Collinear Interface Cracks Research Articles

Moving EMPS model for semipermeable two equal collinear interface cracks in dissimilar magneto-electro-elastic materials

The moving electric-magnetic polarization saturation (EMPS) model is studied for two equal collinear interface cracks in mode-III dissimilar magneto-electro-elastic (MEE) bimaterial under semipermeable crack face conditions. The closed-form solutions of all three possible cases of the proposed EMPS model are derived using the distributed dislocation technique (DDT) and singular integral method. An iterative scheme and explicit expressions of fracture parameters are used to implement the semipermeable crack-face conditions. The study of local energy release rate based on constant electric and magnetic breakdown strength-based saturated conditions concludes that increasing the mismatch of the MEE bimaterial can improve its fracture toughness.

Thermal and fracture analysis of collinear interface cracks in graded coating systems under ramp-type heating

Ceramic based thermal barrier coatings are extensively employed to shield critical engineering components from harsh temperature environments, where the typical Fourier's law may not be able to provide an accurate assessment of the physical process. This work adopts a more generalized heat conduction approach to reveal the thermal and fracture interaction mechanism of two collinear interface cracks in orthotropic functionally graded thermal coating systems by dual-phase-lag theory. The heating rate of the imposed thermal loading on the exterior bounding surface is modeled by ramp-type function, where the ramping period is comparable to the certain time spent for building the local thermal equilibrium within composites. The methods of Fourier transform and Laplace transform in conjunction with the singular integral equations are applied to solve the complex transient thermoelastic problem. Parametric investigations are conducted to investigate the impacts of ramping time, thermal lags, nonhomogeneous parameters, and crack spacing on the thermal and fracture characteristics. According to the maximum hoop stress criterion, higher fracture risk is discovered with the approaching of collinear interface cracks.

Analytical fracture parameters of two unequal collinear interface cracks in an orthotropic bimaterial

This paper presents an analytical solution for the fracture parameters of two unequal collinear interface cracks (UCIC) in an infinite orthotropic or isotropic bimaterial subject to in-plane loading. The analytical expressions for the stress intensity factors (SIF), Jk-integrals and crack opening displacements of two UCIC in an infinite orthotropic bimaterial plate are derived using the complex variable method and evaluated in conjunction with the Jacobian elliptic functions and elliptic integrals. The presented theory is verified using the boundary element method. The results show that the fracture parameters are greatly influenced by mismatch of the engineering constants and proximity of the cracks. The inner tip of the longer crack always experiences the maximum SIFs and Jk values. These fracture parameters will increase exponentially when the distance between the cracks inner tips decreases. This study provides a baseline for the verification of future numerical and experimental studies of two UCIC which is not currently available in the SIFs handbooks.

Interaction of two collinear interface cracks with different electrical conditions at their faces in a one-dimensional piezoelectric quasicrystal

Interaction of two collinear interface cracks with different electrical conditions at their faces in a one-dimensional piezoelectric quasicrystal

The Anti-Plane Problem of Collinear Interface Cracks Emanating From a Circular Hole in 1D Hexagonal Quasicrystal Bi-Materials

The Anti-Plane Problem of Collinear Interface Cracks Emanating From a Circular Hole in 1D Hexagonal Quasicrystal Bi-Materials

Role of crack length, crack spacing and layer thickness ratio in the electric potential and temperature of thermoelectric bi-materials systems

The influence of dual collinear interface cracks on the electric potential and temperature of thermoelectric bi-materials system under the electric load and thermal load is reported. The nonlinear governing equations of thermoelectric materials are transformed into the Laplace equations with the help of the driving force of the electric current density and the energy flux introduced. Firstly, based on the boundary conditions about the electric potential and the temperature, the interface electric current density and the interface energy flux the boundary of crack-free system are obtained. Then, the problem of the dual interface cracks is transformed into a Riemann-Hilbert problem, and analytical solutions of the electric current density and the energy flux are achieved. Furthermore, we provide the intensity factors of electric current density and energy flux around the crack tip. Finally, we unveil the crucial role of crack length, crack spacing and layer thickness ratio in the electric potential and temperature of thermoelectric bi-materials by numerical experiments.

Interaction of collinear interface cracks between dissimilar one‐dimensional hexagonal piezoelectric quasicrystals

AbstractIn this paper, the interaction of collinear interface cracks between dissimilar one‐dimensional (1D) hexagonal quasicrystals with piezoelectric effect under anti‐plane shear and in‐plane electric loading has been studied. By using complex variable method the mixed boundary value problem for the interface cracks was reduced to the solution of Riemann‐Hilbert problem. Analytic full‐field solution for phonon and phason stresses, electric fields, electric displacement in the cracked bi‐materials has been obtained based on the electrically permeable crack model. The electric field and electric displacement inside the interface cracks are found to be nonlinearly distributed under line loadings. The field intensity factors of the interface cracks depend on both the mechanical and electric load for the line loading case, but the field intensity factors depend only on mechanical loading when the uniform loadings are applied at infinity. The investigation of the SIFs of neighboring interface cracks has been used to predict possible crack propagation. It is found that when the neighboring cracks are close enough, the inner crack tips are more likely to propagate and when the neighboring cracks are far away from each other, the outer crack tip of the bigger crack has more possibility to propagate.

