Permeable Crack Research Articles

Multiple electrically limited permeable cracks in the interface of piezoelectric materials

A bimaterial piezoelectric space with collinear electrically limited permeable cracks along the material’s interface is considered under plane strain conditions. The distances between the cracks, their location and number can be arbitrary. The problem of linear relationship is formulated and solved exactly. The electric flux over the crack regions is found. The closed-form expressions for stresses and electric displacement outside cracks and also for displacement jumps over cracks regions are found. The energy release rates at the crack tips are also derived in an analytical form. Numerical analysis is performed for different loading, cracks permittivity, their number, lengths, and locations.

Dynamic fracture of a partially permeable crack in a functionally graded one-dimensional hexagonal piezoelectric quasicrystal under a time-harmonic elastic SH-wave

The dynamic fracture of a crack in a functionally graded one-dimensional (1D) hexagonal piezoelectric quasicrystals (PEQCs) subjected to a time-harmonic elastic SH-wave is studied by using integral transform technique and Copson method. It is assumed that the crack surface is a partially permeable boundary condition and the material properties vary continuously as an exponential function. With the help of the Fourier transform, the boundary value problem of partial differential equation describing fracture problem is formulated to three pairs of dual integral equations, which are numerically solved by Copson method. Explicit expressions for the electroelastic field including phonon and phason stresses and electric field on the crack face are determined. The dynamic intensity factors of the electroelastic field are obtained in closed form, and some special cases of obtained results are discussed. On the basis of theoretical analysis and numerical simulation of the established models, numerical analysis was then conducted to discuss crack length, gradient parameter, electric boundary condition, electric loading, incident angle, amplitude, and wave number on the fracture characteristics of material. The research of this paper will provide a theoretical basis for nondestructive testing, optimal design, and reliability analysis of materials and will enrich the research content of fracture mechanics of multi-field coupling materials.

On energy release rate for an electrically permeable interface crack between two different 1D hexagonal piezoelectric QCs

A bi-material composed of two 1D piezoelectric hexagonal quasicrystals with a crack along the material interface was considered. Phonon and phason remote loading providing plane strain conditions were applied at infinity and an open crack model was adopted. Because electromechanical fields have an oscillating singularity at the crack tip, the energy release rate (ERR) is the most important fracture parameter in this case. The main purpose of this study is to define ERR in an analytical form. Using the obtained earlier asymptotic presentations of the phonon and phason fields at the crack tip and the crack closure integral approach, the desired formula is obtained in a simple form. The eligibility of the formula is verified by means of a crack in the bi-material composed of two 1D piezoelectric hexagonal quasicrystals and by considering a crack in homogeneous materials of this type. An additional comparison of the results obtained for a particular case of an isotropic material with known values confirmed the validity of the obtained formula.

Arbitrary number of electrically permeable cracks on the interface between two one-dimensional piezoelectric quasicrystals with piezoelectric effect

A set of finite number collinear cracks along the interface of two 1D piezoelectric hexagonal quasicrystals is considered. The cracks can have arbitrary lengths and distances between their tips and they are considered as electrically permeable. Remote phonon and phason loading, which results in plane strain state, are applied at infinity and the cracks are assumed to be open. By using the presentations of phonon and phason characteristics through sectionally-analytic functions, the problem of linear relationship is formulated and solved in an analytical form. Phonon and phason stresses outside cracks and also correspondent crack faces displacement jumps are presented in the closed forms. It is found out that all fields have an oscillating singularity at the crack tips, therefore, the energy release rate (ERR) is the most appropriate fracture parameter in this case. Using the asymptotic presentations of the phonon and phason fields at the crack tips and the crack closure integral approach, the analytical formula for the ERR have been obtained. The variations of the phonon and phason crack faces displacement jumps, stresses along the interface and the ERR are presented in graph and table forms for different crack tips, loading, crack lengths and their locations. New valuable conclusions have been made concerning the influence of the cracks interaction, their number and locations on the ERR, phonon and phason fields.

