Crack-tip process zone as a bifurcation problem
| Autor: | Alexei Boulbitch, Yury M. Gufan, Alexander L. Korzhenevskii |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Physics
Phase transition Condensed matter physics Order (ring theory) Saddle-node bifurcation 02 engineering and technology 021001 nanoscience & nanotechnology 01 natural sciences Stress field Pitchfork bifurcation 0103 physical sciences 010306 general physics 0210 nano-technology Stress intensity factor Stress concentration Phase diagram |
| Zdroj: | Physical review. E. 96(1-1) |
| ISSN: | 2470-0053 |
| Popis: | Stress concentration at a crack tip generates a solid structural transformation in its vicinity, the process zone. We argue that its formation represents a local phase transition described by a multicomponent order parameter. We derive a system of equations describing the dynamics of the order parameter driven by an inhomogeneous, time-dependent stress field in the solid and show that it exhibits a bifurcation. The latter corresponds to the emergence of a process zone characterized by the distribution of the order parameter localized in the vicinity of the crack tip. The emergence temperature T_{*} considerably differs from the temperature of the bulk phase transformation T_{c}. We demonstrate that T_{*} exhibits a universal behavior T_{*}-T_{c}∼K_{I}^{4/3}, in terms of the stress intensity factor K_{I}, and that the zone universally vanishes upon achieving a critical velocity. These facts together give rise to a universal dynamic phase diagram. |
| Databáze: | OpenAIRE |
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