Elastoplastic Analysis of Layered Metal Matrix Composite Cylinders—Part I: Theory

An exact elastic-plastic analytical solution for an arbitrarily laminated metal matrix composite tube subjected to axisymmetric thermo-mechanical and torsional loading is presented. First, exact solutions for transversely isotropic and monoclinic (off-axis) elastoplastic cylindrical shells are developed which are then reformulated in terms of the interfacial displacements as the fundamental unknowns by constructing a local stiffness matrix for the shell. Assembly of the local stiffness matrices into a global stiffness matrix in a particular manner ensures satisfaction of interfacial traction and displacement continuity conditions, as well as the external boundary conditions. Due to the lack of a general macroscopic constitutive theory for the elastic-plastic response of unidirectional metal matrix composites, the micromechanics method of cells model is employed to calculate the effective elastic-plastic properties of the individual layers used in determining the elements of the local and thus global stiffness matrices. The resulting system of equations is then solved using Mendelson’s iterative method of successive elastic solutions developed for elastoplastic boundary-value problems. Part I of the paper outlines the aforementioned solution strategy. In Part II (Salzar et al., 1996) this solution strategy is first validated by comparison with available closed-form solutions as well as with results obtained using the finite-element approach. Subsequently, examples are presented that illustrate the utility of the developed solution methodology in predicting the elastic-plastic response of arbitrarily laminated metal matrix composite tubes. In particular, optimization of the response of composite tubes under internal pressure is considered through the use of functionally graded architectures.