Mode III stress intensity factors in an interfacial crack in dissimilar bonded materials

The antiplane shear deformation problem of two edge-bonded dissimilar isotropic wedges is considered. In the case when the sum of the two apex angles is equal to 2π, the problem reduces to that of two edge-bonded dissimilar materials with an interfacial crack subjected to concentrated antiplane shear tractions on the crack faces. An explicit expression is extracted for the stress intensity factor at the crack tip. In the special cases of different combinations of the apex angles, the obtained expression for the stress intensity factor may be simplified and relations of a simpler form are given for the stress intensity factor. It is shown that the stress intensity factor is dependent on the material properties as well as the geometry and loading. However, in special cases of equal apex angles as well as the case of similar materials the dependency of the stress intensity factor on the material properties disappears.     

Mode-III interface edge crack between two bonded quarter-planes of dissimilar piezoelectric materials

Summary  The problem of an interface edge crack between two bonded quarter-planes of dissimilar piezoelectric materials is considered under the conditions of anti-plane shear and in-plane electric loading. The crack surfaces are assumed to be impermeable to the electric field. An integral transform technique is employed to reduce the problem under consideration to dual integral equations. By solving the resulting dual integral equations, the intensity factors of the stress and the electric displacement and the energy release rate as well as the crack sliding displacement and the electric voltage across the crack surfaces are obtained in explicit form for the case of concentrated forces and free charges at the crack surfaces and at the boundary. The derived results can be taken as fundamental solutions which can be superposed to model more realistic problems. Received 10 November 2000; accepted for publication 28 March 2001     

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.     

Stress intensity factors for a moving cylindrical crack in a nonhomogeneous cylindrical layer in composite materials

Stresses are determined for a finite cylindrical crack that is propagating with a constant velocity in a nonhomogeneous cylindrical elastic layer, sandwiched between an infinite elastic medium and a circular elastic cylinder made from another material. The Galilean transformation is employed to express the wave equations in terms of coordinates that are attached to the moving crack. An internal gas pressure is then applied to the crack surfaces. The solution is derived by dividing the nonhomogeneous interfacial layer into several homogeneous cylindrical layers with different material properties. The boundary conditions are reduced to two pairs of dual integral equations. These equations are solved by expanding the differences in the crack surface displacements into a series of functions that are equal to zero outside the crack. The Schmidt method is then used to solve for the unknown coefficients in the series. Numerical calculations for the stress intensity factors were performed for speeds and composite material combinations.     

Orthotropic semi-infinite medium with a crack under thermal shock

A cracked orthotropic semi-infinite plate under thermal shock is investigated. The thermal stresses are generated due to sudden cooling of the boundary by ramp function temperature change. The superposition technique is used to solve the problem. The crack problem is formulated by applying the thermal stresses obtained from the uncracked plate with opposite sign to be the only external loads on the crack surfaces as the crack surface tractions. The Fourier transform technique is used to solve the problem leading to a singular equation of the Cauchy type. The singular integral equation is solved numerically using the expansion method. The influence of the material orthotropy on the stress intensity factors is shown by comparing the results obtained for different orthotropic materials and isotropic materials in the case of plane stress. The numerical results of the stress intensity factors are demonstrated as a function of time, crack length, location of the crack and the duration of the cooling rate.     

Stress intensity factor for a kinked interfacial crack in dissimilar anisotropic materials under antiplane deformation

The asymptotic problem of a kinked interfacial crack in dissimilar anisotropic materials under antiplane deformation is investigated. The linear transformation method for the problem of the anisotropic bimaterial with a straight interface is proposed. The stress intensity factor for the kinked interfacial crack in the anisotropic composite is obtained from the solution of the transformed problem of the kinked interfacial crack in the isotropic bimaterial based on the linear transformation method. The effects of the material parameters as well as the kink angle on the stress intensity factor are discussed from numerical results of the stress intensity factor. The finite element analysis is carried out to verify the stress intensity factor obtained by using the linear transformation. The influence of the material orientations on the stress intensity factor is investigated for the kinked crack in the bimaterial consisting of dissimilar inclined orthotropic materials.     

Analytical solution for bending stress intensity factor in an orthotropic elastic plate containing a crack and subjected to concentrated moments

The problem of estimating the bending stress distribution in the neighborhood of a crack located on a single line in an orthotropic elastic plate of constant thickness subjected to out-of-plane concentrated moments is examined. Using classical plate theory and integral transform techniques, the general formulae for the bending moment and twisting moment in an elastic plate containing cracks located on a single line are derived. The solution is obtained in a closed form for the case in which there is a single crack in an infinite plate subjected to symmetric concentrated moments.     

