Incubation & Incubation & Nucleation Validation Nucleation Validation

StudyStudy

SIPS TIM, October 22nd 2007

Cornell and RPI

Eight peer-reviewed journal papers will be produced from the SIPS-related work being completed by Cornell and our M&S colleagues:

January, 2008 – “A geometric approach to creating and meshing statistically accurate finite element models of AA7075-T651 microstructures ”

January, 2008 – “A geometric approach to modeling microstructurally small crack fatigue crack formation part I: probabilistic simulation of constituent particle cracking in AA7075-T651”

May, 2008 – “A three-dimensional multiscale procedure for microstructurally small fatigue crack nucleation”

May, 2008 – “A geometric approach to modeling microstructurally small crack fatigue crack formation part II: verification and validation of incubation and nucleation criteria”

July, 2008 – “A geometric approach to modeling microstructurally small crack fatigue crack formation part III: simulation of stage I, intra-granular crack propagation in AA7075-T651”

January, 2009 – “A geometric approach to modeling microstructurally small crack formation, part IV: simulation of stage I, trans-granular crack propagation in AA7075-T651”

March, 2009 – “A geometric approach to modeling microstructurally small crack formation, part V: probabilistic simulation of stage I crack propagation in AA7075-T651”

May, 2009 – “A geometric approach to modeling microstructurally small crack formation, part VI: a probabilistic multiscale method for predicting microstructurally small fatigue life of AA7075-T651

Outline

Previous Work

• Incubation Filter

• Nucleation Damage Metrics Calibration & Validation

• Objectives Microstructure Replication Process

• Model Generation

• Preparation & Analysis

• Results & Observations

3

4

p cr noyes

RD

ND

Determine particle strength, cr ~ KIC / sqrt(particle size)

Previous Work: Incubation FilterPrevious Work: Incubation Filter

5

Max. accumulated slip on a single system:

Max. accumulated slip on a single plane:

Total accumulated slip:

Work-based damage:

Fatemi-Socie damage:

max1D

ppD max2

3D

systemonslipdaccumulate

pplaneonslipdaccumulatep

systems slip allonslipdaccumulate

tpp dtpD

0

3

1 max4

systemandpplane

onstressshearp

pplaneonstressnormaln

systemeachonp sli

toresistanceinitialg

o dtgpD

t

o

pn

p

0

3

15.01max5

Criterion: Nucleation occurs when Di ≥ Di,0

Previous Work: Nucleation Damage Previous Work: Nucleation Damage MetricsMetrics

Definitions of relevant slip-based damage metrics:

6

Maximum particle stress is accurately obtained when:

• idealizing particle as an ellipsoid

• only attaching the surrounding grain Parameter ‘C’ is a material constant

Using 13 additional observations, validate incubation criterion assumptions :

Do any of the 5 slip-based damage metrics predict nucleation events for all observations?Evaluate nucleation criteria using 5 additional observations:

Using 1 experimental observation of crack incubation, back calculate the parameter ‘C’

Using 1 experimental observation of crack nucleation, calibrate the parameter ‘Di,0’ for each damage metric

Calibrate incubation & nucleation criteria:

p

IC

f

ICcr Ca

K

a

K

Calibration & Validation: Objectives

Outline

Previous Work

• Incubation Filter

• Nucleation Damage Metrics Calibration & Validation

• Objectives Microstructure Replication Process

• Model Generation

• Preparation & Analysis

• Results & Observations

7

8

Physical Data(from Northrop

Grumman)

Computational Modeling

SEM OIM

Particle Particle

Detailed Microstructure

• Take detailed microstructure from EBSD/OIM

• Generate a simplified microstructure derivative based on phenomenological information

• Assign crystal plasticity model, with measured orientations, to each grain

• Mesh and apply notch strain

• Test effect of simplifying the microstructure by comparing with results from detailed geometry

• Record results, check for mesh convergence, and note numerical advantages for each simplified microstructure derivative

Microstructure Replication Process

9

Model Generation: Detailed Microstructure

10

All Grains

Surrounding Grains Only

Small Grains Above/Below No Small Grains

No Small Grains @ Distance

Model Generation: Simplified Microstructure Derivatives

11

Model Generation: Automated Routine

12

All grains Surrounding grains only

Preparation and Analysis: Mesh

13

Preparation and Analysis: Notch Strain

Questions for Northrop Grumman Inc.:

What is the exact notch strain for the first load cycle?

What is the notch strain history for subsequent load cycles?

Coarse MeshMedium Mesh

xx

MPa

100 m 75 m

x

Surrounding Grains OnlyAll Grains

Fine Mesh

Results and Observations

14