The Maximum Stress Failure Criterion and the Maximum Strain Failure Criterion: Their Unification and Rationalization

Shuguang Li

doi:10.3390/jcs4040157

Abstract

The maximum strain failure criterion is unified with the maximum stress failure criterion, after exploring the implications of two considerations responsible for this: (1) the failure strains for the direct strain components employed in the maximum strain criterion are all defined under uniaxial stress states, not uniaxial strain states, and (2) the contributions to the strain in a direction as a result of the Poisson effect do not contribute to the failure of the material in that direction. Incorporating these considerations into the maximum strain criterion, the maximum stress criterion is reproduced. For 3D stress/strain state applications primarily, the unified maximum stress/strain criterion is then subjected to further rationalization in the context of transversely isotropic materials by eliminating the treatments that undermine the objectivity of the failure criterion. The criterion is then applied based on the maximum and minimum direct stresses, the maximum transverse shear stress and the maximum longitudinal shear stress as the invariants of the stress state, instead of the conventional stress components directly.

Highlights

The most well-known failure criteria for modern composites are the maximum stress criterion and the maximum strain criterion. They are, so well-known that nobody can be bothered to trace back to where they were introduced in the first instance, it is apparent that each stemmed from a conventional failure criterion for conventional isotropic materials established way before modern composites became available
They remain popular in applications due to their simplicity, especially amongst designers in situations where a rough but quick estimate is required. This status is likely to remain so for a long time to come. Their other benefits include that they offer a clear indication about the failure modes, and that they are applicable to genuinely orthotropic materials, rather than transversely isotropic materials alone
The key observation underlying the unification is the fact that the direct failure strains employed in the maximum strain criterion are defined under uniaxial stress states, the same stress states as those for strengths employed in the maximum stress criterion

Summary

Introduction

The most well-known failure criteria for modern composites are the maximum stress criterion and the maximum strain criterion. They are, so well-known that nobody can be bothered to trace back to where they were introduced in the first instance, it is apparent that each stemmed from a conventional failure criterion for conventional isotropic materials established way before modern composites became available They are being incorporated into modern engineering design tools, such as Abaqus [1] and Ansys [2], to name but a few. A much wider range and more extensive studies are available in the literature; some of them have been included in the World Wide Failure Exercises (WWFE-I~III) [6,7,8], of which references [4,5] were a part Another popular criterion is the Tsai-Wu criterion, which has been recently rationalized by the author and his co-workers in [9]. The outcomes are twofold: the unification of these two criteria, and a rational, and improved, presentation of them

The Conventional Maximum Stress Failure Criterion

The Conventional Maximum Strain Failure Criterion

Further Rationalization

An Example of Case Study

C11 C23 C33