Mathematical Model of Fluid Filtration to the Production Wells in the Reservoirs with Discontinuities

Recently, it has been proved very important to study the filtration process in the reservoir with discontinuities of permeability. These discontinuities may be either natural, like tectonic fault, or artificial, like hydraulic fractures, and it may have various permeability values. This paper considers the steady-state flow process of incompressible fluid to the production well in a reservoir of constant height and permeability. There is a thin area in the reservoir with constant permeability kf, which might be highly permeable crack or low permeable barrier. The characteristics of filtration process are studied for various kf values. The nature of fluid flow to the wellbore is analyzed at different locations of the well and the crack for different values of the fracture conductivity in this paper and the analytical expression for skin effect is defined.

An interaction of electrically conductive and electrically permeable collinear cracks in the interface of piezoelectric materials

An interaction of electrically conductive and electrically permeable collinear cracks in the interface of piezoelectric materials

An EFGM approach for permeable, semi-permeable and impermeable crack interaction study in 2D piezoelectric domains

This paper presents the numerical simulation of permeable, semi-permeable and impermeable crack interaction study in 2D piezoelectric domains using an element-free Galerkin method (EFGM). The electric and displacement fields are described by introducing the singularity terms into an approximation function. This study is performed with respect to effects of electrical loading, crack surface boundary conditions, crack orientation angles, aspect ratio and number of cracks in order to examine these effects on fracture parameters. Multiple inclined equidistant cracks are considered in piezoelectric domain under different crack surface boundary conditions. The proposed enrichment criterion accurately estimates fracture parameters which shows the robustness, efficacy and applicability of EFGM approach.

The Analysis of a Cracked Material under Combined Unsymmetric Thermal Flux and Symmetric Linear Mechanical Loading

An improved partially permeable crack model is put forward to deal with the problem of a single crack embedded in an orthotropic or isotropic material under combined unsymmetric thermal flux and symmetric linear mechanical loading. With the application of the Fourier transform technique (FTT), the thermoelastic field is given in a closed form. Numerical results show combined unsymmetric linear thermal flux, symmetric linear mechanical loading, and dimensionless thermal conductivity, and the coefficient has influences on fracture parameters. For the improved partially permeable crack, the mode II stress intensity factor and the energy release rate might be zero or positive under combined unsymmetric thermal flux and symmetric linear mechanical loading. Therefore, closure of the crack tip region need not be considered under combined unsymmetric thermal flux and symmetric linear mechanical loading when making use of fracture parameters as a criterion.

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.

Dynamic fracture behavior for functionally graded piezoelectric bi-materials with interfacial cracks near a circular hole

This work aims to develop an effective method for evaluating the stress concentration at the tip of permeable interfacial cracks near a circular hole in functionally graded piezoelectric bi-materials. The structure is loaded by anti-plane incident SH-wave and all material parameters are assumed to obey exponential variations. Fracture analysis is performed by the Green function method, which is used to solve the boundary conditions problem. The mechanical model of the cracks is constructed by crack-conjunction and crack-deviation techniques so that the crack problem is simplified as solving a series of the first kind of Fredholm’s integral equations, from which the dynamic stress intensity factors (DSIFs) at the inner and the outer crack tips can be derived. The validity of the present method is verified by comparison with references. Numerical cases reveal parametric dependence of DSIFs on the geometry of circular holes and cracks, the characteristics of the incident waves and the inhomogeneity of materials. The method proposed in this paper can circumvent the limitations of using dual integral equations to deal with asymmetric defects and opens up a new way for the research on fracture problems in functionally graded piezoelectric materials with more complex defects.

Dynamic performance for piezoelectric bi-materials with an interfacial crack near an eccentric elliptical hole under anti-plane shearing

The purpose of this paper is to evaluate the stress concentration at the tip of a permeable interfacial crack near an eccentric elliptical hole in piezoelectric bi-materials under anti-plane shearing. Fracture analysis is performed by Green’s function method and the conformal mapping method, which are used to solve the boundary conditions problem. The mechanical model of the interfacial crack is constructed by interface-conjunction and crack-deviation techniques so that the crack problem is simplified as solving a series of the first kind of Fredholm’s integral equations, from which the dynamic stress intensity factors (DSIFs) at the inner and the outer crack-tips can be derived. The validity of the present method is verified by comparing with a crack emerging from the edge of a circular hole as a reference. Numerical cases reveal parametric dependence of DSIFs on the geometry of eccentric elliptical holes and interfacial cracks, the characteristics of the incident wave, the equivalent piezoelectric elastic modulus and piezoelectric parameters. The results illustrate that the eccentric distance has a great effect on the stress concentration at the crack tip, which may be harmful to the normal service of piezoelectric devices and materials. In addition, the method proposed in this paper can also deal with non-eccentric problems and has wider applicability.

