SYMPOSIA PAPER Published: 01 January 1994

Two-Parameter Fracture Mechanics: Theory and Applications


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.

Author Information

O'Dowd, NP
Imperial College of Science, Technology & Medicine, London, United Kingdom
Shih, CF
Brown University, Providence, RI
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Developed by Committee: E08
Pages: 21–47
DOI: 10.1520/STP13698S
ISBN-EB: 978-0-8031-5270-0
ISBN-13: 978-0-8031-1990-1