氏名　傅　列東
学位の種類　博士（工学）
学位記番号　博甲第305号
学位授与の日付　平成16年3月25日
学位論文題目　Study on elasto-plastic interface mechanics and its applications （弾塑性界面力学及びその応用に関する研究）
論文審査委員
　主査　教授　武藤　睦冶
　副査　教授　長井　正嗣
　副査　教授　古口　日出男
　副査　助教授　井原　郁夫
　副査　上海交通大学　教授　許　金泉

• 論文目次
• 論文要旨

［平成15（2003）年度博士論文題名一覧］ ［博士論文題名一覧］に戻る．

Contens

Abstract
Contents

Chapter1 Introduction　p.1
1.1 Back of interface mechanics　p.1
1.2 Interface model and conditions of continuity at interface　p.2
1.3 Dunders'parameters　p.3
1.4 Elastic singular stress field of the interface edge　p.4
1.5 Dvelopment of interface mechancis　p.6
1.6 Scope and constitution of this thesis　p.7

Chapter2 Two dimensional elasto-plastic BEM program　p.9
2.1 Introduction　p.9
2.2 Intergral equations and analysis procedure　p.9
2.3 Methods for sinular integrals　p.13
2.4 Improving of the inerating effciency　p.14
2.5 Analysis example　p.14

Chapter3 Elasto-plastic analysis of bonded linear hardening materials　p.16
3.1 Introduction　p.16
3.2 Theoretiacl solution of the elasto-plastic singular stress field of interface edge　p.17
3.3 Elasto-plastic BEM analysis on the stress near feild the interface edge　p.19
3.4 Conclusions　p.26

Chapter4 Elasto-plastic analysis of bonded power law hardening materials　p.27
4.1 Introduction　p.27
4.2 Theoretiacl solution of the singular stress field of the interface edge　p.27
4.3 FEM analysis of the stress near feild the interface edge　p.40
4.4 Conclusions　p.46

Chapter5 Elasto-plastic analysis and strength evaluation of Si3N4/S45C joint　p.47
5.1 Introduction　p.47
5.2 FEM analysis of the residual stress of Si3N4/S45C joint with a copper interlayer　p.48
5.3 Evaluation of the fracture toughness of Si3N4/S45C joint　p.55
5.4 Evaluation of the strength of orthogonal Si3N4/S45C joint　p.63
5.5 Conclusions　p.68

Chapter6 Fundamental solution of concentrated force on the surface of coating material　p.70
6.1 Introduction　p.70
6.2 Solution of plane problem　p.71
6.3 Solution of three dimensional normal force　p.80
6.4 Solution of three dimensional tangential force　p.85
6.5 Numerical examination and discussion of three dimensional problem　p.92
6.6 Conclutions　p.97

Chapter7 Summary　p.99

Feferences　p.102

Acknowledgements

Due to the mismatch of the material properties of the composing materials, the bonded dissimilar materials have some unique mechanical behaviors, such as the stress singularity at the interface edge and the thermal residual stress. These behaviors severely degraded the strength of bonded dissimilar materials and make the strength evaluation difficult. Understanding of the mechanical behavior is substantial for the evaluation and improving of the strength of bonded dissimilar materials.
In the present study, the elasto-plastic analyses were carried out for stress field near the interface edge.
The theoretical solutions of the elasto-plastic singular stress fields of the interface edge were analyzed and the details of the stress field near the interface edge were investigated by BEM and FEM.
For linear hardening materials, it is found that the elasto-plastic singular stress field of the interface edge is substantially the same as that of elastic material whose Young's modulus and Poisson's ratio are and , respectively. For bonded materials composed of an elastic material and a linear hardening material, the singular stress field near the interface edge can be well approximated by the elastic singular stress field with the Dunders' parameters of , for plane strain problem and , for plane stress problem. The thermal residual stress of cylindrical Si3N4/S45C joint with a copper interlayer was analyzed with S45C and copper assumed as the linear hardening materials. It is found that the stress intensity factor of the elasto-plastic singular stress field has a minimum value when interlayer thickness is about 1/8 of the radius.
For bonded materials composed of two power law hardening materials with different hardening exponent, it is found that the stress singularity of the interface edge depends only on the bonding angle and the hardening exponent of the material with higher hardening exponent. The stress singularity increases with an increase of the bonding angle as well as a decrease of the hardening exponent. For plane strain problem, stress singularity will disappear when the bonding angle becomes less than 45o, while two different singularities will appear when the bonding angle becomes larger than 135o. For plane stress problem, the stress singularity will disappear when the bonding angle becomes less than 54.7o, while two different stress singularities will appear when the bonding angle becomes larger than 125.7o.
Fracture toughness tests were carried out on Si3N4/S45C joint specimens with interface cracks of different lengths. Due to the effect of the residual stress, the specimen with a crack length of 4mm has higher apparent fracture toughness than those with crack lengths of 1mm and 2mm. A crack propagated into Si3N4 directly from the initial crack tip in the direction of 40o for crack lengths of 1mm and 2mm, while it propagated along the interface for the crack length of 4mm. Evaluation of the fracture path and fracture toughness was carried out based on the elasto-plastic analysis in which S45C was assumed as a linear hardening material. It is found that the maximum criterion based on the elasto-plastic singular stress field could be successfully applied for evaluating the fracture path and fracture toughness value. The value due to the residual stress decreases in the sequence of a=2.0mm, a=1.0mm and a=4.0mm. This is the same sequence of fracture loads of the specimens with a=2.0mm, a=1.0mm, a=4.0mm. The applied stress results in a decrease of the value of . The decrease of for a=4.0mm is significant and the value of for a=4.0mm is much smaller than those for a=1.0mm and a=2.0mm. This agrees with the experimental result that the specimens with a=1.0mm and a=2.0mm fractured with an angle of about 40o to the interface, while the specimens with a=4.0mm fractured along the interface. The values at the fracture of specimens are almost the same regardless of the crack length and were close to the value of Si3N4. Evaluation of the strength of orthogonal Si3N4/S45C joint was also carried out. It is found that it's possible to evaluate the strength of orthogonal dissimilar material involving the thermal residual stress with the stress intensity factor of the elasto-plastic singular stress field although it is impossible to evaluate the strength with elastic stress intensity factor only.
As a numerical analyzing tool for bonded dissimilar materials, a two dimensional elasto-plastic BEM program was developed.
Besides, the fundamental solution of concentrated force on the surface of coating material was derived. Considering of the geometric and loading conditions, the problem was divided into plane problem, three dimensional normal force problem and three dimensional tangential force problem. The corresponding solutions were derived independently.