A Stress-Based Non-Proportionality Parameter for Considering the Resistance of Slip Systems of Shear Failure Mode Materials

Multiaxial loading on mechanical products is very common in the automotive industry, and how to design and analyze these products for durability becomes an important, urgent task for the engineering community. Due to the complex nature of the fatigue damage mechanism for a product under multiaxial state of stresses/strains which are dependent upon the modes of loading, materials, and life, modeling this behavior has always been a challenging task for fatigue scientists and engineers around the world. As a result, many multiaxial fatigue theories have been developed. Among all the theories, an existing equivalent stress theory is considered for use for the automotive components that are typically designed to prevent Case B cracks in the high cycle fatigue regime. The focus of this paper is on the introduction of the equivalent stress model with an emphasis on characterizing a non-proportionality parameter to account for material dependent resistance of interactions between slip systems under nonproportional loading. This parameter is determined experimentally by comparing stress-life curves for two extreme loading cases, in-phase and 90° out-of-phase axial-torsional fatigue tests. However, multiaxial testing is very expensive and time consuming. As a result, an empirical formula was developed for the non-proportionality parameter, α_LTJ, based on readily available material properties.