Interfacial Edge Crack Research Articles

Analysis of composite finite wedges under anti-plane shear

Problems of composite finite wedges under anti-plane shear applied on a circular arc are analyzed in this study. The considered conditions of radial edges are free–free, free–fixed, and fixed–fixed. A procedure that uses the finite Mellin transform and the Laplace transform is developed to solve these problems. Explicit solutions for displacement and stress fields are derived. Stress intensity factors (SIFs) of composite circular shafts with an interfacial edge crack are extracted from the derived stress fields, and the distributions for various loading angles are presented and discussed. It was found that if the loading angles are the same, free–free and fixed–fixed edge problems can be degenerated into single material problems. Uniform stresses were found along the interface in free–free and fixed–fixed edge problems. Solutions of a general loading case deduced from the derived results compare well with those obtained from finite element (FE) analyses.

Stress intensity factors for an interface crack between an epoxy and aluminium composite plate

A cracked composite specimen, comprised of an epoxy and an aluminium plate, was fractured under a tensile load. In this paper, two crack configurations were investigated. The first was an artificial center crack positioned in the epoxy plate parallel to the material interface. The other was for two edge cracks in the epoxy plate, again, parallel to the interface. A tensile test was carried out by gradually increasing the applied load and it was verified that the cracks always moved suddenly in an outward direction from the interface. The d/a ratio was gradually reduced to zero, and it was confirmed that the maximum stress intensity factor value for the artificial center crack, <TEX>$K_{{\theta}{\theta}}^{max}$</TEX>, approached that of an artificial interface crack,<TEX>$K_{{\theta}{\theta}}^{ifc\;max}$</TEX> (where: 2a is the crack length and d is the offset between the crack and interface). The same phenomenon was also verified for the edge cracks. Specifically, when the offset, d, was reduced to zero, the maximum stress intensity factor value, <TEX>$K_{{\theta}{\theta}}^{max}$</TEX>, approached that of an artificial interface edge crack.

Impact of Thermal, Moisture, and Mechanical Loading Conditions on Interfacial Fracture Toughness of Adhesively Bonded Joints

Interfacial delamination is a common failure mode in multilayered IC packages. In this paper, an experimental technique using Brazil-nut specimens is employed to determine the interfacial fracture toughness of an adhesively sandwiched joint with the introduction of edge interfacial crack. The design of experiments (DOE) is applied to study variations in strain rates and the thickness of the sandwich structure. In addition, the effects of moisture content and temperature on the interfacial adhesion are investigated. For the DOEs conducted, as the loading angle increases from 20° to 90°, the interfacial fracture toughness decreases. The fracture toughness and its corresponding mode mixity are determined from the measured critical load by finite element modeling computation.

Analysis of Interface Crack in Polymer Liner Subjected to Hygrothermal Stress

Polymeric materials such as epoxy are widely used as coating layers for the containment building of the nuclear power plant. These layers may be damaged through a hygrothermal process and residual stresses can reach significant levels near the free edges, possibly leading to interface debonding or delamination. Interfacial stress singularities induced in a laminate model consisting of the epoxy coating layer and the concrete substrate is investigated using the time-domain boundary element method. The epoxy layer is assumed to be a linear viscoelastic material and moisture effects are assumed to be analogous to thermal effects. The overall stress intensity factor for the case of a small interfacial edge crack of length a has been computed.

Hybrid Special Finite Element Method for Bi-Material Crack

In the paper, two novel 2-D hybrid special finite elements each containing an interfacial edge crack, which lies along or vertical to the interface between two materials, are developed. These proposed elements can assure the high precision especially in the vicinity of crack tip and provide a better description of its singularity with only one hybrid element surrounding one interfacial crack, thus, the numerical modeling of fracture analysis on bi-material crack can be greatly simplified. Numerical examples are provided to demonstrate the validity and versatility of the proposed method.

