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Multi. Stage Fatigue (MSF) Modeling Dr. Mark F. Horstemeyer (Mississippi State University) Outline Introduction/motivation Micromechanics: Computations and experiments Multi. Stage Fatigue (MSF) model Summary Main Reference Mc. Dowell, D. L. , Gall, K. , Horstemeyer, M. F. , and Fan, J. , “Microstructure-Based Fatigue Modeling of Cast A 356 -T 6 Alloy, ” Engineering Fracture Mechanics, Vol. 70, pp. 49 -80, 2003.
ISV-MSF Model Implementation/Use initial microstructureinclusion content ISV model Note: models can be implemented in other FE codes mesh finite element Code (ABAQUS) boundary conditions loads temperature strain rate history MSF Model life Damage/failure design
MSU MSF Model History • First started on a cast A 356 al alloy for automotive application (1995 -2000) • Extended to aerospace aluminum alloys (7075, 7050 al) (2002 -2006) • Extended to automotive cast Mg alloys (2002 -present) • Recently used for several steel alloys (2005 present) • Just started polymers 4 J. , “Microstructure-Based Fatigue Modeling of Mc. Dowell, D. L. , Gall, K. , Horstemeyer, M. F. , and Fan, Cast A 356 -T 6 Alloy, ” Engineering Fracture Mechanics, Vol. 70, pp. 49 -80, 2003.
MSU Multi. Stage Fatigue Modeling • Based upon three thresholds – Incubation – Microstructurally Small Crack Growth – Long Crack Growth • Based on microstructure sensitivity • Multiscale modeling was used to first develop the equations in the absence of experiments; experiments later validated the 5 equations
Multi. Stage Fatigue Microstructure-Sensitive Model Ntotal=Ninc+NMSC+NPSC+NLC Ntotal = total number of cycles to failure Ninc = number of cycles to incubate a fatigue crack NMSC = Microstructurally Small Crack growth (ai < a < k. DCS) NPSC = Physically Small Crack growth (~1 -2 DCS < a < ~10 DCS) NLC = Long Crack growth (a > ~10 DCS) Inclusion Severity 1. Large oxides greater than 200 microns 2. Large pores near free surface (length scale ~ 100 microns) 3. Large pores (length scale ~ 50 -100 Microns) 4. High volume fraction of microporosity; no large pores/oxides (length scale < 50 microns) 5. Distributed microporosity and silicon; no significant pores/oxides 6
Ilustration of Different Stages
Different Defects Induce Different Crack Growth Rates 8
Fatigue Micromechanisms LCF and HCF Regimes. Mechanisms LCF - Extensive Plasticity HCF – Microstructure Scale Plasticity Crack incubation largest grains or Initiation-dominated: largest grains or inclusions control inclusions establish number of cycles to form a crack or to propagate past arrest initial crack length in limits propagation analysis MSC growth Cracks grow in elastic-plastic field with less microstructure influence First few microstructural barriers control fatigue limit and scatter of lifetime PSC and LC growth Elastic-plastic growth persists well into crack growth history; coalescence of multisite cracks can occur Transition to LEFM-dominated homogeneous crack growth; single dominant crack is common
Fatigue Stages: Incubation (b) Fatigue damage of AA 7075 -T 651 was found mostly initiated at fractured particles • NINC: The number of cycles required to nucleate a crack at a constituent particle and then to grow the crack a short distance from the particle; in this state, the fatigue damage evolution is under the influence of micronotch root plasticity. • NINC uses modified Coffin-Manson law : micro-notch root max plastic shear strain a : Remote Strain; l : plastic zone size D : particle diameter; R : min/ max ainc = 0. 5 Dp + 1/16 Dp, the crack size is 2 ainc • Experiments/Simulation for Incubation Life Measurement/evaluation of notch root plastic strain amplitude : • 2 -D micromechanics simulation of fractured particles for local plasticity as a function of remote loading (MSU) • Conducting interrupted HCF tests in-situ SEM on polished rectangular specimens with laser cut micronotch of particles (MSU) • Measure at micron scale the local plastic strain (amplitude and plastic zone size) using Micro-X-Ray diffraction to evaluate the micronotch plasticity to understand/validate the incubation model (ORNL) 13
