Three-dimensional Interface Crack Research Articles

The Multi-Virtual Crack Closure Technique for three-dimensional interface crack problems

The Virtual Crack Closure Technique (VCCT) is a simple method that was found in the past to produce good results for determining stress intensity factors of cracks in homogeneous bodies and poor results for interface cracks. In recent papers, the VCCT was found to produce excellent results for two-dimensional interface cracks where many elements were used in the virtual crack extension (VCE). This approach is called here the Multi-VCCT. A criterion for the optimal number of elements used in the VCE was also found. Here, the M-VCCT is extended to three-dimensional interface crack problems. Results for three-dimensional problems containing a straight through finite length interface crack and a penny-shaped interface crack are presented. The interfaces include that between two homogeneous and isotropic dissimilar materials, as well as two transversely isotropic materials.

Some Aspects of the Three-Dimensional Interface Cracks Analysis

Some Aspects of the Three-Dimensional Interface Cracks Analysis

Analysis of semi-elliptical surface cracks in the interface of bimaterial plates under tension and bending

A semi-elliptical surface crack widely exists in the multilayered electronic devices, fibre reinforced laminated composites and solder joints. To ensure the safety of these structural components, three-dimensional interface fracture mechanics analysis is required. In this study, three-dimensional finite element analyses have been conducted to calculate the fracture mechanics parameters, including the stress intensity factors (SIFs), the strain energy release rate G and two phase angles ψ and φ for semi-elliptical interface surface cracks in finite thickness plates. A wide range of crack aspect ratios and relative depths are considered. The SIF computations are presented along the front of a three-dimensional bimaterial interface cracks with a/t values of 0.2, 0.4, 0.6 or 0.8 and a/c values of 0.2, 0.4, 0.6 or 1.0. In particular, far-field loads i.e., remote tension and bending, and various combinations of bimaterials are investigated. These fracture mechanics parameters’ solutions are suitable for fracture and fatigue life prediction for semi-elliptical bi-material interface surface cracks in engineering components.

Analysis of a three-dimensional arbitrarily shaped interface crack in a one-dimensional hexagonal thermo-electro-elastic quasicrystal bi-material. Part 1: Theoretical solution

The extended displacement discontinuity boundary integral-differential equation method is adapted to analyze a three-dimensional interface crack of arbitrary shape in a one-dimensional, hexagonal thermo-electro-elastic quasicrystals bi-material. The extended displacement discontinuities include phonon and phason displacement discontinuities, electric potential discontinuity, as well as temperature discontinuity across the interface crack; while the extended stresses represent phonon and phason stresses, electric displacement and heat flux, respectively. An analysis method is proposed based on the analogy between the governing equations for one-dimensional hexagonal electro-thermo-elastic quasicrystals and three-dimensional transversely isotropic magnetoelectrothermoelastic media. By using the analogy method, the fundamental solutions for unit-point extended displacement discontinuities on the interface are obtained. Using the superposition principal, the extended displacement discontinuity boundary integral-differential equations are established. The singular indices and the singular behaviors of the near crack border fields are studied, and the combined extended stress intensity factors (SIFs) are derived in terms of the EDDs.

Enriched finite element method for three-dimensional viscoelastic interface crack problems

The enriched finite element method is developed for three-dimensional problems of an interface crack between elastic and viscoelastic (including dissimilar viscoelastic) materials. According to the displacement fields of elastic interface crack, the displacement fields of viscoelastic interface crack are derived through the correspondence principle. By incorporating the displacement expressions into the displacement model of regular element, the incremental formulations of enriched element are derived. The stress intensity factors and strain energy release rates can be solved based on the enriched degree of freedoms. A 3-D through interface crack at the center of jointed dissimilar viscoelastic plate subjected to remote tension and a quarter-circular viscoelastic interface corner crack subjected to uniform thermal loading was investigated using the enriched finite element method. It is shown that the present solutions are consistent with the analytical solutions, which indicates the present method is correct and efficient.

