spot weld for the 2 sheets and the nugget
• Stress histories are calculated from :
where k = static loadcase ID, or results from transient FEA • Life is calculated using Linear Damage Summation (Miner's Rule)
SPOT WELD DAMAGE CALCULATION PROCEDURE
σ (t) = σkPk�
Pk(t)�∑�
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POSTPROCESSING SPOT WELD RESULTS
• Listing the results files, life, damage, crack location, etc...
• Plotting in Patran (Insight)
• Polar plotting of damage
• What if ? scenarios ...
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EXAMPLE FATIGUE RESULTS FOR SHOCK TOWER
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EXAMPLE POLAR PLOT OF FATIGUE DAMAGE
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SEAM WELD FATIGUE
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VOLVO/CHALMERS/NCODE METHOD
• Designed and validated for thin sheet automotive structures (1-3 mm sheet thickness)
• Based on structural stress at weld toe
• Simple shell meshing rules
• Differentiates between “flexible” and “stiff” joints
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MODELLING WELDS
E(i)
E(j)
σ⊥Α
σ⊥Β
sheet B
sheet A
tB
t A
effective throat, a
● Sheets and welds modelled predominantly with 4-noded shells ● Sheets described by mean surfaces ● Thickness of weld elements equals effective throat, or about 2x sheet thickness ● Element length of about 5 mm ● Small radii not modelled
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DAMAGE PARAMETER (STRESS) DEFINITION
Damage parameter is principal stress at weld toe, based on weld toe elements.
Use Nastran with options:
STRESS,CUBIC
PARAM, SNORM, 55
Stresses are unaveraged
Stress is determined based on the nodal displacements and rotations of the weld toe elements
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S-N CURVE DETERMINATION
“Flexible”
“Stiff”
● Different specimen geometries are tested
● FE-models must be built to calculate stress
● Results fall on 2 curves depending on the nature of the joint
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“FLEXIBLE” AND “STIFF” JOINTS
● Bending ratio r is calculated based on top and bottom surface stresses ● Flexible joints have more bending at weld toe, and high values of r ● S-N curve is selected based on values of r ● Stiff joints have lower fatigue strength
Flexible
rσ
bσb σn+-------------------------- 0 r 1≤ ≤= = =
Stiff
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● Initial results are positive ● Predictions on real components tend to be with a factor of 2 or 3 ● Mainly conservative
SUMMARY
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Other Fatigue Considerations
• Corrosion Fatigue
– Combined action of repeated loading and corrosive environment.
– Presence of corrosive medium results in essentially two phenomena. • Weakening of interatomic link in surface layer producing minute cracks. • Accumulation of corrosion products in microcracks further reducing fatigue
strength.
– A corrosive fatigue failure has a rough, craggy appearance.
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Other Fatigue Considerations
• Surface Treatments
– Most common processes are Anodization, Chrome Plating and Cadmium Plating.
– Both anodization and chrome plating have detrimental effect on fatigue life.
– Cadmium plating is not considered to have a detrimental effect on fatigue life. ‘Soft’ process.
– Approach used for fatigue analysis • S-N analysis - preference to have data appropriate to the particular
treatment, otherwise factors are available. • δ-N analysis - factors available.
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Other Fatigue Considerations
• Fretting
– The term is applied to contacting surfaces, which are not expected to show relative movement.
– Fretting characteristic is that most of the debris produced is retained at the fretting site, ‘das Bluten des Eisens’ – the bleeding of the iron.
– Common sites are bolted joints and attachment lugs.
– Fretting itself may not lead to failure, but produces small cracks which can then lead to conventional fatigue failure.
– Use of interfay materials in joints can reduce fretting fatigue effects, however reduced friction can reduce fatigue life.
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Fatigue Life Improvement Techniques
• Techniques are widely used to increase initiation life, such as:
– Installation of interference fit fasteners.
– Cold working the fastener holes.
– Peening the surface layers of a component.
