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J-Integral
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Definition: A mathematical expression for the characterization of a line of the local stress-strain field around a crack front. The J-integral expression for a two-dimensional crack in the x-z plane with the crack front parallel to the z axis is the line integral:

where

W = loading work per unit volume or for elastic bodies, strain energy density
γ = path of the integral which encloses or contains the crack tip
ds = increment of the contour path
T = outward traction vector on ds
p = displacement vector at ds.
Definition Copyright ©1989 CRC Press LLC. All rights reserved.

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