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Thermodynamically Consistent Phase Field Modeling of Interaction Between Crack Propagation and Phase Transformation

Jafarzadeh, Hossein | 2019

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 52383 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Farrahi, Gholam Hossein; Javanbakht, Mahdi
  7. Abstract:
  8. According to the widespread application of shape memory alloys, their study in the presence of cracks has received lots of attention in the last two decades. The phase transformation ahead of the crack tip may change the stress field and the fracture behavior, especially at the nanoscale. Thus, modeling this phenomenon helps to recognize the affecting factors on crack propagation and prediction of material behavior when cracks exist. In the first step of this thesis, a phase field approach for crack propagation was presented, first by considering fracture as phase transformation and then as bond breaking. According to the scaling-up strategy, the developed theory is applicable from the atomistic to the macroscopic scales by relating the length scale to the number of cohesive interatomic planes at the crack tip. The surface stresses (tension) were introduced by employing some geometrical nonlinearities in both small and large strains frameworks. In addition, an approach, consistent to the J-integral expression, was presented to avoid fracture under compressive (closing) stresses. The applicability of the theory for a broad spectrum of the stress-strain relationships was shown by analysis of the thermodynamic potential in terms of stress-strain curves. Calibration of the model were depicted by utilizing the published experimental or first principle results. In the second step, a thermodynamically consistent phase field approach to the interaction of fracture and phase transformation was developed. This model includes the change in surface energy during phase transformation and the effect of unexplored scale parameter proportional to the ratio of the widths of the crack surface and the phase interface, both at the nanometer scale. Variation of these two parameters causes unexpected qualitative and quantitative effects (change in the structure and geometry of the transformed region, crack trajectory, and process of interfacial damage evolution, as well as transformation toughening) and new physics (shift of phase transformation away from the crack tip and “wetting” of the crack surface by martensite). The results suggest additional controlling parameters, i.e. ratios of the length scales and the surface energies of fracture and phase transformation, on coupled fracture and phase transformation
  9. Keywords:
  10. Phase Field Model ; Fracture and Phase Transformation Interaction ; Surface Stress ; Martensitic Phase Transformation ; Surface Energy

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