eFunda: Linear Elastic Fracture Mechanics (LEFM)
engineering fundamentals Linear Elastic Fracture Mechanics
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Introduction

Linear Elastic Fracture Mechanics (LEFM) first assumes that the material is isotropic and linear elastic. Based on the assumption, the stress field near the crack tip is calculated using the theory of elasticity. When the stresses near the crack tip exceed the material fracture toughness, the crack will grow.

In Linear Elastic Fracture Mechanics, most formulas are derived for either plane stresses or plane straines, associated with the three basic modes of loadings on a cracked body: opening, sliding, and tearing. Click here for the illustrations of these modes.

Again, LEFM is valid only when the inelastic deformation is small compared to the size of the crack, what we called small-scale yielding. If large zones of plastic deformation develop before the crack grows, Elastic Plastic Fracture Mechanics (EPFM) must be used.

Fracture Analysis Using LEFM

The basic LEFM analysis can be outlined as follows:

Based on linear elasticity theories, the stress field near a crack tip is a function of the location, the loading conditions, and the geometry of the specimen or object.

In practice, engineers calculate the stress intensity factor K based on the stress field at the crack tip and compare it against the known fracture toughness of the material:
  1. 

The crack tip stress field is a function of the location, loading, and geometry

where location can be represented by r and theta using the polar coordinate system whereas the loading and geometry terms can be grouped into a single parameter K, called the stress intensity factor.

K(Loading, Geometry)

(The stress intensity factor K for a few simple loading and geometry conditions are provided and grouped in three categories: classic, specimen, and structure.)

  2.  The fracture toughness of a material can be obtained by experiment. It is material specific.

The stress intensity factor associated with the fracture toughness of the material is called the critical stress intensity factor Kc where Kc is material dependent.


(The critical stress intensity factors Kc's for a few common engineering materials are listed in this table.)
  3.  The stress intensity factor K should NOT exceed Kc.

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