Constitutive and damage evolution equations for elastic-plastic-damaging materials based on thermodynamics theory
Hayakawa Kunio; Murakami Sumio
Abstract:An irreversible thermodynamics theory is developed for the constitutive and damage evolution equations for elastic-plastic-damaging materials with special emphasis on the anisotropic aspect of material damage. The internal state of the material is described first by an isotropic hardening variable t , a second rank symmetric damage tensor D and a scalar damage variable b related to the further development of the damage. The effect of crack closure under compression is described by introducing a modified elastic strain tensor ee. The Helmholtz free energy y is decomposed into the terms related to global elastic deformation of the damaged material, local elastic distortion due to plastic deformation, and the surface energy generated by material damage. A dissipation potential function F in the space of the conjugate forces of the internal state variables is expressed as the sum of the plastic and the damage parts. The constitutive and evolution equations resulting from these potentials are applied to elucidate the damage process of tubular specimens of spheroidized graphite cast iron under uniaxial tension and torsion. Key Words:elastic-plastic-damage, constitutive equation, irreversible thermodynamics, internal state variables, Helmholtz free energy, dissipation potential