氏名　Dinh Van Hai
学位の種類　博士（工学）
学位記番号　博甲第453号
学位授与の日付　平成19年3月25日
学位論文題目　Constitutive Modeling for High Temperature Deformation Behavior of Magnesium Alloys and Its Application to FEM Simulation of Sheet Forming　（マグネシウム合金の高温変形挙動の構成式のモデルかとその板形成シミュレーションへの応用）
論文審査委員
　主査　教授　鎌土　重晴
　副査　教授　福澤　康
　副査　教授　田辺　郁男
　副査　准教授　永澤　茂
　副査　准教授　南口　誠

• 論文目次
• 論文要旨
• 論文審査の結果の要旨

［平成19（2007）年度博士論文題名一覧］ ［博士論文題名一覧］に戻る．

1　Introduction　p.1
　1.1　Overview of Magnesium and Its Alloys　p.1
　1.2　Sheet Metal Forming　p.5
　1.2.1 Sheet Metal Forming Process　p.5
　1.2.2 Process Modeling and Simulation in Sheet Metal Forming　p.8
　1.3　FE Simulation of Sheet Forming for Magnesium Alloys　p.12
　1.4　Objective of This Thesis　p.13
　1.5　Outline　p.14
2　Evaluation of high temperature deformation of magnesium alloys　p.15
　2.1　Specimen Preparation　p.15
　2.2　Material Characterization　p.17
　2.3　Conclusions　p.21
3　Material modeling　p.22
　3.1　Constitutive Modeling　p.22
　3.1.1 Determination of the material constants for the constitutive equation　p.30
　3.2　Investigation on the Anisotropy of the Sheets　p.33
　3.3　Yield Criterion　p.36
　3.3.1 Isotropic Yield Criterion　p.37
　3.3.2 Anisotropic Yield Criterion　p.38
　3.3.2.1 Hill's Quadratic Yield Criterion　p.39
　3.3.2.2 Hill's Non-Quadratic Yield Criterion　p.41
　3.3.2.3 Barlat's Non-Quadratic Yield Criterion　p.42
　3.3.3 Conclusions　p.43
4　Application of FEM simulation to sheet forming.　p.45
　4.1　2-D Finite Element Analysis for Deep Drawing Process　p.45
　4.1.1 Finite Element Model　p.45
　4.1.1.1 Geometry model and meshing　p.46
　4.1.1.2 Material data and model　p.47
　4.1.1.3 Contact and boundary conditions　p.48
　4.2　Deep Drawing Test　p.50
　4.2.1 Results and discussion　p.54
　4.2.2 Conclusions　p.56
　4.3　3-D Finite Element Analysis　p.65
　4.3.1 Deep Drawing Process　p.65
　4.3.1.1 Finite element model　p.66
　4.3.1.2 Results and discussion　p.66
　4.3.2 Stretching Process　p.74
　4.3.2.1 Stretching test　p.75
　4.3.2.2 Finine element model　p.75
　4.3.2.3 Results and discussion　p.77
　4.3.3 Conclusions　p.80
5　Summary　p.85
A　Appdx A Thermal-Rigid-Viscoplastic FEM　p.88
　A.1　Rigid-Viscoplastic FEM　p.88
　A.2　Heat Transfer Analysis　p.89
　References　p.95

