Some Phenomena of Cracks Perpendicular to an Interface Between Dissimilar Orthotropic Materials

1996 ◽  
Vol 63 (1) ◽  
pp. 190-203 ◽  
Author(s):  
J. C. Sung ◽  
J. Y. Liou ◽  
Y. Y. Lin
Keyword(s):  
Stress Intensity ◽  
Characteristic Equation ◽  
Stress Intensity Factors ◽  
Dissimilar Materials ◽  
Singular Integral Equations ◽  
Kernel Functions ◽  
Orthotropic Materials ◽  
Intensity Factors ◽  
Present Context ◽  
Real Forms

The problem of two aligned orthotropic materials bonded perfectly along the interface with cracks embedded in either one or both of the materials while their directions being perpendicular to the interface is considered. A system of singular integral equations for general anisotropic materials is derived. Employing four effective material parameters proposed by Krenk and introducing four generalized Dundurs’ constants, the kernel functions appearing in the integrals are converted into real forms for the present problem which are keys to the present study. The kernel functions for isotropic dissimilar materials can be deduced from the present results directly, no any limiting process is needed. These kernel functions are then employed to investigate the singular behaviors for stresses at the point on the interface. Characteristic equation which determines the power of singularity for stresses is given in real forms for the case of cracks that are going through the interface. Studies of the characteristic equation reveal that the singular nature for the stresses could vanish for some material combinations and the singular nature for the stresses is found to be independent of the replacement of the material parameter Δ by Δ-1. The kernel functions developed are further used to explore analytically some interesting phenomena for the stress intensity factors, which are discussed in detail in the present context. Some numerical results for the stress intensity factors for a typical dissimilar materials are also given.

Analysis of a Crack Embedded in a Linear Elastic Half-Plane Solid

1995 ◽  
Vol 62 (1) ◽  
pp. 78-86 ◽  
Author(s):  
J. C. Sung ◽  
J. Y. Liou
Keyword(s):  
Stress Intensity ◽  
Half Plane ◽  
Singular Integral ◽  
Stress Intensity Factors ◽  
Orthotropic Material ◽  
Singular Integral Equations ◽  
Kernel Functions ◽  
Intensity Factors ◽  
Material Parameters ◽  
Linear Elastic

A crack embedded in a half-plane solid traction-free on the infinite straight boundary is analyzed. The response of the material is linear elastic. A system of singular integral equations for the unknown dislocation densities defined on the crack faces is derived. These equations are then specialized to the problem of a crack located arbitrarily in an orthotropic material which are found to depend on two material parameters only. For a crack oriented either perpendicular or parallel to the infinite straight boundary, the kernel functions appearing in the singular integral equations are obtained in real form which are valid for arbitrary alignment of the orthotropic material. Furthermore, these kernel functions are found to be valid even for degenerate materials and can directly lead to those kernel functions for isotropic materials. Numerical results have been carried out for horizontal or vertical crack problems to elucidate the effect of material parameters on the stress intensity factors. The effect of the alignment of the material on the stress intensity factors is also presented for degenerate materials.

scholarly journals Two interfacial collinear Griffith cracks in thermo-elastic composite media

2018 ◽  
Vol 22 (1 Part B) ◽  
pp. 423-433 ◽  
Author(s):  
Prashant Mishra ◽  
Subir Das
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Singular Integral Equations ◽  
Orthotropic Materials ◽  
Intensity Factors ◽  
Temperature Coefficients ◽  
Interfacial Cracks ◽  
Steady State Temperature ◽  
Elastic Composite ◽  
Physical Quantities

The objective of the article is to find the stress intensity factors and crack energy for a pair of collinear Griffith cracks situated at the interface of the two orthotropic materials under steady-state temperature field. The problem is reduced to a pair of singular integral equations, which are solved using Jacobi?s polynomials. Numerical computations are carried out for two different pairs of orthotropic materials for different particular cases, which are depicted through figures. The effect of material constants and temperature coefficients on the behavior of physical quantities viz., stress intensity factors and crack energy of the interfacial cracks is the key feature of the present article.

