On the stress state of a piezoceramic body with a flat crack under symmetric loads

A static-equilibrium problem is solved for an electroelastic transversely isotropic medium with a flat crack of arbitrary shape located in the plane of isotropy. The medium is subjected to symmetric mechanical and electric loads. A relationship is established between the stress intensity factor (SIF) and electric-displacement intensity factor (EDIF) for an infinite piezoceramic body and the SIF for a purely elastic material with a crack of the same shape. This allows us to find the SIF and EDIF for an electroelastic material directly from the corresponding elastic problem, not solving electroelastic problems. As an example, the SIF and EDIF are determined for an elliptical crack in a piezoceramic body assuming linear behavior of the stresses and the normal electric displacement on the crack surface __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 11, pp. 67–77, November 2005.     

Stress state of a piezoelectric ceramic body with a plane crack under antisymmetric loads

The static equilibrium of an electroelastic transversely isotropic space with a plane crack under antisymmetric mechanical loads is studied. The crack is located in the plane of isotropy. Relationships are established between the stress intensity factors (SIFs) for an infinite piezoceramic body and the SIFs for a purely elastic body with a crack of the same form under the same loads. This makes it possible to find the SIFs for an electroelastic body without the need to solve specific electroelasitc problems. As an example, the SIFs are determined for a piezoelastic body with penny-shaped and elliptic cracks under shear __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 2, pp. 32–42, February 2006.     

Stress state of a piezoceramic body with a plane crack opened by a rigid inclusion

The paper establishes a relationship between the solutions for cracks located in the isotropy plane of a transversely isotropic piezoceramic medium and opened (without friction) by rigid inclusions and the solutions for cracks in a purely elastic medium. This makes it possible to calculate the stress intensity factor (SIF) for cracks in an electroelastic medium from the SIF for an elastic isotropic material, without the need to solve the electroelastic problem. The use of the approach is exemplified by a penny-shaped crack opened by either a disk-shaped rigid inclusion of constant thickness or a rigid oblate spheroidal inclusion in an electroelastic medium __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 7, pp. 47–60, July 2008.     

Closed form solution for two unequal collinear semi-permeable straight cracks in a piezoelectric media

The problem of two unequal collinear straight cracks weakening a poled transversely isotropic piezoelectric ceramic is addressed under semi-permeable electric boundary conditions on the crack faces. The plate has been subjected to combined in-plane normal(to the faces of the cracks) mechanical and electric loads. Problem is formulated employing Stroh formalism and solved using complex variable technique. The elastic field, electric field and energy release rate are obtained in closed analytic form. A case study is presented for poled PZT-5H cracked plate to study the effect of prescribed mechanical load, electric load, inter-crack distance and crack lengths on crack arrest parameters stress intensity factor (SIF), electric displacement intensity factor (EDIF) and mechanical and total energy release rates (ERR). Moreover a comparative study is done of impermeable and semi-permeable crack face boundary conditions on SIF, EDIF and ERR, and results obtained is presented graphically. It is observed that the effect of dielectric medium in the crack gap cannot be ignored.     

Elastic state of a transversely isotropic piezoelectric body with an arbitrarily oriented elliptic crack

The elastic stress state in a piezoelectric body with an arbitrarily oriented elliptic crack under mechanical and electric loads is analyzed. The solution is obtained using triple Fourier transform and the Fourier-transformed Green’s function for an unbounded piezoelastic body. Solving the problem for the case of a crack lying in the isotropy plane, for which there is an exact solution, demonstrates that the approach is highly efficient. The distribution of the stress intensity factors along the front of a crack in a piezoelectric body under uniform mechanical loading is analyzed numerically for different orientations of the crack __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 2, pp. 39–48, February 2008.     

