Dissimilar Anisotropic Media Research Articles

A moving screw dislocation near interfacial rigid lines in two dissimilar anisotropic media

This paper attempts to investigate the problem for the interaction between a uniformly moving screw dislocation and interface rigid lines in two dissimilar anisotropic materials. Integrating Riemann-Schwarz’s symmetry principle with the analysis singularity of complex functions, we present the general elastic solutions of this problem and the closed form solutions for interfaces containing one and two rigid lines. The expressions of stress intensity factors at the rigid line tips and image force acting on moving dislocation are derived explicitly. The results show that dislocation velocity has an antishielding effect on the rigid line tip and a larger dislocation velocity leads to the equilibrium position of dislocation closing with the rigid line. The presented solutions contain previously known results as the special cases.

Heat Conduction in Dissimilar Anisotropic Media with Bonding Defects/Interface Cracks

AbstractAs an essential foundation for the associated thermoelasticity analysis in the boundary element method (BEM), this article proposes an expedient, yet powerful, approach to analyze the heat conduction in multiply jointed anisotropic media with bonding defects/interface cracks. The direct domain mapping technique (DDM) is applied to treat a domain consisting of dissimilar anisotropic sub-regions in the potential theory of BEM. The heat transfer across a crack is modeled with a gap conductance equation specially formulated for the BEM analysis. Two numerical examples are provided as illustrations of the validity and the applicability of this proposed scheme.

Strain energy release rates for an interface crack in orthotropic media––a finite element investigation

Strain energy release rate (SERR) components for an interface crack in two-dimensional orthotropic media were obtained using finite element (FE) analysis. The elastic analysis of interface cracks results in oscillatory singularity. This is prevalent over a very small zone near the crack-tip, where the traction free crack faces undergo unacceptable deformations resulting in the interpenetration of crack faces. The individual and total strain energy release rates are calculated using modified crack closure integral (MCCI) method. Although the total SERR converges, it is observed that the individual SERR components are dependent on the values of the smallest element size (Δ a) at the crack-tip. It is observed that both the crack opening and sliding displacements are oscillatory when the interpenetration is allowed in the contact zone. The contact zone length ( r c) calculated using Suo's analytical expression [Singularities, interfaces and cracks in dissimilar anisotropic media. Proc. Royal Soc. London, Ser A427 (1990) 331] is in good agreement with the results from FE analysis and MCCI calculations. However, for the chosen material properties, the estimated contact zone length based on the analytical expression proposed by Ni and Nemat-Nasser [J. Mech. Phys. Solids 39 (1991) 113] exhibits a large deviation from the present FE results. It is seen that the mode-II behavior dominates the crack growth, even under mode-I loading.

Calculation of stress intensity factors for an interfacial crack between dissimilar anisotropic media, using a hybrid element method and the mutual integral

Using Beom and Atluri's complete eigen-function solutions for stresses and displacements near the tip of an interfacial crack between dissimilar anisotropic media, a hybrid crack tip finite-element is developed. This element, as well as a mutual integral method are used to determine the stress intensity factors for an interfacial crack between dissimilar anisotropic media. The hybrid element has, for its Galerkin basis functions, the eigen-function solutions for stresses and displacements embedded within it. The “mutual integral” approach is based on the application of the path-independent J integral to a linear combination of two solutions: one, the problem to be solved, and the second, an “auxiliary” solution with a known singular solution. A comparison with exact solutions is made to determine the accuracy and efficiency of both the methods in various mixed mode interfacial crack problems. The size of the hybrid element was found to have very little effect on the accuracy of the solution: an acceptable numerical solution can be obtained with a very coarse mesh by using a larger hybrid element. An equivalent domain integral method is used in the application of the “mutual” integral instead of the line integral method. It is shown that the calculated mutual integral is domain independent. Therefore, the mutual integral can be evaluated far away from the crack-tip where the finite element solution is more accurate. In addition, numerical examples are given to determine the stress intensity factors for a delamination crack in composite lap joints and at plate-stiffener interfaces.

