Nonlinear Constant Fatigue Life Diagrams for CFRP Laminates

Transcription

1 CompTest26, Porto Nonlinear Constant Fatigue Life Diagrams for CFRP Laminates M. Kawai and M. Koizumi Department of Engineering Mechanics and Energy Graduate School of Systems and Information Engineering University of Tsukuba, Japan University of Tsukuba

2 Outline Background Objectives Experimental Results Modeling & Predictions Conclusions

3 Fatigue Failure Analysis R 3 R 1 n 2 n 1 n 3 N f R 2 Linear Damage Accumulation Rule n 1 N 1 + n 2 N 2 + n 3 N Basic fatigue strength as a function of Alternating stress Mean stress Wave sequence Frequency

4 Mean Stress Sensitivity to Fatigue Unidirectional Multidirectional Salkind (1972) Hahn (1979) Sims & Brogdon (1977) El-Kadi & Ellyin (1994) Miyano et al. (1995) Philippidis & Vassilopoulos (22) Kawai & Suda (24) Ramani & Williams (1977) Bonfield & Ansell (1991) Ansell et al. (1993) Harris & coworkers: Adam et al. (1989, 1992) Harris et al. (199, 1997) Beheshty & Harris (1998)

5 Constant Fatigue Life (CFL) Diagram [/±3] 3S Ramani & Williams (1977) Asymmetry about alternating stress axis Attributed to strength differential Linear CFLD approximation Khaya Bonfield & Ansell (1991) Asymmetry about alternating stress axis Complex shape of CFLD C Peak at the stress ratio equal to = T Ansell et al. (1993) [(±45, 2 ) 2 ] S Beheshty & Harris (1998) Asymmetry about alternating stress axis Complex shape of CFLD Bell-shaped CFLD approximation

6 Objectives 1. Examination of the shape of CFL diagram 2. Development of an efficient fatigue life prediction method 1 Fatigue behavior of a [45/9/-45/] 2s CFRP laminate 2 Experimental CFL diagram 3 Fatigue life prediction method based on a theoretical CFLD 4 [/6/-6] 2s 5 [/9] 3s

7 Material Systems Kind Prepreg Lay-up CFRP CFRP CFRP T8H/Epoxy #3631 T8H/Epoxy #3631 T8H/Epoxy #25 [45/9/-45/] 2s [/6/-6] 2s [/9] 2s

8 Specimens Static tension & T-T fatigue tests: (unit:mm) Based on JIS K773 Static compression & T-C, C-C fatigue tests: Based on ASTM D695,Haberle & Matthews (1993)

9 max min max min Frequency: 1 Hz Temperature: RT Fatigue Tests max T-T fatigue min max t Stress Ratio R = min max R = 1 min C-C fatigue

10 max A critical stress ratio min Tensile failure Frequency: 1 Hz Temperature: RT T R = 1 R C = = T max t Stress Ratio min R = min max C Compressive failure Equal tendency to static failure T-C fatigue

11 Experimental Results t R =-1. R =-.681 R = 1 T-T T-C C-C t t max, MPa T8H/Epoxy#3631 UTS UCS Experimental (RT) R = 1 [+45/9/-45/] 2s T-T C-C max, MPa T8H/Epoxy#3631 UTS UCS Experimental (RT) R = R = -1 [+45/9/-45/] 2s T-T T-C N f 2N f [+45/9/-45/] 2s

12 Construction of CFLD max, MPa CFLD a 2 T8H/Epoxy#3631 Experimental (RT) [+45/9/-45/] 2s N f max for a given life m a = 1 2 (1 R) max m = 1 2 (1 + R) max 2N f

13 Experimental CFL Diagram a Fatigue T8H/Epoxy#3631 RT 1Hz [+45/9/-45/] 2s R = -1. R = Experimental N f =1 1 N f =1 2 + N f =1 3 N f =1 4 N f =1 5 N f =1 6 Compressive Tensile c C-C regime R = 1 = C / T =.681 T-T regime t [+45/9/-45/] 2s m Static failure envelope

14 Linear Approximation of CFL Diagram a m m, T m m a a T m = a m m, C m < m C m Fatigue T8H/Epoxy#3631 RT 1Hz [+45/9/-45/] 2s R = R = -1. R = Experimental N f =1 1 N f =1 2 + N f =1 3 N f =1 4 N f =1 5 N f =1 6 C R = 1 (, ) T m a Good at a short fatigue life [+45/9/-45/] 2s m

15 Parabolic Approximation of CFLD

16 a Parabolic Approximation of CFLD a a a = m m T m m m C m Fatigue T8H/Epoxy#3631 RT 1Hz [+45/9/-45/] 2s R = R = -1. R = Experimental N f =1 1 N f =1 2 + N f =1 3 N f =1 4 N f =1 5 N f = c, T m m, C m < m R = 1 ( m, a ) Good at a longer fatigue life t [+45/9/-45/] 2s m

17 Modeling of Anisomorphic CFLD Assumptions: (1) The alternating stress component of the maximum fatigue stress for a given constant value of fatigue life becomes largest at the critical stress ratio equal to the ratio of the compressive strength to tensile one. (2) A progressive change in shape of CFL curves from a straight line to a parabola occurs with increasing fatigue life. (3) The CFL diagram is bounded by the static failure envelope made up of two straight lines connecting the peak position of the CFL diagram with the tensile and compressive strengths respectively.

