Stress and strain under external load

Before we examine the phenomenological models that relate microscopic features to brittle or ductile behavior, we will present the continuum elasticity picture 

This is an intriguing result, indicating that very near the crack tip, r 0, the stress diverges as 1/Vr. The general solution for the stress near the crack has the form 

For the geometry of Fig. 10.13, which is referred to as plane strain , since by symmetry the strain is confined to the xy plane (m = 0), the above expression put 

Comparing this result to that for the penny crack loaded in mode /, we find that in the latter case the stress intensity factor is given by A / = (TooVira. The expression for the displacement field, evaluated on either side of the opening behind the crack ((x 0, y = 0) or 0 = 7t, see Fig. 10.13), gives 

The generalization of these results to mode II and mode III loading gives 

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