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122 Fracture Mechanics: Fundamentals and Applications
where d is a dimensionless constant, given by
n
ασ 1/ n
2 u y π n ˜ (,) o u x π n {˜ (, ) + u y π n ˜ (, )}
d = E I n (3.49)
n
Figure 3.18 shows plots of d for a = 1.0, which exhibits a strong dependence on the strain-
n
hardening exponent and a mild dependence on as /E. A comparison of Equation (3.41) and
o
FIGURE 3.18 Predicted J-CTOD relationships for plane stress and plane strain, assuming a = 1. For a ≠ 1,
1/n
the above values should be multiplied by α . Taken from Shih, C.F. ‘‘Relationship between the J-Integral
and the Crack Opening Displacement for Stationary and Extending Cracks.’’ Journal of the Mec hanics and
Physics of Solids, Vol. 29, 1981, pp. 305–326.