18 a Asymmetric Anisomoriphic CFLD 2 ψ m m, T m m a a T m = 2 ψ a m m, C m < m C m Fatigue T8H/Epoxy#3631 R = RT 1Hz [+45/9/-45/] 2s R = Experimental N f =1 1 N f =1 2 + N f =1 3 N f =1 4 N f =1 5 N f =1 6 linear parabolic (, ) m a ψ = = max 1 f (2 N f ) B Reference S-N relationship [+45/9/-45/] 2s C m T

19 Comparison With Experimental Data 2 ψ m m, T m m a a T m = 2 ψ a m m, C m < m C m 8 a T8H/Epoxy#3631 [+45/9/-45/] 2s Experimental (RT) N f =1 1 N f =1 2 + N f =1 3 N f =1 4 N f =1 5 N f =1 6 R = 1 R = [+45/9/-45/] 2s m where ψ R = Static strength line Predicted CFD = = max 1 f (2 N f ) B Good agreements with experiment!

20 Predicted S-N Relationships t 1 T8H/Epoxy#3631 [+45/9/-45/] 2s T-T fatigue loading 8 [+45/9/-45/] 2s max, MPa Experimental (RT) Predicted N f

21 Predicted S-N Relationships R = 1 t R =-1. R =-.681 t C-C fatigue loading T-C fatigue loading max, MPa T8H/Epoxy#3631 [+45/9/-45/] 2s Experimental (RT) R = 1 Predicted N f R = 1 max, MPa T8H/Epoxy#3631 [+45/9/-45/] 2s R = Predicted (R = -1) Fitted (R = -.681) R = N f Experimental (RT) 2N f R = -1. R = = 2 K * (1 ψ ) a (ψ ) n [+45/9/-45/] 2s

22 Further Verification (1) Application to a [/6/-6] 3s Laminate a T8H/Epoxy#3631 R = [/6/-6] 2s Experimental (RT) N f =1 1 N f =1 2 + N f =1 3 N f =1 4 N f =1 5 N f =1 6 R = 1 R = -1. Static strength line Predicted CFD m

23 Predicted S-N Relationships t R = 1 t T-T fatigue loading C-C fatigue loading 12 1 T8H/Epoxy#3631 [/6/-6] 2s 1 8 T8H/Epoxy#3631 [/6/-6] 2s max, MPa Experimental (RT) Predicted max, MPa Experimental (RT) R = 1 Predicted R = N f [/6/-6] 3s 2N f

24 Further Verification (2) Application to a [/9] 3s Laminate a T8H/Epoxy#25 [/9] 3s Experimental (RT) N f =1 1 N f =1 2 + N f =1 3 N f =1 4 N f =1 5 N f =1 6 R = 1 R = -1. R = Static strength line Predicted CFD m

25 Predicted S-N Relationships t R = 1 t T-T fatigue loading C-C fatigue loading T8H/Epoxy#25 [/9] 3s max, MPa 1 T8H/Epoxy#25 [/9] 3s 5 Experimental (25 C) Predicted N f max, MPa Experimental (25 C) R = 1 Predicted R = N f [/9] 3s

26 Comparison Between CFLDs for different CFRP laminates a a a T8H/Epoxy#3631 [+45/9/-45/] 2s Experimental (RT) N f =1 1 N f =1 2 + N f =1 3 N f =1 4 N f =1 5 N f =1 6 R = 1 R = m R = Static strength line Predicted CFD 8 7 T8H/Epoxy#3631 R = [/6/-6] 2s 6 Static strength line 5 Experimental (RT) N f =1 1 R = N f =1 2 + N f =1 3 3 N f =1 4 R = 1 2 N f =1 N f =1 6 1 Predicted CFD T8H/Epoxy#25 [/9] 3s Experimental (RT) N f =1 1 N f =1 2 + N f =1 3 N f =1 4 N f =1 5 N f =1 6 R = 1 R = -1. m m R = Static strength line Predicted CFD

27 Failure Under T-C & C-C Fatigue R =-.681 t R =-1. max, MPa R = 1 T8H/Epoxy#3631 [+45/9/-45/] 2s R = R = 1 Experimental (RT) R = -1. Fitted (R = -.681) Predicted N f R = -1. R = Compressive Tensile

28 Conclusions Experimental and theoretical studies to identify a full shape of a CFL diagram were attempted for three kinds of symmetric CFRP laminates of [45/9/-45/] 2s, [/6/-6] 2s and [/9] 3s lay-ups. From experiments: It was confirmed that the CFL diagram becomes asymmetric about the alternating stress axis. A peak position of the asymmetric CFL diagram corresponds to the fatigue loading near the critical stress ratio equal to the ratio of compressive strength to tensile one. (These features of the CFL diagram are similar to the findings of Ansell et al. and Harris et al. )

29 Conclusions (continued) From experiments: It was found that the shape of the asymmetric CFL curves progressively changes from a straight line to a nonlinear curve as a given constant value of life increases. The nonlinear shape of the CFL curves in the range of a longer fatigue life can be described approximately by using a parabola. Similar features in the shape of CFLD were observed for all the CFRP laminates tested in this study. This fact elucidates that the three types of CFRP laminates have a similar mean stress sensitivity to fatigue.

30 Conclusions (continued) From modeling: A procedure to predict an anisomorphic CFL diagram by using the static strengths in tension and compression and the reference S-N relationship for the critical stress ratio was developed. The asymmetric anisomorphic CFL diagrams predicted using the proposed procedure agree well with the experimental CFL diagrams for the types of CFRP laminates. The S-N relationships predicted using the theoretical anisomorphic CFL diagram agree well with experimental results for all the stress ratios in the range of fatigue life up to 1 6 cycles, regardless of the types of CFRP laminates.

31 Advantage & Expectation It is an advantage of the proposed procedure that only a limited amount of data obtained from relatively simple experiments is required for identification of mean stress sensitivity to fatigue of the material. Further validation for different types of composite laminates. The predictive capability demonstrated suggests its application as an essential ingredient to fatigue failure analysis of CFRP structures subjected to complex fatigue loading.

32 Thank you for kind attention!