A Synergistic Multiscale Modeling Approach to Damage in Composites

1. A Synergistic Multiscale Modeling Approach to Damage in Composites Ramesh Talreja Aerospace Engineering Texas A&M University, College Station, Texas

2. Contents • The Engineering Motivation • Damage Scenarios • Multiple Scales  of heterogeneities  of damage entities • Hierarchical approach (“up-the-scales”) • Motivated (need-based) treatment of scales • Conclusion

6. Question: What is the best sequence of modeling: Right to Left, Or Left to Right, Or Combined (Synergistic)?

7. Damage classification “Damage” in composites: Multiple cracking where shear-lag (at interfaces) is involved • Pre-damage regime • Damage regime • Post-damage regime • (Localization and fracture)

8. Pre-Damage Regime Example: Unidirectional Composite in Transverse Tension σ Debonding induces matrix cracking Matrix cracking causes debonding σ Length scales of microstructure: Fiber diameter, Inter-fiber spacing

9. Local Stress State resulting from transverse loading of fiber composites σ Dilatational • Depends on • Fiber and matrix properties • Fiber distribution σ Distortional

10. Effect of Dilatational (hydrostatic tension) stress Cavitation, presumably from free volume in polymers Unstable growth of cavitation at critical dilatational energy

11. Effect of Dilatational (hydrostatic tension) stress σ When dilatational energy reaches a critical value, cavities burst open causing debonding Length scales of damage: Cavity diameter (before debonding) Fiber diameter (after debonding) σ Asp, Berglund, Talreja (1996)

12. Effect of Distortional stress σ Distortional Matrix cracks form by Yielding, Void growth and Coalescence, crazing Length scales of damage: Cavity diameter (before cracking) Inter-fiber spacing (after cracking) Models: Rice, Tracey (1969) Boyce, Parks, Argon (1988) Gearing, Anand (2004) σ

13. Polymer Fracture Through Crazing E D B C A

14. Damage Regime Example 1: Unidirectional Ceramic Matrix Composite in Tension Fiber-bridged matrix crack Fibers Increasing load

15. Damage Regime Example 2: Cross-Ply Polymer Matrix Composite in Fatigue Transverse cracks Delaminations Axial splits

16. Cross Ply Composites and Woven Fabric Composites

17. Damage Regime Example 3: General laminate with off-axis ply cracking

18. Damage in Composites • Multiple matrix cracks, interfacial disbonds, delaminations, fiber breaks, microbuckled fibers, and more • Multiple orientations • Multiple scales of damage entities • Multiple rates of evolution • Multiple effects on material response

19. The Multi-Scale Nature ofDamage in Composites • What is the Lowest Damage Scale? • A Purist (Scientific) View: • The first (basic) scale at which dissipative mechanism(s) occur. • A Pragmatist (Engineering) View: • The first significant scale (manifesting behavior of lower scales, if any) that governs the property of interest. Preferably, scale of observable entities.

20. The Choice of Scales in an Engineering Approach • Should be guided by the purpose (Model) • -- To predict properties and performance, or • -- To design properties for selected performance • Should account for the scale of inhomogeneities • (fibers, particles, plies, etc.) • -- Damage entities are often initiated by • inhomogeneities, and evolve under their influence

21. Damage Mechanisms Unidirectional Ceramic Matrix Composite in Tension Increasing Load Increasing Crack Density

22. Stress-Strain Response Unidirectional Ceramic Matrix Composite in Tension

23. Stage II Damage Mechanism sliding debonding Fiber-bridged Matrix Cracking

24. Length Scales of Stage II Damage Mechanism Damage Entity Length Scale: Crack length RVE Length Scale: Crack spacing Microstructural Length Scale: Fiber diameter

25. Damage Mechanisms Cross-Ply Polymer Matrix Composite in Fatigue Delaminations Multiple Damage Modes: Transverse Ply Cracks Axial Splits

26. Length Scales - Ply Cracking in Laminates Damage Entity Length Scale: Ply thickness, tc RVE Length Scale: Crack spacing, s Microstructural Length Scale: Ply thickness, t0

27. Ply Cracking with Delamination Damage Entity Length Scale: Ply thickness, tc RVE Length Scale: Crack spacing, s Microstructural Length Scale: Ply thickness, t0

28. A Continuum Characterization of Damage

31. A Tensorial Representation of Damage RVE ni:Unit normal to damage entity surface ai:Represents pre-specified influence of damage entity on the surrounding medium

33. The damage tensor for intralaminar-cracking is given as follows: tc: Thickness of the cracked ply tT: Total laminate thickness s1: Spacing between cracks κ: Effect of constraint on the crack opening displacement imposed by the uncracked laminae

34. The Internal Variable of Damage • All terms are measurable, except κ • κ depends on “microstructure” and its • length scales, and can be experimentally • “identified” or calculated by analytical or computational micromechanics

35. κ

36. Examples of SDM: • Multiple cracking in UD CMC (Sørensen,Talreja, 1993) • Multiple ply cracking in cross ply laminates (Varna, Akshantala, Talreja , 1999) • Multiple transverse cracking with varying constraints (Varna, Akshantala, Talreja, 1999; Varna, Joffe, Talreja, 2001) • Linear viscoelastic cross ply laminates with transverse cracks (Kumar, Talreja, 2003; Varna, Krasnikovs, Kumar, Talreja, 2004) • Off-axis multiple cracking – one mode (Varna, Joffe, Akshantala, Talreja, 1999; Singh, Talreja, 2008) • Off-axis multiple cracking – two modes (Singh, Talreja, 2009) • Review papers: • Talreja, R., Journal of Materials Science, 2006 • Talreja, R. and Singh, C.V., In Multiscale Modeling • and Simulation of Composite Materials and Structures, • Y. Kwon, D.H. Allen and R. Talreja, Eds., Chapter 12, Springer, 2007.

37. Conclusion • Damage in composite materials is complex (multitude of size, shape, orientation) and not suited for “up-the scale” multi-scale approach • For application to complex shaped structures in service loading (time-varying multiaxial stress, temperature) continuum damage mechanics is the most suitable approach • Synergistic approach (CDM with “access” to judiciously selected micromechanics results) has been demonstrated for elastic and linear viscoelastic composites. • Damage evolution, not discussed here, is treated by micromechanics