Shakedown Limits for a Metal Matrix Composite

The paper discusses a method for the evaluation of the yield values of a metal matrix composite material when subjected to a variation in temperature. A direct shakedown analysis method is described which produces a shakedown stress value as a result of a sequence of incompressible linear solutions with a spatially varying modulus. The process converges to the minimum upper bound associated with the class of displacement fields when implemented in a finite element method (Ponter and Carter [1,2]). The solutions for an Aluminum/alumina system loaded in a direction perpendicular to the direction of the fibers demonstrate the high sensitivity of this material to fluctuations in temperature. Simple approximate equations for strength values are presented in terms of nondimensional variables.