An orthotropic theory of viscoplasticity based on overstress for thermomechanical deformation and its application to laminated metal matrix composites

An infinitesimal, orthotropic theory of viscoplasticity based on overstress for both isothermal and thermal loading cases is presented. The theory is based on existing isotropic formulations of the viscoplasticity theory based on overstress. All material constants and functions can be functions of temperature. No influence of temperature history on the asymptotic solutions is modeled. A yield surface and a loading/unloading condition is not used in the theory. Since invariance requirements constrain the orthotropic growth laws for the state variables, a comparatively simple theory is obtained. The theory models creep, relaxation, rate sensitivity, hysteresis, work, hardening, and tension/compression symmetry and can be reduced to the transversely isotropic, cubic symmetric, and isotropic cases. The theory can be specialized for the cases of inelastic incompressibility, invariance of inelastic properties under superimposed pressure, and tension/compression symmetry. The uniaxial behaviors of the thermal theory are investigated for three different materials. The elastic, inelastic, and cyclic behaviors as well as a temperature rate effect of each material are demonstrated and compared for various thermochemical loading conditions.; The orthotropic, thermal viscoplasticity theory based on overseas (OTVBO) is specialized for plane stress in a simple laminate theory. The geometric assumptions of the classical laminate theory are maintained but that the orthotropic linear elasticity law is replaced by OTVBO. 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 couples, first order, nonlinear differential equations which must be numerically integrated for a given mechanical and thermal history to yield the laminate and ply stresses or the laminate total strain as a function of time. Two metal matrix composites are constructed theoretically for numerical analysis. One of them shows the initial increase of strength with temperature. The increase in strength can be found in Nickel Aluminides and MMC2 is patterned after an Al{dollar}sb2{dollar}O{dollar}sb3{dollar}/Ni{dollar}sb3{dollar}Al composite.