Boundary Element Analysis of an Interface Crack in a Bonded Viscoelastic Thin Film

Interfacial stress singularities induced in a laminate model consisting of the viscoelastic thin film and the elastic substrate have been investigated using the time-domain boundary element method. First, the interfacial singular stresses between the viscoelastic thin film and the elastic substrate subjected to a uniform moisture ingression have been investigated near the free surface, but without any edge crack. The thin film is assumed to be a linear viscoelastic material and moisture effects are assumed to be analogous to thermal effects. Then, the overall stress intensity factor for the case of a small interfacial edge crack of length a has been computed. The numerical procedure does not permit calculation of the limiting case for which the edge crack length vanishes.

Determination of interface fracture toughness of adhesive joint subjected to mixed-mode loading using finite element method

In this study, a compact mixed-mode (CMM) specimen, which comprises an adhesive joint and a loading fixture, is employed to determine interface fracture toughness of an adhesively sandwiched joint with an interface edge crack subjected to global mixed-mode loading. An interface mechanics-based finite element (FE) method is developed to simulate the stress and displacement distributions around the tip of an interface edge crack situated in the sandwiched joint. A small region crack-tip opening displacement (CTOD)-based linear extrapolation method is developed to determine stress intensity factors (SIFs) at the crack-tip. Effect of pre-crack length on the SIFs is studied and a length range of pre-crack is proposed for the determination of SIFs. Furthermore, these methodologies are applied to characterize the critical interface fracture toughness of the sandwiched joint. Three types of fracture criteria, i.e., modes I and II critical fracture toughness-based failure assessment diagram (FAD), effective critical fracture toughness-based failure assessment criterion (FAC), and strain energy release rate-based FAC, are established for the reliability design and failure assessment of the adhesively bonded sandwich joint.

Some problems in the antiplane shear deformation of bi-material wedges

The antiplane shear deformation of a bi-material wedge with finite radius is studied in this paper. Depending upon the boundary condition prescribed on the circular segment of the wedge, traction or displacement, two problems are analyzed. In each problem two different cases of boundary conditions on the radial edges of the composite wedge are considered. The radial boundary data are: traction–displacement and traction–traction. The solution of governing differential equations is accomplished by means of finite Mellin transforms. The closed form solutions are obtained for displacement and stress fields in the entire domain. The geometric singularities of stress fields are observed to be dependent on material property, in general. However, in the special case of equal apex angles in the traction–traction problem, this dependency ceases to exist and the geometric singularity shows dependency only upon the apex angle. A result which is in agreement with that cited in the literature for bi-material wedges with infinite radii. In part II of the paper, Antiplane shear deformation of bi-material circular media containing an interfacial edge crack is considered. As a special case of bi-material wedges studied in part I of the paper, explicit expressions are derived for the stress intensity factor at the tip of an edge crack lying at the interface of the bi-material media. It is seen that in general, the stress intensity factor is a function of material property. However, in special cases of traction–traction problem, i.e., similar materials and also equal apex angles, the stress intensity factor becomes independent of material property and the result coincides with the results in the literature.

Interaction of a screw dislocation with an interfacial edge crack in a two-phase piezoelectric material

The interaction of a screw dislocation with an interfacial edge crack in a two-phase piezoelectric medium is investigated. Closed-form solutions of the elastic and electrical fields induced by the screw dislocation are derived using the conformal mapping method in conjunction with the image principle. Based on the electroelastic fields derived, the stress and electric displacement intensity factors, the image force acting on the dislocation are given explicitly. We find that the stress and electric displacement intensity factors depend on the effective electroelastic material constants. In the case where one of two phases is purely elastic, the stress intensity factor and image force are plotted to illustrate the influences of electromechanical coupling effect, the position of the dislocation and the material properties on the interaction mechanism.