有限厚度板穿透裂纹前缘附近三维弹性应力场分析

通过三维有限元计算来研究有限宽度、有限厚度含有穿透裂纹板的裂纹前缘应力场，从中找出应力强度因子与板的厚度、裂纹长度之间的关系，同时还分析了裂尖的三维约束程度和三维约束区的大小。分析结果表明：应力强度因子沿厚度的分布是不均匀的，应力强度因子的最大值及其位置与厚度有关；有限厚度板中面应力强度因子(KI)m-p及最大应力强度因子(KI)max均大于平面应力或平面应变的应力强度因子。对有限厚度裂纹问题，按平面应力或平面应变来考虑是不安全的；板中面的应力强度因子(KI)m-p及最大应力强度因子(KI)max是厚度B／a的函数；板的中面离面约束系数Tx最大，自由面(z=B)Tx=0。沿厚度方向裂尖附近的离面约束系数Tx也是z／B和B／a的函数，随着厚度的增加离面约束系数Tx增大，离中面越近离面约束系数Tx越大。Tx随着x的增大急剧减小，三维约束影响区域大小大约为板厚的一半，且裂纹长度a／W对应力强度因子沿厚度变化规律及Tx影响区域大小影响较小。     

Stress state of a transversely isotropic magnetoelectroelastic body with a plane crack under antisymmetric loads

The static equilibrium of a transversely isotropic magnetoelectroelastic body with a plane crack of arbitrary shape in the isotropy plane under antisymmetric mechanical loading is studied. The relationships between the stress intensity factors (SIFs) for an infinite magnetoelectroelastic body and the SIFs for a purely elastic body with the same crack and under the same antisymmetric loading are established. This enables the SIFs for a magnetoelectroelastic body to be found directly from the analogous problem of elasticity. As an example of using this result, the SIFs for penny-shaped, elliptic, and parabolic cracks in a magnetoelectroelastic body under antisymmetric mechanical loading are found Translated from Prikladnaya Mekhanika, Vol. 44, No. 10, pp. 37–51, October 2008.     

Thermoelastic state of a half-space having a thermally active crack parallel to its boundary

Using the boundary integral equation method, the problem of stationary heat conduction and thermoelasticity for a semi-infinite body with a crack parallel to its boundary is solved. Temperature or heat flow on the crack is prescribed. The body boundary is heat-insulated or is at zero temperature. The dependence of the stress intensity factor on the depth of occurrence of a circular crack at a constant temperature or under a constant heat flow is studied. In contrast to mechanical loading, thermal loading shows less SIF values than in an infinite body __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 4, pp. 46–54, April 2007.     

Axially symmetric thermal stress of an external circular crack under general thermal conditions

Summary The paper presents a solution for the linear thermoelastic problem of determining axisymmetric stress and displacement fields in an isotropic elastic solid of infinite extent weakened by an external circular crack under general mechanical loadings and general thermal conditions. The mechanical loadings and thermal conditions applied on the crack faces are axisymmetric, being non-symmetric about the crack plane. In similar lines of [7], equations of equilibrium of an elastic solid conducting heat have been solved using Hankel transforms and Abel operators of the first kind. Expressions for stress, displacement, temperature and heat flux functions are obtained in terms of Abel transforms of the first kind of the jumps of stress, displacement, temperature and heat flux at the crack plane. Two types of thermal conditions, that is, general surface temperatures and general heat flux on faces of the crack are considered. In both the cases, closed form solutions have been obtained for the unknown functions solving Abel type of integral equations. Explicit expressions for stresses, displacements, temperature fields, stress intensity factors have been obtained. Two special cases of thermal conditions in which: (i) crack faces are subjected to constant non-symmetric temperatures over a circular ring area, (ii) crack faces are subjected to constant non-symmetric heat flux over a circular ring area, have been considered. In some special cases, results have been compared with those from the literature.     

