Field Intensity Factors Research Articles

Dynamic instability, free vibration, and buckling analysis of MR fluid sandwich plates with FG face layers using the HSDT-based finite strip method

In the present study, by using a higher-order shear deformation plate theory (HSDT) and considering the second model proposed by Frostig and Thomsen, Dynamic instability, static buckling, and free vibration of the Magneto-Rheological (MR) fluid sandwich plates subjected to an axial periodic force is investigated. MR fluids are a group of smart materials whose rheological properties change rapidly with the application of a magnetic field. The upper and lower layers of the core (face layers) are selected from two different types. In the first group, they are made of functionally graded materials (FGMs), and the second group, consists of a matrix phase reinforced with carbon nanotubes (CNTs). The mechanical properties of the nanocomposite are considered in accordance with the extended rule of mixtures. The governing equations are derived using Hamilton’s principle and discretized by the finite strip method. The results obtained from the finite strip method are compared with the results of available literature. The impact of various parameters such as magnetic field intensity, core thickness, static and dynamic load factors, different boundary conditions, and the CNT distribution on the critical static buckling, natural frequency, and instability zone of the structure are investigated. The results show that increasing the MR fluid thickness has a stabilizing effect on the dynamic instability of the MR fluid sandwich plates.

DYNAMIC FRACTURE PROPAGATION MECHANISM AND APPLICATIONIN TIGHT OIL RESERVOIR

Tight oil reservoirs have achieved certain oil increase effect by supplementing formation energy with water-injection huff and puff. However, formation pressure and production decrease rapidly after multiple rounds of water injection. In order to improve the oil enhancement effect of tight oil reservoirs, changing the development method quickly became hotspot research. This paper analysis the stress field distribution near the tip of type I fracture considered the complex fracture morphology of tight oil reservoirs based on Irwin theory and elastic mechanics. A multi-fracture cross-fracture propagation model is established based on seepage mechanics, fractured tight reservoir characteristics and dynamic fracture seepage characteristics. The fracture propagation length is obtained based on the fracture propagation mechanism and the energy conservation principle. It is proposed to turn water-injection huff and puff into unstable pulse water injection according to the principle of reverse imbibition in tight oil reservoirs. Comparative analysis of two energy supplementary generation methods, water-injection huff and puff and pulse water injection, predicting cumulative oil production, pressure and remaining oil distribution in 10 years. The results show that the net internal pressure of the fracture increases with the increase of water injection, and the stress field intensity factor also increases. When the stress field intensity factor reaches the fracture toughness, it will expand at the fracture tip. The expanded and extended natural fractures communicate with each other, presenting irregular and complex fracture networks. Reverse imbibition mainly occurs in the complex fracture networks. Pulse water injection has a high cumulative oil production, a wide area of water injection and strong reverse imbibition. The findings of this study can help for better understanding of the transformation of water-injection huff and puff into pulsed water injection from horizontal wells in fractured tight oil reservoirs. It can give full play to the effects of reverse imbibition and linear displacement. This research provides guidance for it can achieve the purpose of effective oil displacement of the dynamic fracture network.

In-plane stress analysis in a cracked functionally graded piezoelectric plane

The fracture behavior of a cracked functionally graded piezoelectric plane was investigated under in-plane mechanical and electrical loading. The electro-elastic properties of the plane exponentially varied along the y-axis. Employing the Fourier transform, stress analysis containing a Volterra edge dislocation in a functionally graded piezoelectric plane was carried out. These solutions were used to derive a system of Cauchy singular integral equations for analyzing the straight and curved cracks. Linear, arc, parabolic and sine wave-shaped cracks were evaluated. The integral equations were numerically solved using the Lobatto–Chebyshev integration formula for dislocation density functions on the crack face which were employed to calculate field intensity factors. The effects of the shaped crack, loading parameters, and non-homogeneity parameter on the stress and electric intensity factors were considered.

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.

Transient non-Fourier thermoelastic fracture analysis of a cracked orthotropic functionally graded strip

In this work, the fracture problem of an orthotropic functionally graded strip containing an internal crack parallel to its surfaces subjected to thermal shocks is examined. To eliminate the paradox of infinite heat propagation speed and take the microstructural interactions of thermal energy carriers into account, the non-Fourier, dual-phase-lag theory is employed to investigate the transient heat conduction and the associated thermal stresses response. By utilizing Laplace transform and Fourier transform, the thermoelastic problems are finally reduced to the Cauchy-type singular integral equations, which are solved by the Lobatto–Chebyshev technique numerically. The temperature field and thermal stress intensity factors are evaluated by the numerical inversion of Laplace transform to illustrate the effects of two thermal lags and nonhomogeneous parameters. The results show the fracture risks accompanied by the dual-phase-lag heat conduction can be higher than the classical analysis and it would be more conservative to consider non-Fourier effects in designing the orthotropic functionally graded materials.

