Abstract
A family of self-similar fields provides the two parameters required to characterize the full range of high- and low-triaxiality crack tip fracture states. The two parameters J and Q have distinct roles: J sets the size scale over which large stresses and strains develop, while Q scales the near-tip stress distribution relative to a high triaxiality reference stress state. Careful investigations show that Q accurately describes the evolution of near-tip stress triaxiality over a wide range of loading and crack geometries. The J - Q theory provides a framework which allows the toughness locus to be measured and utilized in engineering applications. Methods for evaluating Q in fully yielded crack geometries and a scheme to interpolate for Q over the entire range of yielding are presented. An indicator of the robustness of the J - Q fields is introduced; Q as a field parameter and as a pointwise measure of stress level are discussed.
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