Hereditary creep of isotropic composites of random structure under a complex stress state

Abstract

Nonlinear hereditary creep problem of the mechanics of composites is solved within the framework of a second-order theory. The hereditary functionals are used to construct general constitutive relations. A stochastic boundary value problem for determining the stress concentration and its relaxation in metal matrix composite (PMC) is solved in Laplace-Carson image space. Shapery's correspondence principle for quasi-linear viscoelastic media is generalised on the hereditary creep problem and the method of successive approximation is used. The reduced creep functions and the stress concentration parameters are determined. Examples are given showing the importance of the mutual influence of nonlinear elastic and viscous properties of the components on stress redistribution near inclusions with possibility to predicting the long-term strength.