Surface effects on a mode-III reinforced nano-elliptical hole embedded in one-dimensional hexagonal piezoelectric quasicrystals

To effectively reduce the field concentration around a hole or crack, an anti-plane shear problem of a nano-elliptical hole or a nano-crack pasting a reinforcement layer in a one-dimensional (1D) hexagonal piezoelectric quasicrystal (PQC) is investigated subject to remotely mechanical and electrical loadings. The surface effect and dielectric characteristics inside the hole are considered for actuality. By utilizing the technique of conformal mapping and the complex variable method, the phonon stresses, phason stresses, and electric displacements in the matrix and reinforcement layer are exactly derived under both electrically permeable and impermeable boundary conditions. Three size-dependent field intensity factors near the nano-crack tip are further obtained when the nano-elliptical hole is reduced to the nano-crack. Numerical examples are illustrated to show the effects of material properties of the surface layer and reinforced layer, the aspect ratio of the hole, and the thickness of the reinforcing layer on the field concentration of the nano-elliptical hole and the field intensity factors near the nano-crack tip. The results indicate that the properties of the surface layer and reinforcement layer and the electrical boundary conditions have great effects on the field concentration of the nano-hole and nano-crack, which are useful for optimizing and designing the microdevices by PQC nanocomposites in engineering practice.

Ultrahigh mid-infrared electric field enhancement via nanoantenna plasmonic resonance coupled to a novel hyperbolic metalens

Concentrating optical energy to areas much smaller than the diffraction limit, with high field enhancement in mid-infrared (MIR) using noble metals such as gold (Au) or silver (Ag), is not feasible because of high losses, lack of tunability, low resolution, and low-intensity enhancement. Our methods are based on appropriate metamaterial selection, coupling system (a hyperbolic metalens and a nanoantenna), and optimizations of their geometries. Doped indium arsenide (InAs) is used as an alternative to plasmonic metals when designing a Fresnel zone plate (FZP). A hyperbolic metamaterial (HMM), placed under FZP, is formed by stacking layers of doped and undoped InAs. By combining the focal spot of the metalens with the excited plasmons of a nanoantenna, the resulting structure exhibits an ultrahigh field-intensity enhancement factor of about 1012 with a high absorption cross-section and a focusing resolution of up to 10−3 λ at the operating wavelength of 7.8 μm.

Study on prediction method of crack propagation in absorber weld by experiment and simulation

As an important equipment for purifying crude oil and natural gas in energy industry, absorber is subjected to harsh working environment of high stress and severe corrosion. Especially, weld is the weak region of the absorber, which faces significant risk of crack propagation due to residual stress caused by the welding process, working pressure and temperature. Meanwhile, crack propagation in absorbers with high pressure, high temperature and toxic media can often cause disastrous consequences. Therefore, to solve this problem, a systematic method considering welding, heat treatment and working process is presented in this paper to predict crack propagation completely in the weld. In the case, based on actual conditions, a finite element model (FEM) of welding process considering transient heat transfer and heat radiation for residual stress field analysis is established to obtain the far-field stress for cracks. Then, the detailed analysis of stress field and stress intensity factor (KI) under the obtained far-field stress at the crack tip is carried out through the method of integrating the strain energy density (SED) in the crack tip region. Finally, experiments of fracture toughness (KIC) of undamaged weld specimens and post-corrosion weld samples are carried out to compare with KI obtained by FEM and evaluate the safety of existing cracks. The method presented in this paper is a complete system that can provide a universal technological basis for crack propagation prediction and safety assessment of pressure vessel.

Field intensity factors of three cracks originating from a circular hole in a thermoelectric material

Field intensity factors of three cracks originating from a circular hole in a thermoelectric material

Transient analysis of a piezoelectric-orthotropic laminate weakened by multiple embedded and interface cracks under impact loads

The transient response of a piezoelectric layer bonded to an orthotropic layer under anti-plane mechanical and in-plane electrical impacts is investigated in this paper. The problem consist of two parts. In the first part, the analysis is based on the stress and electric displacement fields caused by electro-elastic dislocation in the piezoelectric layer, while the second part consist of the interfacial crack formulation by introducing the dislocation situated at the interface of two bonded layers. For both problems, the dislocation solution are obtained utilizing Fourier and Laplace transforms. These solutions lead naturally to singular integral equations for dislocation density functions in the both cases of embedded and interface cracks. The integral equations are solved numerically to obtain dislocation density functions on the surface of crack, which are used to calculate dynamic field intensity factors.

