A LOADING HISTORY AGNOSTIC FREE ENERGY BASED FRACTURE CRITERION

Rather than energy release rate, the proposed framework starts from the energy function itself. Instead of strain energy density, it considers the change in volume-specific free energy density from mechanical deformation. The free energy function must capture strain induced orthotropy, known to be critical for polymers but also important for metals plasticity. To capture strain induced orthotropy, free energy is defined in terms of principal strains and by separating deformation into dilatational and distortional contributions. The separation does not utilize deviatoric strain. Rather, it leverages a new distortional strain definition and the new concept of orthotropic dilataion, enabling clean separation to large strain.

The proposed framework clarifies how a generalized Maxwell model spring-dashpot mechanical analog cleanly interperets the First and Second Laws of Thermodynamics. A transition state theory based nonlinear viscoelastic (NLVE) model is mated to the Maxwell model. Nonlinear Maxwell springs feature an instability in their constitutive law, providing a viscoelastic failure criterion. Embedding the instability into the springs in an NLVE model provides a failure criterion that accommodates complex temperature histories, rate dependence, and self generated heat from cyclic loading.
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