• However, there are advantages & disadvantages associated with such techniques.
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Processing Stresses Obtained from FE Models
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• Equivalent stresses σσV :
There is a 3–dimensional stress behaviour in an arbitrary part.
Experimental data have been received from a tension specimen (1-dimensional stress behaviour).
The equivalent stress is used to compare 3-dimensional stress behavior with the 1-dimensional stress behaviour of the tension test.
Different strength hypotheses have been developed.
Equivalent stresses
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• Equivalent stresses σσV :
Normal stress hypothesis :
Assumption : The maximum normal stress value is responsible for the material load
σσV = σσ1
Used for : brittle materials (and, for fatigue analysis, ductile also)
Equivalent stresses
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• Equivalent stresses σσV :
von Mises stress hypothesis : (named after Huber (1872-1950), v. Mises (1883-1953) and Hencky (1885-1951))
Assumption : The material load is characterized by the energy which is used for the change of the shape without a change in the volume of the part
Plane Stress:
σσV = [ σσ12 + σσ2
2 - σσ1σσ2 ]½ = [ σσx2 + σσy
2 - σσxσσy + 3 ττxy2 ]½
Used for : ductile materials
Equivalent stresses (von Mises)
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• Equivalent stresses σσV :
Shear stress hypothesis : (1864 described by H.Tresca)
Assumption : The material load is characterized by the maximum stress value.
Plane Stress:ττMax = ½ (σσ1 - σσ2 ) => σσV = σσ1 - σσ2
σσV = [( σσx - σσy)2 + 4 ττxy2 ]½
Equivalent stresses (Tresca)
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Assessing stresses on an FEA model
� Stress state can be characterised by ratio of principal stresses and their orientation (angle)
� If orientation and ratio are fixed, loading is proportional. � Otherwise loading is non-proportional � Biaxiality analysis:
� ae = -1: Pure Shear � ae = +1: Equi-Biaxial � ae = 0: Uni-axial
ae =σσ
2
1
Ratio of Principals or Biaxiality Ratio:
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Example: Near Proportional Loading
0 2 4 6 8 10 12-392.3
1301Strain(UE) S131A.DAC
Seconds
Sample = 409.6Npts = 9446Max Y = 1301Min Y = -392.3
0 2 4 6 8 10 12-284.3
121.1Strain(UE) S131B.DAC
Seconds
Sample = 409.6Npts = 9446Max Y = 121.1Min Y = -284.3
0 2 4 6 8 10 12-298.7
2663Strain(UE) S131C.DAC
Seconds
Sample = 409.6Npts = 9446Max Y = 2663Min Y = -298.7
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Example: Near Proportional Loading
-1 -0.5 0 0.5 1-1000
0
1000
2000
3000
4000
5000
S131.ABSStrainUE
Biaxiality Ratio (No units)
Time range : 0 secs to 23.06 secs
Screen 1-50 0 50
-1000
0
1000
2000
3000
4000
5000
S131.ABSStrainUE
Angle (Degrees)
Time range : 0 secs to 23.06 secs
Screen 1
Biaxiality ratio vs. σ1 Orientation of σ1 vs. σ(range)
• The left plot indicates that the ratio of the principal stresses is nearly fixed at around 0.4, especially if the smaller stresses are ignored.
• The right hand plot shows that the orientation (φp) of the principal stresses is more or less fixed.
• This is effectively a proportional loading (these calculation assume elasticity)
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Example: Non-Proportional Loading
-1 -0.5 0 0.5 1-200
-100
0
100
200
GAGE1.ABSStressMPa
Biaxiality Ratio (No units)
Time range : 0 secs to 183.6 secs
Screen 1-50 0 50
-200
-100
0
100
200
GAGE1.ABSStressMPa
Angle (Degrees)
Time range : 0 secs to 183.6 secs
Screen 1
Both the ratio and orientation of s1 and s2 vary considerably: non-proportional loading.