Thermoelectric field disturbed by two unequal cracks adjacent to a hole in thermoelectric materials

In this paper, the two-dimensional problem of a circular hole with two unequal cracks in infinite thermoelectric materials subjected to a uniform electric current and thermal flux is studied. Meanwhile, the boundary conditions at hole and cracks are assumed to be electrically impermeable and thermally impermeable. By using the complex function method and the conformal mapping theory, the exact solutions of the electric current density and the total energy flux are obtained. Furthermore, according to the theory of fracture mechanics, the intensity factors of electric current density, total energy flux density and stress at the crack tip have been obtained, which are proportional to the applied far-field loads, respectively. On the other hand, these field intensity factors are closely related to the radius of the circular hole and the lengths of cracks. The analytical solution is in good agreement with the regularized simulation results given by COMSOL commercial finite element code. Further numerical experiments reveal the effects of circular hole radius and lengths of cracks on the dimensionless thermoelectric and stress field intensity factors.

Mixed mode analysis of multiple cracks in magneto-electro-elastic plane

In this paper, the mixed mode problem for a magneto-electro-elastic (MEE) material containing multiple cracks under in-plane magneto-electro-mechanical loads is analyzed. First, the solution to an generalized dislocation is obtained in the infinite MEE plane. The Fourier transform is employed to derive closed-form expressions for the stress, electric displacement and magnetic induction components. The solution to the problem is consequently reduced to derive singular integral equations for dislocation density functions on the surfaces of cracks. The equations are then solved numerically to determine field intensity factors for cracks. At the final step, the numerical results of calculated field intensity factors are presented for multiple curved cracks under certain ratios of the applied magnetical and electrical loads to mechanical loads. Also, the field intensity factors are calculated for various crack patterns with different geometries. Moreover, the analysis can be applied for any number of cracks with arbitrary arrangement in the MEE regions under in-plane condition.

Exact Solutions for Interaction of Parallel Screw Dislocations with a Wedge Crack in One-Dimensional Hexagonal Quasicrystal with Piezoelectric Effects

The purpose of this paper is to consider the interaction between many parallel dislocations and a wedge-shaped crack and their collective response to the external applied generalized stress in one-dimensional hexagonal piezoelectric quasicrystal, employing the complex variable function theory and the conformal transformation method; the problem for the crack is reduced to the solution of singular integral equations, which can be further reduced to solving Riemann–Hilbert boundary value problems. The analytical solutions of the generalized stress field are obtained. The dislocations are subjected to the phonon field line force, phason field line force, and line charge at the core. The positions of the dislocations are arbitrary, but the dislocation distribution is additive. The dislocation is not only subjected to the external stress and the internal stress generated by the crack, but also to the force exerted on it by other dislocations. The closed-form solutions are obtained for field intensity factors and the image force on a screw dislocation in the presence of a wedge-shaped crack and a collection of other dislocations. Numerical examples are provided to show the effects of wedge angle, dislocation position, dislocation distribution containing symmetric configurations and dislocation quantities on the field intensity factors, energy release rate, and image force acting on the dislocation. The principal new physical results obtained here are (1) the phonon stress, phason stress, and electric displacement singularity occur at the crack tip and dislocations cores, (2) the increasing number of dislocations always accelerates the crack propagation, (3) the effect of wedge angle on crack propagation is related to the distribution of dislocations, and (4) the results of the image force on the dislocation indicate that the dislocations can either be attracted or rejected and reach stable positions eventually.

Cracked elastic layer with surface elasticity under antiplane shear loading

A mode-III crack embedded in a homogeneous isotropic elastic layer of nanoscale finite thickness is studied in this article. The classical elasticity incorporating surface elasticity is employed to reduce a nonclassical mixed boundary value problem, where the layer interior obeys the traditional constitutive relation and the surfaces of the layer and the crack are dominated by the surface constitutive relation. Using the Fourier transform, we convert the problem to a hypersingular integro-differential equation for the out-of-plane displacement on the crack faces. By expanding the out-of-plane displacement as series of Chebyshev polynomials, the Galerkin method is invoked to reduce the singular integro-differential equation with Cauchy kernel to a set of algebraic linear equations for the unknown coefficients. An approximate solution is determined, and the influences of surface elasticity on the elastic field and stress intensity factor are examined and displayed graphically. It is shown that surface elasticity decreases the bulk stress and its intensity factor near the crack tips for positive surface shear modulus and gives rise to an opposite trend for a negative surface shear modulus.

