Dissimilar Anisotropic Materials Research Articles

Прочность при изгибе анизотропных составных плит со свободными краями

Modern technology shows increased demands on the strength properties of machines, their parts, as well as various structures, reducing their weight, volume and size, which leads to the need to use anisotropic composite materials. Finding criteria to determine the ultimate strength characteristics of structural elements, engineering structures is one of the urgent problems of solid mechanics. Strength problems in structures are often reduced to finding out the nature of the local stress state at the vertices of the joints of the constituent parts. The solution of this urgent problem for composite anisotropic plates can be found in this article, where the author continues the research in this area, extending them to the bending of anisotropic composite plates. The aim of the work is to study the limit stress state of anisotropic composite plates in the framework of the classical theory of plate bending. The outer edges of the plate are considered to be free. Using the classical theory of anisotropic plate bending in the space of physical and geometric parameters, the hypersurface equations determining the low-stress zones for the edge of the contact surface of a composite cylindrical orthotropic plate are obtained. Modern technological processes of welding, surfacing, soldering and bonding allow to produce structural elements of monolithic interconnected dissimilar anisotropic materials. The combination of different materials with qualities corresponding to certain operating conditions opens up great opportunities to improve the technical and economic characteristics of machines, equipment and structures. It can contribute to a significant increase in their reliability, durability, reduce the cost of production and operation. On this basis, the solution proposed in this work can be useful to increase the strength of composite materials.

Near-tip singular fields for an interface anticrack between dissimilar anisotropic elastic materials

We study the near-tip singular fields for an interface anticrack between dissimilar anisotropic elastic materials using the sextic Stroh formalism. The stress and strain fields exhibit an oscillatory singularity and a square root singularity at the anticrack tip. A complex and a real strain/rotation intensity factors are introduced to scale, respectively, the two singularities. An explicit expression for the negative anticrack contraction force is obtained in terms of the proposed intensity factors. We illustrate our results using an example in which the bimaterial is orthotropic. In this typical case, a complex stress intensity factor can also be defined to replace the complex strain/rotation intensity factor.

On joint efficiency of composite anisotropic plate rigidly fixed along outside edges

Introduction. Modern processes of welding, surfacing, soldering and bonding provide producing structural elements of monolithic interconnected dissimilar anisotropic materials. The combination of different materials with qualities corresponding to certain operating conditions offer comprehensive facilities to improve the technical and economic characteristics of machines, equipment and structures. It can contribute to a significant increase in their reliability, durability, and to reduction of the production and operation costs. Materials and Methods. The work objective is to study the boundary state of stress of anisotropic composite plates in the framework of the classical theory of plate bending. The outer edges of the plate are considered free. Using the classical theory of bending of an anisotropic plate in the space of physical and geometric parameters, hypersurface equations are obtained that define low-stressed zones for the contact surface edge of a cylindrical orthotropic composite plate.Research Results. Finding the criteria for engineering structures to determine the limiting strength characteristics of structural elements is one of the urgent tasks of the deformable solid mechanics. Strength problems in structures are often reduced to elucidating the nature of the local stress state at the tops of the joints of the constituent parts. This paper is devoted to solving this problem for composite anisotropic plates in the area of their bending.Discussion and Conclusions. The solution proposed in this paper may be useful for increasing the strength of composite products.

Compatibility of singular stress fields around a three-dimensional corner between dissimilar anisotropic materials and around a two-dimensional corner between dissimilar anisotropic materials

Compatibility of singular stress fields around a three-dimensional corner between dissimilar anisotropic materials and around a two-dimensional corner between dissimilar anisotropic materials

Interaction between semicoherent interfaces and Volterra-type dislocations in dissimilar anisotropic materials

Abstract

Crack propagation in anisotropic composite structures

A crack approaching a material interface between two elastic materials may stop or may advance by either penetrating the interface or deflecting into the interface (cf. N.Y. He and J.W. Hutchinson, Int. J. Solids Struct. 25 (1989), 1053-1067). Mathematical models for crack path prediction are based on the asymptotic behavior near the crack tip. In this work, an idea to compute the asymptotic expansion of the displacement field for structures composed of two dissimilar elastic anisotropic materials is shown, if the crack impinges the material interface. In contrast to the well-known case of isotropic materials, logarithmic terms can appear in the asymptotic decomposition of the displacement field in anisotropic composites. Based on this results, the energy release rate is calculated for different scenarios of crack propagation in composite structures.

