16.2 Statistical Prediction of Creep Failure Time of Unidirectional CFRP 16.2.1 Formulation for Statistical Static Strength of CFRP Laminates Based on Viscoelasticity of Matrix Resin We have proposed the formulation for the statistical static strengthσs of CFRP based on the viscoelasticity of matrix resin as shown in the following equation in our previous paper [8], logσs Pf; t; T ð Þ¼logσ0 t0; T0 ð Þþ 1 αs log ln 1 Pf ð Þ ½ nR log D t; T ð Þ Dc t0; T0 ð Þ ð 16:1Þ where, Pf is the failure probability, t is the failure time, t0 is the reference time, T is the temperature, T0 is the reference temperature, σ0 and σs are the scale parameter and the shape parameter on Weibull distribution of static strength, nR is the viscoelastic parameter, and Dc and D* are the creep and viscoelastic compliances of matrix resin. The viscoelastic compliance D* for the static load with a constant strain rate is shown by the following equation. D t; T ð Þ¼Dc t=2, T ð Þ ð16:2Þ The failure probability of unidirectional CFRP under static load with a constant strain rate can be shown by the following equation. Pf ¼1 exp F ð Þ, logF¼αs log σs σ0 þ αsnR log Dc t=2, T0 ð Þ Dc t0; T0 ð Þ ð 16:3Þ 16.2.2 Failure Probability of Unidirectional CFRP Under Static Load It was cleared in our previous paper that the viscoelastic parameter nR in Eqs. (16.1) and (16.3) is shown by the following equation for the unidirectional CFRP based on Rosen’s model [11]. nR ¼ 1 2αC ð 16:4Þ where, αc is Weibull shape parameter for the tensile strength of carbon fiber mono-filament. 16.2.3 Statistical Creep Failure Time of Unidirectional CFRP The relationship between the creep failure time and the static failure time can be shown by Fig. 16.1 [14]. This figure shows the creep strength and the static strength versus failure time. The creep strength curve can be obtained by shifting horizontally the static strength curve. The shifting amount log A determined by the slope of the static strength curve is shown by the following equation. logA¼log 1þ1=kR ð Þ ð16:5Þ Figure 16.2a shows the slope mRof the creep compliance of matrix resin against time. Figure 16.2b shows the slope kRof the static strength of CFRP against failure time. The slope kR can be obtained from the following equation. 132 Y. Miyano et al.
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