MultiStage Fatigue (MSF) Modeling Dr. Mark F. Horstemeyer (Mississippi State University) Outline Introduction/motivation Micromechanics: Computations and experiments MultiStage Fatigue (MSF) model Summary Main Reference McDowell, D.L., Gall, K., Horstemeyer, M.F., and Fan, J., “Microstructure-Based Fatigue Modeling of Cast A356-T6 Alloy,” Engineering Fracture Mechanics, Vol. 70, pp.49-80, 2003.

initial microstructure- ISV-MSF Model Implementation/Use mesh initial microstructure- inclusion content finite element Code (ABAQUS) MSF Model life ISV model Damage/failure boundary conditions loads temperature strain rate history design Note: models can be implemented in other FE codes

MSU MSF Model History First started on a cast A356 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 McDowell, D.L., Gall, K., Horstemeyer, M.F., and Fan, J., “Microstructure-Based Fatigue Modeling of Cast A356-T6 Alloy,” Engineering Fracture Mechanics, Vol. 70, pp.49-80, 2003.

MSU MultiStage 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 equations

MultiStage 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 < kDCS) NPSC = Physically Small Crack growth (~1-2DCS < a < ~10DCS) NLC = Long Crack growth (a > ~10DCS) 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

Ilustration of Different Stages

Different Defects Induce Different Crack Growth Rates

Strain-Life Data

Fatigue Micromechanisms LCF and HCF Regimes. Mechanisms LCF - Extensive Plasticity HCF – Microstructure Scale Plasticity Crack incubation largest grains or inclusions establish initial crack length in propagation analysis Initiation-dominated: largest grains or inclusions control number of cycles to form a crack or to propagate past arrest limits 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-T651 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 2ainc 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)

Incubation (Ninc) Measurement/evaluation of Incubation Life 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 2ainc 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, 0.1, 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, 0.1, 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

Fatigue Incubation Indicators Exhaustion of irreversible strain (slip band decohesion): Suresh, 1990 cf. Dunne et al. Irreversibility factor or

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 (McDowell & 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 process zone volume Refs 1 Coffin-Manson 2. Venkataraman et al., 1991 3. Dowling, 1979 4. Ting and Lawrence, 1993 5. McDowell et al., 2003 RHS-constants correlated from uniaxial fatigue exps 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 McDowell 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 ~ 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 McDowell 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 eper=strain percolation limit for microplasticity at inclusion (0.0054-0.0055, eper=0.00545) Determined by cyclic yield strength (=0.8Sy/E(1-R)) Determined by micromechanical FE sims Determined by ORNL micro X-ray diffraction method eth=strain threshold for microplasticity inclusion (0.002-0.00225, eth=0.0021) Determined by Su of material (=.29Su/E/(1-R)) Determined by fatigue strength (=Sf/E)

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 Y1=nonlocal microplastic shear strain range coefficient (100-200,Y1=116) determined by micromechanical FE sims Y2=nonlocal microplastic shear strain mean stress coefficient (100-1000, Y2=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 McDowell 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

MSC Regime’s Different Plasticity Character

MSC Regime (Grain effects) Multiaxial term Crystal plasticity fatigue simulation on crack propagation validate grain orientation effects (MSU or Cornell)

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

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, 0.1, 0.5 Single Edge Notch Tension tests (SENT) with R = -1, 0.1, 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) (LaVision system) Sequence experiments for Kt=1 specimens Periodic overload experiments for Kt=1 specimens for just CI

MSC Regime (q1 and q2) Multiaxial term Multi-axial tests to determine 1 and 2.

MSC CTD Drops Indicate Resistance from Particles

MSC Showing Tortuousity via FEA Fan, McDowell, 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

MSC

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 Laird et. al., 1965 McClintock, 1965 3. McDowell et al., 2003

DCTD calculation HCF LCF Refs Dugdale Couper et al., 1990 Shiozawa et al., 1997 McDowell et al., 2003 HCF LCF 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 (1e4-6e4 microns, CI=1.6e4) 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 McDowell 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 Refs McDowell et al., 2003 Hayhurst et al., 1985 maximum principal stress 0 < q < 1 q = 0 fatigue controlled by q = 1 fatigue controlled by q determined by torsion-tension/compression fatigue exps

Long crack growth NLC FASTRAN used for long crack growth

Transition from small crack growth to long crack growth

initial microstructure- Use of Fatigue Model mesh initial microstructure- inclusion content finite element Code (ABAQUS) Number of cycles to failure Fatigue model Note: coupon tests from a component are typically uniaxial, but the stress state of a region in the component is typically multiaxial boundary conditions loads temperature strain rate history

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 A356 Al alloy with a focus on local defects

Fracture surface of 0.2% strain amplitude sample Fatigue crack Nucleation site Al oxide cavity where the growth of microstructurally small cracks occurred Fracture surface of 0.2% strain amplitude sample specimen surface

FCG =fatigue crack growth Same fracture surface of 0.2% strain amplitude sample as before showing progressive damage alpha intermetallics FCG =fatigue crack growth

SEM pictures at (a) 15x and (b) 200x of specimen tested under uniaxial fatigue at a strain amplitude of 0.0015 with an R-ratio of –1. This specimen ran for 2.05x106 cycles illustrating the degrading effect of the 150 micron size casting pore.

SEM pictures at (a) 15x and (b) 200x 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 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 Mean stress term Porosity term LC Growth LC growth model will be FASTRAN. This model is temporary.

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 NT > 10,106,046 cycles 20,000 lbs 21,000 lbs NT > 10,079,826 cycles NT > 10,060,891 cycles 22,000 lbs 23,000 lbs

Powder Metal Finite Element Analysis of Performance and Fatigue Higher Bound (Low Homogeneous Porosity 9.5%) Fatigue Life Shaft Loading (lbs) 20,000 21,000 22,000 23,000 NINC > 10,000,000 NSC 2 1 NLC 142,942 106,044 79,826 60,890 NTOTAL > 10,142,944 > 10,106,046 > 10,079,828 > 10,060,891 Failure PASS Lower Bound (High Homogeneous Porosity 19.0%) Fatigue Life Shaft Loading (lbs) 20,000 21,000 22,000 23,000 NINC 2,399,554 1,658,665 1,176,098 778,410 NSC 1 NLC 173,956 129,105 97,223 74,187 NTOTAL 2,573,511 1,787,771 1,273,322 852,598 Failure FAIL Interpolation I (Heterogeneous Porosity) Fatigue Life Shaft Loading (lbs) 20,000 21,000 22,000 23,000 NINC > 10,000,000 9,902,806 8,341,563 7,109,965 NSC 1 NLC 163,212 121,115 91,194 69,579 NTOTAL > 10,163,213 10,023,922 8,432,758 7,179,545 Failure PASS CRACK FAIL Interpolation II (Heterogeneous Porosity) Fatigue Life Shaft Loading (lbs) 20,000 21,000 22,000 23,000 NINC > 10,000,000 8,553,476 7,485,101 NSC 1 NLC 163,212 121,115 91,194 69,579 NTOTAL > 10,163,213 > 10,121,116 8,644,671 7,554,681 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 Porosity 25% INC 60% INC 65% MSC 30% MSC 10% LC 10% LC N=Number of Cycles NINC=Incubation NMSC=Microstructurally Small Crack NLC=Long Crack N=NINC+NMSC+NLC Powder metal compaction/sintering Porosity 99% INC 0% MSC 1% LC Defect size (m) 10-7 10-6 10-5 10-4 10-3 Fatigue Failure Defect volume fraction 10-5 10-4 10-3 10-2 10-1 10-0