J integral

The J-integral represents a way to calculate work (energy) per unit fracture surface area in a material.^[1] J_1c defines the point at which large-scale plastic yielding during propagation takes place under mode one loading.^[1] This value is difficult to determine experimentally, however in 1968 Jim Rice developed the J-integral test that allows one to calculate fracture toughness (K_1c) for materials in which sample sizes are too small (on the order of < 1 meter) for direct determination of K_1c. Physically the J-integral is related to the area under curve of a load versus load point displacement.^[2].

Additional recommended knowledge

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Essential Laboratory Skills Guide

J-Integral and Fracture Toughness

The J-integral can be described as follows^[1]

where

• F is the force applied at the crack tip
• A is the area of the crack tip
• is the change in energy per unit length
• σ is the stress
• is the change in the strain caused by the stress

Fracture toughness is then calculated from the following equation^[1]

where

• K_1c is the fracture toughness in mode one loading
• v is the Poisson's ratio
• E is the Young's Modulus of the material

See also

• Fracture toughness
• Toughness

References