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Crack-tip process zone as a bifurcation problem.

Alexei Boulbitch1, Yury M Gufan2, Alexander L Korzhenevskii3

  • 1IEE S.A. ZAE Weiergewan, 11, rue Edmond Reuter, L-5326 Contern, Luxembourg.

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Crack tip stress induces a phase transition, forming a process zone. This dynamic transformation, governed by an order parameter, exhibits universal behavior with stress intensity and critical velocity, creating a unique phase diagram.

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Area of Science:

  • Solid mechanics
  • Materials science
  • Phase transitions

Background:

  • Stress concentration at crack tips initiates localized structural transformations, known as process zones.
  • The formation of these zones is analogous to phase transitions in materials.

Purpose of the Study:

  • To model the formation of crack tip process zones as a local phase transition.
  • To derive and analyze the dynamics of the order parameter governing this transformation.
  • To establish a universal dynamic phase diagram for crack tip behavior.

Main Methods:

  • Derivation of a system of equations for a multicomponent order parameter.
  • Analysis of the order parameter dynamics under time-dependent stress fields.
  • Investigation of bifurcation phenomena corresponding to process zone emergence.

Main Results:

  • The process zone emerges via a bifurcation in the order parameter dynamics.
  • The emergence temperature (T *) differs from bulk transformation temperature (T c) and scales universally with stress intensity factor (K I) as T * - T c ∼ K I^{4/3}.
  • The process zone universally vanishes at a critical velocity.

Conclusions:

  • Crack tip process zone formation is a universal dynamic phase transition.
  • A universal dynamic phase diagram can be constructed based on stress intensity and critical velocity.
  • This framework provides new insights into fracture mechanics and material behavior under stress.