　In recent years, magnesium alloys have been considered as a promising alternative material for high-strength steel and aluminum alloy in some applications and expected to be widely used for structural components in the automotive and aerospace industries due to their advantages such as low density, high specific strength etc. However, the application of magnesium wrought alloy components is still restricted due to lack of knowledge for processing magnesium alloys at elevated temperatures. According to the great attractiveness of magnesium alloy sheet parts, there is a strong demand for a reliable modeling of the virtual process chain including the specification of required mechanical properties. The aim of the present study was to investigate the formability of magnesium alloy sheets at different conditions through non-isothermal deep drawing and stretching tests experimentally and numerically. The simulation was carried out by using 2D and 3D finite element code Deform.
　In order to be able to simulate the forming process, the most important requirement is to construct a proper material model. An important part of the numerical model is the modeling of the material behaviors. Both the hardening and softening behaviors including temperature and strain rate dependencies, and the stress-strain response of the sheet were considered. Two hardening models were developed and used in this study: a phenomenological model in which the parameters of a power law strain rate relation and a physical based model according to Arrhenius equation in which the effects of the temperatures and strain on the deformation behaviors can be represented by Zener-Hollomon parameter in an exponent-type equation were taken into consideration.
　Anisotropy is one of the well known mechanical properties of magnesium alloy sheet. In order to achieve the accuracy in simulation, the anisotropic properties of the materials were investigated by a high temperature tensile test up to 573K. The results recommend that both isotropic and anisotropic material should be used in the simulation to capture the real mechanical behaviors of the alloys at elevated temperatures. Therefore, in this thesis, isotropic Von-Mises and anisotropic Hill's models were used. In comparison between experimental and simulation results at temperatures higher than the rescrystallization temperature （ ）, the prediction of both Von-Mises and Hill's models achieve good agreement with experimental results. However, at temperatures lower than　, Hill's mode is able to capture the deformation behavior of the sheets better than Von-Mises model.
　Besides, the comparison also shows that the numerical code was well capable of predicting the observed deformation behaviors, failure location and distribution of strain, temperature change during the forming process. Concerning the parameter identification procedure, it is observed that the simulated force versus displacement response shows some deviations from the experimentally observed curves. The main reasons of this phenomenon are either due to the materials models used in simulation for determining yielding of the material may over / under predict the yield stress in the flange or high interface friction in experiment.It is found that the coupled thermo-plastic finite element code can be used to analyze and optimize the non-isothermal sheet forming processes for magnesium alloys at elevated temperatures. It is, however, important to note that simulations must be performed alongside carefully experimental conditions.

　本論文は、「Constitutive modeling for high temperature deformation behavior of magnesium alloys and its application to FEM simulation of sheet forming （マグネシウム合金の高温変形挙動の構成式のモデル化とその板成形シミュレーションへの応用）」と題し、5章より構成されている。
　第1章「Introduction」では、マグネシウム合金の板成形技術およびそのシミュレーションに関する従来の研究の概要および既存技術の問題点を示すとともに、本研究の目的と範囲を述べている。
　第2章「Evaluation of high temperature deformation of magnesium alloys」では、Mg-Al系合金のアルミニウム含有量を変化させた合金の圧延まま材を用いて、異方性の強い再結晶温度以下の150℃から、動的再結晶による結晶粒微細化により、粒界すべりの寄与が大きくなり、等方的な変形が可能になる300℃までの温度範囲で、変形挙動のひずみ速度依存性を調べるとともに、圧延方向に対する試験片採取方向の影響を調べている。その結果、温度の上昇およびひずみ速度の低下とともに強度は低下し、延性が著しく向上するが、均一伸びは極端に減少することを明らかにしている。
　第3章「Materials Modeling」では、得られた応力-ひずみ曲線のひずみ速度および温度依存性から動的析出、動的再結晶を伴う変形挙動を表すための材料定数をZener-Hollomonパラメータと流動応力から求め、さらに、変形異方性を表すためのパラメータとしてランクフォード値を求め、高温変形構成モデル式を導出している。
　第4章「Application of FEM simulation to sheet forming」では、第3章で導出した高温変形構成モデル式を用いて代表的な板成形加工である深絞りおよび張出し加工の高温成形シミュレーションを等方的変形とみなす二次元Von－Misesモデルおよび変形異方性を考慮可能な三次元Hillモデルを用いて行ない、再結晶温度以上では等方的変形とみなす二次元モデル式でも実験値と良く一致するが、再結晶温度以下では異方性も考慮できる三次元Hillモデル式が実験値と良く一致し、異方性の強い再結晶温度以下でも、成形加工中のひずみ分布、温度分布、荷重変化、破断位置等を精度良く予測可能であることを明らかにしている。
　第5章「Summary」では本研究で得られた結果を要約し、総括している。
　以上のように、本論文は高温変形中に変形異方性および相変態が生じるマグネシウム合金の高温変形構成モデル式を導出し、板成形FEMシミュレーションに応用展開することにより、その妥当性を検証している。よって、本論文は工学上及び工業上貢献するところが大きく、博士（工学）の学位論文として十分な価値を有するものと認める。