Analytical stress intensity factors and Jk‐integrals of periodic and collinear interface cracks between dissimilar orthotropic materials

AbstractThis paper introduces an analytical expression for the stress intensity factors at the crack tips of a row of periodic and collinear cracks between infinite dissimilar orthotropic materials. The analytical Jk‐integrals of these traction‐free cracks have been presented for different material combinations, ‘crack length’/‘interval width’ ratios (λ) and various in‐plane loading conditions. Some of the analytical Jk‐integrals have been compared with the numerical values computed using the boundary element crack shape sensitivities which are in good agreement. For any in‐plane loading condition of a bimaterial plate with periodic and collinear interface cracks, the normalised J1‐integral is almost independent of λ, but there is a slight variation in the normalised J2‐integral with respect to λ. This is provided that the normalising factor is the strain energy release rate of a homogeneous plate made from one of the materials with the same ratio of λ and subject to the same loading condition.

Stress intensity factors for four interface-close cracks between a nonhomogeneous bonding layer and one of two dissimilar elastic half-planes

Abstract Stress intensity factors are estimated for four collinear interface cracks that are situated at the interface between a nonhomogeneous elastic bonding layer and one of two dissimilar elastic half-planes. Tensile stress is applied normal to the cracks. The material properties of the bonding layer vary continuously from those of the lower half-plane to those of the upper half-plane. To solve this problem, two solutions are combined: the solution for two inner collinear cracks and the solution for two outer collinear cracks. To satisfy the boundary conditions for the combined solution, the differences in the crack surface displacements are expanded as a series of functions that are zero outside the cracks. The unknown coefficients in the series are solved using the Schmidt method so they satisfy the conditions inside the four cracks. The stress intensity factors are calculated numerically for the selected crack configurations.

D-16 4個の共線界面き裂の応力拡大係数について

D-16 4個の共線界面き裂の応力拡大係数について

Electro-elastic analysis of bonded piezoelectric finite wedges with two collinear interface cracks under anti-plane deformation

This paper studies two collinear impermeable interface cracks in bonded piezoelectric finite wedges. The radial edges are subjected to anti-plane concentrated forces and in-plane electric surface charges. The circular boundary is considered as traction free and electrically insulated. The finite complex transform developed in the literature for elastic wedges is extended to electro-elasticity for piezoelectric wedges. Based on the finite Mellin transforms and series expansions, the crack surface conditions are expressed analytically in the form of a set of simultaneous standard singular integral equations, which can be solved numerically by the Lobatto–Chebyshev method. The Normalized Intensity Factors (NIFs) around crack tips are obtained for the elastic and electric field in explicit forms. Dependence of the NIFs on the crack length and crack interval, as well as the wedge angle, is discussed in detail. Crack interaction is graphically demonstrated and analyzed. Results show that extension of one crack length generally enhances the NIFs for both tips of the other crack. Crack interval significantly affects the NIFs of the inner crack tips of the collinear cracks. The formulation and results in this paper include, as special cases, some wedge problems presented in the literature. These analyses are expected to provide some guidance for the design of piezoelectric composite wedges.

Thermal Stresses Around Two Collinear Interface Cracks between a Nonhomogeneous Bonding Layer and One of the Two Dissimilar Elastic Half-Planes Under Uniform Heat Flux

In composite materials, in which two dissimilar elastic half-planes are bonded by a nonhomogeneous elastic layer, two collinear cracks are situated at the interface between the nonhomogeneous elastic layer and one of the two dissimilar half-planes. The stress intensity factors are solved under uniform heat flux normal to the cracks. The material properties of the bonding layer vary continuously from the lower half-plane to the upper half-plane. The boundary conditions are reduced to dual integral equations using the Fourier transform technique. In order to satisfy the boundary conditions outside the cracks, the differences in temperature and displacements at the crack surfaces are expanded in a series of functions that vanish outside the cracks. The unknown coefficients in each series are evaluated using the Schmidt method. The stress intensity factors were calculated numerically for selected crack configurations.

An exact analysis for mode III cracks between two dissimilar magnetoelectroelastic layers

This paper develops a closed-form solution for an interface crack in a layered magnetoelectroelastic strip of finite width. The strip is subjected to anti-plane mechanical and in-plane electric and magnetic fields. Explicit expressions for the stress, electric, and magnetic fields, together with their intensity factors, are obtained for two extreme cases of an impermeable and a permeable cracks. The stress intensity factor does not depend on the electromagnetic boundary conditions assumed for the crack. However, the electrically and magnetically permeable boundary conditions on the crack profile have a significant influence on the crack-tip electromagnetic field intensity factors. Solutions for some special cases, such as a central crack, an edge crack, two symmetric collinear cracks, and a row of collinear interface cracks, are also obtained in closed forms.