Electric field intensity factors for conducting paths in anisotropic dielectric bimaterials

Conducting paths in an anisotropic dielectric bimaterial as well as in a homogeneous anisotropic material subjected to electric loading are investigated. The conducting path problems are formulated by using a linear transformation method. Electric field intensity factors are obtained for conducting paths emanating from a surface electrode in an orthotropic material. The asymptotic problem of a kinked conducting path in dissimilar anisotropic dielectric materials is considered. The electric field intensity factor for the asymptotic problem is obtained in the infinite product form. To ascertain validity of the solution obtained from the linear transform method, numerical computations are carried out by using finite element method. The electric field intensity factor for a conducting path emanating from the vertex of a bimaterial wedge with a tilt boundary is also obtained in the closed form.

Energy release rates near the interface between two anisotropic solids

If a crack starts from an interface between two dissimilar anisotropic materials, or is approaching the interface, various scenarios can happen. The question whether the crack will reach or even penetrate the interface depends on the mismatch of elastic moduli in the two materials. This contribution is devoted to the question how to calculate the change of the potential energy if the crack starts with its tip is on the interface or approaching it from a small distance. The energy release is calculated using the method of matched asymptotic expansions. Other than for the energy release rate in homogeneous materials it may happen here that the ERR is zero or infinity. The method is universal in the sense that it does not depend on the particular geometry and is even applicable if the crack tip meets a junction of several materials, or an angular point of the material interface e.g.

Integral identities for a semi-infinite interfacial crack in anisotropic elastic bimaterials

The focus of the article is on the analysis of a semi-infinite crack at the interface between two dissimilar anisotropic elastic materials, loaded by a general asymmetrical system of forces acting on the crack faces. Recently derived symmetric and skew-symmetric weight function matrices are introduced for both plane strain and antiplane shear cracks, and used together with the fundamental reciprocal identity (Betti formula) in order to formulate the elastic fracture problem in terms of singular integral equations relating the applied loading and the resulting crack opening. The proposed compact formulation can be used to solve many problems in linear elastic fracture mechanics (for example various classic crack problems in homogeneous and heterogeneous anisotropic media, as piezoceramics or composite materials). This formulation is also fundamental in many multifield theories, where the elastic problem is coupled with other concurrent physical phenomena.

3A2 三次元異方性異種材接合角部の特異応力場解析(<OSI>機械工学における計算力学3)

3A2 三次元異方性異種材接合角部の特異応力場解析(<OSI>機械工学における計算力学3)

A Crack Emanating from a Wedge In Dissimilar Anisotropic Materials Under Antiplane Shear

A crack in a composite wedge consisting of two dissimilar anisotropic materials under concentrated antiplane loads is analyzed. The problem of a crack in an isotropic composite wedge is solved first by using the Mellin transform and the Wiener-Hopf method. Using a linear transformation of the original composite wedge into an isotropic composite wedge consisting of dissimilar isotropic materials, the antiplane displacement and stresses for the anisotropic composite wedge are obtained from the solution for the transformed wedge. The stress intensity factor for the crack in the original anisotropic composite wedge is obtained from the solution of the crack in the transformed wedge. Special attention is given to the asymptotic problem of a wedge crack in an anisotropic bimaterial. Numerical computations are carried out to obtain the energy release rate for various apex angles and anisotropic parameters as a function of crack angle.

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.

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.

