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Experimental and Theoretical Investigations of Calibration Methods and Factors Influencing the Forming Limit Diagrams

Ghazanfari, Amir | 2012

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 42612 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Assempour, Ahmad
  7. Abstract:
  8. In designing of sheet metal forming processes, knowledge of the maximum permissible strains in the sheet is of prime importance for the design engineer. Thus, a large amount of experimental and theoretical researches have been carried out to estimate these limiting strains. A renowned and prevalent theoretical method for prediction of forming limits is the Marciniak and Kuczynski model. In this model, it is assumed that a small groove exists in the sheet even before applying the loads; and due to the weakness of this region, necking starts from there. The major problem of the M-K model is requiring of an experimental point to “calibrate” the results. Furthermore, while experiments indicate the significant effect of strain rate and sheet thickness, these parameters are omitted from the equations. Another method for prediction of limiting strains is using the NADDRG relation. However, it is applicable only to low-carbon steels and is not accurate for other materials. In this project, effective solutions have been proposed to solve these problems. To solve the calibration problem, three different approaches have been presented. In the first method, the M-K model has been modified and a “material” inhomogeneity has been replaced with the geometrical inhomogeneity. Using this assumption, an empirical law has been developed which is able to predict the Forming Limit Diagrams with a reasonable error in the absence of experimental data. In the second method, the calibration point of the classical M-K model has been modified and it is demonstrated that using the point corresponding to the uniaxial tension state has several important advantages over the classical plane strain point. In the third method for calibration of FLDs, the NADDRG relation has been modified. It is shown that adding the strain rate sensitivity index to the existing parameters enables this relation to predict FLDs of other materials as well. As another research, the M-K model has been improved to be able to take into account the effect of strain rate on FLDs. In another part of the project, a comprehensive theoretical and experimental study has been done to investigate the influence of sheet thickness on formability. Firstly, it has been tried to explain the effect of thickness theoretically. To do this, a recently-proposed constitutive relation has been employed. Then, some experiments have been carried out to demonstrate that “the influence of thickness is due to variations of microstructure resulted from the thickness reduction processes”. In other words, it has been shown that “if the thickness reduction process is performed so as not to alter the microstructure of the material, the formability will not change significantly with variations of thickness”. This small dependency is also explained via theoretical methods. Finally, to illustrate the application of FLDs, the forming process of a circular cup has been designed, simulated and optimized using the concept of FLDs
  9. Keywords:
  10. Sheet Metal Forming ; Marciniak-Kuczynski Model ; Thickness Effect ; Calibration ; Forming Limit Diagram (FLD)

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