Elliptic hole in a biaxially stressed material

The path-integral along T is a line integral in the plane perpendicular to the curve C at each of its points. This integral is the negative of the vectorvalued two-dimensional J-integral of fracture mechanics (Eshelby (1951), Rice (1968a)) 

a configurational force per unit length along the crack edge that is work-conjugate to crack edge motion with respect to free energy is 

This quantity is perhaps not appropriately called a chemical potential, but it has the character of chemical potential as being developed here, where the corresponding material volume is the amount of crack surface area. The equilibrium condition X = 0 corresponds to the Griffith crack growth criterion introduced in Section 4.2.1. These ideas are applied in a discussion of cohesive contact in Section 8.6. 

With reference to the discussion in Section 8.2, the surface S in the present case is the cylindrical surface of the hole. The equation of this surface in the plane of deformation is 

Stress analysis of this configuration reveals that the in-plane tensile stress at a point on the boundary of the hole, acting in the direction tangent to the surface of the hole, is (Timoshenko and Goodier 1987) 

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Elliptic hole in a biaxially stressed material Then (8.27) becomes... 

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