Analysis of Branched Interface Cracks Between Dissimilar Anisotropic Media

1989 ◽  
Vol 56 (4) ◽  
pp. 844-849 ◽  
Author(s):  
G. R. Miller ◽  
W. L. Stock
Keyword(s):  
Stress Intensity ◽  
Singular Integral ◽  
Stress Intensity Factors ◽  
Crack Problem ◽  
Singular Integral Equations ◽  
Crack Branching ◽  
Intensity Factors ◽  
Function Solution ◽  
Special Cases ◽  
Branch Crack

A solution is presented for the problem of a crack branching off the interface between two dissimilar anisotropic materials. A Green’s function solution is developed using the complex potentials of Lekhnitskii (1981) allowing the branched crack problem to be expressed in terms of coupled singular integral equations. Numerical results for the stress intensity factors at the branch crack tip are presented for some special cases, including the no-interface case which is compared to the isotropic no-interface results of Lo (1978).

Reliability Evaluation of Flip Chip Using Stress Intensity Factors of an Interface Crack

2003 ◽  
Author(s):  
Won-Keun Kim ◽  
Toru Ikeda ◽  
Noriyuki Miyazaki
Keyword(s):  
Stress Intensity ◽  
Interface Crack ◽  
Stress Intensity Factors ◽  
Flip Chip ◽  
Liquid Crystal Display ◽  
Dissimilar Materials ◽  
Circuit Board ◽  
Electrical Performance ◽  
Intensity Factors ◽  
Adhesive Film

Anisotropic Conductive Adhesive Film (ACF) has been used for electronic assemblies such as the connection between a Liquid Crystal Display (LCD) panel and a flexible print circuit board (FPC). ACF is expected to be a key technology for flip chip packaging and chip size packaging. The goal of our work is to provide an optimum design scheme to achieve the best combination of electrical performance and mechanical reliability for electronic packages using the ACF. This study presents an evaluation technology for the delamination of the ACF connections. We utilized the stress intensity factors of an interface crack between jointed dissimilar materials. The evaluation technology presented herein was found to provide reliability of an electronic package using the ACF connection during the solder reflow process.

The Effect of Transverse Shear in a Cracked Plate Under Skew-Symmetric Loading

1979 ◽  
Vol 46 (3) ◽  
pp. 618-624 ◽  
Author(s):  
F. Delate ◽  
F. Erdogan
Keyword(s):  
Stress Intensity ◽  
Transverse Shear ◽  
Stress Intensity Factors ◽  
Orthotropic Materials ◽  
Shear Load ◽  
Intensity Factors ◽  
Mode Iii ◽  
Shear Loads ◽  
Elasticity Solutions ◽  
Symmetric Loading

The problem of an elastic plate containing a through crack and subjected to twisting moments or transverse shear loads is considered. By using a bending theory which allows the satisfaction of the boundary conditions on the crack surface regarding the normal and the twisting moments and the transverse shear load separately, it is found that the resulting asymptotic stress field around the crack tip becomes identical to that given by the elasticity solutions of the plane strain and antiplane shear problems. The problem is solved for uniformly distributed or concentrated twisting moment or transverse shear load and the normalized Mode II and Mode III stress-intensity factors are tabulated. The results also include the effect of the Poisson’s ratio and material orthotropy for specially orthotropic materials on the stress-intensity factors.

scholarly journals Crack Paralleling an Interface Between Dissimilar Materials

1987 ◽  
Vol 54 (4) ◽  
pp. 828-832 ◽  
Author(s):  
J. W. Hutchinson ◽  
M. E. Mear ◽  
J. R. Rice
Keyword(s):  
Stress Intensity ◽  
Interface Crack ◽  
Stress Intensity Factors ◽  
Dissimilar Materials ◽  
Complex Stress ◽  
External Loading ◽  
Universal Relation ◽  
Intensity Factors ◽  
Elastic Solids ◽  
Complex Stress Intensity Factor

