Modelling the strengths of engineering materials in three dimensions

A general, three-dimensional failure criterion is presented. This criterion is formulated in terms of the first and third stress invariants of the stress tensor, and it involves only three independent material parameters. Although these parameters interact with one another, each parameter corresponds to one of three failure characteristics of material behaviour. These material parameters may be determined from any type of strength test, including the simplest possible, such as uniaxial compression and tension tests or biaxial tests for materials with cohesion and tensile strength, and by triaxial compression tests for materials without tensile strength. The procedure for determination of the three material parameters is demonstrated and comparisons between the failure criterion and experimental results are presented for different types of engineering materials.