Calculation of stress intensity factors for an interfacial crack between dissimilar anisotropic media, using a hybrid element method and the mutual integral

Calculation of stress intensity factors for an interfacial crack between dissimilar anisotropic media, using a hybrid element method and the mutual integral

General solution to the hygrothermoelastic interface problem with discontinuity between dissimilar anisotropic media

A general solution to the hygrothermoelastic problem associated with an interface discontinuity between dissimilar anisotropic media is presented. The complex variable representation of Lekhnitskii [Theory of Elasticity of an Anisotropic Elastic Body (Holden-Day, San Francisco, CA, 1963)] is extended into the hygrothermoelastic problem by means of five complex functions including three stress functions, one temperature function, and one moisture function. A special technique of analytical continuation is used to deal with the continuous conditions of dissimilar media. Based on the Hilbert problem formulation, the linear relation between the boundaries of discontinuity can be derived into a type of Cauchy integral, which makes the solution in a compact version. The result shows that the heat or moisture flux exhibits an inverse square-root singularity at the tips of discontinuity while the nature of singularity of the hygrothermal stresses possess the same trig-log character as those obtained for the elastic problem.

Fracture parameters for the orthotropic bimaterial interface cracks

In order to define a proper bimaterial stress intensity factor, a general solution for the collinear interface cracks between dissimilar anisotropic media is applied to the near tip of an interface crack. Through the operation of normalization, scaling, nondimensionalization and transformation, a comparable definition which can be reduced to the classical stress intensity factors for a crack tip in homogeneous media has been obtained. For special cases of orthotropic bimaterial interface cracks, the explicit solutions are derived in terms of engineering constants.

Steady-state heat conduction problem of the interface crack between dissimilar anisotropic media

A solution is given for the steady-state heat conduction problem of the interface crack between dissimilar anisotropic media. Based on the Hilbert problem formulation and a special technique of analytical continuation, exact expressions are obtained for the temperature and temperature gradients for both the heat flux prescribed and temperature prescribed boundary conditions. It is found that the temperature gradients near the crack tip always possess the characteristic inverse square root singularity in rectilinearly anisotropic bodies provided the heat conductivity coefficients are positive definite and symmetric. Moreover, the temperatures or temperature gradients associated with the dissimilar media can be easily obtained from the corresponding problem associated with the homogeneous media by a simple substitution. Special examples are given to the homogeneous and isotropic materials and the solutions reduce to the results given in the literature. The strength of heat flux singularities related to the crack dimension is also discussed.

Explicit solutions for collinear interface crack problems

By combining Stroh's formalism, the method of analytical continuation and the translating technique introduced in this paper, the explicit full domain solutions for the problems of collinear interface cracks between dissimilar anisotropic media have been presented. To define a proper bimaterial stress intensity factor, the full domain solution is applied to the near tip of an interface crack. The results show that the effect of material properties is totally reflected through the oscillation index ε, and the bimaterial constants D11, D22 and D33 which have inverse relations with Young's moduli E1, E2 and shear modulus √G23G31, respectively. For the purpose of illustration, three typical examples are solved explicitly such as a semi-infinite interface crack, a finite interface crack and two collinear interface cracks.

Thermal interface crack problems in dissimilar anisotropic media

The fundamental nature of an interface crack between dissimilar anisotropic media under the uniform heat flux is studied. Based on the Hilbert problem formulation and a special technique of analytical continuation, a simple and compact version of general solutions for the thermal field are given. The temperature gradients or heat fluxes are found to possess the characteristic inverse square-root singularity in terms of the radial distance from the crack tip. Due to this singular behavior, the heat flux intensity factor is then introduced to quantify the thermal energy cumulated in the neighborhood of the crack tip. Some numerical examples are given for the application of the final results to the intensity factor of heat flux as well as the full field solutions of temperature. It is very interesting to see that the solutions associated with the dissimilar media can be easily obtained from the corresponding problem associated with the homogeneous media by a simple substitution of their own material properties. In general, the system possesses the symmetric properties of the thermal conductivity coefficients which can make the heat flux intensity factor smaller. Consequently, the thermal energy intensification is diminished.

