Exact solutions of two semi-infinite collinear cracks in piezoelectric strip

Using the complex variable function method and the conformal mapping technique, the fracture problem of two semi-infinite collinear cracks in a piezoelectric strip is studied under the anti-plane shear stress and the in-plane electric load on the partial crack surface. Analytic solutions of the field intensity factors and the mechanical strain energy release rate are derived under the assumption that the surfaces of the crack are electrically impermeable. The results can be reduced to the well-known solutions for a purely elastic material in the absence of an electric load. Moreover, when the distance between the two crack tips tends to infinity, analytic solutions of a semi-infinite crack in a piezoelectric strip can be obtained. Numerical examples are given to show the influence of the loaded crack length, the height of the strip, the distance between the two crack tips, and the applied mechanical/electric loads on the mechanical strain energy release rate. It is shown that the material is easier to fail when the distance between two crack tips becomes shorter, and the mechanical/electric loads have greater influence on the propagation of the left crack than those of the right one.

Exact analytic solutions for an elliptic hole with asymmetric collinear cracks in a one-dimensional hexagonal quasi-crystal

Using the complex variable function method and the technique of conformal mapping, the anti-plane shear problem of an elliptic hole with asymmetric colfinear cracks in a one-dimensional hexagonal quasi-crystal is solved, and the exact analytic solutions of the stress intensity factors （SIFs） for mode Ⅲ problem are obtained. Under the limiting conditions, the present results reduce to the Griffith crack and many new results obtained as well, such as the circular hole with asymmetric collinear cracks, the elliptic hole with a straight crack, the mode T crack, the cross crack and so on. As far as the phonon field is concerned, these results, which play an important role in many practical and theoretical applications, are shown to be in good agreement with the classical results.

Interaction between many parallel screw dislocations and a semi-infinite crack in a magnetoelectroelastic solid

Based on the fundamental equations of magnetoelectroelastic material and the analytic theory, and using the Muskhelishvili-introduced well-known elastic techniques combined with the superposition principle, the closed form solution of the generalized stress field of the interaction between many parallel screw dislocations and a semi-infinite crack in an infinite magnetoelectroelastic solid is obtained, on the assumption that the surface of the crack is impermeable electrically and magnetically. Besides, the Peach-Koehler formula of n parallel screw dislocations is given. Numerical examples show that the generalized stress varies with the position of point z and is related to the material constants. The results indicate that the stress concentration occurs at the dislocation core and the tip of the crack. The result of interaction makes the system stay in a lower energy state.

THE BEHAVIOR OF TWO COLLINEAR CRACKS IN MAGNETO-ELECTRO-ELASTIC COMPOSITES UNDER ANTI-PLANE SHEAR STRESS LOADING

In this paper, the behavior of two collinear cracks in magneto-electro-elastic compos- ite material under anti-plane shear stress loading is studied by the Schmidt method for permeable electric boundary 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 displacements across the crack surfaces. In solving the triple integral equations, the unknown variable is expanded in a series of Jacobi polynomials. Numerical solutions are obtained. It is shown that the stress feld is independent of the electric feld and the magnetic fux.

Anti-plane analysis of semi-infinite crack in piezoelectric strip

Using the complex variable function method and the technique of the conformal mapping, the fracture problem of a semi-infinite crack in a piezoelectric strip is studied under the anti-plane shear stress and the in-plane electric load. The analytic solutions of the field intensity factors and the mechanical strain energy release rate are presented under the assumption that the surface of the crack is electrically impermeable. When the height of the strip tends to infinity, the analytic solutions of an infinitely large piezoelectric solid with a semi-infinite crack are obtained. Moreover, the present results can be reduced to the well-known solutions for a purely elastic material in the absence of the electric loading. In addition, numerical examples are given to show the influences of the loaded crack length, the height of the strip, and the applied mechanical/electric loads on the mechanical strain energy release rate.

Interaction between infinitely many dislocations and a semi-infinite crack in one-dimensional hexagonal quasicrystal

By means of analytic function theory, the problems of interaction between infinitely many parallel dislocations and a semi-infinite crack in one-dimensional hexagonal quasicrystal are studied. The analytic solutions of stress fields of the interaction between infinitely many parallel dislocations and a semi-infinite crack in one-dimensional hexagonal quasicrystal are obtained. They indicate that the stress concentration occurs at the dislocation source and the tip of the crack, and the value of the stress increases with the number of the dislocations increasing. These results are the development of interaction among the finitely many defects of quasicrystals, which possesses an important reference value for studying the interaction problems of infinitely many defects in fracture mechanics of quasicrystal.

INVESTIGATION OF ANTI-PLANE SHEAR BEHAVIOR OF TWO COLLINEAR CRACKS IN PIEZOELECTRIC MATERIALS BY A NEW METHOD

In this paper, the interaction between two collinear cracks inpiezoelectric materials under anti-plane shear loading wasinvestigated for the impermeable crack face conditions. By using theFourier transform, the problem can be solved with two pairs of tripleintegral equations. These equations are solved using Schmidt'smethod. This process is quite different from that adopted previously.This makes it possible to understand the two collinear cracksinteraction in piezoelectric materials.

