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Experimental and Numerical Evaluation of Grain Morphology Effect on Formability of Sheet Metals Using Coupled Crystal Plasticity and Damage Mechanics

Amelirad, Omid | 2021

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 54334 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Assempour, Ahmad
  7. Abstract:
  8. In this dissertation, using experimental and numerical methods, the effects of grain morphology on the formability of sheet metals are investigated. In this regard, in the first stage, by conducting heat treatment on two different sheet metals with bcc and fcc crystal structures, different grain sizes are produced. Using metallographic observations, these grain structures are examined and the grain sizes are measured. Tensile test and Nakazima formability test have been implemented on these specimen. The grains are also shaped in the rolling process and different grain morphologies are created. In the second stage, a software has been developed to generate various grain structures and morphologies with crystalline textures in any given meshed geometries. Subsequently, a crystal plasticity model compatible with the second law of thermodynamics in large deformation space is introduced. This model is also combined with anisotropic damage mechanics based on the definition of damage tensor and potential function. To combine these two mathematical models, the fundamental relationships governing the continuum mechanics have been used. In order to conduct numerical calculations, the presented model has been implemented in UMAT subroutine in Abaqus software. To this aim, existing Huang's crystal plasticity code has been modified and hyper-elastic and damage relations have been added to the code. In third step, aiming to reduce the computational costs, the minimum geometric size of finite element models (in terms of number of grains per volume, number of grains in thickness and number of elements per grain) is determined in which the uniaxial tensile behavior of polycrystalline is converged. The parameters of the developed mathematical model are calibrated for different sheet samples. High correlation is observed between numerical and experimental stress-strain curves before and after the necking. Forming limits have been calculated for various grain morphologies with and without taking damage into account. The obtained results show that the proposed model can predict the forming limit curve to an acceptable level, especially on the left side of the diagram. Applying compressive stresses in the direction of thickness and considering the effects of damage, the right side of the graphs become closer to the experimental results. Error of calculation in the case without considering damage is from 14% to 34%. The error is reduced to less than 18% by considering damage and compressive stresses. Applying compressive stresses comparable to the ultimate strength of the material results in a 23% increase in the forming limit. For sheets in the annealed condition, grain size effects on the forming limit curves are small, as long as the grain size is not comparable to the thickness of the sheet. When the grain size is large and comparable to the thickness of the sheet, a significant reduction in formability is observed due to the influential role of single grains. Elongated grains also increase ductility by 7% when they have the same hardening properties as spherical grains. The results of analyses on the effects of crystalline texture on formability show that changing the crystalline texture from ϵ-fiber to γ-fiber in bcc structure, ductility can be increased up to 23%. In the case of fcc structure, the effect of changing the crystalline texture is more and by changing the texture with Copper orientation to Cube orientation, the ductility can be increased up to 30%
  9. Keywords:
  10. Damage Mechanics Model ; Large Deformation ; Finite Element Method ; Crystal Plasticity ; Grain Morphology ; Ductility Limit ; Sheet Metal Forming

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