Fracture Mechanics

  • Dominique François
  • André Pineau
  • André Zaoui
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 191)


After an overlook about the aim of fracture mechanics, the strain energy release rate is defined in linear as well as in nonlinear elasticity. Perturbation to the stress field produced by the presence of an elliptical hole allows introducing the notion of stress intensity factor. Stress and strain fields at the tip of a crack are calculated. The relation between the strain energy release rate and the stress intensity factor is demonstrated. The presence of a crack produces displacements, which can be calculated. Various methods exist to determine the stress intensity factor: experimental, superposition, relation with the stress concentration factor, compliance, numerical methods. Consideration is given on three-dimensional cracks.

The plastic zones at the tip of cracks are different in plane stress and in plane strain. Various approximations give their dimensions as well as the crack opening displacement, in small scale yielding and also in large scale yielding. The way to measure fracture toughness is described. The “R” curve effect explains some of the standard procedures. In elastoplastic fracture mechanics, the “R6” method provides an assessment of the safety of a structure, while the measurement of the critical value of J, or of the CTOD is explained. Fracture mechanics of creeping solids follows the analysis of Riedel and Rice. It is shown how to determine the time to fracture.

The local approach to fracture mechanics is introduced. It leads to the use of cylindrical notched specimens. The ways to experiment and to analyse the results are presented.


Fracture Toughness Stress Intensity Factor Crack Length Plastic Zone Plane Stress 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Dominique François
    • 1
  • André Pineau
    • 2
    • 3
  • André Zaoui
    • 3
    • 4
  1. 1.École Centrale de ParisParisFrance
  2. 2.École des Mines de Paris Paris Tech Centre des Matériaux UMR CNRSÉvry CedexFrance
  3. 3.Academy of EngineeringParisFrance
  4. 4.French Académie des SciencesParisFrance

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