Incubation (Ninc) : micro-notch root max plastic shear strain a : Remote Strain; l : plastic zone size D : particle diameter; R : min/ max ainc = 0. 5 Dp + 1/16 Dp, the crack size is 2 ainc Measurement/evaluation of Incubation Life NInc: • In-situ SEM fatigue test using dogbone shape rectangular specimens with micronotches to observe the crack incubation and growth with R = -1, 0. 5. This provides accurate incubation life prediction and crack size and crack growth rate measurement to submicron scale. (MSU) • Single Edge Notch Tension tests (SENT) with R = -1, 0. 5 observation on small crack initiation and propagation using 1) optical tools (~50 mm), 2) plastic repliset (~10 mm). This provides incubation life estimation and crack size and crack growth rate measurement to micron scale. (MSU, for FASTRAN as well) • Interrupted strain-life fatigue experiments with R=-1, 0. 1 on Kt 3 specimens (previous done at Alcoa) that estimate incubation life as a function of stress states 14
Fatigue Incubation Indicators Exhaustion of irreversible strain (slip band decohesion): cf. Dunne et al. or Irreversibility factor Suresh, 1990
Fatigue Incubation Indicators Modified Coffin-Manson laws for crack formation (incubation), assuming cyclically stable conditions: cf. Mura et al. (1991) Fatemi-Socie Parameter (1988) decohesion plus crack behavior (Mc. Dowell & Berard, FFEMS, 1992) (cf. Dang-Van (1993), Papadopoulos (1995), others for similar multiaxial parameters applied at grain scale)
Fatigue Incubation Indicators Zener mechanism or Stress normal to boundary
Incubation life NINC = maximum plastic shear strain range at particle/matrix interface averaged in a Refs process zone volume 1 Coffin-Manson 2. Venkataraman et al. , 1991 RHS-constants correlated from 3. Dowling, 1979 uniaxial fatigue exps 4. Ting and Lawrence, 1993 5. Mc. Dowell et al. , 2003 LHS-constants determined from micromechanical FE simulations
Solving for Right Hand Side of Incubation Eqtn: Partition of HCF/LCF based upon local Plasticity HCF strain coefficient at micronotch LCF strain coefficient at micronotch Threshold between constrained and unconstrained microplasticity determined from micromechanical FE sims Refs Mc. Dowell et al. , 2003 Gall et al. , 2000 Gall et al. , 2001
Solving for Right Hand Side of Incubation Eqtn: HCF Mean Stress Effect Local microstructure-based fatigue ductility coefficient Cn ~ material constant 0. 2 ~ 0. 6 (Cn=0. 48) Cm ~ material constant 0. 08 ~ 1. 0 (Cm=0. 3) C-M Fatigue ductility exponent a~ material constant -0. 4 ~ -0. 9 (a = -0. 7)
Solving for Left Hand Side of Incubation Eqtns: transfer functions needed Micromechanical simulations relate global applied strain range to maximum plastic shear strain range at particle/matrix interfaces Refs Mc. Dowell et al. , 2003 Gall et al. , 2000 Gall et al. , 2001
Solving for Left Hand Side of Incubation Eqtns: Micro FE Sims
Solving for Left Hand Side of Incubation Eqtns: Micro FE Sims § per=strain percolation limit for microplasticity at inclusion (0. 0054 -0. 0055, per=0. 00545) § Determined by cyclic yield strength (=0. 8 Sy/E(1 -R)) § Determined by micromechanical FE sims § Determined by ORNL micro X-ray diffraction method § th=strain threshold for microplasticity inclusion (0. 002 -0. 00225, th=0. 0021) § Determined by Su of material (=. 29 Su/E/(1 -R)) § Determined by fatigue strength (=Sf/E) § Determined by micromechanical FE sims § Determined by ORNL micro X-ray diffraction method
Solving for Left Hand Side of Incubation Eqtns: Micro FE Sims § hlim=l/D at the strain percolation limit (0. 2 -0. 4, hlim=0. 3) determined by micromechanical FE sims § r=l/D exponent (0. 1 -0. 5, r=0. 4) determined by micromechanical FE sims § q=nonlocal microplastic shear strain range exponent (2. 1 -2. 8, q=2. 27) determined by micromechanical FE sims § Y 1=nonlocal microplastic shear strain range coefficient (100 -200, Y 1=116) determined by micromechanical FE sims § Y 2=nonlocal microplastic shear strain mean stress coefficient (100 -1000, Y 2=0) determined by micromechanical FE sims § x=strain intensification multiplier (1 -9, x=1. 6) determined by micromechanical FE sims
size of incubated crack Refs Smith and Miller, 1977 Mc. Dowell et al. , 2003
When does the transition occur between stages? Incubation (Current method has more influence on HCF than LCF) MSC (current method assumes long crack starts at 250 microns)
