Thermodynamic Criterion for Quasi-Static Tearing of Elastic and Elastic–Plastic Fracture Specimens, and Its Validation from the Empirical Structure of Load–Displacement Diagrams

A global thermodynamic criterion is formulated for quasi-static crack extension in elastic and elastic-plastic fracture specimens. It accounts for crack extension accompanied by both large-scale plastic deformation and elastic unloading, which are excluded in LEFM and J-integral theories. Underlying assumptions are the first and second laws of thermodynamics, and an internal energy function where the independent variables are load-point displacement, entropy and crack extension, with the latter assuming the role of internal state variable. The criterion takes the form I = D, where I is an elastic-plastic crack driving force and D is the energy dissipation rate, identified thermodynamically as the sum of heat dissipated per unit of crack extension plus the rate of change of a residual Helmholtz energy parameter admitting non-dissipative irreversible energy forms such as residual elastic energy and Griffith surface energy. The thermodynamic criterion is validated by comparison with energy relations implicit in the structure of experimental load–displacement diagrams. For elastic–plastic specimens exhibiting linear elastic unloading behavior, a simple relation arises between thermodynamic driving and resistance forces and an excess elastic stress field ahead of growing cracks. Instability criteria are formulated for fixed grips and fixed load conditions. The original Griffith and Irwin fracture criteria are derived from the thermodynamic criterion.