Micromechanics for SMAs Aging in Polymer Composites

1. McCormick School of Engineering Micromechanics for SMAs & Aging in Polymer Composites Professor Cate Brinson Dr. Miinshiou Huang Kathy Issen Alex Bekker Xiujie Gao

2. McCormick School of Engineering Outline Simple 1-D Modeling SMA Multivariant Model Single Crystal Model Polycrystalline model Comparisons with experimental data Recent Experimental Data Implications for Further Work

3. McCormick School of Engineering Basic Shape Memory Phenomena Shape Memory Effect Pseudoelasticity

4. McCormick School of Engineering Simple 1-D SMA Model Phenomenological Constitutive Law Split Martensite Volume Fraction: Kinetic Law based on Phase Diagram Multivalued, path-dependent function Simple algebraic kinetic description possible Location and direction of loading path determines kinetics

5. McCormick School of Engineering “Phase Diagram” Kinetics Divide any thermomechanical loading path into segments

6. McCormick School of Engineering Simple 1-D Constitutive Law Robust and accurate Easy to program Used in control algorithms Used in finite element codes Coupled with Heat Transfer equations Limited to 1-D, wire response Need 3D model as convenient!

7. McCormick School of Engineering Finite Element Example - Active Frequency Tuning

8. McCormick School of Engineering SMA Microstructure of Single Crystal Self-accommodated variants (T-induced) Hierarchical twin microstructure Reorientation and Detwinning key for single and polycrystal response Experimental data for 3D severely lacking

9. McCormick School of Engineering A Multivariant SMA Model

10. McCormick School of Engineering A Multivariant SMA Model

11. McCormick School of Engineering Groups of Variants

12. McCormick School of Engineering Multivariant Single Crystal Model

13. McCormick School of Engineering Habit Plane and Correspondence Variants

14. McCormick School of Engineering Conversion Process Under Load

15. McCormick School of Engineering Single Crystal Comparison: Biaxial Load

16. McCormick School of Engineering Orientation Dependence

17. McCormick School of Engineering Orientation Dependence The anisotropy factor in the cubic system is defined as A = 2 C44 /(C11 - C12) = 12.8 for Cu-14Al-4.1Ni (wt%) The ratio of the maximum Young’s modulus to the minimum in the same alloy Emax / Emin = 10 Multivariant Model: A = 1 Emax / Emin = 1 (assumed A, M isotropic with same modulus) Strong anisotropy of austenite should be accounted for in modeling different initial moduli, transformation stresses Difficulty: Eshelby inclusion analysis difficult for anisotropy CuAlNi has 2H periodic stacking structure model currently optimized for 9R/18R

18. McCormick School of Engineering Orientation Dependence

19. McCormick School of Engineering Polycrystalline Model

20. McCormick School of Engineering Temperature Induced Transformation

21. McCormick School of Engineering Shape Memory Effect

22. McCormick School of Engineering Pseudoelasticity

23. McCormick School of Engineering Pseudoelasticity

24. McCormick School of Engineering Reuss Approximation

25. McCormick School of Engineering Uniaxial and Triaxial Stress States

26. McCormick School of Engineering Experiment & Prediction

27. McCormick School of Engineering Experiment and Prediction

28. McCormick School of Engineering Experiment and Prediction

29. McCormick School of Engineering Model Prediction for DV>0

30. McCormick School of Engineering Multivariant Model Summary Multivariant Model predicts a variety of shape memory phenomena Multivariant Model can account for: tension/compression asymmetry multiaxial stress states modulus dependent on stress state Polycrystalline model has trouble with: transformation stress magnitudes strain hardening Anisotropy of material could be key Modification for 2H/3R crystallography Code is computationally intensive More Experiments needed

31. McCormick School of Engineering Recent Experimental Studies Single crystal CuAlNi experiments Optical Microscopy SEM EBSD All with in situ loading Experiments designed to provide key modeling information Experiments on NiTi planned

32. McCormick School of Engineering SEM Experimental Set-Up

33. McCormick School of Engineering SEM Loading Stage

34. McCormick School of Engineering SEM Image Showing Habit Plane, Twins SEM image at 2000x Uniaxial loading Variant ID possible when habit plane and twin plane visible

35. McCormick School of Engineering EBSD in Austenite Phase

36. McCormick School of Engineering Digital Camera Observation in MTS

37. McCormick School of Engineering Stress-Strain Response For previous thermal/loading cycle

38. McCormick School of Engineering Implications of Experiments Model criterion for b1’ and g1’ should differ Resistance gap between b1’ and g1’ Note single M-variant across width of specimen NiTi: need to account for detwinning (HV CV) Work best criteria for variant selection (from tension/compression experiments) Still need biaxial, bending experiments for more complex load states Need microscopy resolution to ID variants

39. McCormick School of Engineering

40. McCormick School of Engineering Future Modeling Take one step back: Remove interaction energy Simplify Calculations Retain and expand variant structure Account for CV, HV: Detwinning possible Implement resistance gap:

41. McCormick School of Engineering Preliminary Result Interaction Energy removed Speedy computation Ultimately, can remove other layers as discover necessary and unnecessary baggage for 3D polycrystalline response

42. McCormick School of Engineering Summary SMA Polycrystalline 1-D Modeling Tractable SMA Variant structure and response complex Microscopy Experiments with in situ loading help provide insight Micromechanics modeling appropriate and promising Several micromechanics methods under development