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Definition of J Integral

Consider a nonlinear elastic body containing a crack,

the J integral is defined as

J Integral

where is the strain energy density, is the traction vector, Gamma is an arbitrary contour around the tip of the crack, n is the unit vector normal to Gamma; Stress, Strain, and u are the stress, strain, and displacement field, respectively.

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:

J

where Pi=U-W 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.

The dimension of J is

J vs. G and K

For linear elastic materials, the J integral J is in fact the strain energy release rate, G, and both are related to the stress intensity factor K in the following fashion:

Glossary
STEM Career Outlook

Wages, employment opportunities, and growth projections for STEM jobs.

Mechanical Engineers Outlook

Guide for those interested in becoming a mechanical engineer. Includes qualifications, pay, and job duties.

Selecting the Right 3D Printer

Discover how to choose the right 3D printer for your needs and the key performance attributes to consider.

Essentials of Manufacturing

Information, coverage of important developments and expert commentary in manufacturing.