Breakage criterion
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:
- Tresca criterion
- Mohr and Coulomb's criterion
- Criterion according to Drucker and Prager
- Criterion after loading
- Matsuoka and Nakai criterion
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 .
Web links
- To assess the structural safety of existing reinforced concrete structures, see p. 23
- Crack, Fracture and Fatigue (accessed September 20, 2018)
- Experimental determination and mathematical description of the multi-axial strength of ultra-high-strength concrete. (accessed on September 20, 2018)
- Parameters for the strength assessment of components (accessed on September 20, 2018)