Fatigue Stages: MSC/PSC • NMSC/PSC : the number of cycles required for a microstructurally small crack and physically small crack propagating to a long crack; in this state, the crack growth are influenced by microstructural noncontinuous features, such as particle, particle distribution, grain size and orientation, and textures. • Fatigue Model Multiaxial term 27
MSC Regime’s Different Plasticity Character 28
MSC Regime (Grain effects) Multiaxial term Crystal plasticity fatigue simulation on crack propagation validate grain orientation effects (MSU or Cornell) 29
MSC Regime (CIII) • Crystal plasticity fatigue simulation on crack propagation overload or load sequence effects • Periodic overload experiments for Kt=1 specimens • Sequence experiments for Kt=1 specimens 30
MSC Regime (CI and CII) • In-situ SEM fatigue test using dogbone shape rectangular specimens with micronotch to observe the crack initiation and growth with R = -1, 0. 5 • Single Edge Notch Tension tests (SENT) with R = -1, 0. 5 observation on small crack propagation using 1) optical tools (~50 mm), 2) plastic repliset (~10 mm). This provides MSC life estimation and crack size and crack growth rate measurement to micron scale. (MSU, for FASTRAN as well) (La. Vision system) • Sequence experiments for Kt=1 specimens • Periodic overload experiments for Kt=1 specimens for just CI 31
MSC Regime ( 1 and 2) Multiaxial term • Multi-axial tests to determine 1 and 2. 32
MSC CTD Drops Indicate Resistance from Particles
MSC Showing Tortuousity via FEA Fan, Mc. Dowell, Horstemeyer, and Gall, K. A. , Eng Fract Mech, 68, No. 15, pp. 1687 -1706, 2001. Resistance of particles and pores to small cracks is illustrated
Microstructurally Small Crack, NMSC crack growth rate is a function of crack tip displacement range G ~ constant for given microstructure with 0. 30 < G < 0. 50 G=0. 32 for 7075 al alloy G is being evaluated from Crystal Plasticity and atomistic sims DCTDTH ~ Burgers vector b Refs 1. 2. 3. Laird et. al. , 1965 Mc. Clintock, 1965 Mc. Dowell et al. , 2003
DCTD calculation HCF LCF Refs Dugdale Couper et al. , 1990 Shiozawa et al. , 1997 Mc. Dowell et al. , 2003 GS = grain size (19 -74 microns, GS=40), determined by CMU Su = ultimate strength (635 MPa) determined by NGC exps n = MSC HCF exponent (4. 0 -4. 3, n=4. 24) determined by small crack exps a = crack length CI=MSC LCF Coefficient (1 e 4 -6 e 4 microns, CI=1. 6 e 4) determined by in-situ SEM (now it is determined by strain-life exps) CII= MSC HCF Coefficient (1. 0 -3. 0, CII=1. 82) determined by in-situ SEM (now It is determined by strain-life exps) w=Hall-Petch fatigue exponent (0 -1, w=0)
U considers crack closure simple approximation Refs Mc. Dowell et al. , 2003 Fan et al. , 2001 R<0 So = 0 U = 1/(1 -R) R>0 So = Smin U=1 So is determined by small crack mean stress experiments, in-situ SEM, and micromechanical crack growth FE sims
Multiaxial stress effects deviatoric von Mises stress maximum principal stress 0
Long crack growth NLC FASTRAN used for long crack growth
Transition from small crack growth to long crack growth
Use of Fatigue Model mesh initial microstructureinclusion content finite element Code (ABAQUS) boundary conditions loads temperature strain rate history Fatigue model Number of cycles to failure Note: coupon tests from a component are typically uniaxial, but the stress state of a region in the component is typically multiaxial
Notch Root Radii Effects on Incubation and MSC
MSC: Debonding dominant because driving force is relatively small LC: Cracking of second phase particles dominant because driving force is relatively strong
Strain-life for A 356 Al alloy with a focus on local defects
cavity where the growth of microstructurally small cracks occurred Fracture surface of 0. 2% strain amplitude sample speci men surfa ce Fatigue crack Nucleation site Al oxide
Same fracture surface of 0. 2% strain amplitude sample as before showing progressive damage alpha intermetallics FCG =fatigue crack growth
SEM pictures at (a) 15 x and (b) 200 x of specimen tested under uniaxial fatigue at a strain amplitude of 0. 0015 with an R-ratio of – 1. This specimen ran for 2. 05 x 106 cycles illustrating the degrading effect of the 150 micron size casting pore.
