Two-Parameter Fracture Mechanics: Theory and Applications

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Abstract
A family of self-similar fields provides the two parameters required to characterize the full range of high- and low-triaxiality crack tip states. The two parameters, J and Q, have distinct roles: / sets the size scale of the process zone over which large stresses and strains develop, whereas Q scales the near-tip stress distribution relative to a high-triaxiality reference stress state. An immediate consequence of the theory is this: it is the toughness values over a range of crack-tip constraint that fully characterize the material's fracture resistance. It is shown that Q provides a common scale for interpreting cleavage fracture and ductile tearing data, thus allowing both failure modes to be incorporated in a single toughness locus. The evolution of Q, as plasticity progresses from small-scale yielding to fully yielded conditions, has been quantified for several crack geometries and for a wide range of material strain hardening properties. 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 is discussed.