Interfacial fracture of layered magnetoelectroelastic materials

A problem for an interface crack located in a layered magnetoelectroelastic material strip of semi-infinite length is solved. A closed-form solution is obtained for anti-plane mechanical and in-plane electric and magnetic fields. Explicit expressions for stresses and electric and magnetic fields, together with their intensity factors and the energy release rate, are obtained. The extreme cases of impermeable and permeable cracks are discussed. Using the basic solution for a single crack, solutions for two collinear interface cracks in an infinitely long layered magnetoelectroelastic medium, an interface crack in an infinitely long layered magnetoelectroelastic medium, and an edge crack at the interface of a semi-infinitely long layered magnetoelectroelastic medium are also obtained.

Dynamic behavior of two collinear interface cracks between two dissimilar functionally graded piezoelectric/piezomagnetic material strips

The dynamic interaction of two collinear interface cracks between two dissimilar functionally graded piezoelectric/piezomagnetic material strips subjected to the anti-plane shear harmonic stress waves was investigated. By using the Fourier transform, the problem can be solved with the help of a pair of triple integral equations in which the unknown variable is jump of displacement across the crack surfaces. These equations are solved using the Schmidt method. Numerical examples are provided to show the effect of the functionally graded parameter, the circular frequency of the incident waves and the thickness of the strip upon stress, electric displacement and magnetic flux intensity factors of cracks.

The scattering of the harmonic anti-plane shear stress waves by two collinear interface cracks between two dissimilar functionally graded piezoelectric/piezomagnetic material half-infinite planes dynamic loading

In this paper, the dynamic behaviour of two collinear interface cracks between two dissimilar functionally graded piezoelectric/piezomagnetic material half-infinite planes subjected to the harmonic anti-plane shear stress waves is investigated. To make the analysis tractable, it is assumed that the material properties vary exponentially with coordinate vertical to the crack. By using the Fourier transform technique, the problem can be solved with the help of a pair of triple integral equations, in which the unknown variable is the jump of the displacements across the crack surfaces. These equations are solved by using the Schmidt method. The relations among the electric field, the magnetic flux field, and the dynamic stress field near the crack tips can be obtained. Numerical examples are provided to show the effect of the functionally graded parameter, the distance between two interface cracks, and the circular frequency of the incident waves upon the stress, the electric displacement, and the magnetic flux intensity factors of cracks.

Two Collinear Interface Cracks between Two Dissimilar Functionally Graded Piezoelectric/Piezomagnetic Material Layers under Anti-Plane Shear Loading

In this paper, the behavior of two collinear interface cracks between two dissimilar functionally graded piezoelectric/piezomagnetic material layers subjected to an anti-plane shear loading is investigated. To make the analysis tractable, it is assumed that the material properties vary exponentially with coordinate vertical to the crack. By using the Fourier transform, the problem can be solved with the help of a pair of triple integral equations in which the unknown variable is the jump of the displacement across the crack surfaces. These equations are solved using the Schmidt method. The normalized stress, the electrical displacement and the magnetic flux intensity factors are determined for different geometric for the permeable electric boundary conditions. The relations among the electric filed, the magnetic flux field and the dynamic stress field near the crack tips can be obtained. Numerical examples are provided to show the effect of the functionally graded parameter and the thickness of the strip upon the stress, the electric displacement and the magnetic flux intensity factors of the crack.

Analyzing the interaction between collinear interfacial cracks by an efficient boundary element-free method

A new traction boundary integral equation is presented for analyzing the interaction effect of any number of collinear interface cracks in a two-dimensional bimaterial. The dislocation densities on every crack surface are expressed in the products of the characteristic terms and the weight functions, and the unknown weight functions are approximated using the moving least-squares technique based on the constructed orthogonal basis functions. An efficient numerical integral method is employed to evaluate the Cauchy principal integrals that appear in the meshless method. The boundary element-free method is established, and a series of numerical results is presented. The interaction between the collinear interfacial cracks is analyzed.

The dynamic behavior of two collinear interface cracks in magneto-electro-elastic materials

In this paper, the dynamic behavior of two collinear symmetric interface cracks between two dissimilar magneto-electro-elastic material half planes under the harmonic anti-plane shear waves loading is investigated by Schmidt method. By using the Fourier transform, the problem can be solved with a set of triple integral equations in which the unknown variable is the jump of the displacements across the crack surfaces. To solve the triple integral equations, the jump of the displacements across the crack surface is expanded in a series of Jacobi polynomials. Numerical solutions of the stress intensity factor, the electric displacement intensity factor and the magnetic flux intensity factor are given. The relations among the electric filed, the magnetic flux field and the stress field are obtained.

Two collinear interface cracks in magneto-electro-elastic composites

In this paper, the behavior of two symmetric interface cracks between two dissimilar magneto-electro-elastic composite half planes under anti-plane shear stress loading is investigated by Schmidt method for the permeable crack surface conditions. By using the Fourier transform, the problem can be solved with a set of triple integral equations in which the unknown variable is the jump of the displacements across the crack surfaces. In solving the triple integral equations, the jump of the displacements across the crack surface is expanded in a series of Jacobi polynomials. Numerical solutions of the stress intensity factor are given. The relations among the electric filed, the magnetic flux and the stress field can be obtained.