Nonlinear Hereditary Creep of Isotropic Composites of Random Structure

The problem of nonlinear hereditary creep of composites of random structure is solved within the framework of a second-order nonlinear theory. Hereditary functionals are used to develop general constitutive equations of complex stress state. The Schapery correspondence principle is generalized to quasilinear viscoelastic media concerning hereditary creep problems. The solution of the stochastic boundary value problem for determining the stress concentration and relaxation in a metal-matrix composite (MMC) is obtained. The method of successive approximations is used to obtain a complete system of second-order viscoelastic equations. Locally averaged relaxation functions are determined in the case of viscoelastic matrix and elastic inclusions. Stress concentration parameters are also determined. Examples that show the importance of the mutual effect of nonlinear elastic and viscous properties of components on the redistribution of stresses near inclusions in multicomponent MMCs are given. The possibility of predicting the long-term strength of the material when the field of viscoelastic stresses is known as a result of computer modeling in the vicinity of inclusions is noted.