Bi-material Half Space Research Articles

Dynamic response of a multi-layer inclusion embedded in right side of bi-material half space by SH waves

Dynamic response of a multi-layer inclusion embedded in right side of bi-material half space by SH waves

Dynamic stress intensity factor for periodic interfacial cracks in a bi-material half space disturbed by SH waves

The dynamic anti-plane properties of mode III interfacial collinear periodic cracks in a bi-material half space are investigated by the complex function and Green’s function methods. The responses of a rectangular domain under the action of an out-plane point source are solved, i.e. the required Green’s function is found. Periodic cracks at the interface are constructed by using the “cutting” method. Using the continuity conditions at the bi-material interface, the Fredholm integral equations of the first kind including the out-of-plane force system are established by the interface “conjunction” technique. Analytical expressions for the dynamic stress intensity factors (DSIFs) at crack tips are derived. Numerical analyses of DSIFs are conducted, and results discussed in depth.

Scattering of SH waves in a bi-material half space with a circular hole and periodic type III interfacial cracks

The dynamic anti-plane response of a bi-material half space including a circular hole and periodic interfacial cracks is investigated. An analytical model is established for periodic type III cracks that adopt the idea of “conjunction” modeling. The definite integral equations suitable for modeling the existence of multiple interfacial cracks are derived that satisfy the continuity conditions at the interface. Numerical calculations are carried out to find the dynamic stress concentration factor (DSCF), whose results indicate that the number of interfacial cracks has a significant effect on the dynamic stress concentration around the hole edge, especially for low-frequency incident SH waves.

Dynamic analysis for a vertical interface crack and the nearby circular cavity located at the piezoelectric bi-material half-space under SH-waves

The present problem aims to study the scattering behavior of SH-waves by a circular cavity near two symmetrically permeable interface cracks in the piezoelectric bi-material half-space. The steady-state response of the problem is obtained, with the aid of the Green’s function method and the complex function method. Above all, the essential expression of Green’s function is constructed by the mirror method. This expression satisfies the conditions of being stress-free and electric insulation on the horizontal boundary of the orthogonal space where the circular cavity is located, and the condition of bearing a harmonic out-plane line source force on the vertical boundary. Next, on the basis of dividing the bi-material medium into two parts along the vertical boundary, the first kind of Fredholm integral equation with uncertain anti-plane forces is established by using the conjunction method and the crack-division technology. Then, the solution is obtained by solving an algebraic equation with finite terms, which is an effective truncation of the integral equation. Finally, the dynamic stress concentration factor around the edge of the circular cavity and the dynamic stress intensity factor at the crack tip are calculated numerically. On this basis, the effects of incident wave frequency, crack length, crack location and circular cavity position on the dynamic stress concentration factor and dynamic stress intensity factor are discussed.

Anti-plane Response of a Dike near Bi-material Interface to SH Waves

In the present work, we study the scattering of SH waves by a dike embedded near the interface of bi-material half space. For this, a simple model is utilized to discuss the response of a dike near the interface. Complex function method, image principle, region-matching technique and Green function method are introduced to obtaine the total displacement fields along the free surface of the dike. The results are presented graphically considering the different material parameters. The results show that the displacement along the dike is greatly dependent upon the properties of bi-material interface.

Dynamic analysis of SH wave by a three-layer inclusion near interface in bi-material half space

In this paper, the scattering of SH waves by a three-layer inclusion near the bi-material interface has been studied. A complex function method is employed to solve a two-dimensional wave propagation problem. The displacement fields in the bi-material half space and inside the linings of the inclusion are constructed, satisfying the governing equation, and unknown coefficients are solved from boundary conditions. The bi-material half space is separated into two quarter spaces, and the region matching method is used to determine the extra-forces on the interface. With the aid of the Green function method, the displacement fields owing to the forces are obtained. Then, the dynamic stress concentration factors (DSCFs) around the inner and outer surfaces of the inclusion are presented graphically, considering different medium parameters. Results are compared with those of earlier investigations, and the effect of parameters on the DSCF is discussed.

Scattering of SH Wave by a Semi-Circle Inclusion Embedded in Bi-Material Half Space Surface

ABSTRACTInvestigation of SH wave scattering by inclusions in bi-material half space is an important issue in engineering. The purpose of this work is to study the dynamic response of a semi-circle inclusion embedded in bi-material half space surface by SH wave. Graf's addition theorem, Green function method and region-matching technique are used to determine the displacement fields in the bi-material half space and the inclusion. The distributions of dynamic stress concentration factor (DSCF) around the semi-circle inclusion are depicted graphically considering different material parameters. The results show that the frequency and the incidence angle of SH wave, the rigidities of the inclusion and bi-material half space, and the distance from the inclusion to the interface have a great effect on the distribution of DSCF around the inclusion.

