Energy-based universal failure criterion and strength-Poisson's ratio relationship for isotropic materials

Abstract

The prediction of material failures has been one of the most important topics in engineering design since the onset of human civilization. To date, a plethora of failure criteria have been developed, particularly for homogeneous isotropic materials. However, many of them have limited usage for specific groups of materials, are obscure in their origin, or different from the actual phenomena at the microscopic and macroscopic scales. Therefore, based on the most fundamental concept of energy, this study aims to establish a universal failure criterion for homogeneous full-density isotropic materials. The developed failure criterion requires three independent load-bearing capabilities of the material, that is, tensile (T), compressive (C), and shear (S) strengths, as criterion calibrators for applicability to a wide range of materials, including those with extremely ductile to exceedingly brittle behaviors. Energy and polynomial invariants expansion approaches were used to formulate the universal failure criterion, and both yielded a perfect dual relationship. The criterion in the energy form revealed a new physical insight into the zero-energy bound or fracture criterion, which corresponds to an intrinsic cut-off plane in a failure envelope. Comparisons between the experimental data across a broad spectrum of material types and the proposed failure criterion were in excellent agreement in both the stress and energy spaces. The strength-Poisson's ratio relationship was also derived for the first time, demonstrating that only two strength properties are independent and that three important bounding conditions for isotropic materials exist: (1) S/C = 0 when T/C = 0; (2) when T/C = 1 and S/C = 1/3, Poisson's ratio v = 0.5; and (3) v = −1 when T/S and C/S approach zero.