SEM pictures at (a) 15 x and (b) 200 x of specimen tested under uniaxial fatigue at a strain amplitude of 0. 0015 with an R-ratio of – 1. This specimen ran for 51, 000 cycles illustrating the degrading effect of the 100 micron size casting pore at the specimen edge.
Number of cycles versus maximum pore size (micron) measured for specimens tested at a strain amplitude of 0. 0015.
Number of cycles versus nearest neighbor distance (micron) measured for specimens tested at a strain amplitude of 0. 0015. .
Number of cycles versus number of pores measured for specimens tested at a strain amplitude of 0. 0015.
Number of cycles versus porosity (void volume fraction) measured for specimens tested at a strain amplitude of 0. 0015.
Number of cycles versus (pore size*pore size)/(nearest neighbor distance*dendrite cell size) measured for specimens tested at a strain amplitude of 0. 0015.
Current State: Multistage Fatigue Model Incubation Initial crack size MSC/PSC Growth Note: not used for PM alloys HCF loading dominated LCF loading dominated Multiaxial term Porosity term LC Growth LC growth model will be FASTRAN. This model is temporary. Mean stress term
Used to determine functional form of incubation equation particularly the 0. 3 limit
Micromechanics simulations showing variation of driving force because of pore/particle resistances
Strain-Life as a function microstructure Long Crack Regime
Number of Cycles as a function of inclusion size
Strain-Life Model Correlation with MSF Model
Finite Element Analysis of Performance and Fatigue Total Fatigue Life NTOTAL = NINC + NSC + NLC for Higher Bound (Low Homogenous Porosity 9. 5%) NT > 10, 142, 944 cycles 20, 000 lbs NT > 10, 106, 046 cycles 21, 000 lbs NT > 10, 079, 826 cycles 22, 000 lbs NT > 10, 060, 891 cycles 23, 000 lbs
Powder Metal Finite Element Analysis of Performance and Fatigue Higher Bound (Low Homogeneous Porosity 9. 5%) Lower Bound (High Homogeneous Porosity 19. 0%) Shaft Loading (lbs) Fatigue Life 20, 000 21, 000 22, 000 NINC > 10, 000, 000 NSC 2 NLC Shaft Loading (lbs) 23, 000 Fatigue Life 20, 000 21, 000 22, 000 23, 000 > 10, 000, 000 NINC 2, 399, 554 1, 658, 665 1, 176, 098 778, 410 2 2 1 NSC 1 1 142, 942 106, 044 79, 826 60, 890 NLC 173, 956 129, 105 97, 223 74, 187 NTOTAL > 10, 142, 944 > 10, 106, 046 > 10, 079, 828 > 10, 060, 891 NTOTAL 2, 573, 511 1, 787, 771 1, 273, 322 852, 598 Failure PASS Failure FAIL Interpolation I (Heterogeneous Porosity) Interpolation II (Heterogeneous Porosity) Shaft Loading (lbs) Fatigue Life 20, 000 21, 000 22, 000 NINC > 10, 000 9, 902, 806 NSC 1 NLC Shaft Loading (lbs) 23, 000 Fatigue Life 20, 000 21, 000 22, 000 23, 000 8, 341, 563 7, 109, 965 NINC > 10, 000, 000 8, 553, 476 7, 485, 101 1 NSC 1 1 163, 212 121, 115 91, 194 69, 579 NLC 163, 212 121, 115 91, 194 69, 579 NTOTAL > 10, 163, 213 10, 023, 922 8, 432, 758 7, 179, 545 NTOTAL > 10, 163, 213 > 10, 121, 116 8, 644, 671 7, 554, 681 Failure PASS CRACK FAIL Failure PASS FAIL
Relationship of Manufacturing Process, Defect, and Fatigue Mechanisms Rolling/Extrusion/Forging/Stamping Particles 15% INC 70% MSC 15% LC Manufacturing process Defect type Dominant damage mechanism under cyclic loads Casting Particles 25% INC 65% MSC 10% LC N=Number of Cycles NINC=Incubation NMSC=Microstructurally Small Crack NLC=Long Crack N=NINC+NMSC+NLC 10 -7 10 -5 10 -6 10 -4 Porosity 60% INC 30% MSC 10% LC Powder metal compaction/sintering Porosity 99% INC 0% MSC 1% LC 10 -5 10 -3 10 -4 10 -2 10 -3 10 -1 Defect size (m) Fatigue Failure 10 -0 Defect volume fraction