TJ1008 : tixtle Theoretical and Experimental Analysis of Anisotropy Change in the Deformation Process using Hardening Evolution and Digital Image Correlation (DIC) Method
Thesis > Central Library of Shahrood University > Mechanical Engineering > PhD > 2025
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Abstarct: Abstract
In the present study, theoretical and experimental analysis of the anisotropy evolution in sheet mextals during deformation was conducted. Initially, mechanical properties of DC04 steel sheets were extracted through standard uniaxial tensile tests. Subsequently, quadratic anisotropic yield criterion (Hill 1948) and the non-quadratic BBC 2005 criterion were adopted to describe the material’s plastic behavior, along with the Swift hardening model for approximating strain hardening behavior. The anisotropy parameters of the BBC 2005 yield criterion were identified using uniaxial tensile data and error function optimization via the Levenberg–Marquardt algorithm. To investigate the anisotropy evolution experimentally under strain, the Digital Image Correlation (DIC) method was employed with targeted measurement points. Anisotropy behavior of the sheet was analyzed across various strain levels and modeled using a sixth-order polynomial. DIC analysis revealed that the average anisotropy evolution across the specimen surface could serve as a comprehensive foundation for defining strain-dependent anisotropy functions. Moreover, it was observed that applying an equivalent strain of 0.5 reduced the normal and planar anisotropy of the sheet by 57% and 84%, respectively, indicating that as mextal forming progresses, anisotropic characteristics and, consequently, resistance to thinning diminish. Validated empirical anisotropy evolution functions were integrated into ABAQUS via UMAT subroutines, replacing the constant coefficients of the yield criteria. Uniaxial tension processes were simulated numerically using the Hill 1948(ε ̅) and BBC 2005(ε ̅) models. Comparative simulations were also performed with constant-coefficient Hill 1948 and BBC 2005 yield functions. This segment of the study demonstrated notable improvement in modeling accuracy for the plastic behavior of DC04 steel under in-plane loading conditions by incorporating anisotropy evolution into the yield criteria. In the final stage, to validate the proposed model under out-of-plane processes, Nakajima experimental tests and corresponding numerical simulations were performed on DC04 sheets. Through strain path modeling and prediction of force–displacement curves and Forming Limit Diagrams (FLDs) baxsed on the four discussed yield functions and two time-dependent necking criteria, simulation results were compared with experimental data. Findings showed that evolving yield criteria, despite certain limitations, particularly in equiaxial tension, provided relatively accurate reproduction of experimental FLDs and significantly improved FE simulation predictions of forming limits. Moreover, the area under the punch force–displacement curve was computed as the absorbed energy in the Nakajima test for each simulation scenario and subsequently compared with the experimental data.
Keywords:
#Keywords: Anisotropy evolution #Hill 1948 yield criterion #BBC 2005 yield criterion #Digital image correlation (DIC) #Hardening evolution #Forming limit diagram (FLD) #DC04 steel. Keeping place: Central Library of Shahrood University
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