The orthotropic, thermal viscoplasticity theory based on overstress (TVBO) is specialized for plane stress in a simple laminate theory. It maintains the same geometric assumptions as the classical laminate theory except that the orthotropic linear elasticity law is replaced by TVBO. In this way, rate sensitivity, creep, and relaxation can be modeled without the use of a yield surface and loading/unloading conditions. The laminate theory is intended for thermal analysis of metal matrix composites operating at high temperature under simultaneous mechanical and thermal loadings.
The rate-dependent laminate behavior is described by a set of coupled, first order, nonlinear differential equations that must be numerically integrated for a given mechanical and thermal history to yield the laminate and ply stresses as well as the laminate total strain as a function of time. To describe the behavior, the elastic constants and the coefficients of thermal expansion need to be known in addition to two material functions and six constants that describe the inelastic deformation behavior. Two metal matrix composites, MMC1 and MMC2, are constructed theoretically. For MMC1, the strength in the fiber and the transverse directions decrease with temperature. The strength in the transverse direction of MMC2, patterned after Ni3Al/Al2O3, increases with temperature before it decreases and the strength in the fiber direction is nearly constant. First, the ply behavior is simulated by off-axis m-phase and out-of-phase thermomechanical numerical tests. Then the behavior of a [±45]s laminate under a temperature excursion is computed both when it is free to expand and when the laminate is clamped in one direction. After the temperature returns to the datum point, residual stresses are shown to redistribute in time. They are induced by prior inelastic deformation.