Applications of two parameter approaches in elastic-plastic fracture mechanics

Two parameter approaches to elastic-plastic fracture mechanics were introduced to remove some of the conservatism inherent in the one parameter approach based on the J integral [J. R. Rice, J. appl. Mech. 35, 379 (1968)] and to account for observed "size effects" on fracture toughness. It was shown in refs [C. F. Shih, N. P. O'Dowd and M. T. Kirk, Constraint Effects in Fracture, ASTM STP 1171, 2 (1993)], [J. W. Hancock, W. G. Reuter and D. M. Parks, Constraint Effects in Fracture, ASTM STP 1171, 21 (1993)] and [J. D. G. Sumpter and A. T. Forbes, Proc. TWIIEWIIIS Int. Conf. Shallow Crack Fracture Mechanics and Applications, Cambridge, U.K. (1992)], that much of the dependence of fracture toughness on specimen geometry could be explained by two parameter fracture theories based on T or Q. This paper briefly reviews the two parameter J-Q theory and examines some of the pertinent issues with regard to the application of the theory. In particular, the use of existing Q solutions for characterising constraint in real materials is investigated. Interpolation schemes for Q based on the T stress and pure power law solutions are also discussed. Two parameter toughness curves for failure by cleavage and ductile tearing are presented.