AN ANALYTICAL MODEL FOR THE INELASTIC AXIAL SHEAR RESPONSE OF UNIDIRECTIONAL METAL-MATRIX COMPOSITES

An analytical solution is presented for the inelastic response of an a rbitrarily layered concentric cylinder assemblage under axial shear lo ading of the type that produces homogeneous deformation in an equivale nt homogenized medium. This solution forms the basis for the model for the axial shear response of unidirectional metal matrix composites ba sed on the multiple concentric cylinder geometry. First, analytical so lutions are developed using a Fourier series representation of the dis placement field in each layer of the cylindrical assemblage. These sol utions are subsequently reformulated in terms of the interfacial displ acement harmonics as the fundamantal unknowns by constructing a local stiffness matrix for each layer. Assembly of the local stiffness matri ces into a global stiffness matrix in a particular manner ensures sati sfaction of interfacial traction and displacement continuity condition s as well as the external boundary conditions. The resulting system of equations, in which integrals of the inelastic strain distributions ( which depend implicitly on the interfacial displacements) appear as fo rce-like terms, is then solved using Mendelson's iterative method of s uccessive solutions developed for elastoplastic boundary value problem s. Results are presented that illustrate the convergence characteristi cs of the solution, comparison with the predictions of Aboudi's well-e stablished generalized method of cells, and the effects of fiber aniso tropy on the inelastic axial shear response of unidirectional graphite /aluminum composites. (C) 1997 Elsevier Science Ltd.