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Multiscale Modeling SIPS TIM, October 22nd 2007 Cornell University Jeff Bozek, Jake Hochhalter, Mike Veilleux, Gerd Heber, Wash Wawrzynek, Tony Ingraffea Outline Microstructure Realization Models • Evolution of Microstructure Geometry Models • Current Mesh Generation Flow Chart • Qualitative Comparison of Meshing Tools Probability Framework • Flow Charts • Filters: Incubation, Nucleation, and Intra- & Transgranular Propagation – Stage I, Intragranular Crack Propagation Criteria • High Fidelity Probability Framework • Screening Microstructure Realization Models 2 Evolution of Microstructure Geometry Models SEM’s of 7075-T651 (R. Campman, CMU) SOFTWARE DEVELOPERS YEAR DESCRIPTION PyXL Cornell 2003 One phase; convex, equi-axed grains mBuilder, Equi-axed CMU, Cornell 2004 One phase; non-convex, equi-axed grains Lumber RPI 2005 One phase; rectangular prismatic grains mBuilder, Elongated CMU, Cornell 2005 One phase; non-convex, elongated grains PINC Cornell 2006 Inserts particles into one-phase models Progress Toward Reality 3 New Microstructure Geometry Model SEM’s of 7075-T651 (R. Campman, CMU) Improvements on past methods: 1. More accurate representation of grain aspect ratios 2. No “exaggerated” re-entrant corners along grain boundaries Current status: 1. CMU has generated a model with a surface mesh 2. Cornell is developing tools to interpret new model and create volume mesh Progress Toward Reality 4 Current Mesh Generation Flowchart Geometry Geometry Surface Mesh READ INPUT EXTRACT GEOMETRY Edge Subdivisions SUBDIVIDE EDGES Edge Subdivisions SUBDIVIDE EDGES Surface Mesh MESH FACES Surface Mesh MESH FACES Volume Mesh Volume Mesh MESH REGIONS MESH WITH ABAQUS MESH REGIONS MESH WITH PolyMesh 5 Qualitative Comparison of Meshing Tools ABAQUS Positives Negatives High quality Incompatibility elements with some inhouse tools Industry support Not open source Robustness Scripting interface Automation requires new scripts PolyMesh Positives In-house, open Negatives Not robust Low quality source Already fully automated Compatible with inhouse tools Designed specifically for meshing microstructures elements 6 Outline Microstructure Realization Models • Evolution of Microstructure Geometry Models • Current Mesh Generation Flow Chart • Qualitative Comparison of Meshing Tools Probability Framework • Flow Charts • Filters: Incubation, Nucleation, and Intra- & Transgranular Propagation – Stage I, Intragranular Crack Propagation Criteria • High Fidelity Probability Framework • Screening Microstructure Realization Models 7 The Big Picture Stochastic input Probabilistic life prediction Finite element model of structure including boundary/environmental conditions Material system & pertinent microstructural statistics Best available physicsbased damage models CU’s Black Box Time to failure, N 8 CU’s Black Box Low fidelity life predictor: Stochastic input • Level I for Ntotal = NMSC+NMLC • Level I for NMSC Low fidelity life prediction PT N PT ( NTotal ) “predictor” “corrector” nodes P( N | a ) P(a ) i i i Pm High fidelity life prediction Hot-spot (HS) iterator: N Low fidelity conditional life pdf • Level II for NMLC • Combine conditional probabilities for Ntotal PT N Pm P( NMSC | ai @ HS) High Fidelity Probability: • Level III for NMSC N High fidelity conditional life pdf P( NMSC | ai @ HS) 9 High Fidelity Probability Framework Stochastic Microstructural Input Screening Tool (Filters): IntermediateFidelity Reliability NMSC R N Multiscale Analysis: Probability Procedure: High-Fidelity Reliability NMSC R N 10 Incubation Filter A response surface for the particle stress and strength was generated based on grain orientation, particle aspect ratio, and strain level • Based on series of finite element analyses x (RD) z (ND) y (TD) Develop series of filters: • • • • Incubation Nucleation Intragranular crack growth Transgranular crack growth M. Liu et al. A Geometric Approach to Modeling Microstructurally Small Crack Formation, Part I: Probabilistic Simulation of Constituent Particle Cracking in AA7075-T651. To Appear, 2007. 