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The Strain Gradient Approach for Forming Analysis of Sheet Metals

Safikhani, Alireza | 2008

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 40702 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Assempour, Ahmad
  7. Abstract:
  8. In this study, the forming limit stress and strain diagrams have been determined based on the strain gradient plasticity theory. Forming limit stress diagram (FLSD) has been reported as being much less path-dependent and much more favorable than the forming limit diagram (FLD) in representing forming limits in the numerical simulation of sheet metal forming processes. Therefore, the purpose of this study is to develop a methodology for prediction of the forming limits both in strain and stress spaces. All simulations are based on strain gradient theory of plasticity in conjunction with the so-called Marciniak-Kuczynski (M-K) approach. This method introduces an internal length scale into conventional constitutive equations and takes into account the effects of deformation in-homogeneity and material softening. The nonlinear second order boundary valued (BVP) ordinary differential equation of the thickness of sheet metal has been solved by different shooting methods and also combination of collocation and Newton-Raphson methods. When shooting method is used, various initial value problem (IVP) techniques are employed and their efficiency is examined. It is shown that combination of collocation and Newton-Raphson methods is a very efficient and robust technique for solving the current BVP differential equation. This technique has not numerical instabilities and need for accurate initial guess which is crucial for the shooting methods. Comparison with the experimental data shows that calculated FLDs and FLSDs based on the strain gradient theory are more accurate than those of the classical plasticity theory. In other words, strain gradient plasticity theory which takes into account a length scale parameter is more accurate in predicting the behavior of materials. Moreover, the predicted FLDs and FLSDs that take into account the strain gradient effects are less sensitive to the magnitude of initial imperfection factor when a very small value of this factor is used. This is a major improvement over the traditional M-K method whose predicted results vary dramatically with the change of initial imperfection factors. Also, as a research beyond the main scope of this thesis, an analytical method for predicting the elastic-plastic behavior of a rotating cylinder in plane strain conditions and using strain gradient theory is presented. In this solution, explicit relations for the displacement, strain and stress components are derived. It is shown that the solution is dependent to the dimensions of the cylinder, while the results of the classical plasticity theory is independent of the dimensional parameters.

  9. Keywords:
  10. Forming ; Forming Limit Diagram (FLD) ; Marciniak-Kuczynski Model ; Forming Limit Stress Diagram ; Strain Gradient Plasticity

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