J Integral - J-integral and Fracture Toughness | J-integral Fracture Toughness

J-integral and Fracture Toughness

For isotropic, perfectly brittle, linear elastic materials, the J-integral can be directly related to the fracture toughness if the crack extends straight ahead with respect to its original orientation.

For plane strain, under Mode I loading conditions, this relation is

$J_{\rm Ic} = G_{\rm Ic} = K_{\rm Ic}^2 \left(\frac{1-\nu^2}{E}\right)$

where is the critical strain energy release rate, is the fracture toughness in Mode I loading, is the Poisson's ratio, and E is the Young's modulus of the material.

For Mode II loading, the relation between the J-integral and the mode II fracture toughness is

$J_{\rm IIc} = G_{\rm IIc} = K_{\rm IIc}^2 \left$

For Mode III loading, the relation is

$J_{\rm IIIc} = G_{\rm IIIc} = K_{\rm IIIc}^2 \left(\frac{1+\nu}{E}\right)$

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