Comparison of energy release rate and minimum strain energy density for potential failure of composite with bi-material interface

An analytical method is developed to describe the fields of stress and displacement in a bi-material strip specimen with an edge interfacial crack. All of the basic governing equations, boundary conditions on crack surfaces and conditions of continuity along the interface are satisfied by the eigenfunction expansion method. The other boundary conditions are satisfied by the generalized variational principle. The stress intensity factors are calculated for determining the energy release rate and minimum strain energy density factor S min that is used the strain energy density criterion. Problems with oscillatory singularity and contact zone are discussed. Not only the effects of bi-material modulus ratio, thickness ratio, Poisson's ratio and crack length to S min, but also the influences of bi-material modulus ratio, thickness ratio to phase angle are presented. Among these parameters, particular situations where S min become jeopardously high and lead to failure are discussed.

Mode III Interfacial Edge Crack in a Magnetoelectroelastic Bimaterial

This paper deals with a Mode III interfacial edge crack in a magnetoelectroelastic bimaterial subjected to line singularities such as an out-of-plane line force, a line electric charge, a line magnetic charge and a straight screw dislocation. The surfaces (including crack surfaces) of the bimateral are assumed to be electrically open and magnetically closed. The closed-form analytical solution to the problem is obtained by employing the complex variable approach in conjunction with the conformal mapping technique. The intensity factors of stress, electric displacement and magnetic induction are given explicitly. The obtained results can be used as the Green's function to solve more complicated problems.

Relation between Stress Intensity Factor of a Small Edge Interface Crack and Intensity of Free-Edge Stress Singularity of Bonded Dissimilar Materials

When two materials are bonded, the free-edge stress singularity usually develops near the intersection of the interface and the free-surface. Fracture in bonded dissimilar materials may therefore occur from an interface crack which develops at the intersection of interface and free-surface. Free-edge stress singularity is very important in the evaluation of strength of bonded dissimilar materials. In this study, the relationship between the stress intensity factor of a small edge crack on interface of bonded dissimilar materials and the intensity of free-edge stress singularity of bonded dissimilar materials with no crack under external mechanical loading was investigated numerically by using the boundary element method. The relationship was also investigated theoretically by using the principle of superposition. The results of numerical analyses were compared with those of theoretical analyses. It was found that stress intensity factors of small edge crack on interface K1 and K2 were proportional to the intensity of free-edge stress singularity of bonded dissimilar materials Kσ without crack irrespective of the combination of materials. The numerically determined proportional coefficient between K1 and Kσ agreed well with the theoretical one, and was not affected by crack length when proper normalizations were applied. From these results, it is suggested that stress intensity factor of small edge crack on interface can be used as a strength criterion of interface of bonded dissimilar materials.

Anti-Plane Interface Edge Crack between Two Dissimilar Piezoelectric Blocks

The problem of an interface edge crack between two dissimilar piezoelectric materials is analyzed under the conditions of anti-plane shear and in-plane electrical loading. The crack is considered to be traction-free, but electric permeable one across which the normal component of the electric displacement are continuous. A series form of electromechanical solution and field intensity factors are obtained. The results show that all fields including strain, stress, electric field strength and electric displacement are singular in the front of crack tip. At last, the stress intensity factor is solved by the boundary collocation method (BCM), numerical results are given and discussed.

Investigation and Minimization of Underfill Delamination in Flip Chip Packages

A generalized plane strain condition is assumed for an edge interfacial crack between die passivation and underfill on an organic substrate flip chip package. C4 solder bumps are explicitly modeled. Temperature excursions are treated as loading conditions. The design factors studied include underfill elastic modulus, underfill coefficient of thermal expansion (CTE), fillet height, and die overhang. Varying underfill modulus and CTE produces a different stress field at underfill/die passivation interface, different stress intensity factor (SIF), and phase angle (/spl psi/) even under the same loading condition. The baseline case uses underfill with elastic modulus of 6 GPa, CTE of 36 ppm//spl deg/C and fillet height equal to half die thickness. Four more cases involving underfill material properties are investigated by varying elastic modulus between 3 and 9 GPa, and by varying CTE between 26 and 46 ppm//spl deg/C. The effect of fillet height is also studied by assuming no fillet and full fillet, i.e., fillet height equal to die thickness. Finally, two cases concerning the influence of die overhang, defined as the nominal distance between outermost solder joint and die edge, are investigated. Fracture parameters, including energy release rate (G) and phase angle (/spl psi/), are evaluated as a function of dimensions. Underfill material properties (elastic modulus and CTE), fillet configuration, and die overhang can be optimized to reduce the risk of underfill delamination in flip chip or direct chip attach (DCA) applications.