Experimental study of wetting-seepage effect of microemulsion for the coal seam water injection

The microemulsion was used as an injection agent for the coal seam water injection. In this paper, wetting and seepage parameters of microemulsion, water and SDS are studied, and modification mechanism of microemulsion to increase wetting and promote seepage is revealed. The results indicated that microemulsion exhibited stronger spreadability and a smaller contact angle because of surface tension. The content of benzene ring one adjacent H, S = O, OH…N, CH structure was positively correlated with the contact angle. The content of benzene ring three adjacent H and CH3 structure was negatively correlated with the contact angle. The change of functional group content is the main reason for the wettability modification of coal by microemulsion. SDS exhibited the best initial seepage rate, followed by microemulsion, and water was the worst. Microemulsion increased the capillary number and increased the permeable cracks and pores, and finally improved the permeability of coal. Under the action of the capillary force, the permeability effect of non-pressure microemulsion injection was improved.

Laboratory evaluation of hybrid chemical enhanced oil recovery methods coupled with carbon dioxide

Chemically enhanced oil recovery techniques have been considered efficient tertiary methods to improve the oil production from oil reservoirs regarding their compatibility with the reservoir characteristics. Moreover, gravity segregation and viscous fingering during carbon dioxide flooding would be the main problems of oil recovery techniques. In this paper, a hybrid chemical flooding that contained the subsequent flooding of surfactant–polymer​ (henceforth; SP) coupled with supercritical carbon dioxide was performed to enhance the oil recovery factor. The foaming agent that is used in this experiment is solely formed by CO2. It is concluded that SP-foam flooding had witnessed the highest blockage, which is caused to have the maximum cumulative oil recovery factor (about 78%) due to the more mobilization oil in low permeable pores and cracks. Furthermore, direct foam flooding has the second-highest oil recovery factor (nearly 70%), which is considered as the preferable techniques to SP-CO2 flooding (65%). On the contrary, SP-foam flooding has provided the highest pressure drop after the minimum miscible pressure circumstances, which is about 0.27 MPa at the end of the process.

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.

Investigation of Breakthrough Curves in Porous Media with a Crack

Fractured porous media provide an important topic in particular for geologists and for material scientists. Many researchers are concerned with fluid flow. Here we extend the research studies by focussing on transport processes. In order to understand the effect on the micro-scale we examine details of a porous medium with a single fracture, a crack. By numerical experiments using finite element simulations we investigate the effect of crack characteristics on the overall behaviour of the combined flow and transport matrix-crack system that is observed in breakthrough curves. We deal with open cracks and with highly permeable fractures, varying their conductivity in relation to the porous medium conductivity. We also vary the crack orientation relative to the flow direction, and the crack aperture. Aside from the differences between the simulated scenarios, the results show that there is an increased diffusivity with the overall permeability of the system. While the front breakthrough appears earlier for higher permeable cracks, transport in low flow regions is slowed down. As a result, pockets of the replaced fluid remain longer within the system. The latter result can have important implications in application cases.

An analytical approach to the analysis of an electrically permeable interface crack in a 1D piezoelectric quasicrystal

A plane problem is analysed for an electrically permeable crack in a bi-material composed of two semi-infinite 1D piezoelectric quasicrystals bonded together. The polarization direction coincides with the quasiperiodic direction of the materials and is orthogonal to the interface. Uniformly distributed phonon normal and shear in-plane stresses and also phason stress and electric displacement are applied at infinity. The matrix–vector representations for the phonon and phason stresses, the electrical displacement and for the derivatives of the phonon and phason displacements and electrical potentials jumps via the sectional-holomorphic vector-function are derived. Using these relations and satisfying the conditions at the crack faces, the problems of linear relationship are formulated and solved exactly. All required phonon and phason characteristics are given in the form of simple analytical expressions. A numerical analysis is carried out for two different 1D piezoelectric quasicrystals bonded together. The obtained results are presented in graph and table forms.

