ANALYSIS OF ORDER OF STRESS SINGULARITY AT A VERTEX IN 3D TRANSVERSELY ISOTROPIC PIEZOELECTRIC DISSIMILAR BONDED JOINTS

The order of singularity near the vertex of bonded joints is one of the main factors responsible fordebonding under mechanical or thermal loading. The distribution of stress singularity field near the vertex ofbonded joints is very important to maintain the reliability of intelligent materials. In this paper, order of stresssingularity at vertex in 3D transversely isotropic piezoelectric dissimilar bonded joints is analyzed. Eigenanalysis based on FEM is used for stress singularity field analysis of piezoelectric bonded joints. The eigenequation is used for calculating the order of stress singularity, and the angular function. The numerical resultshows that the angular functions have large value near the interface edge than the inner portion of the joint.Therefore, there is a possibility to debond and delamination may occur at the interface edge of the piezoelectricbonded joints due to the higher stress and electric displacement concentration at the free edge.DOI: http://dx.doi.org/10.3329/jme.v44i1.19490

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Investigation of Order of Singularity in 3D Transversely Isotropic Piezoelectric Bimaterial Joints by FEM

Journal of Circuits System and Computers ◽

10.1142/s0218126615400010 ◽

2014 ◽

Vol 24 (02) ◽

pp. 1540001

Author(s):

Md. Shahidul Islam ◽

Hideo Koguchi

Keyword(s):

Electric Displacement ◽

Stress Singularity ◽

Transversely Isotropic ◽

Field Analysis ◽

Elastic Displacement ◽

Bonded Joints ◽

Eigen Analysis ◽

Piezoelectric Bimaterial ◽

Converse Piezoelectric Effect ◽

Interface Edge

The order of singularity near the vertex of bonded joints is one of the main factors responsible for debonding of electronic device under mechanical or electrical loading. The distribution of singularity field near the vertex of bonded joints is very important to maintain the reliability of smart electronic structure. Piezoelectric material, due to its characteristic direct-converse piezoelectric effect, has naturally received considerable attentions. Piezoelectric materials have been extensively used as transducers and sensors due to their piezoelectric effects that take place between electric fields and mechanical deformation. The order of singularity at a vertex and at a point on singularity line in 3D transversely isotropic piezoelectric joints is analyzed. Eigen analysis based on FEM is used for stress singularity field analysis of piezoelectric bimaterial joints. The eigen equation is used for calculating the order of stress singularity and the angular function of elastic displacement, electric potential, stress and electric displacement. The numerical result shows that the angular functions have large value near the interface edge than the inner portion of the joint. Therefore, there is a possibility to debond and delamination occurs at interface edge of the piezoelectric bimaterial joints, due to the higher stress and electric displacement concentration at the free edge.

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Effect of Thickness in Intermediate Layer on Intensity of Stress Singularity at a Vertex in Three-Dimensional Bonded Joints

Fracture and Damage Mechanics V - Key Engineering Materials ◽

10.4028/0-87849-413-8.883 ◽

2006 ◽

pp. 883-886

Author(s):

Hideo Koguchi

Keyword(s):

Intermediate Layer ◽

Three Dimensional ◽

Stress Singularity ◽

Bonded Joints

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Fundamental solutions of two 3D rectangular semi-permeable cracks in transversely isotropic piezoelectric media based on the non-local theory

Multidiscipline Modeling in Materials and Structures ◽

10.1108/mmms-09-2019-0169 ◽

2020 ◽

Vol 16 (6) ◽

pp. 1497-1520

Author(s):

Haitao Liu ◽

Liang Wang

Keyword(s):

Electric Displacement ◽

Transversely Isotropic ◽

Elastic Behavior ◽

Classical Solutions ◽

Local Theory ◽

Dual Integral Equations ◽

Piezoelectric Media ◽

Content Type ◽

Present Solution ◽

Non Local

PurposeThe paper aims to present the non-local theory solution of two three-dimensional (3D) rectangular semi-permeable cracks in transversely isotropic piezoelectric media under a normal stress loading.Design/methodology/approachThe fracture problem is solved by using the non-local theory, the generalized Almansi's theorem and the Schmidt method. By Fourier transform, this problem is formulated as three pairs of dual integral equations, in which the elastic and electric displacements jump across the crack surfaces. Finally, the non-local stress and the non-local electric displacement fields near the crack edges in piezoelectric media are derived.FindingsDifferent from the classical solutions, the present solution exhibits no stress and electric displacement singularities at the crack edges in piezoelectric media.Originality/valueAccording to the literature survey, the electro-elastic behavior of two 3D rectangular cracks in piezoelectric media under the semi-permeable boundary conditions has not been reported by means of the non-local theory so far.

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Analytical Solutions for Laminated Transversely Isotropic Magnetoelectroelastic Plates

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.634-638.2425 ◽

2013 ◽

Vol 634-638 ◽

pp. 2425-2431

Author(s):

Xiao Chuan Li ◽

Qing Li

Keyword(s):

Symplectic Geometry ◽

Separation Of Variables ◽

Electric Displacement ◽

Transversely Isotropic ◽

Hamiltonian Operator ◽

Hamiltonian Matrix ◽

Operator Matrix ◽

Zero Eigenvalue ◽

Dual Variables ◽

Eigen Solutions

The theory of Hamiltonian system is introduced for the problems of laminated transversely isotropic magnetoelectroelastic plates. The partial differential equations of the magnetoelectroelastic solids are derived corresponding to the Lagrange density function and Legendre’s transformation. These equations are a set of the first-order Hamiltonian equations and expressed with displacements, electric potential and magnetic potential, as well as their dual variables--lengthways stress, electric displacement and magnetic induction in the symplectic geometry space. To obtain the solutions of the equations, the schemes of separation of variables and expansion of eigenvector of Hamiltonian operator matrix in the polar direction are implemented. The homogenous solutions of the equations consist of zero eigen-solutions and nonzero eigen-solutions. All the eigen-solutions of zero eigenvalue are obtained in the symmetric deformation. These solutions give the classical Saint-Venant’s solutions because the Hamiltonian matrix is symplectic. The method is rational, analytical method and does not require any trial functions.

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The Effects of Materials Properties & Angle Junction on Stress Concentration at Interface of Dissimilar Materials

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.383-390.887 ◽

2011 ◽

Vol 383-390 ◽

pp. 887-892

Author(s):

Alireza Fallahi Arezoodar ◽

Ali Baladi

Keyword(s):

Stress Concentration ◽

Stress Distribution ◽

Stress Reduction ◽

Stiffness Matrix ◽

Stress Singularity ◽

Dissimilar Materials ◽

Element Analysis ◽

Materials Properties ◽

Main Factors ◽

Elastic Modules

In dissimilar material joints, failure often occurs along the interface between two materials due to stress singularity. Stress distribution and its concentration depend on materials and geometry of the junction as the stress concentration depends on grain orientation and its stiffness matrix of neighboring grains in micro-scale. Inhomogenity of stress distribution at the interface of junction of two materials with different elastic modules and stress concentration in this zone are the main factors resulting in rupture of the junction. Effect of materials properties, thickness, and joining angle at the interface of aluminum-polycarbonate will be discussed in this paper. Computer simulation and finite element analysis by ABAQUS showed that convex interfacial joint leads to stress reduction at junction corners in compare with straight joint. This finding is confirmed by photoelastic experimental results.

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