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Finite Elements & Fracture Mechanics - overview

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The primary fracture mechanics parameters that may be of interest when analysing a defect are:

The stress intensity factor approach was developed by Irwin in the 1950s following on from the elastic strain energy approach to brittle fracture developed by Griffith from the 1920s. Irwin's work led to the foundations for the concept of linear elastic fracture mechanics (LEFM) which is still fundamental in most crack propagation analyses.

An important relationship for stress intensity factors in linear elastic analysis is based on the Westergaard equations that link the stress intensity factors to the displacement field around the crack tip. When used with the finite element method, these equations allow displacement solutions to be used to generate stress intensity factors. This approach does not require any special capability in the finite element code and is available in all of the Zencrack f.e. interfaces.

The calculation of energy release rate in finite element analyses was first demonstrated by Parks and Hellen in independent publications. The method which they both presented, commonly referred to as the stiffness derivative or virtual crack extension technique, was formulated specifically for finite element applications. The change in energy is calculated for a virtual crack extension at the crack front. The accuracy of this method is known to depend upon the magnitude of the applied virtual crack extension.

A differential formulation for the calculation of energy release rate was presented by de Lorenzi. This formulation also uses virtual crack extensions, but is a continuum mechanics approach. The finite element formulation of this technique produces results that do not depend upon the magnitude of the applied virtual crack extension.

These original energy release rate and j-integral methods have been modified and expanded to include additional load terms and implementations are available in Abaqus, Ansys and NX Nastran to allow calculation of energy release rates and j-integrals. Zencrack uses these capabilities to calculate energy release rate and j-integral data.

  • Parks,D.M., "A Stiffness derivative Finite Element Technique For Determination Of Crack Tip Stress Intensity Factors", Int. J. Frac., Vol.10 (487-502), 1974.
  • Hellen,T.K., "On the Method of Virtual Crack Extensions", Int. J. Num. Met. Engn. (187-207) 1975.
  • de Lorenzi,H.G., "On the Energy Release Rate And The J-Integral For 3-D Crack Configurations", Int. J. Frac., Vol.19 (183-193) 1982.
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