DDSim: A Next Generation D amage and D urability Sim ulator

1. DDSim: A Next Generation Damage and Durability Simulator Presenting: John Emery Advising and Supporting: Prof. Tony Ingraffea, John Dailey Jr., Gerd Heber,Wash Wawrzynek funded through NASA’s Constellation University Institutes Project.

2. Outline for the Talk • The Big Picture & Overview • DDSim Level I – Reduced-order filter • Input • Approach • Results & Performance • Level II – Automated crack insertion • Approach • Results • Level III – Multiscale simulation • Statistically accurate microstructural geometry • Multiscale implementation • Conclusions

3. The Big Picture Random input Finite element model of structure including boundary/environmental conditions Probabilistic life prediction PT Material system & pertinent microstructural statistics DDSim Time to failure, N Best available physics-based damage models

4. Overview of the Hierarchical Approach A multiscale approach with 3 hierarchical levels: • Level I: A fast, analytical, reduced-order filter to determine life-limiting hot-spots in complex structures • Level II: Traditional continuum fracture mechanics, FRANC3D, to compute the life of the structure consumed by growth of microstructurally large cracks (NMLC) • Level III: Multiscale simulation to compute the life of the structure consumed by incubation, nucleation and propagation of microstructurally small cracks (NMSC) Assumption: Ntotal = NMLC + NMSC

5. DDSim Level I: Input • Database from FEM without damage • Mesh • Field information • Boundary conditions B (slide 9) • Models and Parameters for Fracture and Damage Mechanics • Models for fatigue crack growth (NASGRO equation*) • Statistical material data & initial damage size A (slide 6) Stress field contour plot: Rib-stiffened element *Forman & Mettu, Fracture Mechanics: Twenty-second Symposium, Vol. 1, ASTM STP 1131

6. Life prediction contour plot on original FE Mesh (29,072 surface nodes, average ai=2.76e-4 in) Stress field contour plot: x-section A (previous), Rib-stiffened element DDSim Level I • Analytical solutions & field data from undamaged FEM used to estimate service life limited by damage at a large number of possible origins (mesh nodes). How to map: Stress  Life prediction? • Initial flaw size from statistical distribution (eg. particle x-sectional area). • These damage origins do NOT become part of the geometrical model in Level I. • These damage origins do NOT interact with each other. • These simplifications readily allow parallel processing. Key Ideas for Level I: High Volume, High Automation, Probabilistic, & Conservative First Order Analysis

7. Stress intensity factor, (ksiin) Crack length, (in) Principal stress on a thermomechanically loaded part (courtesy of FAC) Conservative SIF History b a DDSim Level I is designed to provide conservative estimates of K (compared with FRANC3D here).

8. Level I Results & Performance • Under Fatigue spectrum • Nodes (i.e. initial flaw locations): 63,974 • Random initial flaws (from particle filter): 10,000 • No. of processors @ 3.6GHz w/ 2GB RAM: 16 • Min & Max computed life (cylces): 18542 - 99,999 • Processing time (hr:mm): 5:48 Probability of occurrence Particle diameter, (in) Life prediction contour plot w/ 10,000 initial flaws

9. DDSim Level II Fully 3D crack growth simulation at “hot spots”: • Explicit representation of crack surface in FE model geometry • Automatically inserted at “hot spots” determined by Level I analysis Level I Life prediction contour plot (x-section B slide 5) Automatically inserted, grown and remeshed crack

10. a m b Crack paths Level II Results Low fidelity NMLC = 803 cycles, High fidelity NMLC = 4070 cycles N, (load cycles) NMLC = 4070 Crack length, (in) Level I predictions

11. DDSim Level III: Multiscale Simulation • With a first order, probabilistic analysis completed, focus on the “hot spots” to increase the accuracy of the NMSC prediction using: • Representative digital microstructure • Best available physics • Multiscale simulation • High performance parallel computing Life contour plot from initial prediction Focusing on a “hot spot”, rectangular void for PC model Representative digital microstructure

