Interrelation of crack opening displacement and J-integral

The relationship between $\text{J-}\text{integral}$ and crack opening displacement δ is based on theoretical as well as experimental investigations and is of the general form $\text{J = Mσ}{}_{\mathrm{r\delta }}$. The significance of M and its possible dependence on specimen geometry and material properties is unknown. An attempt is made in the present paper to identify the different variables and to account for them in $\text{H-δ}$ relationship. It is observed that if the material properties remain constant, $\text{M}$ increases with $\text{a/W}$ ratio upto 0.5 and then probably decreases for higher $\text{a/W}$ ratios. If the specimen geometry and size is maintained constant then it is observed that $\text{M}$ increases with decreasing yield strength and a corresponding increase in work hardening exponent.