Stress intensity factor in a contact problem for a plane crack under an antiplane shear wave

The frictional contact interaction of the finite edges of a plane crack under the action of a normally incident harmonic shear wave that produces antiplane deformation is studied. The influence of the forces of contact interaction on the stress intensity factor is analyzed Published in Prikladnaya Mekhanika, Vol. 43, No. 9, pp. 115–119, September 2007.     

Thermal shock analyses for a strip containing an infinite row of periodically distributed cracks normal to its edge

The transient thermal stress problem of a semi-infinite plate containing an infinite row of periodically distributed cracks normal to its edge is investigated in this paper. The elastic medium is assumed to be cooled suddenly on the crack-containing edge. By the superposition principle, the formulation leads to a mixed boundary value problem, with the negating tractions arisen from the thermal stresses for a crack-free semi-infinite plate. The resulting singular integral equation is solved numerically. The effects on the stress intensity factors due to the presence of periodically distributed cracks in a semi-infinite plate are illustrated. For both the edge crack and the embedded crack arrays, the stress intensity factors increase, due to the reduction of the shielding effect, as the stacking cracks are more separated. For the case of embedded crack array, one has the further conclusion that the stress intensity factors decline as the crack array shifts from the plate edge.     

Stress intensity factors for three-dimensional cracks in functionally graded materials using enriched finite elements

A three-dimensional enriched finite-element methodology is presented to compute stress intensity factors for three-dimensional cracks contained in functionally graded materials (FGMs). A general-purpose 3D finite-element based fracture analysis program, FRAC3D, is enhanced to include this capability. First, using available solutions from the literature, comparisons have been made in terms of stresses under different loading conditions, such as uniform tensile, bending and thermal loads. Mesh refinement studies are also performed. The fracture solutions are obtained for edge cracks in an FGM strip and surface cracks in a finite-thickness FGM plate and compared with existing solutions in the literature. Further analyses are performed to study the behavior of stress intensity factor near the free surface where crack front terminates. It is shown that three-dimensional enriched finite elements provide accurate and efficient fracture solutions for three-dimensional cracks contained in functionally graded materials.     

DYNAMIC STRESS INTENSITY FACTORS AROUND TWO CRACKS NEAR AN INTERFACE OF TWO DISSIMILAR ELASTIC HALF－PLANES UNDER IN－PLANE SHEAR IMPACT LOAD

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Interface crack problems for mode II of double dissimilar orthotropic composite materials

The fracture problems near the similar orthotropic composite materials are interface crack tip for mode Ⅱ of double disstudied. The mechanical models of interface crack for mode Ⅱ are given. By translating the governing equations into the generalized hi-harmonic equations, the stress functions containing two stress singularity exponents are derived with the help of a complex function method. Based on the boundary conditions, a system of non-homogeneous linear equations is found. Two real stress singularity exponents are determined be solving this system under appropriate conditions about bimaterial engineering parameters. According to the uniqueness theorem of limit, both the formulae of stress intensity factors and theoretical solutions of stress field near the interface crack tip are derived. When the two orthotropic materials are the same, the stress singularity exponents, stress intensity factors and stresses for mode II crack of the orthotropic single material are obtained.     

Stress intensity factors for ring-shaped crack surrounded by spherical inclusions

Interaction of a ring-shaped crack with inhomogeneities such as inclusions is analyzed for the resulting three-dimensional stress field. Considered for the composite solid with a given volume fraction of inclusions are the two cases of (a) spherical voids and (b) spherical inclusions with elastic moduli different from the matrix. A ring-shaped crack is initiated at the equator of one of the voids or inclusions. A three-phase model is used to examine the interaction between the crack and surrounding inhomogeneities. Finite element method is then applied to calculate the stress intensity factor for different configurations. The effects of volume fraction of inhomogeneities, relative size of crack to inclusions, and material constants on crack behavior are discussed.     

Anti-plane shear of an arbitrary oriented crack in a functionally graded strip bonded with two dissimilar half-planes

An internal crack located within a functionally graded material (FGM) strip bonded with two dissimilar half-planes and under an anti-plane load is considered. The crack is oriented in an arbitrary direction. The material properties of strip are assumed to vary exponentially in the thickness direction and two half-planes are assumed to be isotropic. Governing differential equations are derived and to reduce the difficulty of the problem dealing with solution of a system of singular integral equations Fourier integral transform is employed. Semi closed form solution for the stress distribution in the medium is obtained and mode III stress intensity factor (SIF), at the crack tip is calculated and its validity was verified. Finally, the effects of nonhomogeneous material parameter and crack orientation on the stress intensity factor are studied.     

