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Modeling Brittle Fracture Under Thermo-mechanical Loading with Discrete Volterra Dislocation Arrays

  • Author(s): Sheng, Andrew
  • Advisor(s): Ghoniem, Nasr M
  • et al.
Abstract

The Discrete Crack Mechanics method (DCM) is a dislocation-based crack modeling technique in which crack models are constructed using discrete Volterra dislocation loops. The method allows for the natural introduction of displacement discontinuities, avoiding numerically expensive techniques. Mesh-dependence that is observed in many existing computational modeling of crack growth is eliminated by utilizing a superposition procedure. The elastic field of a crack in a finite geometry is separated into two parts: the infinite-medium solution of the dislocation-based crack model, and an FEM solution of a correction problem that ensures external boundary conditions are satisfied. In DCM, a crack is represented by a dislocation array with a fixed outer loop that determines the crack tip position. This leading dislocation encompasses additional concentric loops free to expand or contract. Solving for the equilibrium positions of the inner loops gives the crack shape and stress field. The equations governing crack tip motion are developed for quasi-static growth problems based on the Principle of Maximum Entropy Production rate. Convergence and accuracy of the DCM method is verified with 2D and 3D problems with well-known solutions. The DCM method is then coupled with heat transfer to simulate thermo-mechanical fracture.

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