12. a b c 10 mm Level III: Microstructurally Small Damage • Important geometrical features: • Grains • Particles • Damage processes and events: • (a) Crack incubation process – damage accumulation until the particle cracks • (b) Crack nucleation event – • (c) Microstructurally small crack propagation – process of crack growth within grains and across grain boundaries Crack Incubation Crack Nucleation Crack Propagation

13. Level III: Current Microstructural Geometry Models The lumber model (right) approximates the average grain size and aspect ratios of AA 7075 in a randomly assorted stack The Voronoi model (left) approximates random crystallographic structure of an unrolled alloy The rolled Voronoi model (right) is our most statistically accurate geometry for rolled AA 7075, approximating grain morphology and average size.

14. DDSim Level III: Multiscale Simulation Life contour plot from initial prediction Representative digital microstructure Focusing on a “hot spot”, rectangular void for PC model Multiscale model = Continuum + mstructure!

15. Conclusions Our assumption is: Ntotal = NMLC + NMSC • DDSim Level I provides a high volume, highlyautomated, probabilistic, and conservativelife prediction (Ntotal) for real structures & locates areas of high interest for the Level II & III simulations • Level II uses the current best practice fracture mechanics life predictions methodologies for high fidelity NMLC • The Level III microstructural models incorporate state-of-the-art physics and accounts for microstructural stochasticity for high fidelity NMSC. • DDSim, as a multiscale system, will provide microstructurally educated life predictions for real structures.

16. Safety slides • Intentionally blank

17. Level III: Microstructural Geometry and Damage 0.6 mm Composite Metallic Dissimilar materials…similar microstructural geometrical features 50 mm Metallic micrographs courtesy of A. Rollett, CMU. Composite micrographs from: Nicoletto G., Enrica R., Composites: Part A, 35, 2004, 787 – 795, & S. Stanzl-Tschegg, personal communication

18. Particle Tensile Stress (σxx) Probability Density Function Probability Probability • Particle aspect ratio • Grain orientation • Strain level Particle Tensile Stress Low orientation sxx Intermediate orientation Y f High orientation Q Level III: Particle Crack Incubation Criterion Affect of grain orientation on particle stress, 3 categories: • High stress orientation • Intermediate stress orientation • Low stress orientation

19. Putting It All Together Currently, we have these loose ends: • Monte Carlo simulation is feasible for the low fidelity life prediction of DDSim Level I, however, it is NOT feasible for the multi-scale simulation • One microstructural model requires millions of DOF • Required number of samples makes MC intractable • Level II computes the life consumed by continuum length scale damage evolution • Level III computes the life consumed by micro-scale damage evolution Recall our assumption was: Ntotal = Nmacro + Nmicro

20. PT N PT N Pm Pm N N Putting It All Together Low fidelity life predictor: DDSim Level I Random input Low fidelity life prediction “predictor” “corrector” Damage site iterator: DDSim Level II, Nmacro Combine conditional probabilities High fidelity life prediction High fidelity “post” conditional life cdf Low fidelity “prior” conditional life cdf Multi-scale simulation: DDSim Level III, Nmicro Bayesian estimation

21. Level III: Multi-scale 3-D Realistic Microstructure Model 3-D Continuum Field Analysis 3-D Continuum Model Simulate damage evolution: steam enhanced delamination (with models from collaborating CUIP IFST teams) particle debonding/cracking crystal plasticity/cohesive constitutive models intra/intergranular microcracking Analyze microstructure for to capture microstructural damage evolution, update continuum damage state and fields Apply B.C.’s from Macroscale Model

22. sx (ksi) y sx (ksi) x 45.17 ksi Continuum Model E=10,500 ksi n=0.33 Close-Up of Bolt-Hole Update Stiffness Polycrystal Scale Continuum Scale Grain Boundary Decohered Polycrystal Model Level III: Multi-scale, 2D Example Gather Boundary Conditions and Apply to Polycrystal Model Calculate New Modulus for Each Gauss Point in the Continuum Model E=10,500 +/- 1,000 ksi n=0.33 tp=72.5 ksi

23. y x Level III: Multi-scale, 2D Example ex Smeared Crack Updated Continuum Model