Stress intensity factor analyses of three-dimensional interface cracks using tetrahedral finite elements

A numerical method is proposed for evaluating the stress intensity factors of a three-dimensional bimaterial interfacial crack using tetrahedral finite elements. This technique is based on the M1-integral method and employs the moving least-squares approximation. Stress or strain in the M1-integral equation is automatically approximated from the nodal displacements obtained by the finite element analysis using the moving least-squares method. Therefore, the presented method needs no elemental information from the finite element analysis. In this study, stress intensity factor analyses of some typical three-dimensional interface crack problems using the tetrahedral finite elements are demonstrated.

Stress intensity factor analysis of a three-dimensional interface crack between dissimilar anisotropic materials under thermal stress

A numerical method for evaluating the stress intensity factors (SIFs) of a three-dimensional interface crack between dissimilar anisotropic materials subjected to thermal and mechanical stresses is proposed. The M1-integral method was applied to an interfacial crack between three-dimensional anisotropic bimaterials under thermal stress. The moving least square approximation was utilized to calculate the value of the M1-integral. The M1-integral in conjunction with the moving least square approximation can be used to calculate the SIFs from nodal displacements obtained by finite element analysis. SIF analyses were performed for double edge cracks in jointed dissimilar isotropic semi-infinite plates subjected to thermal load. Excellent agreement was achieved between the numerical results obtained by the present method and the exact solution. In addition, we computed the SIFs of an external circular interfacial crack in jointed dissimilar anisotropic solids under thermal stress and showed the distributions of SIFs along the crack front. The distribution of stress and the crack opening displacement obtained by the asymptotic solution using the computed SIFs were compared with those obtained by the finite element analysis with fine mesh. They were almost identical to each other, except for the minor component of SIFs that is much smaller than the major component of SIFs. These results indirectly demonstrate the accuracy of the obtained SIFs.

Boundary Element Analysis of Three-Dimensional Interface Cracks in Transversely Isotropic Bimaterials Using the Energy Domain Integral

It is presented in this paper a three-dimensional Boundary Element Method (BEM) implementation of the Energy Domain Integral for the fracture mechanical analysis of three-dimensional interface cracks in transversely isotropic bimaterials. The J-integral is evaluated using a domain representation naturally compatible with the BEM, in which the stresses, strains and derivatives of displacements at internal points are evaluated using their appropriate boundary integral equations. Several examples are solved and the results compared with those available in the literature to demonstrate the efficiency and accuracy of the implementation to solve straight and curved crack-front problems.

Analysis of stress intensity factors for three-dimensional interface crack problems in electronic packages using the virtual crack closure technique

In this study the fracture mechanics parameters, including the strain energy release rate, the stress intensity factors and phase angles, along the curvilinear front of a three-dimensional bimaterial interface crack in electronic packages are considered by using finite element method with the virtual crack closure technique (VCCT). In the numerical procedure normalized complex stress intensity factors and the corresponding phase angles (Rice, J Appl Mech 55:98–103, 1988) are calculated from the crack closure integrals for an opening interface crack tip. Alternative procedures are also described for the cases of crack under inner pressure and crack faces under large-scale contact. Validation for the procedure is performed by comparing numerical results to analytical solutions for the problems of interface crack subjected to either remote tension or mixed loading. The numerical approach is then applied to study interface crack problems in electronic packages. Solutions for semi-circular surface crack and quarter-circular corner crack on the interface of epoxy molding compound and silicon die under uniform temperature excursion are presented. In addition, embedded corner delaminations on the interface of silicon die and underfill in flip-chip package under thermomechanical load are investigated. Based on the distribution of the fracture mechanics parameters along the interface crack front, qualitative predictions on the propensity of interface crack propagation under thermomechanical loads are given.

Stress Intensity Factors Analyses of a Three-Dimensional Interface Crack Between Anisotropic Dissimilar Materials Under Thermal Stress

A new numerical method was presented for stress intensity factors (SIFs) analyses of a three-dimensional interface crack between dissimilar anisotropic materials subjected to thermal stress. The M-integral method was applied to the thermoelastic interfacial crack in three-dimensional anisotropic bimaterials. The moving least square method was used to calculate the value of the M-integral. The M-integral in conjunction with the moving least square method can calculate the SIFs from only nodal displacements obtained by the finite element analysis. We analyzed the SIFs of external circular interfacial cracks in jointed dissimilar anisotropic solids subjected to thermal load and showed the distributions of SIFs along the crack front. The distribution of stress and the crack opening displacement obtained by the asymptotic solution with the SIFs are compared with those obtained by the FEM with fine mesh. They are almost identical each other.

