载流金属材料裂纹尖端电磁应力的数值模拟

用数值模拟方法研究了金属裂纹尖端电磁应力的分布情况,给出了电流分布、磁场分布和电磁应力的分布.模拟结果表明,金属材料裂纹尖端受的电磁应力是最大的,并且这个力的大小随着电流密度的增加而增大,裂纹尖端的电磁力指向金属的内部.通过具体算例表明,在金属能承受的电流密度下,金属材料裂纹尖端的电磁应力约能达到1MPa的数量级.因此,在研究电磁场处理金属裂纹时,不能忽略电磁应力.     

A Griffith crack shielded by a dislocation pile-up

The dislocation free zone at the tip of a mode III shear crack is analyzed. A pile-up of screw dislocations parallel to the crack front, in anti-plane shear, in the stress field of a crack has been solved using a continuous distribution of dislocations. The crack tip remains sharp and is assumed to satisfy Griffith's fracture criteria using the local crack tip stress intensity factor. The dislocation pile-up shield the sharp crack tip from the applied stress intensity factor by simple addition of each dislocation's negative contribution to the applied stress intensity value. The analysis differs substantially from the well known BCS theory in that the local crack tip fracture criteria enters into the dislocation distributions found.     

Determination of Crack Bridging Stresses from Crack Opening Displacement Profiles

This paper discusses the development of an optimization procedure to deduce the bridging stress from the crack opening displacements (COD) measured during fatigue crack growth. Finite element analysis was conducted using the center-cracked geometry to verify the optimization procedure. The proposed procedure successfully predicted the bridging stress distributions with zero stresses at the crack tip and the bridging stress distributions with non-zero stresses at the crack tip. The results also showed that COD measurements spaced at ≈ 0.8-1.0 mm are sufficient for reliable prediction of bridging stresses. Accurate prediction of bridging stresses near the crack tip required COD data within ≈ 0.1 mm from the crack tip. The application of the proposed procedure to a metal matrix composite (SCS-6/TIMETAL®21S) is also discussed.     

A path-independent integral for 2-dimensional cracks in homogeneous isotropic conductive plate

A path-independent integral which is denoted by j_e, is introduced for the 2-dimensional crack problems in the homogeneous isotropic conductor in which the steady current flows. By utilizing the j_e-integral the distributions of the electric potential, current density and the Joule heating rate near the crack tip are derived. It is shown that the j_e-integral provides a parameter which dominates the distributions of the electric potential and current density near the crack tip as the square of the amplitude.     

Electric Current-Induced Stresses at the Crack Tip in Conductors

The electromagnetic and thermal effects on the stress distribution around the crack tip in conducting materials due to electric current are investigated. Emphases are placed on quantifying the crack growth behavior affected by the interplay between these effects. A two-dimensional finite element analysis is conducted to examine the coupled problems. The results show that the compressive stress state around the crack tip plays a decisive role in preventing the crack from further growth. The resulting normal stress in front of the crack tip caused by the Joule heat generation tends to suppress the crack growth, while the stress induced by the electromagnetic forces provides a tensile normal stress with smaller magnitude in the vicinity of the crack tip, hence promotes the crack growth. Favorable agreements between numerical analysis results and existing experimental results are achieved. By utilizing these phenomena, the electric current may be used to actively control the damage propagation, hence catastrophic failure can be prevented. This revised version was published online in July 2006 with corrections to the Cover Date.     

The Interaction between a Piezoelectric Screw Dislocation Dipole and an Elliptic Blunt Crack in Elliptical Inhomogeneity

The interaction problem of a piezoelectric screw dislocation dipole with a confocal elliptic blunt crack in elliptical inhomogeneity subjected to remote anti-plane stress field and in-plane electric field is investigated by using the complex method of elasticity. The exact closed-form solutions of a series of quantities, such as singularity stress field, image force and image torque acting on the center of screw dislocation dipole, stress intensity factor and electric displacement intensity factor of crack tip, energy release rate, and generalized strain energy density are obtained. Then the influence laws of remote load, the dip angle of dislocation dipole, the size of blunt crack, and the material constants on the quantities are analyzed. The numerical results show that the image force, image torque, stress intensity factor, and electric displacement intensity factor make periodic variation as the dip angle of dislocation dipole; the energy release rate of crack tip is negative when subjected to pure electric field, however, it can be positive or negative when subjected to the combined action of mechanical field and electric field; the sharp crack is not easy to expand in some combined action of mechanical field and electric field.     

