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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)

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.

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

- 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.

- 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

Fatigue Micromechanisms

LCF and HCF Regimes.

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)

: 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

= 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

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

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)

- 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

- 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

- 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

Incubation (Current method has more influence on HCF than LCF)

MSC (current method assumes long crack starts at 250 microns)

Multiaxial term

- 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

- 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

- 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

Multiaxial term

- Multi-axial tests to determine 1 and 2.

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

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

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)

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

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

FASTRAN used for long crack growth

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

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

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

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*pore size)/(nearest neighbor distance*dendrite

cell size) measured for specimens tested at a strain amplitude of 0.0015.

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.

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

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