Analysis of three-dimensional interface cracks using enriched finite elements

Many important interface crack problems are inherently three-dimensional in nature, e.g., debonding of laminated structures at corners and holes. In an effort to accurately analyze three-dimensional interface fracture problems, an efficient computational technique was developed that utilizes enriched crack tip elements containing the correct interface crack tip asymptotic behavior. In the enriched element formulation, the stress intensity factors K I, K II, and K III are treated as additional degrees of freedom and are obtained directly during the finite element solution phase. In this study, the results that should be of greatest interest are obtained for semi-circular surface and quarter-circular corner cracks. Solutions are generated for uniform remote tension and uniform thermal loading, over a wide range of bimaterial combinations. Of particular interest are the free surface effects, and the influence of Dundurs’ material parameters on the strain energy release rate magnitudes and corresponding phase angles.

Stress intensity factor analysis of a three-dimensional interface crack between dissimilar anisotropic materials

A new numerical method to calculate the stress intensity factors (SIFs) of a three-dimensional interface crack between dissimilar anisotropic materials was developed. In this study, the M-integral method was employed for mode separation of the SIFs. The moving least-square method was utilized to calculate the M-integral. Using the M-integral with the moving least-square method, SIFs can be automatically calculated with only the nodal displacements from the finite element method (FEM). Here, SIFs analyses of some typical three-dimensional problems are demonstrated. Excellent agreement was achieved between the numerical results obtained by the present method and the corresponding results proposed by other researchers. In addition, the SIFs of a single-edge crack, a through crack, and a semi-circular crack between two anisotropic solids in three-dimensional structures were analyzed.

J-INTEGRAL FOR A 3-D INTERFACE CRACK CONFIGURATION IN WELDS OF DISSIMILAR STEELS

In this study, path-independent values of the J-integral in the finite element context for an arbitrary three-dimensional interface crack configuration in welds of dissimilar steels are presented. For the fracture mechanics analysis of an interface crack in welds of dissimilar steels, residual stress analysis and fracture analysis must be performed sequentially. In the analysis of cracked bodies containing residual stress, the usual domain integral formation results in path-dependent values of the J-integral. And unlike cracks in homogeneous materials, an interface crack in welds of dissimilar steels always induces both opening and shearing modes of stress in the vicinity of the crack tip. Therefore, this paper discusses modifications of the conventional J-integral that yield path independence in the presence of residual stress and the total J values which can characterize the severity of an interface crack tip in welds of dissimilar steels. A finite element method which can evaluate the J-integral for an interface crack in three-dimensional residual stress bearing bodies is developed using the modified J-integral definition and total J values. The situation when residual stresses only are present is studied as is the case when mechanical stresses are applied in conjunction with a residual stress field.

367 熱応力下の三次元異方性異種材界面き裂の応力拡大係数解析(界面と接着・接合の力学2,OS10 界面と接着・接合の力学)

367 熱応力下の三次元異方性異種材界面き裂の応力拡大係数解析(界面と接着・接合の力学2,OS10 界面と接着・接合の力学)

Stress Intensity Factors Analyses of Three-Dimensional Interface Crack between Anisotropic Dissimilar Materials

A new numerical method to calculate the stress intensity factors (SIFs) of a three-dimensional interface crack between dissimilar anisotropic materials was developed. In this study, the M-integral method, usually used as a post-processing step of the finite element method, was employed for the mode separation of the SIFs. The moving least square method was used to calculate the M-integral. Using the M-integral with the moving least square method, the SIFs can be automatically calculated without the need for a complex, time-consuming procedure. The SIFs analyses of some typical three-dimensional problems are demonstrated. Excellent agreement was achieved between the numerical results obtained by the present method and corresponding results proposed by other researchers.

