The distribution of the Ĵ-integral, an extension of the J-integral, is calculated along the crack front of compact specimens of varying thicknesses by a three-dimensional elastic-plastic finite-element method. The Ĵ-integral takes the maximum value at the midthickness and smaller values near the plate surfaces, and the Ĵ-value at the midthickness coincides with the J-value determined from the computed load versus load-line displacement curve by using the Merkle-Corten formula. These results explain why the plane-strain fracture toughness value J_Ic can be experimentally determined by using specimens of moderate thickness.

To avoid the expense of three-dimensional computations, an empirical formula based on a two-dimensional finite-element method is proposed to determine the J-value which coincides with the Ĵ-value at midthickness in a cracked structure. Experimental results on compact specimens of 304 and 4340 steels and also on rotating disks of 4340 steel indicate that the onset of crack growth in a structure with finite thickness can be estimated by using the empirical formula and the J_Ic-value of the compact specimen.