Effect of Shape of Bonded Dissimilar Materials on Stress Intensity Factor of Small Edge Interface Crack

Effect of Shape of Bonded Dissimilar Materials on Stress Intensity Factor of Small Edge Interface Crack

Mode III stress intensity factors for edge-cracked circular shafts, bonded wedges, bonded half planes and DCB’s

Antiplane shear deformation of several edge-cracked geometries is considered. Analytical expressions are derived for the mode III stress intensity factor (SIF) of circular shafts with edge cracks, bonded half planes containing an interfacial edge crack, bonded wedges with an interfacial edge crack and also DCB’s. The results are extracted for simple isotropic materials as well as anisotropic materials and also bonded dissimilar materials and it is shown that the same expressions are obtained for the SIF under the same geometries but with different above-mentioned material properties. Different boundary conditions are assumed and the SIF relations are derived in each case. As the special cases, the SIF’s of the two bonded quarter planes containing an edge crack at the interface and infinite strip with a semi-infinite edge crack are extracted which coincide with the results cited in the literature.

Interfacial edge crack between two bonded dissimilar orthotropic strips under antiplane point loading

AbstractA closed‐form solution is obtained for the interfacial edge crack between two bonded dissimilar orthotropic strips loaded by antiplane point loading in form of screw dislocation or line force. Conformal mapping and existing dislocation solutions are utilized for constructing the fundamental solution of the problem. The stress intensity factor (SIF) and the energy release rate (ERR) are obtained explicitly.

Energy Release Rate of Functionally Graded Materials with Interface Edge-Cracks under Uniform Temperature Change

Energy Release Rate of Functionally Graded Materials with Interface Edge-Cracks under Uniform Temperature Change

A maximum allowable flaw size for debond-resistant bimaterial layers

Free-edge debonding and subsequent interface crack extension are common modes of failure in a variety of engineering applications in which bonded layers of dissimilar materials are subject to differential expansion stresses. In this study, the susceptibility to debonding of short interface edge cracks is investigated for the global plane elasticity problem of a bimaterial strip with a uniform edge load applied to the top layer (a general model of differential expansion). The goal of this study is to determine the maximum crack length L for which interface crack extension is inhibited, or more specifically, for which the singular interface normal stresses are compressive. This is equivalent to a maximum allowable flaw size, which is of interest to both designers and inspectors of bimaterial systems. The critical crack length L has been extracted from parametric finite element analyses over a wide range of bimaterial configurations using the commercial software package ABAQUS. Results indicate that the critical crack length L increases with both the relative stiffness and thickness of the contracting layer, and may represent a significant inspectable flaw size for a variety of practical bimaterial configurations.

Closed-form solution for a mode-III interfacial edge crack between two bonded dissimilar elastic strips

A closed-form solution is obtained for the problem of a mode-III interfacial edge crack between two bonded semi-infinite dissimilar elastic strips. A general out-of-plane displacement potential for the crack interacting with a screw dislocation or a line force is constructed using conformal mapping technique and existing dislocation solutions. Based on this displacement potential, the stress intensity factor (SIF, K III) and the energy release rate (ERR, G III) for the interfacial edge crack are obtained explicitly. It is shown that, in the limiting special cases, the obtained results coincide with the results available in the literature. The present solution can be used as the Green’s function to analyze interfacial edge cracks subjected to arbitrary anti-plane loadings. As an example, a formula is derived correcting the beam theory used in evaluation of SIF ( K III) and ERR ( G III) of bimaterials in the double cantilever beam (DCB) test configuration.