11 Stage I Intragranular Cracks: Direction Criterion Observed phenomena: Loading Direction Illustration of Stage I crack at no load (a), full tensile load (b), and back to no load (c), from: Grain C. Laird, 1967. ~3 mm SEM/OIM images courtesy of Northrop Grumman Corporation Particles are modeled as linear elastic, isotropic and grains are modeled as FCC crystal plastic Five possible direction criteria – same as nucleation damage metrics: D max 1 D max p p 2 t 3 D max p p dt p 1 4 0 D 3 n D max p 1 0.5 dt p 0 1 5 go t 3 p 12 Stage I Intragranular Cracks: Rate Criterion Observed phenomena: Loading Direction Illustration of Stage I crack at no load (a), full tensile load (b), and back to no load (c), from: Grain C. Laird, 1967. ~3 mm SEM/OIM images courtesy of Northrop Grumman Corporation Particles are modeled as linear elastic, isotropic and grains are modeled as FCC crystal plastic One possible rate criterion – change in crack tip displacement*, CTD: Recorded for observed particles da GCTD CTDTH dN computed known material parameter unknown value material parameter * McClintock, 1999. Fan, et al., 2001. McDowell, et al., 2003. 13 Stage I Intragranular Crack Growth Filter Series of finite element analyses • Vary grain properties Consolidate in response surface • Relationship Nucleated Crack Front in Matrix between: – Grain properties – Crack front Location Crack through – Strain level Particle – Crack growth rate x (RD) y (TD) z (ND) Monitor several points along the crack front 14 Stage I Transgranular Crack Growth Filter Series of finite element analyses • Vary properties between adjacent grains – Mainly misorientation Consolidate in response surface • Relationship for number of cycles to propagate into adjacent grain based on: – Grain Properties – Crack Front Location – Strain Level Monitor several points along the crack front M. Janssen, J. Zuidema, and R. Wanhill. Fracture Mechanics. 2nd Ed. Spon Press, 2004. 15 Generating High-Fidelity NMSC Reliability Curve Two possibilities: • Large number of approximated microstructural analyses • Small number of highly-detailed microstructural analyses ‘Critical Region’ Choose both: • Entire curve with approximate analyses • ‘Critical Region’ with highlydetailed analyses 16 High Fidelity Probability Framework Screening Tool (Filters): Stochastic Microstructural Input • High Volume • Based on Previous Finite Element Analyses • Approximate NMSC Reliability Curve • Selection of Microstructural Realizations for Multiscale Analysis Multiscale Analysis: • • Automated Series of Multiscale Analyses Limited Number (e.g. 20) Probability Procedure: • Combine to Generate HighFidelity Reliability Curve IntermediateFidelity Reliability NMSC R N High-Fidelity Reliability NMSC R N 17 Screening Microstructural Realizations Incubation Incubation Nucleation Nucleation Intragranular Intragranular Transgranular Transgranular N=23,500 N=8,000 N=5,600 N=2,300 N=300 N=200 N=9,700 N=4,700 N=400 Keep Track of Location and Life at Approximation of NMSC Crack Front Multiple Points Along Each 18 Combining Probabilities ‘Critical Region’ N1 N2 N3 N4 N5 N6 P( N i ) N7 N8 N Ai P( N h 20,000) P( N h 20,000| N i Ai )P( N i Ai ) P( N h 20,000 | N i Ai ) A1 A2 A3 A4 1 I h 8 j 1 ( N j 20,000 ) A5 19