Strip-coalesced interior zone model for two unequal collinear cracks weakening piezoelectric media

In this paper, a mathematical strip-saturation model is proposed for a poled transversely isotropic piezoelectric plate weakened by two impermeable unequal-collinear hairline straight cracks. Remotely applied in-plane unidirectional electromechanical loads open the cracks in mode-I such that the saturation zone developed at the interior tips of cracks gets coalesced. The developed saturation zones are arrested by distributing over their rims in-plane normal cohesive electrical displacement. The problem is solved using the Stroh formalism and the complex variable technique. The expressions are derived for the stress intensity factors （SIFs）, the lengths of the saturation zones developed, the crack opening displacement （COD）, and the energy release rate. An illustrative numerical case study is presented for the poled PZT-5H ceramic to investigate the effect of prescribed electromechanical loads on parameters affecting crack arrest. Also, the effect of different lengths of cracks on the SIFs and the local energy release rate （LERR） has been studied. The results obtained are graphically presented and analyzed.

Interaction between collinear periodic cracks in an infinite piezoelectric body

The problem of collinear periodic cracks in an infinite piezoelectric body is studied. Effect of saturation strips at the crack-tips is taken into account. By means of the Stroh formalism and the conformal mapping technique, the general periodic solutions for collinear cracks are obtained. The stress intensity factors and the size of saturation strips are derived analytically, and their dependencies on the ratio of the periodicity on the half-length of the crack are analyzed in detail. Numerical results show the following two facts. （1） When h/l 〉 4.0, the stress intensity factors become almost identical to those of a single crack in an infinite piezoelectric body. This indicates that the interaction between cracks can be ignored in establishing the criterion for the crack initiation in this case. （2） The speed of the saturation strip size of periodic cracks approaching that of a single crack depends on the electric load applied at infinity. In general, a large electric load at infinity is associated with a slow approaching speed.

First fundamental problems of anisotropic elastic plane weakened by periodic collinear cracks

Using the method of complex functions, we discuss the first fundamental problems of an anisotropic infinite elastic plane weakened by periodic collinear cracks and with periodic boundary loads on both sides of the cracks. This problem was considered by Cai [Engineering Fracture Mechanics 46（1）, 133-142 （1993）]. However, the previous method is imperfect. Therefore, the results are incorrect. Here, we revise the method and give a correct solution.

Green's function for T-stress of semi-infinite plane crack

Green’s function for the T-stress near a crack tip is addressed with an analytic function method for a semi-infinite crack lying in an elastical, isotropic, and infinite plate. The cracked plate is loaded by a single inclined concentrated force at an interior point. The complex potentials are obtained based on a superposition principle, which provide the solutions to the plane problems of elasticity. The regular parts of the potentials are extracted in an asymptotic analysis. Based on the regular parts, Green’s function for the T-stress is obtained in a straightforward manner. Furthermore, Green’s functions are derived for a pair of symmetrically and anti-symmetrically concentrated forces by the superimposing method. Then, Green’s function is used to predict the domain-switch-induced T-stress in a ferroelectric double cantilever beam （DCB） test. The T-stress induced by the electromechanical loading is used to judge the stable and unstable crack growth behaviors observed in the test. The prediction results generally agree with the experimental data.

The dynamic behavior of two collinear cracks in magneto-electro-elastic composites under harmonic anti-plane shear waves

The dynamic behavior of two collinear cracks in magneto-electro-elastic composites under harmonic anti-plane shear waves is studied using the 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. It can be obtained that the stress field is independent of the electric field and the magnetic flux.

SINGULARITIES AND EXPLICIT SOLUTIONS OF COLLINEAR CRACK PROBLEM IN ANISOTROPIC MEDIA

The singularities of collinear cracks both in anisotropic single medium and at the interface of anisotropic bimaterials are studied by combining Stroh formalism and the analytic function method. The formulae for calculating the field potential and stress intensity factor (SIF) are obtained. It is found that the field potentials are explicitly related to material matrix L and the in-plane and anti-plane fields can be separately calculated when orthotropic bimaterials are considered.