Stress State of a Transversely Isotropic Ferromagnetic with an Elliptic Crack in a Homogeneous Magnetic Field

The magnetoelastic stress-strain problem for a transversely isotropic ferromagnetic body with an elliptical crack in the isotropy plane is solved explicitly. The body is in an external magnetic field perpendicular to the isotropy plane. The magnetic field induces elastic strains and an internal magnetic field in the body. The main characteristics of stress-strain state and induced magnetic field are determined and their features in the neighborhood of the crack are analyzed. Formulas for the stress intensity factors of the mechanical and magnetic fields near the crack tip are presented__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 1, pp. 48–59, January 2005.     

热、机械载荷作用下夹杂对应力强度因子的影响

推导了远场应力、热应力耦合作用下含夹杂裂纹体的应力强度因子求解公式,改进了体积力法中的裂纹面合力平衡条件,将应力强度因子的求解归结为解一组积分方程,再将积分方程转化为线性方程组进行数值求解。算例分析结果表明方法正确、有效。将该算法应用于含Al2O3夹杂的FGH95材料应力强度因子分析中,计算结果表明热应力对应力强度因子影响很小。     

A mode III crack crossing the magnetoelectroelastic bimaterial interface under concentrated magnetoelectromechanical loads

A mode III crack cutting perpendicularly across the interface between two dissimilar semi-infinite magnetoelectroelastic solid is studied under the combined loads of a line force, a line electric charge and a line magnetic charge at an arbitrary location. The impermeable conditions are implied on the crack faces. The technique developed in literature for the elastic bimaterial with a crack cutting interface is exploited to treat the magnetoelectroelastic bimaterial. The Riemann-Hilbert problem can be formulated and solved based on complex variable method. Analytical solutions can be obtained for the entire plane. The intensity factors around crack tips can be defined for the elastic, electric and magnetic fields. It shows that, no matter where the load position is, the electric displacement intensity factors (EDIFs), as well as the magnetic induction intensity factors (MIIFs), are identical in magnitude but opposite in sign for both crack tips, on condition that a line force is solely applied. Alternatively, if only a line electric charge is considered, then the stress intensity factors (SIFs) and the MIIFs exhibit the behavior. Likewise, if only a line magnetic charge is applied, it turns to the SIFs and the EDIFs instead. In addition, the dependence of the intensity factors is graphically shown with respect to the location of a line force. It is found that the SIF for a crack tip tends to be infinite if the applied force is approaching the tip itself, but the EDIF, with the complete opposite trend, tends to be vanishing. Finally, focusing on the more practical case of piezoelectric/piezomagnetic bimaterial, variation of the SIF along with the moduli as well as the piezo constitutive coefficients is explored. These analyses may provide some guidance for material selection by minimizing the SIF. It is also believed that the results obtained in this paper can serve as the Green’s function for the dissimilar magnetoelectroelastic semi-infinite bimaterial with a crack cutting the interface under general magnetoelectromechanical loads.     

THE THREE-DIMENSIONAL STRESS INTENSITY FACTOR UNDER MOVING LOADS ON THE CRACK FACES

The dynamic stress intensity factor history for a half plane crack in anotherwise unbounded elastic body,with the crack faces subjected to a tractiondistribution consisting of two pairs of combined mode point loads that move in adirection perpendicular to the crack edge is considered.The analytic expression for thecombined mode stress intensity factors as a function of time for any point along thecrack edge is obtained.The method of solution is based on the application of integraltransform together with the Wiener-Hopf technique and the Cagniard-de Hoop method.Some features of the solution are discussed and graphical results for various point loadspeeds are presented.     

