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Experimental and Numerical Study of Sheet Metals Formability based on Crystal Plasticity and Presentation of High Formability Fibers

Hajian, Masoud | 2015

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 47048 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Assempour, Ahmad
  7. Abstract:
  8. In the classical theories of plasticity, plastic deformation of material is modeled with a macro- scopic viewpoint and without considering the existing physical mechanisms at the crystal scale. However, plastic deformation stems from slip phenomena and evolution of crystalline structure. Furthermore the effects of initial texture of material on its mechanical properties, like formability, and also texture evolution of material can only be calculated by considering these physical mecha- nisms.The main purpose of this thesis is to predict forming limit diagrams of sheet metals based on crystal plasticity approach by considering the effect of initial material texture and presentation of initial orientations which have better formability properties. To this purpose, rate dependent crystal plasticity model along with power hardening law and Taylor averaging model are employed. The governing equations at the continuum scale are combined with the rate dependent equations governing on slip at the crystal scale.The resulting nonlinear equations are linearized and solved for magnitudes of crystallographic slip by Newton-Raphson method. These processes are programed by FORTRAN in the form of UMAT and are linked to the ABAQUS software to complete the FEM simulation. In order to extract forming limit diagram of the material, squared geometry sheet metals under various boundary conditions are simulated to produce different strain paths. In a manner like M-K method, a groove is embedded in each sample to enable the simulation to capture necking of the material. Occurrence of instability in the second order derivative of thickness strain variations with respect to time is considered as a measure to identify occurrence of necking in the material.In the experimental section of this thesis, aluminum alloy 1050 with FCC crystal structure and 1010 steel sheet with BCC crystalstructure are selected to be studied according to their widespread
    use. Initial textures of selected sheet metals are measured based on Bragg’s law by using x-ray diffraction machine and goniometer. Then, simple tension test samples for both materials are made according to ASTME8 standard and their stress strain curves are extracted by performing simple tension test. Also, the required samples to determine forming limit diagrams of two materials are made and their FLDs are extracted by performing hemi spherical punch test. The mentioned
    experimental results present the complete required input data for crystal plasticity based simulation of 1010 steel and 1050 aluminum sheets along with the required experimental data for verification of FLD prediction for these two materials. The predicted FLDs based on crystal plasticity simulations are compared with the experimental results obtained from hemi spherical punch tests which shows acceptable agreement between simulation and experiment for both materials. Afterwards, the latent hardening modeling approach is more exactly investigated in order to im- prove the FLD prediction accuracy for FCC crystal structures. To this purpose, three different latent hardening models-including isotropic, two parameter and Weng models-are employed and the associated FLDs are extracted.The results show that Weng model predicts FLD with more 149 accuracy especially in the right hand side of the curve.In the next step, the textures which result in better formability properties are studied. To this purpose,a combination of crystal orientations equivalent to each of BCC ideal rolling fibers-including α, η, γ, ξ and ϵ fibers - is designed and the associated FLD for each ideal fiber is extracted. Comparison of the extracted FLDs shows that γ fiber has higher formability with respect
    to other fibers almost in all FLD regions. Also, α fiber although not interesting in the right hand side of FLD, but in the left, shows considerable formability. Based on these observations, increase of γ fiber density in general and increase of α fiber in the special cases where only formability in left hand side of FLD is of importance seems appropriate and is suggested through texture control in the sheet metal manufacturing process
  9. Keywords:
  10. X Ray Diffraction ; Crystal Plasticity ; Formability ; UMAT Subroutine ; Aluminum Alloy 1050 ; Formability Improvement ; Ideal Fiber ; Experimental Texture Measurement

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