Dynamic response of two adjacent semi-cylindrical alluvial inclusions embedded in a bi-material half space surface by SH waves

One model is utilized to investigate the dynamic response of two adjacent semi-cylindrical alluvial inclusions in the bi-material half space. Graf’s addition theorem, method of separation of variables (MSV), image method and region-matching technique (RMT) are used to construct the displacement fields in the two inclusions and the bi-material half-space subjected to an extra force. With the help of Green function and interfacial conjunction, the displacements in them are obtained, so that the dynamic stress concentration factors (DSCFs) around the two inclusions are calculated. The results demonstrate that the DSCF around an inclusion is influenced by material properties of the other inclusion and the bi-material interface.

Дослідження усталених крутних коливань біматеріалу півпростір з тріщиною—шар з використанням ефективних крайових умов

Дослідження усталених крутних коливань біматеріалу півпростір з тріщиною—шар з використанням ефективних крайових умов

The scattering of steady-state SH waves in a bi-material half space with multiple cylindrical elastic inclusions

The scattering of steady-state SH waves in a bi-material half space with multiple cylindrical elastic inclusions is presented analytically. Mirror method and multi-polar coordinate systems are developed to solve the complex boundary value problem. Considering the displacement and stress continuity conditions, a series of integral equations for unknown coefficients are obtained and solved by truncation. The solution is used to calculate the dynamic stress concentration factor around the edge of the inclusion, and the analysis and numerical results are discussed. The results show that degree of dynamic stress concentration around the circular inclusion is influenced by the incident angle, the incident wave number, and the parameters of medium.

Scattering of SH wave by a semi-cylindrical salient near vertical interface in the bi-material half space

With the aid of the Green function method and image method, the problem of scattering of SH-wave by a semi-cylindrical salient near vertical interface in bi-material half-space is considered to obtain its steady state response. Firstly, by the means of the image method, Green function which is the essential solution of displacement field is constructed to satisfy the stress-free condition on the horizontal boundary in a right-angle space including a semi-cylindrical salient and bearing a harmonic out-of-plane line source force at any point on the vertical boundary. Secondly, the bi-material is separated into two parts along the vertical interface, then unknown anti-plane forces are applied on the vertical interface, and according to the continuity condition, the first kind of Fredholm integral equations is established to determine unknown anti-plane forces by “the conjunction method”, then the integral equations are reduced to the linear algebraic equations by effective truncation. Finally, the dynamic stress concentration factor (DSCF) around the edge of semi-cylindrical salient is calculated, and the influences of incident wave number, incident angle, effect of interface and different combination of material parameters, etc. on DSCF are discussed.

Scattering of SH-Wave by a Circular Inclusion Near the Interfacial Cracks in the Piezoelectric Bi-Material Half-Space

AbstractWith the aid of the Green's function method and complex function method, the scattering problem of SH-wave by a circular inclusion near the two symmetrically permeable interfacial cracks in the piezoelectric bi-material half -space is considered to obtain the steady state response. Firstly, by means of the image method, the essential function of Green's function is constructed, which satisfies the stress free and electric insulation conditions on the horizontal boundaries in a right-angle space including a circular inclusion and bearing a harmonic out-plane line source force on the vertical boundary. Secondly, the bi-material media is divided into two parts along the vertical boundary. According to continuity condition, the first kind of Fredholm integral equations containing undetermined anti-plane forces are established by “the conjunction method” and “the crack-division technology”, then the integral equations are reduced to the algebraic equations including finite items by effective truncation. Finally, the dynamic stress concentration factor around the edge of circular inclusion and dynamic stress intensity factor at the crack tip are calculated, then the influences of the frequency of incident wave, the length of crack, the position of the crack, the position of circular inclusion, etc. on the dynamic stress concentration factor and dynamic stress intensity factor are discussed.

