On some general properties of strength criteria

Abstract

In this paper the concept of strength criteria is analyzed from a fracture mechanics point of view. A potential function is introduced to examine strength criteria using the results of catastrophe (singularity) theory. Although the diversity of failure behavior is enormous, there exist a few generic elements, so that only some standard modes occur in most cases. Four example problems in fracture mechanics with two and three independent loading parameters are studied in detail. These examples are shown to be representative and the set of failure states in the space of loading parameters generally appears to form a certain sub-space (manifold) which has the same dimension and is called failure domain, so that depending on the loading path, a failure can either occur or not occur at the given point of the failure domain. The brittle strength criteria are shown to depend on the loading history in the general case. The classical concept of a failure criterion and the postulate of convexity of the limiting fracture surface in the space of loading parameters are discussed. It is shown that importation of the convexity postulate from the plasticity theory to the theory of strength is not necessarily legitimate. Finally, two failure criteria are suggested; one characterizing a lower bound for some possibilities of a total failure, and the other guaranteeing the total failure. In the intermediate domain between both criteria, total failure can either occur or not, depending on the loading path.