Fracture Analyses for Interface Corners in Elastic Materials Subjected to Thermal Loading

By employing the Stroh formalism for two-dimensional anisotropic thermoelasticity, fracture analyses of interface corners between two dissimilar anisotropic elastic materials under thermal loadings are considered in this paper. It was proved that the consideration of thermal effects will not influence the stress singularity but will induce heat flux singularity if the singularity of the temperature field is not permissible. To calculate the stress intensity factors via path independent H-integral, it was found that the one proposed previously for the mechanical loading conditions should be modified by adding an additional surface integral accounting for the thermal effects. Two examples considering cracks and corners in isotropic plates are presented to show the correctness and validity of the modified H-integral.

A Unified Two-Phase Potential Method for Elastic Bi-material: Planar Interfaces

This paper gives a unified approach to analyze two-dimensional elastic deformations of a composite body consisting of two dissimilar anisotropic or isotropic materials perfectly bonded along a planar interface. The Eshelby et al. formalism of anisotropic elasticity is linked with that of Kolosov-Muskhelishvili for isotropic elasticity by means of two complex matrix functions describing completely the arising elastic fields. These functions, whose elements are holomorphic functions, are defined as the two-phase potentials of the bimaterial. The present work is concerned with bi-materials whose constituent materials occupy the whole space and are connected by a planar interface. The elastic fields arising in such a bimaterial are given by universal relationships in terms of the two-phase potentials. Then, the general results obtained are implemented to study two interesting bimaterial problems: the problem of a uniformly stressed bimaterial with a perfect interfacial bonding, and the interface crack problem of a bimaterial with a general loading. For both problems, all combinations of the elastic properties of the constituent materials are considered. For the first problem, the constraints, which must be imposed between the components of the applied uniform stress fields, are established, so that they are admissible as elastic fields of the bimaterial. For the interface crack problem, the solution is obtained for a general loading applied in the body. Detailed results are given for the case of a remote uniform stress field applied to the bimaterial constituents.

Stress Singularity Analysis at an Interfacial Corner between Dissimilar Crystals and Evaluation of Mixed Modes Fracture Criteria Using Molecular Statics

The asymptotic solution of an interfacial corner between dissimilar crystals is expressed by the theory of anisotropic linear elasticity. However, it is not elucidated if the stress field obtained by the molecular analysis corresponds with the anisotropic linear elastic solution. We analyzed the stress fields around interfacial corners between dissimilar crystals using the molecular statics, and compared them with the asymptotic solutions. The stress intensity factor (SIF) is one of the basic fracture mechanics parameters, but there are few applications of the SIF to the fracture criteria of interfacial corners. We proposed a new definition of the SIFs of an interfacial corner between dissimilar anisotropic materials in our previous paper. In this study, the mixed mode fracture criteria of interfacial corners between dissimilar crystals modeled by the molecular statics were evaluated using the proposed SIFs.

Existence of one-component Rayleigh waves, Stoneley waves, Love waves, slip waves and one-component waves in a plate or layered plate

It is known that one-component surface (Rayleigh) waves exist in an anisotropic elastic half-space. Since the solution shows that the displacement normal to the free surface vanishes everywhere, a onecomponent surface wave is also a one-component slip wave in the half-space if the boundary of the half-space is a slippery surface. We show that no other one-component slip waves exist for the halfspace. As to steady waves in a bimaterial that consists of two dissimilar anisotropic elastic materials, one-component slip waves can be constructed from two one-component surface waves. There are no other one-component slip waves for a bimaterial. By imposing the continuity of the displacement at the interface on the one-component slip wave, a one-component Stoneley wave is obtained. Although one-component waves for the half-space can also propagate in a homogeneous plate, we present new one-component waves in a plate for which the Stroh eigenvalue p is real. By superposition of the onecomponent waves in the layer and in the half-space, one-component Love waves can be constructed. Finally, we show that one-component waves can propagate in a layered plate.

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.

702 熱応力下の三次元接合構造物中に存在する異方性異種材接合角部の応力拡大係数解析(OS19.界面と接着・接合の力学,オーガナイズドセッション)

702 熱応力下の三次元接合構造物中に存在する異方性異種材接合角部の応力拡大係数解析(OS19.界面と接着・接合の力学,オーガナイズドセッション)

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.