A stress function based viscoelastic model for relaxation of free edge stresses in composite laminates

Abstract

In this study, the relaxation of free edge stresses in viscoelastic composite laminates is investigated by means of a stress function based viscoelastic model. A linear viscoelastic model using Prony series is adopted for time-dependent material behavior. The stress functions are taken from the Lekhnitskii stress functions and expressed in terms of in-plane stress functions and out-of-plane stress functions, where the out-of-plane stress functions are assumed as a combination of harmonic and hyperbolic functions for developing a Ritz-type solution procedure. By enforcing the complementary virtual work, the fourth order and second order coupled differential equations are obtained and further solved by a standard eigenvalue problem. The benefit of stress function based approach is not merely computationally efficient and accurate. The stress boundary conditions can also be strictly satisfied at the free edges since they are prescribed in the assumed functions. Finally, some of the results will be given for discussion considering different layup stacking sequences. It can be found that by using the present method and Prony series, the relaxation effect on the free edge stresses can be clearly observed and well simulated for the viscoelastic laminates under uniaxial tensile load.