M. Kawai Institute of Engineering Mechanics and Systems,

1. A New Strength Parameter and a Damage Mechanics Model for Off-Axis Fatigue of Unidirectional Composites Under Different Stress Ratios M. Kawai Institute of Engineering Mechanics and Systems, University of Tsukuba, Tsukuba 305-8573, JAPAN

2. Outline Background Objectives Experimental Results Strength Measures Modeling & Verification Conclusions

3. Fiber Matrix Local off-axis loading of inclined plies Matrix-Dominated Behavior Fatigue Failure Analysis of Composites UD Lamina: MD Laminate:

4. Loading Mode Dependence of Fatigue  time Service Loading of Structural Laminates (in general) ・Alternating stress (Amplitude) ・Mean stress ・Waveshape ・Frequency

5. Unidirectional Carbon/Epoxy (Kawai, M., Suda, H. and Koizumi, M., 2002) Unidirectional Glass/Epoxy (El Kadi, H. and Ellyin, F., 1994) Effects of Mean Stress on Off-Axis Fatigue Behavior of PMCs —Experimental Data—

6. Stress Ratio: Mean time Objectives Mean Stress Effects on Off-Axis Fatigue Behavior of UD PMCs for the range –1 ≤ R ≤ 1 Fatigue Strength Measure Fatigue Model Considering Mean Stress Effects

7. Unidirectional Carbon/Epoxy (Kawai, M., Suda, H. and Koizumi, M., 2002) Unidirectional Glass/Epoxy (El-Kadi, H. and Ellyin, F., 1994) Effects of Mean Stress on Off-Axis Fatigue Behavior of PMCs —Experimental Data—

8. Material System Carbon/Epoxy (T800H/2500) Specimens: 10 100 50 50 1 2 (unit:mm) q = 0°  20 100 50 50 1 2 (unit:mm) q = 10 , 15 , 30 , 45 , 90°

9. Comparison Between Tensile and Compressive Strengths

10. s smax time smin s s smax smax smin smin time time Fatigue Testing on CFRP Off-Axis Fatigue Testing ・Load control ・Frequency10 Hz ・TemperatureRT ・Stress ratio R = 0.5, 0.1, –0.3 (q = 0°) R = 0.5, 0.1, –1.0 (q > 0°) R = 0.5 R = 0.1 R = –0.3, –1.0

11. Antibuckling Guide Fixtures

12. max , MPa max , MPa ● R = 0.5 ● R = 0.5 ● R = 0.1 ● R = -1.0 ● R = 0.1 ● R = -1.0 ● R = 0.5 ● R = 0.1 ● R = -1.0 ● R = 0.5 ● R = -1.0 ● R = 0.1 Nf Nf max , MPa max , MPa Nf Nf Effects of Stress Ratio on Off-Axis Fatigue (CFRP)

13. Failure along fibers T-T Fatigue Failure Morphology (CFRP)

14. ( R = -0.3 ) Out-of-plane shear, Microbuckling Failure along fibers T-C Fatigue Failure Morphology (CFRP)

15. Effects of Stress Ratio on Off-Axis Fatigue (GFRP)

16. Strength Ratio: where Maximum fatigue stress Static strength Non-Dimensional Fatigue Strength Measure

17. Off-Axis S-N Relationship Using Strength Ratio Unidirectional T800H/Epoxy (R = 0.1)

18. Effect of Stress Ratio on Off-Axis S-N Relationship Unidirectional T800H/Epoxy

19. Non-Dimensional Fatigue Strength Measure Modified Strength Ratio: where

20. R = –1 Master S-N Relationship Modified Strength Ratio

21. Off-Axis S-N Relationship Using Modified Strength Ratio Unidirectional T800H/Epoxy

22. Off-Axis S-N Relationship Using Strength Ratio Unidirectional Glass/Epoxy (R = 0)

23. Off-Axis S-N Relationship Using Modified Strength Ratio Unidirectional Glass/Epoxy

24. A Unified Fatigue Strength Measure —Experimental— Modified Strength Ratio: Stress ratio effect Fiber orientation effect (for the tested range of R)

25. Non-Dimensional Effective Stress Tsai-Hill Static Failure Criterion: X: Longitudinal strength Y: Transverse strength S: Shear strength Non-Dimensional Effective Stress:

26. Theoretical Strength Ratio Off-Axis Fatigue Loading of UD Composites Non-Dimensional Effective Stress Static Failure Condition: Maximum Non-Dimensional Effective Stress

27. Off-Axis S-N Relationship Using Theoretical Strength Ratio Unidirectional T800H/Epoxy

28. Off-Axis S-N Relationship Using Theoretical Strength Ratio Unidirectional Glass/Epoxy

29. Non-Dimensional Effective Stress for Fatigue Modified Non-Dimensional Effective Stress: where

30. R = –1 Master S-N Relationship Theoretical Modified Strength Ratio

31. Off-Axis S-N Relationship Using Theoretical Modified Strength Ratio Unidirectional T800H/Epoxy

32. Off-Axis S-N Relationship Using Theoretical Modified Strength Ratio Unidirectional Glass/Epoxy

33. Fatigue Damage Growth Law: Fatigue Life Equation: Damage Mechanics Modeling of Composite Fatigue : Fatigue strength parameter

34. Off-Axis Fatigue Model S*-Based Fatigue Damage Model: Master S-N Relationship:

35. Master S-N Relationship Unidirectional T800H/Epoxy

36. Transformation of Master S-N Relationship

37. Comparisons With Experimental Results Unidirectional T800H/Epoxy

38. Master S-N Relationship Unidirectional Glass/Epoxy

39. Comparisons With Experimental Results Unidirectional Glass/Epoxy

40. Constant Fatigue Life Diagram (CFLD)

41. Conclusions For ”, A non-dimensional strength measure S* that considers the mean stress as well as fiber orientation effects on the off-axis fatigue behavior of unidirectional polymer matrix composites was proposed. Validity of the fatigue model based on the non-dimensional strength measure S* was evaluated by comparing with experimental results.

42. Conclusions For ”, Using the modified strength ratio S*, we can substantially remove the fiber orientation as well as stress ratio dependence of the off-axis fatigue data to obtain an experimental master S-N relationship. A general expression S* of the modified fatigue strength ratio is obtained as a natural extension of the non-dimensional effective stress based on the Tsai-Hill static failure criterion. A fatigue damage mechanics model that considers the fiber orientation as well as stress ratio effects is formulated using the modified non-dimensional effective stress S*. The proposed fatigue model can adequately describe the off-axis S-N relationships of unidirectional glass/epoxy and carbon/epoxy laminates under constant-amplitude cyclic loading with non-negative mean stresses.

43. Summary Chart Application to Fatigue Experimental Theoretical Metals UD-PMCs Basquin (1910) Awerbuch-Hahn (1981) Landgraf (1970) ?

44. Thank you for your kind attention !