（様式３）
論文の内容の要旨
氏

名 Md. Shahidul Islam

Analysis of 3D Intensity of Singular Stress Fields in Two-phase Transversely Isotropic
Piezoelectric Bonded Joints(２相横等方性ピエゾ接合体における３次元特異応力場の強さに対する解析)

In recent years, intelligent or smart structures and systems have drawn more and moreattention. Piezoelectric materials are playing a key role as active components in many fields ofengineering and technology. Mechanical stress occurs in piezoelectric material for any electric
input. The stress concentrations caused by mechanical or electric loads may lead to crack
initiation and extension, and sometimes the stress concentrations may be high enough to debond
the material parts. Reliable service lifetime predictions of piezoelectric components demand acomplete understanding of the debonding processes of these materials. When two materials arejoined, a free-edge stress singularity usually develops at the intersection of the interface and thefree surface. The stress singularity fields are one of the main factors responsible for debonding
under mechanical or thermal loading. Stress singularity frequently occurs at a vertex in aninterface of joints due to a discontinuity of materials. Stress singularity is related to debonding
and delamination at interface of the bonded joints. Different numerical methods have developed
for determining the singularity field in a 3D dissimilar material joint. Several studies haveinvestigated the stress singularity field in 3D elastic materials. Recently, some researcher
proposed the solution of singular stress field and its stress intensity factors of an interfacial
corner of a 2D dissimilar piezoelectric material joint with crack. However, the singularity at avertex in 3D transversely isotropic piezoelectric dissimilar material joints has not been madeclear until now. In this study, the intensity of singularity at a vertex is investigated intransversely isotropic piezoelectric dissimilar material joints.
The orders of singularity at a vertex and at a point on singularity lines for piezoelectricbonded joints are determined using eigenanalysis based on FEM. Solving eigenequation yields
many roots p and eigenvectors corresponding to each eigenvalue are obtained. However, if theroot p is within the range of 0 < p < 1, this fact indicates that the stress field has singularity. In
the present analysis, the effect of material constants on the order of stress singularity is alsoexamined. The angular functions of elastic displacement, electric potential, stress and electric
displacement are calculated with the help of eigenanalysis. The numerical result shown that theangular functions of stress and electric displacement are larger at the free edge of the joints. The

orders of stress singularity for two cases of isotropic piezoelectric material are also calculated.
One case is an isotropic piezoelectric joint with piezo-effect and the other is that without
piezo-effect. The largest value of vertex decreases in the isotropic joints.
The stress and electric displacement distributions on an interface in two-phase transversely
isotropic piezoelectric dissimilar material joints are investigated using BEM. The distributions ofstress and electric displacement with respect to radial distance, r and angle,  are plotted. The
stress and electric displacement have a larger value at the vertex and near the free edge of thejoint. Therefore, there is a possibility to debond and delamination at the corner and the interface
edge of the bonded joints. The intensities of singularity are calculated by fitting the stress andelectric displacement curves with the help of the result of eigenanalysis at the vertex. The
intensities of singularity for stress and electric displacement are calculated by varying thematerial thickness in joints. It is shown from numerical result that the intensity of stresssingularity increases with the thickness of upper material and the intensity of electric
displacement singularity decreases with the thickness. The intensities of singularity for stress andelectric displacement can be reduced significantly by varying the elastic and piezoelectricconstants.
Finally, three-dimensional intensities of singularity for stress and electric displacement aredetermined. The 3D intensities of singularity are calculated using different boundary conditions
and material combinations. It is shown from the present analysis that the 3D intensity of stresssingularity increases and the 3D intensity of electric displacement singularity decreases with theincrease of material thickness. Also the 3D intensities of singularity for stress and electric
displacement are opposite to each other. It is observed from the present analysis that the value of3D
3D
K13D
 is larger than the value of K1r and K1 . It is also found in the present analysis that the3D
3D
ratio of K1r3D and K13D
 , and the ratio of K1 and K1 with respect to the material thickness injoints are nearly constant. This analysis reveals that the effect of the intensity of singularity at a3D vertex for electric displacement on a thin material joint is larger than that of the thickmaterial. Therefore, there is a highest possibility to debond and delamination at the corner of thintransversely isotropic piezoelectric bonded joints. It is also observed from the present analysis
that the variations of material constants affect the intensities of singularity for stress and electric
displacement more significantly.