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Linear Elastic Fracture Mechanics (LEFM) applies when the nonlinear deformation of the material is confined to a small region near the crack tip. For brittle materials, it accurately establishes the criteria for catastrophic failure. However, severe limitations arise when large regions of the material are subject to plastic deformation before a crack propagates. Elastic Plastic Fracture Mechanics (EPFM) is proposed to analyze the relatively large plastic zones.

Elastic Plastic Fracture Mechanics (EPFM) assumes isotropic and elastic-plastic materials. Based on the assumption, the strain energy fields or opening displacement near the crack tips are calculated. When the energy or opening exceeds the critical value, the crack will grow.

Please note that although the term elastic-plastic is used in this approach, the material is merely nonlinear-elastic. In others words, the unloading curve of the so called elastic-plastic material in EPFM follows the original loading curve, instead of a parallel line to the linear loading part which is normally the case for true elastic-plastic materials.

Fracture Analysis Using EPFM

There are two major branches in EPFM: Crack Tip Opening Displacement (CTOD) suggested by Wells, popular in Europe, and the J Integral proposed by Rice, widely used in the United States. However, Shih provided evidence that a unique relationship between J and CTOD exists for a given material. Thus, these two parameters are both valid in characterizing crack tip toughness for elastic-plastic materials.

The basic EPFM analysis can be summarized as follows:


Calculate the J integral or crack tip opening displacement (CTOD) delta as a function of the loading and the geometry.

  2.  The critical J integral Jc or the critical CTOD can be determined empirically.
  3.  The J integral J should NOT exceed Jc, or, the CTOD delta should not exceed the critial CTOD delta.