Relationship To Energy Release Rate and J-integral
The strain energy release rate for a crack under mode I loading is related to the stress intensity factor by
where is the Young's modulus and is the Poisson's ratio of the material. The material is assumed to be an isotropic, homogeneous, and linear elastic. Plane strain has been assumed and the crack has been assumed to extend along the direction of the initial crack. For plane stress conditions, the above relation simplifies to
For pure mode II loading, we have similar relations
For pure mode III loading,
where is the shear modulus. For general loading in plane strain, the relationship between the strain energy and the stress intensity factors for the three modes is
A similar relation is obtained for plane stress by adding the contributions for the three modes.
The above relations can also be used to connect the J integral to the stress intensity factor because
Read more about this topic: Stress Intensity Factor
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