A Rate Dependent Anisotropic Damage Model for Metal Matrix Composites at Elevated Temperatures.

A rate dependent plastic and anisotropic damage model is developed for a metal matrix composite (MMC) system at elevated temperatures. The developed constitutive model will enable one to predict the inelastic response of the composite material at different loading rates at elevated temperatures. The formulation is thermodynamically based using the concept of internal state variables. Two sets of internal variables are introduced into the thermodynamic potential. One set characterizes the viscoplastic behavior of the ductile matrix and its effect on the overall inelastic response of the composite while the second set characterizes the damage for each constituent of the composite. The rate dependency of the initial yield stress and initial damage threshold are also discussed here and an analytical expression is presented to account for this effect on the inelastic and the damage response of the composite at elevated temperatures. The damage is introduced into the thermodynamic potential as a second order damage tensor from which the fourth order damage operator tensor is obtained using the concept of the effective stress and a suitable symmetrization method. Physical interpretation of the damage is presented using the kinematic description of the reduction in area due to the presence of micro-cracks and micro voids in the material. Computational aspects of both the rate independent and rate dependent models are established. The Newton Raphson itterative scheme is used for the overall laminate system. The main framework return mapping algorithm by Ortiz and Simo (1986) is used here for the correction of the elasto-plastic and viscoplastic states. However, for the case of the damage model these algorithms are redefined according to the governed damage constitutive relations. In order to test the validity of the model, a series of laminated systems (0)8s, (90)8s, (0/90)4s, (45/-45) 2s are investigated at both room and elevated temperatures of 538°C and 649°C. The results obtained from the special purpose developed computer program, DVP-CALSET (Damage and Viscoplastic Coupled Analysis of Laminate Systems at Elevated Temperatures), are then compared with the available experimental results and other existing theoretical material models

A thermomechanically consistent constitutive theory for modeling micro-void and/or micro-crack driven failure in metals at finite strains

Within a continuum approximation, we present a thermomechanical finite strain plasticity model which incorporates the blended effects of micro-heterogeneities in the form of micro-cracks and micro-voids. The former accounts for cleavage-type of damage without any volume change whereas the latter is a consequence of plastic void growth. Limiting ourselves to isotropy, for cleavage damage a scalar damage variable d ϵ [0, 1] is incorporated. Its conjugate variable, the elastic energy release rate, and evolution law follow the formal steps of thermodynamics of internal variables requiring postulation of an appropriate damage dissipation potential. The growth of void volume fraction f is incorporated using a Gurson-type porous plastic potential postulated at the effective stress space following continuum damage mechanics principles. Since the growth of micro-voids is driven by dislocation motion around voids the dissipative effects corresponding to the void growth are encapsulated in the plastic flow. Thus, the void volume fraction is used as a dependent variable using the conservation of mass. The predictive capability of the model is tested through uniaxial tensile tests at various temperatures ϵ [-125°C, 125°C]. It is shown, via fracture energy plots, that temperature driven ductile-brittle transition in fracture mode is well captured. With an observed ductile-brittle transition temperature around - 50°C, at lower temperatures fracture is brittle dominated by d whereas at higher temperatures it is ductile dominated by f