氏名　Wisessint Attaporn
学位の種類　博士（工学）
学位記番号　博甲第514号
学位授与の日付　平成21年6月30日
学位論文題目　3D-Enriched FEM Analysis for Intensity of Singular Stress Field in Dissimilar Material Joints　（異材接合体における特異応力場の強さに対する三次元エンリッチ有限要素法解析）
論文審査委員
　主査　教授　古口　日出男
　副査　教授　武藤　睦治
　副査　准教授　永澤　茂
　副査　准教授　井原　郁夫
　副査　教授　宮下　幸雄

• 論文目次
• 論文要旨
• 論文審査の結果の要旨

［平成21（2009）年度博士論文題名一覧］ ［博士論文題名一覧］に戻る．

Contents
Chapter 1:　Introduction　p.1
　1.1　Dissimilar material joint　p.2
　1.2　Stress singularity　p.5
　1.3　Review of the past study　p.8
　1.4　Objectives　p.13
　1.5　Scope of work　p.14
　1.6　Conclusion　p.16
　References　p.17
Chapter 2:　Analysis methods（FEM）　p.21
　2.1　Finite element method（FEM）　p.22
　2.2　Eigen analysis　p.30
　2.3　Conclusion　p.38
　References　p.39
Chapter 3:　FEM analysis for singular stress field in 2D elaso-plastic material joints　p.42
　3.1　Introduction of elasto-plastic FEM　p.43
　3.2　Two-dimensional elasto-plastic eigen analysis using FEM　p.47
　3.3　Electronic packaging　p.48
　3.4　Procedure of analysis　p.55
　3.5　Elasto-plastic stress singularity analysis in ACF interconnection　p.57
　3.6　Elasto-plastic stress singularity analysis in filp chip joint　p.78
　3.7　Elasto-plastic stress singularity analysis in a bonded joint　p.83
　3.8　Conclusion　p.88
　References　p.89
Chapter 4:　3D-enriched FEM　p.94
　4.1　Three-dimensional enriched FEM　p.95
　4.2　Conclusion　p.108
　References　p.109
Chapter 5:　Intensity of stress singularity analysis using 3D-enriched FEM　p.111
　5.1　Introduction of three-dimensional enidhed FEM　p.112
　5.2　FEM model and boundary conditions　p.114
　5.3　Eigen analusis results　p.115
　5.4　Boundary element analysis　p.118
　5.5　Two-dimensional enriched FEM analysis　p.119
　5.6　Three-dimensional enriched FEM results and discussion　p.121
　5.7　Conclusion　p.128
　References　p.129
Chapter 6:　General conclusions and future works　p.132
　6.1　General conclusions　p.133
　6.2　Future works　p.136
Appendix A　p.137
Acknowledgment　p.143
List of journal publications　p.144
List of internationnal confreences　p.144
List of nationnal conferences　p.145

