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2017
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Magnesium alloy, one of HCP structured material, shows strong anisotropy and asymmetric behavior in tension and compression test especially at room temperature. These characteristics limit the application of finite element method (FEM) which is based on conventional continuum mechanics. To accurately predict the material behavior of magnesium alloy from the microstructural level, the methodology of fully coupled multiscale simulation is presented, which introduces crystal plasticity model as a constitutive equation in the simulation of metal forming process.
First, the existing constitutive equation for rigid plastic FEM is modified in component form to accommodate the polycrystal model as the constitutive equation. Visco-plastic self-consistent (VPSC) model was selected as the polycrystal model because it is regarded as the most robust model compared with Taylor model and Sachs model. The stiffness matrix and the load vector were derived based on a new approach and implemented into DEFORMTM-3D via a user subroutine which handles stiffness matrix in elemental level.
Secondly, the extrusion and rolling process of pure magnesium were simulated and it was shown that basal slip and tension twin are the dominant deformation mode which corresponds well with the known texture information from the literature in those processes.
Thirdly, fully coupled multiscale simulation of Erichsen test was done for the two Mg alloys which show distinct difference in initial texture. The texture evolution, activity of each deformation mode, r-value and forming load of both alloys during the test were analyzed and compared based on the numerical simulation as well as experimental result. The simulated texture evolutions conform well to the experimental ones, and also the simulated forming load shows reasonably good approximation with the test loads. It was shown that ZX40 (Mg-4Zn-0.3Mn-0.3Ca) alloy, which has more broadened distribution of (0002) pole figure with the addition of Ca element, has good stretch formability at room temperature via the dominant basal slip mode and activation of tension twin during the whole deformation process.
Through the several multiscale simulations of typical metal forming processes, it is confirmed that the developed methodology can be applied in large deformation problem of metal. This approach can be a powerful tool in not only analyzing the forming process of a product but also designing rolling process which enhances the formability of sheet and analyzing the characteristics of texture evolution in alloy design research.
First, the existing constitutive equation for rigid plastic FEM is modified in component form to accommodate the polycrystal model as the constitutive equation. Visco-plastic self-consistent (VPSC) model was selected as the polycrystal model because it is regarded as the most robust model compared with Taylor model and Sachs model. The stiffness matrix and the load vector were derived based on a new approach and implemented into DEFORMTM-3D via a user subroutine which handles stiffness matrix in elemental level.
Secondly, the extrusion and rolling process of pure magnesium were simulated and it was shown that basal slip and tension twin are the dominant deformation mode which corresponds well with the known texture information from the literature in those processes.
Thirdly, fully coupled multiscale simulation of Erichsen test was done for the two Mg alloys which show distinct difference in initial texture. The texture evolution, activity of each deformation mode, r-value and forming load of both alloys during the test were analyzed and compared based on the numerical simulation as well as experimental result. The simulated texture evolutions conform well to the experimental ones, and also the simulated forming load shows reasonably good approximation with the test loads. It was shown that ZX40 (Mg-4Zn-0.3Mn-0.3Ca) alloy, which has more broadened distribution of (0002) pole figure with the addition of Ca element, has good stretch formability at room temperature via the dominant basal slip mode and activation of tension twin during the whole deformation process.
Through the several multiscale simulations of typical metal forming processes, it is confirmed that the developed methodology can be applied in large deformation problem of metal. This approach can be a powerful tool in not only analyzing the forming process of a product but also designing rolling process which enhances the formability of sheet and analyzing the characteristics of texture evolution in alloy design research.
목차
목 차List of Tables ............................................................................. iList of Figures ............................................................................. ii1. 서론 ........................................................................................... 11.1 연구 배경 ............................................................................ 11.2 연구 동향 ........................................................................... 71.3 연구 목적 및 내용 ................................................................ 112. 이론적 배경 .............................................................................. 142.1 집합조직 .............................................................................. 142.1.1 집합조직 개요 ................................................................ 142.1.2 집합조직의 표현 및 측정 방법 …………………………… 202.2 금속의 소성 변형기구 …………………………………………… 252.2.1 금속의 변형기구 개요 ……………………………………… 252.2.2 마그네슘 합금에서의 슬립과 쌍정 시스템 ……………… 282.3 단결정의 운동학(kinematics) ………………………………… 312.4 점소성 자기일관성 다결정 모델 …………………………… 362.4.1 결정립과 다결정체에 대한 구성방정식 ………………… 362.4.2개재물 모델 공식화 ...................................................... 402.4.3 Voce 경화 모델 .............................................................. 462.4.4 쌍정 모델 ....................................................................... 482.4.5 다결정 모델의 역할 ...................................................... 502.5 강소성 유한요소해석 개요 ................................................... 542.5.1 강소성 유한요소 지배방정식 ........................................ 542.5.2 유한요소 이산화 …………………………………………… 553. 멀티스케일 방법론 .................................................................. 613.1 점소성 자기일관성 다결정 모델과 강소성 유한요소법의 결합.. 613.1.1. 유한요소법에서의 강성행렬식 유도 ............................. 613.1.2. VPSC 코드와의 연계 .................................................. 643.1.3. 강체 영역의 처리 ........................................................ 683.1.4 강소성 유한요소법에서의 VPSC 모델 구현 .................... 693.2 유전자 알고리즘을 적용한 물성 파라미터 최적화 ............. 743.2.1 유전자 알고리즘 개요 ................................................. 743.2.2 유전자 알고리즘을 활용한 물성 파라미터의 확보 ……… 743.3 멀티스케일 해석 개요 ......................................................... 784. 압출 및 압연 공정의 멀티스케일 전산모사 ............................... 804.1 순수 마그네슘 압출 공정의 전산모사 및 분석 .................... 804.2 순수 마그네슘 압연 공정의 전산모사 및 분석 .................... 895. 에릭슨 시험 공정의 멀티스케일 전산모사 .................................. 975.1 에릭슨 시험 전산모사 개요 ................................................. 975.2 마그네슘 합금 판재의 물성 파라미터 확보 ………………… 995.3 인장-압축-인장 하중 사이클에 대한 전산모사 …………… 1035.4 에릭슨 시험 전산모사 모델 …………………………………… 1075.5 에릭슨 전산모사 결과 및 고찰 ………………………………… 1096. 결론 및 향후 과제 …………………………………………………… 1226.1 결론 ……………………………………………………………… 1226.2 향후 과제 ………………………………………………………… 125참고문헌 …………………………………………………………………… 127Abstract …………………………………………………………………… 139
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