0 50 100 150-81.32
161.4GAGE 1X( uS) GAGE103.DAC
Sample = 200Npts = 3.672E4Max Y = 161.4Min Y = -81.32
0 50 100 150-274.6
559.5GAGE 1Z( uS) GAGE102.DAC
Sample = 200Npts = 3.672E4Max Y = 559.5Min Y = -274.6
0 50 100 150-651
716.2GAGE 1Y( uS) GAGE101.DAC
Sample = 200Npts = 3.672E4Max Y = 716.2Min Y = -651
Screen 1
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Effect of Multiaxiality on Plasticity, Notch Modelling and Damage Modelling
Uniaxial
Proportional Multiaxial
Non-Proportional Multiaxial
φp ae
φp constant
φp constant
φp may vary
a = 0
-1 < a < +1
a may vary
Increasing Difficulty
(and Rarity)
OK
??????
Tricky
Decreasing Confidence
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Stress State Characterization
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Elastic Biaxiality Ratio
pφPrincipal Stress Angle
-1 -0.5 0 0.5 1-1000
0
1000
2000
3000
4000
5000
S131.ABSStrainUE
Biaxiality Ratio (No units)
Time range : 0 secs to 23.06 secs
Screen 1
-50 0 50-1000
0
1000
2000
3000
4000
5000
S131.ABSStrainUE
Angle (Degrees)
Time range : 0 secs to 23.06 secs
Screen 1
Multi Axial Stress States
Uni-axial = const = 0
Prop multi-axial = const = const
Non-proportional = may vary may varypφ
ea11 <<− eapφ
pφ
ea
Uni-axial Uni-axial
1
2
σσ
=ea
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Time 0 1 2 3 4 Max range
Max Principal
100 -100 200 -200 500 -200 to 500 = 700
MinPrincipal
50 -150 -500 -250 -10 -500 to 50 =550
Max. Abs Principal
100 -150 -500 -250 500 -500 to 500 = 1000
What is “Maximum Absolute Principal” Stress
and “Signed Von Mises
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Element 1 Element 2
Element 3 Element 4
Nodal values for stress can either be ‘as is’ or
averaged between adjacent elements. Element stresses are
normally at internal positions in the element
and so usually underestimate peak
values.
Average of stresses for all 4 elements at this node
Nodal or element averaging?
Unaveraged nodal results are usually preferred, but the choice of averaged nodal is often a reasonable compromise
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Multiple Vibration Inputs and Derivation of the Appropriate Stresses For a Fatigue Analysis
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Features�
– Multi input loads�
– Correlation effects using Cross PSD s�
– Resolution of stresses onto Principal planes�
– Calculation of response PSD using TF s and input PSD s�
– Calculate fatigue life from PSDs�
Vibration Fatigue in the Frequency Domain:
Input PSD [A]
Transfer Function [B]
Output PSD [C]
1
2
3
4 6
5
1
2
3 4 6
5
1 2 3
654
Transfer Functions on component axes�
Transfer Functions rotated on to Principal planes by MSC.Fatigue�
�
Rainflow histogram and fatigue life calculated by
MSC.Fatigue�
Response PSD’s calculated by MSC.Fatigue�
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One degree of Freedom System With One Random Load Input
Mass M
Stiffness K
Damping C
time
FSinusoidalforce with amplitude Fand frequency w
T
1.0
4.0
2 4 6 8 10 12 14 16 18 20 220
ωfrequency
Transferfunction
The amplitude of the stress σ is found by:
FT ⋅=σ
Sinusoidal ForceSinusoidal Force
Stress at base σ
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Two degree of Freedom System With Two Partially Correlated Random Load Inputs
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Transfer Function is Calculated at 6 Component Stresses
Input I1x
y
zGlobal coordinate axis
SxxSyySzz
Axial Stresses
SxySyzSxz
Shear Stresses
6 Component stresses at output node
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Possible Rotation of the Principal Stresses Caused By Multiaxial Loading
Input I2Output O1
Output O2
Principal stress axis
Output P1
Output P2
Principal stress axis
Multiple input
loadingUniaxialstress statein members
Different input load positions result inchanges in the direction of the principle stress
axis in an element.