裂纹垂直于双相介质界面时的应力强度因子

本文利用Ｊ积分与应力强度因子的关系,采用有限元数值方法研究了当裂纹与双相介质的界面垂直时,其裂纹的近界面端和远界面端的应力强度因子随双相介质参数和裂纹端部到界面的距离的变化规律,同时还分析了当边裂纹逐渐扩展时,应力强度因子的变化特征。     

Thermal fracture analysis of nonhomogeneous piezoelectric materials using an interaction energy integral method

This paper presents a modified interaction energy integral method to analyze the thermal stress intensity factors (TSIFs) and electric displacement intensity factor (EDIF) in nonhomogeneous piezoelectric materials under thermal loading. This modified method is demonstrated to be domain-independent, even when the nonhomogeneous piezoelectric materials contain interfaces with thermo-electro-mechanical properties. As a result, the method is shown to be convenient for determining the TSIFs and EDIF in nonhomogeneous piezoelectric materials with interfaces. Several examples are shown, and they successfully verify the domain-independence of the present interaction energy integral. The study results also show that the mismatch of material properties can significantly influence the TSIFs and EDIF, particularly when the crack tip is close to the interface. Crack angles and temperature boundary conditions are also shown to significantly influence the TSIFs and EDIF.     

Closed-form solution for a mode-III interfacial edge crack between two bonded dissimilar elastic strips

A closed-form solution is obtained for the problem of a mode-III interfacial edge crack between two bonded semi-infinite dissimilar elastic strips. A general out-of-plane displacement potential for the crack interacting with a screw dislocation or a line force is constructed using conformal mapping technique and existing dislocation solutions. Based on this displacement potential, the stress intensity factor (SIF, K_III) and the energy release rate (ERR, G_III) for the interfacial edge crack are obtained explicitly. It is shown that, in the limiting special cases, the obtained results coincide with the results available in the literature. The present solution can be used as the Green’s function to analyze interfacial edge cracks subjected to arbitrary anti-plane loadings. As an example, a formula is derived correcting the beam theory used in evaluation of SIF (K_III) and ERR (G_III) of bimaterials in the double cantilever beam (DCB) test configuration.     

Point forces and point charge applied to a circular crack in a transversely isotropic piezoelectric space

Interaction between an arbitrarily located and oriented point force and point charge with a circular crack is considered. Obtained are the exact expressions for the stress intensity factors (SIFs) k_j (j=1,2,3) and electric displacement intensity factor (EDIF) k_D; they are given in terms of elementary functions. The results are also presented in graphical form.     

Stress intensity factor measurement of cracks using a piezoelectric element

We present a stress intensity factor (SIF) measurement method of cracks using a piezoelectric element and electrostatic voltmeter. In the method, an isotropic piezoelectric element is first adhered near the crack tip. Then, the surface electrodes are attached to the three different positions on the piezoelectric element. The electric potentials of the surface electrodes, which are proportional to the strain sum (ɛ_x+ɛ_y) on the structural member, are measured by an electrostatic voltmeter during load cycling. Mode I and mode II SIFs of the crack are estimated using the relationship between the SIF and (σ_x+σ_y). The applicability of the proposed method is examined through experiments and numerical analysis.     

平面弹性介质多孔多裂纹问题的一种数值方法

提出了平面弹性介质中多孔洞多裂纹相互作用问题的一种数值计算方 法. 通过把适于单一裂纹的Bueckner原理扩充到含有多孔洞多裂纹的一般体系，将原问题 分解为承受远处载荷不含裂纹不含孔洞的均匀问题，和在远处不承受载荷但在裂纹面上和孔 洞表面上承受面力的多孔洞多裂纹问题. 于是，以应力强度因子作为参量的问题可以通过考 虑后者(多孔洞多裂纹问题)来解决，而利用提出的杂交位移不连续法，这种多孔 洞多裂纹问题是容易数值求解的. 算例说明该数值方法对分析平面弹性介质中多孔洞多裂纹 相互作用的问题既简单又有效.     

功能梯度压电材料反平面裂纹问题

基于三维弹性理论和压电理论，导出了材料系数在横观各向同性平面内梯度分布的压电体的状态方程，进而对材料系数指数函数规律分布的半无限大压电体中的反平面裂纹问题进行了求解，利用Fourier变换给出了半无限大压电体中位移，应力，电势及电位移的解析表达式，并求得了裂纹尖端的应力强度因子和电位移强度因子，分析了不同的非均匀材料系数及几何尺寸对它们的影响。