Flow rupture mechanics

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The term flow rupture mechanics (FBM) or elastic-plastic fracture mechanics (EPBM) summarizes all methods of fracture mechanics which, in addition to linear-elastic crack propagation  (LEBM), also take into account plastic deformations (i.e. flow) in the vicinity of a crack . The FBM is particularly suitable for ductile materials. It defines elastic-plastic parameters that are clearly related to the length of the crack and can still be used in the event of crack propagation with simultaneous plastic deformation.

motivation

The linear-elastic fracture mechanics requires a small plastic zone compared to the crack length . This means that a crack spreads unstably after a critical stress intensity factor K c has been exceeded , since the stress conditions at the crack tip do not change. Brittle fracture occurs , as is often observed in ceramics and some steels at low temperatures.

However, many steels behave differently: when crack growth starts, there is initially a significant hardening of the metal mesh around the crack tip. When lattice planes slide off (plastic deformation), many dislocations are formed , which offer resistance to further deformation and thus crack propagation. Macroscopically , this manifests itself as fracture toughness or, in the case of a further increase in stress, as tough fracture . If this effect is significant, it must be described by suitable extensions of the linear-elastic fracture mechanics.

Concepts

Two criteria method

The two-criteria method assumes that small components fail due to plastic instability ( ductile failure ), while the failure of large components can be described by the LEBM ( brittle failure ). For this purpose, two load values ​​are defined, which reflect the relationship between the existing and the maximum tolerable load with regard to crack propagation and instability. These two load parameters define the position of the applied load within a load map . The failure curve, which is determined differently depending on the method, lies in this map. If the applied load exceeds this limit curve, component failure occurs .

COD or CTOD concept

The crack (tip) opening displacement concept assumes a relationship between the crack bank displacement (COD) at the crack tip and the load on the crack tip. It is therefore assumed that when the crack extension begins, the crack bank displacement will reach a critical value.

J-integral method

The J-integral is a closed line integral which completely encloses the crack tip and describes the condition at the crack tip even with a large plastic zone. It has important properties that apply to non-linear-elastic behavior and, under certain restrictions, can also be applied to elastic-plastic behavior . The value of the integral is independent of the integration path as long as the crack tip is completely enclosed. In clear terms, the J integral is the difference between the potential energies of two otherwise identical bodies, the crack length of which varies by  Δa (delta a).

Individual evidence

  1. ↑ Joachim Rösler, Harald Harders, Martin Bäker: Mechanical behavior of materials. 5th edition, Springer Fachmedien, Wiesbaden 2016, ISBN 978-3-658-13794-6 , pp. 159–161.
  2. ↑ Stefan Kolling: Application of non-linear fracture mechanics according to the finite element method using the example of the remaining service life analysis of a steel railway bridge made of riveted solid wall girders. Diplomica Verlag GmbH 1996, ISBN 978-3-83243-227-0 .
  3. ↑ Fracture mechanical properties of cast iron materials (accessed on September 20, 2018)
  4. ↑ Does the application of fracture mechanics make sense (accessed on September 20, 2018)
  5. ↑ Implementation of an optimization algorithm for the inverse parameter identification of cohesive zone models, pp. 8-9. (accessed on September 20, 2018)
  6. ↑ FEM analyzes of crack problems with non-linear material behavior, pp. 18-21. (accessed on September 20, 2018)

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