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 ∈ [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 microvoids 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 Θ ∈ [−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 ductilebrittle transition temperature around −50◦C, at lower temperatures fracture is brittle dominated by d whereas at higher temperatures it is ductile dominated by f.
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