Fracture Mechanics for Linear Elastic Solids

In order to discuss failure phenomena which depend upon the growth of flaws, some criterion for crack propagation is required. One such criterion is given in Eq. (54), 

At the point when the crack propagates, F = F and D = Dc thus the final equation becomes Eq. (57). 

Further discussion concerning linear elastic fracture mechanics can be found in an article by Williams and in the recent book by Kinloch and Young. Equation (57) can be made somewhat easier to handle by introducing the compliance, C, defined in Eq. (58). 

The compliance gives an indication of how much a specimen deflects with an applied force. For linear elastic materials, the compliance is the reciprocal of the slope of the load-displacement curve. Rearranging Eq. (58) to give Eq. (59) and taking partial differentials gives Eq. (60). 

Substitution of this into Eq. (62) gives Eq. (66), which relates the critical strain energy release rate to the applied force at the instant of crack propagation. 

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