Different input load positions do not affectthe direction of the principle stress axis in
an element.
Input I1
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The principle stress axis will oscillate periodicallydue to differential damping between O1 and O2.Also the transfer function becomes non-linear
Output O1
Output O2Input I1
ϕInput I1
Output O1
Output O2
Rotation of the Principal Stresses Caused By Differential Damping
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Visualization of the Principal Stress Vector on the Surface of a Component
0 0.2 0.4 0.6 0.8 1
00.2
0.40.6
0.81
00.20.40.60.8
1
i
jk
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
=
kji
σ
Surfaceelement
Biaxial stressvector σ alongthe surface
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Stress Response Vector For a Component With NO Differential Damping
i
j
σ(t)timetime
σ Amplitude A
ψ
Apply a unit sinusoidal load andrecord the output
The locus of the principalstress vector σ is seen to mapa straight line through vector
space.
The output stress varies sinusoidallywith the same frequency as the input
load. The amplitude A is obtainedfrom the modulus of the vector andthe phase angle ψ by the argument.
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i
j
time
Apply a unit sinusoidal load andrecord the output
The locus of the principalstress vector σ is seen to map
an ellipse through vectorspace as the i and j
components are out of phase.
Angle ofspread θ
Mean Direction Vector
The mean direction of thevector and the angle of
spread are obtained fromequations derived later
σ
Stress Response Vector For a Component With Differential Damping
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Input load
Torsional mode
Bending mode
Vertical input results in combined torsion and bending in the shaft. Thedirection of the principle stress axis will vary with frequency as the load
excites each mode separately
Rotation of the Principal Stresses Caused By Multiaxial Loading
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Area of highdirectionalvariation
Geometrical constraint helps us a lot!
Or, Why Multi Axial Stresses Usually Are Not a Problem
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Typical shaker table problem
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The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again.
Principal stresses from transfer function analysis
With arrow length normalized by stress magnitude
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Composites
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Composites
• Definition. – A composite is defined as a material having two or more distinct
constituent materials.
• Non-metallic composite is considered to consist of the reinforcement (usually continuous fibre) held together by a weaker material – the matrix.
• Composites include; – Fibre Metal Laminates – Honeycomb (Sandwich) construction.
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Composites
• Metallics– Notch sensitive in fatigue. – Almost notch insensitive under static loading.
• CFC – Notch sensitive under static loading. – Relatively notch insensitive in fatigue.
Often referred to as a ‘new’ material. Introduced to the UK engineering fraternity ~1966!
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Composites
In pure form (fibre) the carbon can have immense tensile strength (>5000MPa!). When made into a component, however, many factors reduce this strength significantly. They are:
• Pre-impregnation. • Variability. • Environmental Degradation. • Lay-up. • Notch sensitivity (a fatique concept but required for static analysis for CFC
structure).
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Composites
• Fatigue behaviour dependant on material type and lay-up.
• Fatigue strength generally superior than metallics – considered excellent.
• CFC’s accumulate fatigue damage while loaded in compression.
• CFC is elastic until failure at ultimate stress (no Kt relief due to plasticity).
• Life proven by test – S~N curves quite flat.
• If static strength is sufficient, fatigue problems should not occur. THIS IS THE NORM.
• Failure often quantified in terms of loss of stiffness.
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Composites
Comparison of tensile strengths at room temperature.