A crack paralleling a bonded plane interface between two dissimilar isotropic elastic solids is considered. When the distance of the crack from the interface is small compared to the crack length itself and to other length scales characterizing the geometry, a simple universal relation exists between the Mode I and Mode II stress intensity factors and the complex stress intensity factor associated with the corresponding problem for the crack lying on the interface. In other words, if the influence of external loading and geometry on the interface crack is known, then this information can immediately be used to generate the stress intensity factors for the sub-interface crack. Conditions for cracks to propagate near and parallel to, but not along, an interface are derived.

Stress Intensity Factor Analysis of an Interfacial Corner Between Piezoelectric Bimaterials in a Two Dimensional Structure Using the H-Integral Method

2011 ◽  
Author(s):  
Toru Ikeda ◽  
Hiroshi Hirai ◽  
Mitsutoshi Abe ◽  
Masatsugu Chiba ◽  
Noriyuki Miyazaki
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Piezoelectric Materials ◽  
Dissimilar Materials ◽  
Anisotropic Materials ◽  
Stroh Formalism ◽  
Asymptotic Solutions ◽  
Dimensional Structure ◽  
Electronic Packages ◽  
Intensity Factors

A corner of bonded dissimilar materials is one of the main causes of the failure of electronic packages or MEMS structures. These materials are sometimes anisotropic materials and piezoelectric materials. To evaluate the integrity of a corner of bonded piezoelectric materials is useful for the reliability of electronic packages and MEMS. Asymptotic solutions around the interfacial corner between piezoelectric bimaterials can be obtained by the combination of the Stroh formalism and the Williams eigenfunction expansion method. Based on an extension of the Stroh formalism and the H-integral derived from Betti’s reciprocal principle for piezoelectric problems, we analyzed the stress intensity factors (SIFs) and asymptotic solutions of piezoelectric bimaterials. The eigenvalues and eigenvectors of an interfacial corner between dissimilar piezoelectric anisotropic materials are determined using the key matrix. The H-integral for piezoelectric problems is introduced to obtain the scalar coefficients, which are related to the SIFs. We propose a new definition of the SIFs of an interfacial corner for piezoelectric materials, and we demonstrated the accuracy of the SIFs by comparing the asymptotic solutions with the results obtained by the finite element method (FEM) with very fine meshes. Proposed method can analyze the stress intensity factors of a corner and a crack between dissimilar isotropic materials, anisotropic materials and anisotropic piezoelectric materials.

Asymptotic Field Near the Tip of a Debonded Anticrack in an Anisotropic Elastic Material

2020 ◽  
Vol 73 (1) ◽  
pp. 76-83
Author(s):  
Xu Wang ◽  
Peter Schiavone
Keyword(s):  
Stress Intensity ◽  
Elastic Material ◽  
Stress Intensity Factors ◽  
Orthotropic Materials ◽  
Intensity Factors ◽  
Power Type ◽  
Material Force ◽  
Real Power ◽  
Anisotropic Elastic ◽  
Anisotropic Elastic Material

Summary We use the sextic Stroh formalism to study the asymptotic elastic field near the tip of a debonded anticrack in a generally anisotropic elastic material under generalised plane strain deformations. The stresses near the tip of the debonded anticrack exhibit the oscillatory singularities $r^{-3/4\pm i\varepsilon }$ and $r^{-1/4\pm i\varepsilon }$ (where $\varepsilon $ is the oscillatory index) as well as the real power-type singularities $r^{-3/4}$ and $r^{-1/4}$. Two complex-valued stress intensity factors and two real-valued stress intensity factors are introduced to respectively scale the two oscillatory and two real power-type singularities. The corresponding three-dimensional analytic vector function is derived explicitly, and the material force on the debonded anticrack is obtained. Our solution is illustrated using an example involving orthotropic materials.

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