Constitutive modelling of damage and plasticity in metal matrix composites

Vita.A general m ethod for deriving constitutive equations for damage and plasticity in m etal and ceramic m atrix composites has been presented. The discussion is intended to introduce constitutive m odeling to beginning graduate students. The m ethod consists of identifying the independent variables, known as state variables, th a t determ ine the free energy. An explicit expression for the free energy is then w ritten, and the rate of change of the state variables is given as a function of the therm odynam ic forces and the state variables. The state variables include the reversible strain, the tem perature, and a set of internal variables that account for the free energy of crystalline defects. The plastic eigenstresses were modelled by isotropic and kinem atic hardening internal variables in the free energy. The therm al eigenstresses were not modelled as internal variables, but as contributions to the entropy. The fictitious eigenstresses due to microcracks were modelled by an internal variable th a t results in a negative contribution to both the elastic modulus and the plastic hardening modulus and a positive contribution to the surface free energy. It was shown th at in composite m aterials, the dam age variable and the plastic hardening variables are not independent. A m icropolar model was presented to predict the evolution of damage and plasticity in large-fiber, inhomogeneous composites. The choice of phenomenological constitutive equations was supported by a m icrotherm odynamics derivation of the constitutive equations