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Thermomechanical Constitutive Modeling and Numerical Implementation of Porous Shape Memory Alloys Considering Irrecoverable Strain

Ashrafi, Mohammad Javad | 2015

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 47245 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Naghdabadi, Reza; Sohrabpour, Saeed; Arghavani, Jamal
  7. Abstract:
  8. Porous shape memory alloys (SMAs) were fabricated by many researchers in the last decade and have been initially utilized as bone implants. Also, due to hysteresis in superelastic behavior, and the porous structure, porous SMAs can be used in energy absorbing applications. Such applications call for efficient constitutive modeling of porous SMAs. Moreover, porous SMAs with a wide range of porosity ratios and mechanical properties have been produced in the recent years; therefore, it is necessary to improve the available models and carefully study porous SMA behavior. Different approaches have been utilized for modeling porous SMA behavior. Most of the researchers used homogenization approach while others used phenomenological approach. In this thesis, we use the phenomenological approach for modeling thermomechanical behavior of porous SMAs, which has low computational cost and reasonable accuracy. According to experimental data, porous material behavior is pressure dependent and specifically in porous SMAs, irrecoverable strain is mainly due to plastic strain and incomplete reverse transformation. Therefore, in constitutive model development, we consider the three main behavior of porous SMAs:Pressure dependency, evolution of plastic strain during phase transformation and the coupling effects of transformation and plastic strains. Choosing proper internal variables, limit functions and presenting proper form for Helmholtz free energy function, constitutive equations are derived following standard arguments of continuum thermodynamic. Then we investigate the numerical implementation for the proposed constitutive models. In this regard, solution algorithmand time discrete form for the constitutive equations are presented. Specifically, we use Fischer- Burmeister function instead of the commonly-used Kuhn-Tucker conditions. To validate the models, different examples are considered and the results are compared with experiments. Moreover, by Finite element implementation of the proposed models using UMAT subroutine in ABAQUS, different boundary value problems are solved which show the effectiveness of numerical implementation. The results show that the proposed phenomenological constitutive models,besides beingas simple as possible,are accurate in a wide range of porosities (10% to 60%). According to simulation results, phase transformation starts earlier and becomes more pressure dependent by increasing porosity. Moreover, the models with plasticity effects can predict appropriately the effects of plastic deformation on reverse phase transformation as well as simultaneous evolution of transformation and plastic strains
  9. Keywords:
  10. Constitutive Modeling ; Thermomechanical Processing ; Porous Shapememory Alloy ; Pressure Dependent Behavior ; Transformation Strain

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