Stress intensity factors and energy release rates of delaminations in composite laminates

Due to the oscillatory characteristics of stresses near interface crack tips, the stress intensity factor K i , i = I, II, III, should be modified and the energy release rate G i , i = 1, 2, 3, of each fracture mode calculated by the virtual crack closure method may not exist. Based upon a near-tip solution for interface cracks between dissimilar anisotropic media, a proper definition for the stress intensity factors and energy release rates for general anisotropic bimaterial interface cracks is provided in this paper, which is applicable for the delaminated composites. Moreover, this definition can be reduced to the classical definition for a crack tip in homogeneous media when the two materials become the same. A simple quadratic relation between K i and G i is derived, which is further reduced explicitly for orthotropic bimaterials. The influence of fiber orientation and the coupling among opening, shearing and tearing mode fracture are studied numerically. The results show that the classical stress intensity factors and energy release rates are still the dominant stress intensity and energy release rate of the mixed mode condition induced by the interface.

Thermoelastic interface crack problems in dissimilar anisotropic media

By applying the extended version of Stroh's formalism and a special technique of analytical continuation, a general solution for the thermoelastic collinear interface cracks between dissimilar anisotropic media has been obtained in this paper. Special notification and examples are given for the application of the final results to the whole field solutions of the temperature, heat flux, displacements and stresses. The explicit expressions for the interface stresses and crack opening displacements are also provided. Based upon this general solution, two special examples of single crack problems are solved explicitly. One is homogeneous media, the other is anisotropic bimaterials. The former is studied for the purpose of presenting the detailed calculation, verifying the general solution and discussing the validity of the solution. A closed form solution is obtained for the latter case subjected to a uniform heat flux and loading.

Singularities, interfaces and cracks in dissimilar anisotropic media

For a non-pathological bimaterial in which an interface crack displays no oscillatory behaviour, it is observed that, apart possibly from the stress intensity factors, the structure of the near-tip field in each of the two blocks is independent of the elastic moduli of the other block. Collinear interface cracks are analysed under this non-oscillatory condition, and a simple rule is formulated that allows one to construct the complete solutions from mode III solutions in an isotropic, homogeneous medium. The general interfacial crack-tip field is found to consist of a two-dimensional oscillatory singularity and a one-dimensional square root singularity. A complex and a real stress intensity factors are proposed to scale the two singularities respectively. Owing to anisotropy, a peculiar fact is that the complex stress intensity factor scaling the oscillatory fields, however defined, does not recover the classical stress intensity factors as the bimaterial degenerates to be non-pathological. Collinear crack problems are also formulated in this context, and a strikingly simple mathematical structure is identified. Interactive solutions for singularity-interface and singularity interface-crack are obtained. The general results are specialized to decoupled antiplane and in-plane deformations. For this important case, it is found that if a material pair is non-pathological for one set of relative orientations of the interface and the two solids, it is non-pathological for any set of orientations. For bonded orthotropic materials, an intuitive choice of the principal measures of elastic anisotropy and dissimilarity is rationalized. A complex-variable representation is presented for a class of degenerate orthotropic materials. Throughout the paper, the equivalence of the Lekhnitskii and Stroh formalisms is emphasized. The article concludes with a formal statement of interfacial fracture mechanics for anisotropic solids.

A thermoelastic problem for a crack between dissimilar anisotropic media

The thermoelastic problem of a flat crack of infinite length and constant finite width between bonded dissimilar anisotropic materials is examined. The stress singularities at the crack tips are obtained and compared with those for the corresponding elastic crack problem.

A crack between dissimilar anisotropic media

The problem of a flat crack of infinite length and constant finite width between bonded dissimilar anisotropic materials is examined. The stress distribution throughout the materials is determined for the case when the crack is subjected to a non-uniform applied stress.