A generalized Gompertz model of reliability-dependent hazard rate for composites under cyclic stresses

Abstract

This study aims to investigate the relation of hazard rate in terms of the corresponding reliability for composite laminates under constant-amplitude cyclic stresses when the static strength is described by the Weibull distribution and the S-N curve is given. On the basis of the strength-life equal rank assumption, Yang’s residual strength degradation model is considered to derive the reliability by retrieving the residual strengths to the initials. Thus, a reliability-dependent hazard rate function is proposed as h(R)=e_g+μ(-ln R)^ξ, where e_g denotes the intrinsic weakness of composites during fabrication, μ the hazard scaling parameter, and ξ the curve trend parameter. Parameter e_g can be assumed as a very small positive value. Both ξ and μ are connected to the shape parameter of the Weibull static strength distribution and the parameter of fatigue life distribution, and μ is correlated to a power function of the applied maximum cyclic stress. The proposed model can be reduced to either the Gompertz model as ξ=1 or the Weibull model when e_g=0 and ξ<1. It has been verified that the proposed model agrees well with the fatigue data of composites under cyclic stresses as well as with various failure data of mechanical components.