ON SOME GENERAL-PROPERTIES OF STRENGTH CRITERIA

In this paper the concept of strength criteria is analyzed from a frac ture mechanics point of view. A potential function is introduced to ex amine 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 an d three independent loading parameters are studied in detail. These ex amples are shown to be representative and the set of failure states in the space of loading parameters generally appears to form a certain s ub-space (manifold) which has the same dimension and is called failure domain, so that depending on the loading path, a failure can either o ccur or not occur at the given point of the failure domain. The brittl e strength criteria are shown to depend on the loading history in the general case. The classical concept of a failure criterion and the pos tulate of convexity of the limiting fracture surface in the space of l oading parameters are discussed. It is shown that importation of the c onvexity postulate from the plasticity theory to the theory of strengt h is not necessarily legitimate. Finally, two failure criteria are sug gested; one characterizing a lower bound for some possibilities of a t otal failure, and the other guaranteeing the total failure. In the int ermediate domain between both criteria, total failure can either occur or not, depending on the loading path.