MultiStage Fatigue (MSF) Modeling
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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.

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MultiStage Fatigue (MSF) Modeling Dr. Mark F. Horstemeyer (Mississippi State University)

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Multistage fatigue msf modeling dr mark f horstemeyer mississippi state university

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.


Multistage fatigue msf modeling dr mark f horstemeyer mississippi state university

ISV-MSF Model Implementation/Use

mesh

initial microstructure-

inclusion content

MSF

Model

finite

element

Code

(ABAQUS)

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

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

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 msf modeling dr mark f horstemeyer mississippi state university

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

Ilustration of Different Stages


Different defects induce different crack growth rates

Different Defects Induce Different Crack Growth Rates


Strain life data

Strain-Life Data


Multistage fatigue msf modeling dr mark f horstemeyer mississippi state university

Fatigue Micromechanisms

LCF and HCF Regimes.


Fatigue stages incubation b

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)


Multistage fatigue msf modeling dr mark f horstemeyer mississippi state university

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 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


Multistage fatigue msf modeling dr mark f horstemeyer mississippi state university

Fatigue Incubation Indicators

Exhaustion of irreversible strain (slip band decohesion):

Suresh, 1990

cf. Dunne et al.

Irreversibility factor

or


Multistage fatigue msf modeling dr mark f horstemeyer mississippi state university

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)


Multistage fatigue msf modeling dr mark f horstemeyer mississippi state university

Fatigue Incubation Indicators

Zener mechanism

or

Stress normal to boundary


Incubation life n inc

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

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

Solving for Right Hand Side of Incubation Eqtn: HCF Mean Stress Effect

Local microstructure-based fatigue ductility coefficient

Cn ~ material constant0.2 ~ 0.6 (Cn=0.48)

Cm ~ material constant0.08 ~ 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

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


Multistage fatigue msf modeling dr mark f horstemeyer mississippi state university

Solving for Left Hand Side of

Incubation Eqtns: Micro FE Sims


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)

    • Determined by micromechanical FE sims

    • Determined by ORNL micro X-ray diffraction method


Solving for left hand side of incubation eqtns micro fe sims1

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


Multistage fatigue msf modeling dr mark f horstemeyer mississippi state university

size of incubated crack

Refs

Smith and Miller, 1977

McDowell et al., 2003


When does the transition occur between stages

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

Multiaxial term

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


Msc regime s different plasticity character

MSC Regime’s Different Plasticity Character


Msc regime grain effects

Multiaxial term

MSC Regime (Grain effects)

  • Crystal plasticity fatigue simulation on crack propagation validate grain orientation effects (MSU or Cornell)


Multistage fatigue msf modeling dr mark f horstemeyer mississippi state university

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 c i and c ii

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 q 1 and q 2

Multiaxial term

MSC Regime (q1 and q2)

  • Multi-axial tests to determine 1 and 2.


Msc ctd drops indicate resistance from particles

MSC CTD Drops Indicate Resistance from Particles


Msc showing tortuousity via fea

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


Multistage fatigue msf modeling dr mark f horstemeyer mississippi state university

MSC


Microstructurally small crack n 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


D ctd calculation

DCTD calculation

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

U considers crack closure

simple approximation

Refs

McDowell et al., 2003

Fan et al., 2001

R < 0So = 0U = 1/(1-R)

R > 0So = SminU = 1

So is determined by small crack mean stress

experiments, in-situ SEM, and

micromechanical crack growth FE sims


Multiaxial stress effects

Multiaxial stress effects

deviatoric von Mises stress

Refs

McDowell et al., 2003

Hayhurst et al., 1985

maximum principal stress

0 < q < 1

q = 0fatigue controlled by

q = 1fatigue controlled by

q determined by torsion-tension/compression fatigue exps


Long crack growth n lc

Long crack growth NLC

FASTRAN used for long crack growth


Transition from small crack growth to long crack growth

Transition from small crack growth to long crack growth


Multistage fatigue msf modeling dr mark f horstemeyer mississippi state university

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

Notch Root Radii Effects on Incubation and MSC


Multistage fatigue msf modeling dr mark f horstemeyer mississippi state university

MSC:

Debonding dominant

because driving force

is relatively small

LC:

Cracking of second

phase particles dominant

because driving force

is relatively strong


Multistage fatigue msf modeling dr mark f horstemeyer mississippi state university

Strain-life for A356 Al alloy with a focus on local defects


Multistage fatigue msf modeling dr mark f horstemeyer mississippi state university

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


Multistage fatigue msf modeling dr mark f horstemeyer mississippi state university

Same fracture surface of 0.2% strain amplitude sample as before showing progressive damage

alpha intermetallics

FCG =fatigue crack growth


Multistage fatigue msf modeling dr mark f horstemeyer mississippi state university

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.


Multistage fatigue msf modeling dr mark f horstemeyer mississippi state university

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.


Multistage fatigue msf modeling dr mark f horstemeyer mississippi state university

Number of cycles versus maximum pore size (micron) measured for specimens

tested at a strain amplitude of 0.0015.


Multistage fatigue msf modeling dr mark f horstemeyer mississippi state university

Number of cycles versus nearest neighbor distance (micron) measured for specimens

tested at a strain amplitude of 0.0015.

.


Multistage fatigue msf modeling dr mark f horstemeyer mississippi state university

Number of cycles versus number of pores measured for specimens tested at a

strain amplitude of 0.0015.


Multistage fatigue msf modeling dr mark f horstemeyer mississippi state university

Number of cycles versus porosity (void volume fraction) measured for specimens tested at a strain amplitude of 0.0015.


Multistage fatigue msf modeling dr mark f horstemeyer mississippi state university

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.


Multistage fatigue msf modeling dr mark f horstemeyer mississippi state university

Initial crack size

HCF loading dominated

LCF loading dominated

Multiaxial term

Mean stress term

Current State: Multistage Fatigue Model

Incubation

MSC/PSC Growth

Note: not used

for PM alloys

Porosity term

LC Growth

LC growth model will be FASTRAN. This model is temporary.


Multistage fatigue msf modeling dr mark f horstemeyer mississippi state university

Used to determine functional

form of incubation equation

particularly the 0.3 limit


Multistage fatigue msf modeling dr mark f horstemeyer mississippi state university

Micromechanics simulations showing variation

of driving force because of pore/particle resistances


Multistage fatigue msf modeling dr mark f horstemeyer mississippi state university

Strain-Life as a function microstructure

Long Crack Regime


Multistage fatigue msf modeling dr mark f horstemeyer mississippi state university

Number of Cycles as a function of inclusion size


Multistage fatigue msf modeling dr mark f horstemeyer mississippi state university

Strain-Life Model Correlation with MSF Model


Multistage fatigue msf modeling dr mark f horstemeyer mississippi state university

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


Multistage fatigue msf modeling dr mark f horstemeyer mississippi state university

Powder Metal Finite Element Analysis of Performance and Fatigue


Multistage fatigue msf modeling dr mark f horstemeyer mississippi state university

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

10-3

10-4

Fatigue

Failure

Defect volume

fraction

10-4

10-3

10-2

10-1

10-0

10-5


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