Small edge crack in a semi-infinite solid subjected to thermal stratification

The mode I stress intensity factor for a small edge crack in an elastic half-space is found when the space is in contact with two stratified fluids of different temperatures, the boundary between the fluids oscillating sinusoidally over the solid surface. The variation in the stress intensity factor, which may lead to thermal fatigue crack growth, is examined as a function of time, crack depth, amplitude and temporal frequency of oscillation, surface heat transfer coefficient and material properties of the half-space. It is shown how this ‘boundary layer’ solution may be applied to problems involving finite geometries.     

Stress intensity factors for an edge interface crack in a bonded semi-infinite plate for arbitrary material combination

Although a lot of interface crack problems were previously treated, few solutions are available under arbitrary crack lengths and material combinations. In this paper the stress intensity factors of an edge interface crack in a bonded strip are considered under tension with varying the crack length and material combinations systematically. Then, the limiting solutions are provided for an edge interface crack in a bonded semi-infinite plate under arbitrary material combinations. In order to calculate the stress intensity factors accurately, exact solutions in an infinite bonded plate are also considered to produce proportional singular stress fields in the analysis of FEM by superposing specific tensile and shear stresses at infinity. The details of this new numerical solution are described with clarifying the effect of the element size on the stress intensity factor. It is found that for the edge interface crack the normalized stress intensity factors are not always finite depending upon Dunders’ parameters. This behavior can be explained from the condition of the singular stress at the end of bonded strip. Convenient formulas are also given by fitting the computed results.     

The dynamic stress intensity factor analysis of adhesively bonded material interface crack with damage under shear loading

This paper studies the dynamic stress intensity factor (DSIF) at the interface in an adhesive joint under shear loading. Material damage is considered. By introducing the dislocation density function and using the integral transform, the problem is reduced to algebraic equations and can be solved with the collocation dots method in the Laplace domain. Time response of DSIF is calculated with the inverse Laplace integral transform. The results show that the mode Ⅱ DSIF increases with the shear relaxation parameter, shear module and Poisson ratio, while decreases with the swell relaxation parameter. Damage shielding only occurs at the initial stage of crack propagation. The singular index of crack tip is -0.5 and independent on the material parameters, damage conditions of materials, and time. The oscillatory index is controlled by viscoelastic material parameters.     

A semi-infinite interface crack interacting with subinterface matrix cracks in dissimilar anisotropic materials. II. Numerical results and discussion

Based on the investigation performed in Part I of this series, numerical results for the interaction between a semi-infinite interface crack and multiple subinterface matrix microcracks in three kinds of material combinations are given in Part II. The major interaction behaviors are discussed in detail. Special attention is focused on the influences of the different material combinations, the T-stress, the orientation angles, and the location angles of the microcracks on the local stress intensity factor at the interface crack tip. In addition, the variable tendencies of the interaction effect induced from change of the distance between the interface crack tip and the centers of the microcracks are studied. It is concluded that the different material combinations introduced in this paper have little influence on the variable tendencies of the effect, but have significant influence on the effect in magnitude. Detailed comparisons of the results with those in a homogeneous orthotropic material show that the dissimilar materials shift the maximum amplification angle, the maximum shielding angle, the neutral shielding angle, and the neutral T-stress angle, respectively.     

Stress state of an orthotropic material with an elliptic crack under linearly varying pressure

The static equilibrium of an elastic orthotropic medium with an elliptic crack subject, on its surface, to linearly varying pressure is studied. The stress state of the elastic medium is represented as a superposition of the principal and perturbed states. Use is made of Willis’ approach based on the triple Fourier transform in spatial variables, the Fourier-transformed Green’s function for an anisotropic material, and Cauchy’s residue theorem. The contour integrals are evaluated using Gaussian quadratures. The results for particular cases are compared with those obtained by other authors. The influence of orthotropy on the stress intensity factors is studied __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 7, pp. 73–81, July 2006.     

Dynamic response of a crack in a functionally graded interface of two dissimilar piezoelectric half-planes

Summary  In this paper, the dynamic anti-plane crack problem of two dissimilar homogeneous piezoelectric materials bonded through a functionally graded interfacial region is considered. Integral transforms are employed to reduce the problem to Cauchy singular integral equations. Numerical results illustrate the effect of the loading combination parameter λ, material property distribution and crack configuration on the dynamic stress and electric displacement intensity factors. It is found that the presence of the dynamic electric field could impede of enhance the crack propagation depending on the time elapsed and the direction of applied electric impact. Received 4 December 2001; accepted for publication 9 July 2002 This work is supported by the National Natural Science Foundation of China through Grant No. 10132010.