非共线多裂纹结构的剩余强度分析与评估

针对老龄飞机的广布疲劳损伤(Widespread Fatigue Damage,WFD)评估问题,通过试验方法研究了不同结构参数对非共线多裂纹结构剩余强度的影响,修正原有剩余强度评估方法中的缺陷,提出改进的净截面屈服准则和改进的Irwin塑性区连通准则,获得更准确的评估结果。改进的净截面屈服准则评估结果误差小,适用范围广,可以评估铆钉孔间距和铆钉孔直径对结构剩余强度的影响;改进的Irwin塑性区连通准则在铆钉孔间距大于10mm时,有较准确的评估结果,还可以评估裂纹分布位置对剩余强度的影响。

一维六方压电准晶狭长体中双半无限共线裂纹问题的D-B模型

基于解析函数理论与保角映射方法,通过构造一维六方压电准晶狭长体中双半无限共线裂纹问题的D-B(Dugdale-Barenblatt)模型,研究了一维六方压电准晶狭长体中双半无限共线裂纹的弹塑性断裂力学问题,得到了塑性区尺寸及场强度因子的解析解,推广了材料中裂纹问题的已有结果,扩大了准晶压电材料弹塑性断裂力学问题的研究范围。

一维六方准晶双材料界面共线裂纹的反平面问题

基于复变函数理论,利用Schwarz解析延拓原理,研究一维六方准晶双材料界面共线裂纹的反平面问题,获得了几个典型问题及相应应力强度因子的封闭解.结果表明,当趋于裂纹尖端路径选在双材料界面上时,双材料界面裂纹应力强度因子大小与材料参数无关,仅与裂纹尺寸及裂纹所受外载荷大小有关且成正比,即应力强度因子随着裂纹尺寸和外载荷的增大而增大.

含共线等长双裂纹损伤钢构件的力学试验及分析

在实际工程中,钢构件在同一条直线上的多条裂纹共线排列现象,既是一种较为常见的形式,也是最具有危险性的形式。这种共线裂纹可能导致钢构件发生脆性破坏,所以有必要深入研究共线裂纹对钢构件力学性能的影响。以含共线等长双裂纹损伤钢构件为研究对象,展开了单轴拉伸试验,研究了相对裂纹长度和相对裂纹间距对钢构件的断后伸长率、屈服强度和剩余极限强度的影响规律,且在此基础上提出了含共线等长双裂纹损伤钢构件的剩余极限强度计算公式。通过与试验值进行对比分析,本文所提出的剩余极限强度计算公式的相对误差小于1%,验证了本文所提出公式的有效性和准确性。针对含多裂纹损伤钢构件的安全评估,本文提出的剩余极限强度计算公式,在一定程度上弥补了该领域的空白,为其剩余极限强度分析研究提供了一种行之有效的方法,对含多裂纹损伤钢构件后期的预防和修复等具有一定的理论价值和现实意义。

基于共线超声混频技术的机械结构缺陷评估

为了更高效检测出机械结构出现的裂纹,提出共线超声混频检测技术。首先,基于非线性超声理论,由差频非线性系数与和频非线性系数得到计算非线性超声混频非线性系数的方法。然后对5种不同深度疲劳裂纹的铝合金试件用超声系统RAM-5000SINAP进行检测,并绘制相应频谱图,得出在一定裂纹深度内,裂纹深度与差频非线性系数、和频非线性系数呈正相关的结论。通过对两组实验数据进行拟合曲线分析,建立对应的裂纹深度预测模型。结合混频非线性系数的特征,得到根据其预测裂纹深度的模型,将3种预测模型的平均误差进行比对,结果表明混频非线性系数预测模型预测结果更佳。研究工作对微裂纹的共线超声混频检测及裂纹深度预测进行了有益探索。

一维六方压电准晶双材料界面共线裂纹问题

利用复变函数理论中的解析延拓、奇性主部分析和推广的Liouville定理,求解了一维六方压电准晶双材料在集中载荷作用下界面共线裂纹反平面弹性问题.导出了含有一条和两条有限长界面裂纹的封闭解,同时给出了裂纹尖端场强度因子(包含声子场和相位子场应力强度因子和电位移强度因子)的表达式.数值算例分析了外荷载与耦合系数之比对裂纹尖端场强度因子变化规律的影响.从数值结果中可以看出,当裂纹长度增加时,裂纹尖端场强度因子随之增加;应力强度因子随双材料耦合系数之比的增大而增大,电位移强度因子几乎不变;不同载荷作用下,裂纹尖端场强度因子随着裂纹长度改变时的变化趋势也不尽相同.研究结果可为压电准晶双材料的设计和制备提供一定的理论参考.

一维六方压电准晶双材料界面共线裂纹的反平面断裂问题

目的研究一维六方压电准晶双材料界面共线裂纹的反平面断裂问题。方法利用复变函数理论中的解析延拓、奇性主部分析和推广的Liouville定理,在电渗透边界条件下研究。结果给出了1条界面裂纹受4种不同外载荷作用及2条等长界面裂纹受无穷远均匀载荷作用等几个典型问题的解析解。同时导出了相应问题场强度因子(声子场、相位子场应力强度因子和电位移强度因子)的解析表达式。结论理论结果表明:当趋于裂纹尖端路径选在双材料界面上时,场强度因子大小与材料弹性常数无关,仅与裂纹尺寸及裂纹所受外载荷大小有关且成正比,即随着裂纹尺寸和外载荷的增大,场强度因子随之增大。