The scattering of harmonic elastic anti-plane shear waves by a Griffith crack in a piezoelectric material plane by using the non-local theory

In this paper, the dynamic behavior of a Griffith crack in a piezoelectric material plane under anti-plane shear waves is investigated by using the non-local theory for impermeable crack face conditions. For overcoming the mathematical difficulties, a one-dimensional non-local kernel is used instead of a two-dimensional one for the anti-plane dynamic problem to obtain the stress and the electric displacement near the crack tips. By using the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations. These equations are solved using the Schmidt method. Contrary to the classical elasticity solution, it is found that no stress and electric displacement singularity is present near the crack tip. The non-local dynamic elastic solutions yield a finite hoop stress near the crack tip, thus allowing for a fracture criterion based on the maximum dynamic stress hypothesis. The finite hoop stress at the crack tip depends on the crack length, the circular frequency of incident wave and the lattice parameter. For comparison results between the non-local theory and the local theory for this problem, the same problem in the piezoelectric materials is also solved by using local theory.     

导电薄板内裂纹尖端区域的电磁应力

为了研究电磁应力对导电薄板内裂纹尖端的作用,从基本电磁理论出发,通过对导体表面所受电场力的分析,推得了导电薄板内裂纹边缘处电场力的表达式.在此基础上,通过导电薄板内裂纹尖端区域磁场的确定,得到裂纹尖端区域的电磁应力表达式.裂纹尖端电磁应力的计算表明,金属薄板中裂纹尖端的电磁应力是由裂纹尖端指向金属内部的压应力,并且当电流密度为103～104A/mm2的数量级时,裂纹尖端的压应力数值可达数兆帕到数百兆帕.因此,在研究裂纹止裂问题上,其影响不容忽视.     

Residual stress induced crack tip constraint

This paper studies the effect of welding residual stresses on the near tip stress field in single edge notched bending and tensile specimens. A combined effect of mechanical stresses by the applied load and residual stress on the crack tip constraint is analyzed. Three initial residual stress distributions were considered. It has been shown that the crack tip stress field is strongly influenced by the residual stresses and a new parameter, R, is proposed to characterize the residual stress induced crack tip constraint. The results therefore suggest a three-parameter approach (CTOD, Q and R) to characterize the crack tip stress field in the presence of residual stress where CTOD sets the size scale over which large stresses and large strains develop, and the geometry constraint parameter Q and the new residual stress induced constraint parameter R control the actual crack tip constraint level. For the cases analyzed, R is in general positive, which indicates that residual stress can enhance the crack tip constraint. However, the results also indicate that the R decreases towards zero and the effect of residual stress on crack tip constraint can be neglected when a full plastic condition is approached in the specimen.     

Crack growth in ferroelectric ceramics under electric loading

Summary A crack with growth in ferroelectric ceramics under purely electric loading is analyzed. The crack tip stress intensity factor for the growing crack under small scale conditions is evaluated by employing the model of nonlinear domain switching. The electrical fracture toughness is obtained from the result of the stress intensity factor. It is shown that the ferroelectric material can be either toughened or weakened as the crack grows. Fatigue crack growth in a ferroelectric material under cyclic electric loading is also examined. The incremental fatigue crack growth under cyclic electric loading is obtained numerically. The fatigue crack growth rate is affected strongly by the electrical nonlinear behavior. It is found that the curve of fatigue crack growth rate versus electric field intensity factor is linear on the log-log plot at intermediate values of the electric field intensity factor.     

Nanoscale anti-plane cracking of materials with consideration of bulk and surface piezoelectricity effects

The influence of surface effect, including surface elasticity and surface piezoelectricity, on thefracture behavior of piezoelectricmaterials with an anti-plane crack is studied.Based on the coupled surface andinterface elasticity model, the solutions to the problem are obtained by applying the singular integral method. Bycomparing the solutions influenced by the surface piezoelectricity with those affected by the surface elasticity,it is found that the influence of the surface piezoelectricity on the crack opening displacement, the crackelectric potential jump across the crack center, the crack tip stress and electric displacement intensity factorscannot be ignored. Under various electrical boundary conditions, the influence of surface piezoelectricity onthe sliding displacement, crack tip stress and electric displacement intensity factors exhibits the same tendency.Besides, the influence of surface piezoelectricity on the electric displacement intensity factor is independentof the electrical boundary conditions, which is different from the results where only the surface elasticity isconsidered.     

Micro-crack initiation at tip of a rigid line inhomogeneity in piezoelectric materials

For the square-root singularity shear stress found at the tip of a rigid line inhomogeneity (an anti-crack) in piezoelectric media, one possible way of releasing high strain energy is to initiate a micro-crack at the inhomogeneity tip. In our current study, a dislocation pileup model for micro-crack initiation at the inhomogeneity tip is proposed based on Zener-Stroh crack initiation mechanism. An interesting and important physical result that emerges from the analysis is that the critical stress intensity factor for the anti-crack (the line inhomogeneity) can be related to the fracture toughness of a conventional Griffith crack in the same material. Analytical results further show that under mechanical loading, the critical stress and electric displacement intensity factors of an anti-crack are only related to the corresponding intensity factors of stress and electric displacement of the crack, respectively. While if the anti-crack is under displacement loading (with net dislocation pile-up at the inhomogeneity tip), the critical stress and electric displacement intensity factors of an anti-crack depend on both of the total mechanical dislocations b_T and electricity dislocations b_D.     