ULTIMATE TENSION
STRESS N/mm2
YOUNG'S MODULUS N/mm2
SPECIFIC GRAVITY
SPECIFIC TENSION
STRESS N/mm2
SPECIFIC MODULUS N/mm2
IM7 5379 276,000 1.77 3039 155,932
T300 3550 230,000 1.75 2029 131,429
XAS 3550 235,000 1.81 1960 129,800
STEEL S99 1230 200,000 7.833 157 25,530
ALUMINIUM ALLOY 7075 500 72,000 2.796 179 25,750
TITANIUM ALLOY TA 10 920 113,000 4.512 203 25,000
MATERIAL
CFC (Fibre Only)
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CFC – Comparative Fatigue Performance
Cycles to failure
Spec
ific
fatig
ue
stre
ngth
103 104 105 106 107
800
640560480
400320240
160
800
720
R = 0.1
Unloaded hole
Al Alloy 7075-T6
Graphite/Epoxy
46%0o/50%+/-45o/4%90o)
Ti-6Al-4V 4340 Steel (210ksi)
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Composites
• Fibre-metal laminates (Glare & Arall).
– Thin Aluminium sheets bonded to uni-directional fibre layers.
– Proven to excellent fatigue and especially high damage tolerance.
– Growth rate upto 20 times slower than 2024-T3.
– Used extensively on Airbus A380 fuselage.
– Suitably for thin sheet applications and small fittings, e.g lugs.
– Inherently fail-safe. Built in crack arrest.
– Bombproof!
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Composites
• Honeycomb (Sandwich) construction.
– Thin Aluminium sheets (facings) bonded to metallic (or non-metallic) honeycomb (core).
– High fatigue and crack growth characteristics due to the general absence of features (Kt=1).
– Structurally similar to an ‘I’ section beam.
– Excellent acoustic and impact resistance.
– Suitable for skinning, control surfaces etc.
– Core very sensitive to CORROSION. Careful design of joints, edges and inserts required.
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Computer based example no 1: Exploring a computer based fatigue analysis environment
Copy VF_SA.db in to working directory (ensure that it is not read only)
Double click the file to start Patran in this directory
Then load VF_SA.db database file
Start MSC.Fatigue from the Tools menu
Create a dos command prompt and change the starting location to the working directory
Try starting MSC.Fatigue programs in 1 of the 3 possible ways
(1) MSC.Fatigue form
(2) Tools+ menu
(3) Command prompt
Try plotting a time history file(s) with mQLD and/or mMFD
Read in an existing MSC.Fatigue run file (.FIN file) using Job Control/Read Saved Job
Explore the MSC.Fatigue form – start at the top and work down. Concentrate on 3 forms –
Solution Parameters,
Loading,
Materials
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Computer based example no 2: Tools for pre-processing data Try running
mATD
mDTA
mQLD
mMFD
mART
mCOE
mLEN
mFRM
mFILMNP
mRSTATS
mADA
mFFF
mBFL
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Computer based example no 3: Tools for post-processing data
Try running
mCDA
mCYL
mP3D
mTPD
mPOD
mTCD
mREGEN
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Computer based example no 4: Using a materials database
Try running
PFMAT
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Computer based example no 5: Using a loads management database
Try running
PTIME
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Computer based example no 6: A Stress-Life fatigue analysis
Try running mSLF
Use mART to make a sensible time history – you will need to pick a material S-N curve first in order to decide on a sensible overall stress range. Don t forget to change the units to stress (MPa).
Use PFMAT to pick a material where the maximum range of stress in your time signal corresponds to about 1000 cycles.
Then run mSLF. Put any job name in and fill in all the required fields.
Experiment with the various options, including the stress multiplier.
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Computer based example no 7: Transforming from a Strain-Life curve to a Stress-Life curve
Start from a typical strain-Life curve in PFMAT and then convert 2 or 3 relevant points in to a Stress-Life curve. Remember
N(S-N) = 2Nf (E-N)
Strain is amplitude (E-N) and stress is range (S-N)
Use cyclic Stress-Strain curve for conversion.
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Computer based example no 8: A Strain-Life fatigue analysis
Try running
mCLF
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Computer based examples no 9 & 10:
Calculating a Compliance Function with pksol
Calculating crack growth rates with pcrack
