J integral

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The J-integral represents a way to calculate work (energy) per unit fracture surface area in a material.[1] J1c 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 (K1c) for materials in which sample sizes are too small (on the order of < 1 meter) for direct determination of K1c. Physically the J-integral is related to the area under curve of a load versus load point displacement.[2].

[edit] J-Integral and Fracture Toughness

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

J=\oint_{C} \frac {F}{A}\frac{du}{dl_0}=\int_{}^{}\sigma d\varepsilon\,

where

  • F is the force applied at the crack tip
  • A is the area of the crack tip
  • \frac{du}{dl_0} is the change in energy per unit length
  • σ is the stress
  • d\varepsilon is the change in the strain caused by the stress


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

J_{1c} = K_{1c}^2(\frac{1-v^2}{E})^2

where

  • K1c is the fracture toughness in mode one loading
  • v is the Poisson's ratio
  • E is the Young's Modulus of the material


[edit] See also


[edit] External links

  • Van Vliet, Krystyn J. (2006); "3.032 Mechanical Behavior of Materials", [1]
  • Meyers and Chawla (1999): "Mechanical Behavior of Materials," 445-448.



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