Near-tip fields and intensity factors for interfacial cracks in dissimilar anisotropic piezoelectric media

A complete form of stress and electric displacement fields in the vicinity of the tip of an interfacial crack, between two dissimilar anisotropic piezoelectric media, is derived by using the complex function theory. New definitions of real-valued stress and electric displacement intensity factors for the interfacial crack are proposed. These definitions are extensions of those for cracks in homogeneous piezoelectric media. Closed form solutions of the stress and electric displacement intensity factors for a semi-infinite crack as well as for a finite crack at the interface between two dissimilar piezoelectric media are also obtained by using the mutual integral.     

压电材料中反平面渗透裂纹的解

用复变函数的保角映射法,采用可渗透边界条件,研究了含裂纹的无限大压电材料在平面内电场和反平面荷载作用下的耦合场,得到了精确的解和场强度因子以及能量释放率。结果表明,电场强度在裂尖没有奇异性,应变、应力、电位移具有1/2阶的奇异性,能量释放率总是正的。     

通电瞬时板内半无限长裂纹尖端域的应力场

以导电弹性体的麦克斯威尔方程为出发点,借助于边界条件和初始条件,推得了在向含半无限长直线裂纹的无限大导电薄板内通入电流的瞬时,裂纹尖端附近电流密度的表达式。在此基础上,得到了裂纹尖端区域处温度和应力的具体表达式。算例表明,在电流所产生的焦耳热源的作用下,裂尖区域处的温度将瞬时升高,并伴有压应力的产生,从而可达到阻止裂纹扩展的目的。     

Dynamic steady-state analysis of crack propagation in rubber-like solids using an extended finite element method

In the present study, a computational framework for studying high-speed crack growth in rubber-like solids under conditions of plane stress and steady-state is proposed. Effects of inertia, viscoelasticity and finite strains are included. The main purpose of the study is to examine the contribution of viscoelastic dissipation to the total work of fracture required to propagate a crack in a rubber-like solid. The computational framework builds upon a previous work by the present author (Kroon in Int J Fract 169:49–60, 2011). The model was fully able to predict experimental results in terms of the local surface energy at the crack tip and the total energy release rate at different crack speeds. The predicted distributions of stress and dissipation around the propagating crack tip are presented. The predicted crack tip profiles also agree qualitatively with experimental findings.     

压电-压磁板条中反平面裂纹的电-磁-弹性分析

基于线性电磁弹性理论,获得了压电-压磁板条中反平面裂纹尖端附近的奇异应力、电场和磁场。假设裂纹位于和板条边界平行的中心位置,并且裂纹是电磁渗透型的。利用Fourier变换,将裂纹面的混合边值问题化为对偶积分方程,即而归结为第二类Fredholm积分方程。通过渐近分析,得到了裂纹尖端附近应力、应变、电位移、电场、磁场和磁感的封闭表达式。结果表明,对于电磁渗透裂纹,电场强度因子和磁场强度因子总为0;板条的宽度对应力强度因子有显著的影响;能量释放率总为正值。     

Linear electro-elastic fracture mechanics of piezoelectric materials

The concepts of linear elastic fracture mechanics, generalized to treat piezoelectric effects, are employed to study the influence of the electrical fields on the fracture behavior of piezoelectric materials. The method of distributed dislocations and electric dipoles, already existing in the literature, is used to calculate the electro-elastic fields and the energy-release rate for a finite crack embedded in an infinite piezoelectric medium which is subjected to both mechanical and electric loads. The energy-release rate expressions show that the electric fields generally tend to slow the crack growth. It is shown that the stress intensity factor criterion and the energy-release rate criterion differ when the energetics of the electric field is taken into account. The study of crack tip singular stress field yields a possible explanation for experimentally observed crack skewing in the presence of a strong electric field.     

An accumulation damage model for fatigue fracture of ferroelectric ceramics

The accumulated plastic displacement criterion for crack propagation in traditional materials is extended to develop equations to predict the fatigue crack growth of ferroelectric ceramics subjected to combined electromechanical loads. The crack-line is perpendicular to the poling direction of the medium. An electric saturation zone and a stress saturation zone are assumed to develop at the crack tips when the medium is subjected to external electromechanical loads. This assumption makes it possible to obtain the accumulated plastic deformation in closed form. A fatigue crack growth law, which is a fourth-power function of the effective stress intensity factor, similar to the well-known Paris law, is derived. Graphical results for the effect of electric load on the effective crack tip stress intensity factor and crack growth rate are provided.