Dynamic intensity factors for multiple permeable cracks in piezoelectric materials

AbstractThis article presents the dynamic intensity factors for multiple permeable Mode‐I cracks in piezoelectric materials plane by means of the generalized Almansi's theorem. The Fourier transform is used and the present problem is formulated into two pairs of dual integral equations. The dual integral equations are solved by the Schmidt method. The dynamic stress intensity factors (DSIFs) and the dynamic electric displacement intensity factor (DEDIF) at the crack tips are given. It is shown that the effects of the crack length, the distance between two parallel cracks and the circular frequency of incident wave near the crack tips on the DSIFs and DEDIF.

Interfacial cracks near an eccentric circular hole in piezoelectric bi-materials subjected to dynamic incident anti-plane shearing

Dynamic fracture analysis of piezoelectric materials with eccentric defects is an important criterion for the design of piezoelectric components. This work aims to suggest an effective method for the dynamic anti-plane shearing problem of piezoelectric bi-materials with permeable interfacial cracks near an eccentric circular hole. In the paper, Fredholm’s equations are solved via the Green’s function method and the coordinate transformation method. Based on conjunction and crack-deviation techniques, the dynamic stress intensity factors (DSIFs) at the outer and the inner tips of the left crack are expressed analytically. As cases, the effects of the eccentric distance, the piezoelectric parameters, the ratio of the crack length to the hole radius, and the dimensionless wave number of the incident wave are presented graphically.

Fracture analysis on an infinite row of collinear permeable cracks in a porous medium

The dynamic (frequency-dependent) mode-I stress intensity factor (SIF) is obtained for a porous medium containing an array of equally distributed collinear cracks. Unlike previous work in which the cracks are assumed to be dry and impermeable, this paper studies the case that the crack is fluid-saturated and permeable. The cracks are under the action of a normal incidence of a time-harmonic plane longitudinal (P) wave. The interaction between the collinear cracks and the mechanism of wave-induced fluid flow (scattered slow P wave) can significantly affect the magnitude and frequency-dependent trend of the SIF, in particular at low frequencies. At low frequencies, the magnitude of the SIF increases monotonously with the decreasing distance between the adjacent cracks and can be much larger than that of a single crack, implying that the material strength can be greatly lowered by the interaction of cracks. However, at higher frequencies, the impacts of interacting cracks are negligible. The comparison with the counterpart of dry impermeable cracks reveals that the magnitude of SIF is lower than that of dry impermeable cracks owing to effective normal stress effect. Moreover, unlike the SIF of dry impermeable cracks for which a peak value is observed around elastic wave resonance frequency, the corresponding SIF of fluid-saturated permeable cracks monotonously decreases with the increasing frequency. This frequency-dependent trend is attributed to the conversion of incident energy into the slow P wave. The obtained results reveal significant influences of the presence of pore fluid and interaction of collinear cracks upon the SIF, both magnitudes and frequency-dependent trends. Such information is useful in predicting the fracture strength of saturated porous materials subjected to oscillating loads.

Thermal shock resistance and thermal fracture of a thermopiezoelectric cylinder based on hyperbolic heat conduction

Accurate evaluation of the thermal shock resistance is great importance when estimating both the life and the performance of piezoelectric structures under thermal shock load. Non-Fourier heat conduction law assumed that the speed of heat propagation in a body is finite, which is more exact to evaluate the thermal shock resistance when the thermal shock time reduces to ps/fs scale or the length size of materials reduces to micro/nanoscale. A hyperbolic heat conduction equation was used to study the thermal shock resistance of a cylindrical piezoelectric structure, in which a permeable penny-shaped crack is considered. The analytical solution of non-Fourier temperature filed is determined by the method of separated variable. The formulas of the associating thermal stress and electrical displacement in the piezoelectric cylinder without crack were obtained. The crack problem is solved by the Dual integral equation and Abel integral equation. The thermal shock resistance is evaluated by associating the stress-based and fracture mechanics-based failure criteria.