　It is well known that dissimilar material joints have singularities induced by discontinuities in material properties across an interface. The stress singularities may cause the failure of joints. Actually, most materials behave in an elasto-plastic manner under external forces or a variation of temperature. Hence, dissimilar material joints should be analyzed considering the elasto-plastic properties of materials. Many investigators determined firstly singular stress fields in 2D elastic dissimilar material joints and then those in 2D elasto-plastic dissimilar material joints. Recently, the 2D numerical analysis has been extended to 3D numerical analysis for determining the singular stress fields in elastic dissimilar material joints. However, the 3D numerical analysis requires the large numbers of elements and computational time, so several authors have developed numerical methods that can analyze 3D stress distributions using a small number of elements. These numerical methods have been widely used for elastic dissimilar material joints. By the way, the 3D elasto-plastic dissimilar material joint is still difficult for analyzing in numerical analysis. Therefore, we aim to determine the singular stress fields at singular points in 3D elasto-plastic dissimilar material joints using finite element method （FEM）. However, 2D elasto-plastic and 3D elastic dissimilar material joints are individually studied in this research. The doctoral dissertation is organized into 6 chapters. The description of each chapter is following below:
　Chapter 1, which is entitled as “Introduction”, explains the detail of dissimilar material joints and the characteristics of the stress field. The concept of stress singularity in dissimilar material joints is presented. The past studies on stress fields around singular points in dissimilar material joints are reviewed. The study on this field has been carried out step-by-step using several numerical methods. Finally, the research objectives and the scope of work are also explained.
　Chapter 2, which is entitled as “Analysis methods （FEM）”, explains general finite element formulations for Hexahedron element and 4-node quadratic element. Two and three-dimensional eigen analyses for determining eigen values at singular points in elastic dissimilar material joint are also explained.
　Chapter 3 is entitled as “Intensity of stress singularity for 2D elasto-plastic dissimilar material joints using FEM”. A general finite element method is applied to determine the intensities of stress singularity around singular points in two-dimensional elasto-plastic material joints. The elasto-plastic eigen value is determined using an eigen analysis. Anisotropic conductive film （ACF） interconnections, a flip chip joint using a solder bump and a bonded joint of ceramic, copper and aluminum are the three cases of applications for the elasto-plastic finite element analysis. The ACF interconnection is analyzed in 2 cases of one ACF particle and two ACF particles in ACF interconnections. The flip chip joint using a solder bump is analyzed by applying the large deformation to the interface between an IC chip and the solder bump. Lastly, the bonded joint between ceramics, copper and aluminum is simulated as the same as the four-point bending test procedure in experiment. The possibilities of delamination in each case of the applications are also discussed by considering the intensity of stress singularity results.
　Chapter 4, which is entitled as “3D-Enriched FEM”, presents a new enriched element in three-dimensional enriched FEM formulation. The relation between global and local coordinates and the definition of enriched domains are explained.
　Chapter 5 is entitled as “Intensity of stress singularity analysis using 3D-enriched FEM”. A new three-dimensional enriched FEM that was presented in chapter 4, is applied to determine the intensities of stress singularity at a singularity corner together with those along the free edge of the interface in a elastic dissimilar material joint that has a large difference of Young’s moduli. A mechanical loading is subjected to the FEM model. The orders of stress singularity are individually examined at the singularity corner and along the singularity lines. The intensities of stress singularity at the singularity corner and also along the singularity lines are directly determined by this method without any post-processing. The size of enriched element and the volumes of enriched domains are analyzed. Then using these values to determine the intensities of stress singularity at the singularity corner and along the singularity lines. The intensities of stress singularity results in the present analysis are compared with those in BEM.
　Chapter 6 is entitled as “General conclusions and future works”. The present researches are summarized and future works are given in this chapter. In the future work, the present study for the order of elasto-plastic stress singularity in two-dimensional eigen analysis will be extended to three-dimensional eigen analysis. The order of elasto-plastic stress singularity and displacement fields around the singular points in three-dimensional elasto-plastic dissimilar material joint will be calculated. Then these values and the three-dimensional enriched FEM will be used for determining the intensity of stress singularity.

　本論文は、"3D-Enriched FEM Analysis for Intensity of Singularity Stress Field in Dis-similar Material Joints"（異材接合体における特異応力場の強さに対する三次元エンリッチ有限要素法解析）と題し、6章より構成されている。
　第一章「Introduction」では、異材接合体とその応力場の特徴、本論文に関係する従来の研究の概要を示すとともに、本研究の目的と範囲を述べている。
　第二章「Analysis methods（FEM）」では、六面体要素および4節点四角形要素を用いた一般的な有限要素法を概説している。さらに、接合体界面端部における特異応力場の特異性のオーダーを求めるための二次元および三次元有限要素法による固有値解析法について説明している。
　第三章「Intensity of stress singularity for 2D elasto-plastic dissimilar material joints using FEM」では、汎用有限要素法を用いて二次元接合体の弾塑性特異応力場の強さを求めたことを述べ、三つの解析例を通して、実際の解析手順、解析方法を詳細に説明している。
　第四章「3D-enriched FEM」では、新しいエンリッチ要素を用いた三次元有限要素法および定式化で用いている全体座標系と局所座標系、さらにエンリッチ領域の定義について説明している。
　第五章「Intensity of stress singularity analysis using 3D-enriched FEM」では、第四章で説明した新しいエンリッチ要素を用いて、ヤング率が大きく異なる角柱状の三次元接合体に軸方向に引張り荷重が作用する場合の界面角部および界面と側面との交線（応力特異線）上の特異応力場の強さを求めている。解析に際し、界面角部および応力特異線上の特異性のオーダーを事前に求める必要があるが、解析後のデータを処理することなしに直接角部および応力特異線上の特異応力場の強さを求めることができるとしている。また、エンリッチ要素およびエンリッチ領域の大きさを種々に変えて特異応力場の強さを求め、境界要素法で得られた値と比較し、比較的よく一致することを示している。
　第六章「General conclusions and future works」では、本論文で得られた結果を要約し、二次元弾塑性特異応力場の強さの導出法の妥当性、直接三次元特異応力場の強さを求めることができる新しいエンリッチ要素の有用性を示し、今後の研究課題についても論じている。
　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。