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

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

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

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

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

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

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

9. Comparison Between Tensile and Compressive Strengths

10. Off-Axis Fatigue Testing ・ Load control R = 0.5R = 0.1 ・ Frequency 10 Hz ・ Temperature RT ・ Stress ratio R = 0.5, 0.1, –0.3 (  = 0°) R = 0.5, 0.1, –1.0 (  > 0°) Fatigue Testing on CFRP time   max  min R = –0.3, –1.0  time  max  min  time  max  min

11. Antibuckling Guide Fixtures

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

13. T-T Fatigue Failure Morphology (CFRP)  R = 0.5R = 0.1 0° 10° 15° 30° 45° 90° Failure along fibers

14. T-C Fatigue Failure Morphology (CFRP) ( R = -0.3 )  0°30° 10°45° 15°90° Failure along fibers Out-of-plane shear, Microbuckling

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

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

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

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

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

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

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. Tsai-Hill Static Failure Criterion: Non-Dimensional Effective Stress 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. Modified Non-Dimensional Effective Stress: where Non-Dimensional Effective Stress for Fatigue

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

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

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

35. Unidirectional T800H/Epoxy Master S-N Relationship

36. Transformation of Master S-N Relationship

37. Comparisons With Experimental Results Unidirectional T800H/Epoxy

38. Unidirectional Glass/Epoxy Master S-N Relationship

39. Unidirectional Glass/Epoxy Comparisons With Experimental Results

40. Constant Fatigue Life Diagram (CFLD)

41. A non-dimensional strength measure  * 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  * was evaluated by comparing with experimental results. Conclusions For ”      ,

42. 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  * 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  *. 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. Conclusions For ”      ,

43. Summary Chart ExperimentalTheoreticalApplication to Fatigue MetalsUD-PMCs Basquin (1910) Awerbuch-Hahn (1981) Landgraf (1970) ?

44. Thank you for your kind attention !