Transient analysis of multiple interface cracks between two dissimilar functionally graded magneto-electro-elastic layers

In this paper, we examine the transient response of two bonded dissimilar functionally graded magneto-electro-elastic (MEE) layers with multiple interfacial cracks under magneto-electro-mechanical impacts. Material properties of the MEE layers are assumed to vary exponentially in the thickness direction of the layers. However, the rate of material properties gradation are different. First, the analytical solution is developed by considering a dynamic magneto-electro-elastic dislocation with time-dependent Burgers vector be situated at the interface of bonded layers by means of the Fourier and Laplace transform. The solutions are used to derive singular integral equations for the MEE layers containing interfacial cracks. Then, the integral equations are solved numerically for the density of dislocations on a crack surface. The dislocation densities are employed to determine the field intensity factors and the dynamic energy release rate. The effects of crack spacing and FGM exponent as well as crack interaction are studied.

Multiple mixed-mode cracks in a magneto-electro-elastic half-plane under in-plane loading

The mixed-mode problem of cracked magneto-electro-elastic (MEE) half-plane subjected to in-plane magneto-electro-mechanical loads is considered. The crack is modelled as distributed dislocations with unknown density and the closed form solution of the generalized dislocation is obtained by using the Fourier transform. Furthermore, stress, electric displacement and magnetic induction fields in the intact MEE half-plane, under magneto-electro-mechanical point forces are determined. These solutions are used to construct singular integral equations in the MEE half-plane with multiple cracks. The integral equations are solved numerically to obtain dislocation density functions on a crack surface. These functions are used to determine field intensity factors for cracks. The results show that the stress, electric displacement and magnetic induction intensity factors at the crack tips depend on crack geometry, patterns and the loading conditions. Moreover, the effect of the boundary of the MEE half-plane as well as interaction between cracks upon field intensity factors is investigated.

Interaction between a screw dislocation and an elliptical hole with two asymmetrical cracks in a one-dimensional hexagonal quasicrystal with piezoelectric effect

The interaction between a screw dislocation and an elliptical hole with two asymmetrical cracks in a one-dimensional (1D) hexagonal quasicrystal with piezoelectric effect is considered. A general formula of the generalized stress field, the field intensity factor, and the image force is derived, and the special cases are discussed. Several numerical examples are given to show the effects of the material properties and the dislocation position on the field intensity factors and the image forces.

Anti-plane analysis of a reinforced nano-elliptical cavity or nano-crack in a magnetoelectroelastic matrix with surface effect

Taking the surface effect into account, anti-plane analysis of a reinforced (coated) nano-elliptical cavity or nano-crack embedded in an infinite magnetoelectroelastic (MEE) matrix is considered under remotely mechanical, electrical and magnetic loadings. Analytical treatment of the problem is presented based on the technique of conformal mapping and the method of complex variable function. Exact solutions of stress, electric displacement and magnetic induction in the reinforced layer and matrix are derived explicitly in closed form. Numerical examples are provided to show the influence of material properties of surface layer and reinforced layer, aspect ratio of elliptical hole and coatings, thickness of coatings and crack length on the field concentration around the nano-hole and field intensity factors near the nano-crack tip. The result indicated that the material properties of surface layer and reinforced layer have a great effect on the fields concentration around the nano-hole or nano-crack, which is helpful for optimum design of MEE nanocomposites in engineering practice.

Periodically spaced collinear cracks in a soft ferromagnetic material under a uniform magnetic field

This paper aims at a fundamental perspective of multiple cracks’ interaction on the fracture behavior of magnetoelastic materials. A theoretical study is performed on a soft ferromagnetic solid weakened by an array of periodic cracks under an in-plane magnetic loading. By using the conformal mapping technique and the analytic function boundary value theory, a rigorous analytical solution of the magnetic and stress fields is obtained, and the closed-form expressions for the field intensity factors are presented. Numerical examples of magnetically impermeable and permeable cracks are studied to reveal the relationship of the mode-I stress intensity factor with the period ratio of the cracks, the surrounding medium, and the applied magnetic loading. The analytical solution in this study can serve as a theoretical benchmark for the fracture problem of a magnetoelastic solid containing multiple defects.

Biot number effect and non-Fourier effect on temperature field and stress intensity factor of a cracked strip under thermal shock loading

In this paper, we considered a thermal shock problem of a strip with an inner crack parallel to the heated or cooled surface. The effect of the surface heat transfer properties and the non-Fourier effect, which are modified by effective Biot’s number and the non-Fourier factor, were considered to investigate the transient temperature field and the dynamic stress intensity factors (SIFs). Fourier transform and Laplace transform were used to reduce this mixed boundary value problem to singular integral equations (SIEs). The Gauss-Chebyshev numerical integration method was applied to the SIEs and linear equations are obtained. Finally, numerical inverse Laplace transform was used to obtain the temperature field and SIFs. The numerical results showed that Biot’s number not only affects the uniformity of the temperature field and the magnitude of the SIFs strongly, but also makes contributions to the non-Fourier effect. This finding can help better understanding the fracture behaviors of advanced materials and making a progress to determine the applicable conditions of the non-Fourier effect.