Scattering of SH Wave by a Cylindrical Inclusion and a Semi-Cylindrical Hollow Near Vertical Interface Crack in the Bi-Material Half Space

AbstractWith the aid of the Green's function method and complex function method, the scattering problem of SH-wave by a cylindrical inclusion and a semi-cylindrical hollow in the bi-material half space is considered to obtain the steady state response. Firstly, by the means of the image method, the essential solution of displacement field as well as Green's function is constructed which satisfies the stress free on the horizontal boundary in a right-angle space including a cylindrical inclusion and a semi-cylindrical hollow and bearing a harmonic out-plane line source force at any point on the vertical boundary. Secondly, the bi-material half space is divided into two parts along the vertical interface, and the first kind of Fredholm integral equations containing undetermined anti-plane forces at the linking section is established by “the conjunction method” and “the crack-division method”, the integral equations are reduced to the algebraic equations consisting of finite items by effective truncation. Finally, dynamic stress concentration factor around the edge of cylindrical inclusion and dynamic stress intensity factor at crack tip are calculated, and the influences of effect of interface and different combination of material parameters, etc. on dynamic stress concentration factor and dynamic stress intensity factor are discussed.

Analysis of dynamic stress intensity factors for interfacial crack near shallow circular inclusion in bi-material half-space to SH wave

An analytical approach is used to investigate the SH-wave scattering problems of the bi-material half-space including a circular inclusion embedded and an interfacial crack. Considering the multiple scattering phenomena between the boundaries and the circular inclusion, the “image” principle is used to establish the expressions of the wave field. With the aid of interfacial conjunction, the interfacial crack is constructed. According to the displacement and stress continuity conditions, the Fredholm integral equations of the first kind are obtained to determine the unknown forces attached to the linking sections. Finally, analytical expressions for dynamic stress intensity factors are obtained. The numerical results for dynamic stress intensity factors are presented graphically considering the factors of the crack length, the incident wave number, the inclusion defect and the different media parameters.

Dynamic Analysis for Circular Inclusion Near Interfacial Crack Impacted by SH-Wave in Half Space

ABSTRACTComplex method and Green's function method are used here to investigate the dynamic analysis for circular inclusion near interfacial crack impacted by SH-wave in bi-material half-space. Firstly, the displacement expression of the scattering wave was constructed which satisfied the free boundary conditions, then Green's function could be constructed, which was an essential solution to the displacement field for an elastic right-angle space with a circular inclusion impacted by out-plane harmonic line source loading at vertical surface. Secondly, crack was made out with “crack-division” technique. Meanwhile, the bi-material media was divided into two parts along the bi-material interface based on the idea of interface “conjunction”, and then the vertical surfaces of the two right-angle spaces were loaded with undetermined anti-plane forces in order to satisfy displacement continuity and stress continuity conditions at linking section. So a series of algebraic equations for determining the unknown forces could be set up through continuity conditions and the Green's function. Finally, some examples and results for dynamic stress concentration factor of the circular elastic inclusion were given. Numerical results show that they are influenced by interfacial crack, the incident wave number and the free boundary in some degree.

Scattering of Sh-Wave by Cylindrical Inclusion Near Interface in Bi-Material Half-Space

ABSTRACTGreen's function and complex function methods are used here to investigate the problem of the scattering of SH-wave by a cylindrical inclusion near interface in bi-material half-space. Firstly, Green's function was constructed which was an essential solution of displacement field for an elastic right-angle space possessing a cylindrical inclusion while bearing out-of-plane harmonic line source load at any point of its vertical boundary. Secondly, the bi-material media was divided into two parts along the vertical interface using the idea of interface “conjunction”, then undetermined anti-plane forces were loaded at the linking sections respectively to satisfy continuity conditions, and a series of Fredholm integral equations of first kind for determining the unknown forces could be set up through continuity conditions on surface. Finally, some examples for dynamic stress concentration factor of the cylindrical elastic inclusion are given. Numerical results show that dynamic stress concentration factor is influenced by interfaces, free boundary and combination of different media parameters.

Dislocation tri-material solution in the analysis of bridged crack in anisotropic bimaterial half-space

The problem of an edge-bridged crack terminating perpendicular to a bimaterial interface in a half-space is analyzed for a general case of elastic anisotropic bimaterials and specialized for the case of orthotropic bimaterials. The edge crack lies in the surface layer of thickness h bonded to semi-infinite substrate. It is assumed that long fibres bridge the crack. Bridging model follows from the assumption of “large” slip lengths adjacent to the crack faces and neglect of initial stresses. The crack is modelled by means of continuous distribution of dislocations, which is assumed to be singular at the crack tip. With respect to the bridged crack problems in finite dissimilar bodies, the reciprocal theorem (Ψ-integral) is demonstrated as to compute, in the present context, the generalized stress intensity factor through the remote stress and displacement field for a particular specimen geometry and boundary conditions using FEM. Also the application of the configurational force mechanics is discussed within the context of the investigated problem.