Griffiths Crack Theory of Fracture Strength

Consider, therefore, an infinitely large plate of elastic material of thickness B, containing a through-thickness crack of length 2a, and subjected to uniform biaxial tension (a) at infinity as shown in Fig. 2.5. Let U = potential energy of the system, Uo = potential energy of the system before introducing the crack, Ua = decrease 

Based on Inglis [5], the decrease in potential energy, for generalized plane stress, is given by  

Since Uo is the potential energy of the system without a crack, it is therefore independent of the crack length a. 

Equilibrium of the crack may be examined in terms of the variation in system potential energy with respect to crack length, a (with a minimum in potential energy constituting stable equilibrium, and a maximum, unstable equifibrium). 

For maxima or minima, SU = 0. For a nonzero variation in a (or Sa), then the expression inside the bracket must vanish i.e., 

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