결정 소성 모델을 통한 다양한 결정질 금속 재료의 멀티 스케일 변형 거동 연산 = Multi-scale Deformation Modeling of Various Metals Using Crystal Plasticity Models

다국어 초록 (Multilingual Abstract)

This study aims to quantitatively understand and simulate the complex deformation mechanisms of crystalline metals by applying a mean-field based crystal plasticity model to metals with various crystal structures, and to comprehensively evaluate its calculative capability and limitations. Conventional phenomenological models have been widely employed in industry due to their computational efficiency in reproducing macroscopic mechanical responses of metals. However, they inherently cannot explicitly account for microscopic deformation mechanisms such as crystallographic orientation distribution, slip and twinning activation. To overcome these limitations, the crystal plasticity model was introduced as a physically based framework that links microscopic crystal behavior with macroscopic mechanical responses through the modeling of crystallographic texture, slip and twinning activation, and phase transformation etc.
In this study, representative mean-field based crystal plasticity models- such as VPSC (Visco-Plastic Self-Consistent model), and its elastically extended versions, ΔEVPSC and σEVPSC-were examined and compared in terms of their mathematical formulation, calculation algorithm, and numerical characteristics. These models were applied to various crystalline metals, including austenitic stainless steel (316L STS, FCC), commercially pure titanium (CP-Ti, HCP), magnesium alloy (E-form, HCP) and dual phase steel (DP980, BCC or BCT), under diverse stress and loading conditions such as uniaxial tension, in-plane compression, tension-compression-tension cyclic loading, loading-unloading-reloading, hydraulic bulge and bending tests. The results confirmed that both ΔEVPSC and σEVPSC models while successfully reproducing non-linear elastic behaviors – such as lattice strain evolution, springback, and the Bauschinger effect- by incorporating elastic contributions.
More specifically, the models accurately reproduced 1) the lattice stain, and activation behavior of each deformation mode on CP-Ti under cryogenic temperature conditions, 2) the twin volume fraction evolution and neutral axis shifting of magnesium alloys as a function of initial texture, and 3) springback behavior of dual-phase steel after forming-draw bending process. These results demonstrate that the elasto-visco-plastic crystal plasticity models (ΔEVPSC and σEVPSC) exhibit consistent calculation accuracy across various crystal structures, material types and stress states, effectively capturing the physical linkage between micro-meso-macro scale deformation behaviors. Overall, this work systematically verifies the universality and accuracy of elasto-visco-plastic crystal plasticity models for various crystalline metals, while also identifying their numerical and physical limitations. The findings provide a fundamental basis for developing high-fidelity material models applicable to complex forming process simulations and optimal design in industrial applications.

목차 (Table of Contents)

• 목차
• 1. 서론 1
• 2. 모델 설명 8
• 2.1 VPSC8 10
• 2.2 ΔEVPSC 그리고 σEVPSC 14
• 2.3 ΔEVPSC-FE 모델 18
• 2.4 경화 및 쌍정 모델 23
• 2.4.1 보세 (Voce) 경화 모델 23
• 2.4.2 전위 밀도 기반 경화 모델 25
• 2.4.3 쌍정 모델 28
• 3. 결정 소성 모델 활용 사례 연구 31
• 3.1 316L 스테인리스강의 기계적 물성 변화에 세가지 결정 소성 모델 적용 및 모델간 차이 비교 33
• 3.2 응력 증분 기반 탄점소성 다결정 모델 활용 사례 연구 48
• 3.2.1 극저온 순수 타이타늄의 기계적 물성 향상 원인을 전위 밀도 기반 경화모델을 활용하여 분석 50
• 3.2.2 (유한 요소 해석 적용) 상온 마그네슘 합금의 굽힘성 개선에 초기 집합조직의 영향 분석 79
• 3.2.3 (유한 요소 해석 적용) DP980강의 U자형 드로잉 후 스프링백 거동 모사 113
• 4. 토의 149
• 4.1 세가지 결정 소성 모델의 모사 능력 종합 평가 149
• 4.2 탄점소성 다결정 모델의 범용성 및 정확성 152
• 4.3 탄점소성 다결정 모델의 한계점 157
• 5. 결론 (혹은 요약) 161
• 6. 참고문헌 164
• 7. Abstract 191
• 8. 감사의 글 194