Breakage criterion

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In solid mechanics , a fracture criterion indicates when and under what conditions the breaking strength of a solid is exceeded and it fails due to fracture.

The fracture mechanics and especially the linear-elastic fracture mechanics and flow fracture mechanics deal with fracture criteria and the crack growth behavior of a material. A break is usually characterized by the beginning of the unstable crack propagation . There are various break criteria that depend on the material and the type of break ( brittle break , deformation break , fatigue break , mixed break , etc.). Break criteria are often named after the author who found or developed it. They can also be empirical.

For solids there are u. a .:

  • With the Mohr-Coulomb breakage criterion , breakage occurs when the shear stress is greater than the pressure-dependent shear strength, that is, when it is above the linear break line that represents the Mohr-Coulomb boundary line.
  • In the empirical Hoek-Brown break criterion , the line that was a straight line in the Mohr-Coulomb criterion is curved. Your equation is a root function. It reflects the relationships in three-dimensional compression tests on rock samples better because it comes closer to the non-linear fracture behavior.
  • Drucker-Prager yield condition (failure criterion according to Drucker-Prager)
  • The Griffithsche failure criterion for brittle fracture of 1920 states that a crack propagates when the released energy to break (strain energy), the surface energy, a material-dependent fracture toughness exceeds.

The following breakage criteria are important for soil and granular materials:

For fiber-plastic composites , breakage criteria are treated under failure criteria for fiber-plastic composites . The term failure criterion is more common for this material category.

literature

  • Paul Judt: Numerical stress analysis of cracks and calculation of crack paths using path-independent maintenance integrals. University Press, Kassel 2017, ISBN 978-3-7376-0368-3 .
  • E. Sommer: Fracture mechanical evaluation of surface cracks. Basics - Experiments - Applications, Springer Verlag, Berlin / Heidelberg 1984, ISBN 978-3-662-06176-3 .

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