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Fracture Mechanics |
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Introduction |
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Ranges of Applicability |
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Linear Elastic Fracture Mechanics |
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Fracture Modes |
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Stress Intensity Fac. |
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Elastic Plastic Fracture Mechanics |
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The J Integral |
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Introduction to J Integral |
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Determination of J |
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CTOD |
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Resources |
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Bibliography |
| Definition of J Integral |
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Consider a nonlinear elastic body containing a crack,  the J integral is defined as  where Rice, J. R., 1968, showed that the J integral is a path-independent line integral and it represents the strain energy release rate of nonlinear elastic materials:  where The dimension of J is  |
J vs.  and K |
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For linear elastic materials, the J integral J is in fact the strain energy release rate,  |
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is the strain energy density, 
is the traction vector, 
is an arbitrary contour around the tip of the crack, n is the unit vector normal to 
, 
, and u are the stress, strain, and displacement field, respectively.
is the potential energy, the strain energy U stored in the body minus the work W done by external forces and A is the crack area.