Boundary element method for J-integral and stress intensity factor computations in three-dimensional interface cracks

A general numerical tool for the analysis of three–dimensional bimaterial interface cracks is presented in this paper. The proposed tool is based on a multidomain formulation of the Boundary Element Method (BEM), with the crack located at the interface of the domain. Mixed mode stress intensity factors are computed along the three-dimensional crack fronts using the Energy Domain Integral (EDI) methodology and decoupled via the Interaction Integral. The capability of the procedure is demonstrated by solving a number of examples. The last of these examples consists in a thick centre cracked panel for which the behaviour of the J-integral and the mixed-mode stress intensity factors along the crack front is studied as a function of the material mismatch.

A new variable-order singular boundary element for calculating stress intensity factors in three-dimensional elasticity problems

A new three-dimensional variable-order singular boundary element has been constructed for stress analysis of three-dimensional interface cracks and internal material junctions. The singular fields in the vicinity of crack front or junction have been accurately represented by the singular elements by taking account the variable order of singularities and the angular profiles of field variables. Both the singular stress fields and displacement fields are independently formulated by the element’s shape functions. Different kinds of displacement formulations are investigated. The formulation combining singular and linear terms is found to be the most accurate one. The mixed-mode stress intensity factors are treated as nodal unknowns. The variation of stress intensity factors along the line of singularity can be obtained directly from the final system of equations and thus no post processing, such as three-dimensional J-integral or domain integral, is necessary. Numerical examples involving stress singularity, such as penny-shaped cracks in homogeneous and dissimilar material interface, plates with through-thickness cracks, and a dissimilar inclusion, are investigated. The analysis results are in good agreement with those reported in the literature.

Evaluation of the stress intensity factors for a three-dimensional interfacial crack by the boundary element method

In this paper, three-dimensional interface crack problems are analysed by the boundary element method. A special crack tip element is used to improve the accuracy and the complex stress intensity factors are determined by several techniques, namely the one-point stress formula, the one-point discontinuity displacement formula and an energy technique. Stress intensity factors are presented for single-edge, double-edge and centre cracks in bi-materials.

Three-Dimensional Interface Cracks in Anisotropic Bimaterials: The Non-Oscillatory Case

Two-dimensional interface cracks in anisotropic bimaterials have been studied extensively in the literature. However, solutions to three-dimensional interface cracks in anisotropic bimaterials are not available. In this paper, a penny-shaped crack on the interface between two anisotropic elastic half-spaces is considered. A formal solution is obtained by using the Stroh method in two-dimensional elasticity in conjunction with the Fourier transform method. Fracture mechanics parameters such as the stress intensity factor, crack-opening displacement, and energy release rate are obtained in terms of the interfacial matrix M. To illustrate the solution procedure, a circular delaminations in a unidirectional and a cross-ply composite are considered. Numerical results for the stress intensity factors and energy release rate along the crack front are presented.

Domain integral formulation for stress intensity factor computation along curved three-dimensional interface cracks

New domain integrals for extracting mixed-mode stress intensity factors along curved, three-dimensional bimaterial interface cracks are derived. In the derivation, the asymptotic auxiliary fields for the plane problem of a bimaterial interface crack are imposed along a curved crack front. The general crack-tip interaction integral (a contour integral surrounding a point on the crack front which is evaluated in the limit as the contour is shrunk onto the crack tip) is then expressed in domain form which is more suitable for numerical computation. A consequence of imposing the auxiliary fields along a curved crack front is that the auxiliary stress fields do not satisfy equilibrium, and the auxiliary strain fields do not satisfy compatibility. The terms which arise due to the lack of equilibrium and compatibility are not sufficiently singular to contribute to the crack-tip interaction integral or to affect its path independence; however, these terms become important when domain integral representations are introduced, because they involve fields which are not asymptotically close to the crack tip. In order to compute the pointwise stress intensity factors along the crack front, the domain integrals are evaluated as a post-processing step in the finite element method. In the numerical results, it is demonstrated that it is crucial to incorporate the terms that arise due to lack of equilibrium and compatibility of the auxiliary fields, especially in regions where the local crack front curvature is high. In the paper, we present two numerical examples. As a benchmark, we first consider the problem of a penny-shaped interface crack embedded in a cylinder. The results for the complex stress intensity factor and phase angle are found to be in excellent agreement with the analytical solution. The problem of an elliptical crack embedded between two dissimilar isotropic materials is also considered, and the results are discussed.