基于权函数法的核主泵飞轮应力强度因子研究

采用权函数法确定了含裂纹飞轮在离心力和接触压力作用下的应力强度因子,计算了在同步转速工况下裂纹尖端应力强度因子的值,并与解析法和有限元法计算结果进行了对比。结果表明:权函数法与解析法的误差在3%以内,与有限元法的误差在1%以内,验证了权函数法计算应力强度因子的准确性高;在结构不变的情况下,权函数法可以快速求解不同载荷条件、不同长度裂纹的应力强度因子。通过控制变量法研究了不同参数对应力强度因子的影响,结果表明,飞轮裂纹尖端总应力强度因子随着裂纹尺寸、旋转转速、飞轮尺寸外径与内径比值的增大而增大。     

Stress and electric displacement analyses in piezoelectric media with an elliptic hole and a small crack

In this paper, the interactions between an elliptic hole and an arbitrary distributed small crack in plane piezoelectric medium, which are often happened in engineering problems, are discussed. The Green’s functions in a piezoelectric plate with an elliptic hole for a generalized line dislocation and a generalized line force are presented. The small crack is represented by unknown continuous distributed dislocations. By considering traction free conditions on the surface of the small crack, the problem is then reduced to a group of singular integral equations which are solved by using a special numerical technique. Accuracy of the present method is confirmed by comparing the numerical results with those in literatures for PZT-4 when the elliptic hole is degenerated into a crack. The generalized stress intensity factors of cracks and the generalized stress on the edge of the elliptic hole are shown graphically. It is shown that the small crack may have shielding or amplifying effects on the main elliptic hole or crack, which depends on the location and orientation of the small crack. The hole near a crack can significantly reduce the stress intensity factor of the crack. The direction of the electric field is important to shielding effect.     

A technique for studying interaction between a screw dislocation dipole or a concentrated load and a mode III crack crossing an interface

A method of potentially wide application is developed for deriving analytical expressions of the elastic interaction between a screw dislocation dipole or a concentrated force and a crack cutting perpendicularly across the interface of a bimaterial. The cross line composed of the interface and the crack is mapped into a line, and then the complex potentials are educed. The Muskhelishvili method is extended by creating a Plemelj function that matches the singularity of the real crack tips, and eliminates the pseudo tips’ singularity induced by the conformal mapping. The stress field is obtained after solving the Riemann–Hilbert boundary value problem. Based on the stress field expressions, crack tip stress intensity factors, dislocation dipole image forces and image torque are formulated. Numerical curves show that both the translation and rotation must be considered in the static equilibrium of the dipole system. The crack tip stress intensity factor induced by the dipole may rise or drop and the crack may attract or reject the dipole. These trends depend not only on the crack length, but also on the dipole location, the length and the angle of the dipole span. Generally, the horizontal image force exerted at the center of the dislocation dipole is much smaller than the vertical one. Whether the dipole subjected to clockwise torque or anticlockwise torque is determined by whether the Burgers vector of the crack-nearby dislocation of the dipole is positive or negative. A concentrated load induces no singularity to crack tip stress fields as the load is located at the crack line. However, as the concentrated force is not located on the crack line but approaches the crack tip, the nearby crack tip stress intensity factor K_IIIu increases steeply to infinity.     

Multiple axial cracks in a coated hollow cylinder due to thermal shock

The transient thermal stress problem of an inner-surface-coated hollow cylinder with multiple pre-existing surface cracks contained in the coating is considered. The transient temperature, induced thermal stress, and the crack tip stress intensity factor (SIF) are calculated for the cylinder via finite element method (FEM), which is exposed to convective cooling from the inner surface. As an example, the material pair of a chromium coating and an underlying steel substrate 30CrNi2MoVA is particularly evaluated. Numerical results are obtained for the stress intensity factors as a function of normalized quantities such as time, crack length, convection severity, material constants and crack spacing.     

Orthotropic semi-infinite medium with a crack under thermal shock

A cracked orthotropic semi-infinite plate under thermal shock is investigated. The thermal stresses are generated due to sudden cooling of the boundary by ramp function temperature change. The superposition technique is used to solve the problem. The crack problem is formulated by applying the thermal stresses obtained from the uncracked plate with opposite sign to be the only external loads on the crack surfaces as the crack surface tractions. The Fourier transform technique is used to solve the problem leading to a singular equation of the Cauchy type. The singular integral equation is solved numerically using the expansion method. The influence of the material orthotropy on the stress intensity factors is shown by comparing the results obtained for different orthotropic materials and isotropic materials in the case of plane stress. The numerical results of the stress intensity factors are demonstrated as a function of time, crack length, location of the crack and the duration of the cooling rate.     

Special rotational deformation effect on the emission of dislocations from a crack tip in deformed nanocrystalline solids

The interaction between the special rotational deformation and the crack in deformed nanocrystalline ceramics and metals is investigated by the complex variable method. We have theoretically described the effects of the disclination quadrupole produced by the special rotational deformation on the emission of lattice dislocations from the crack tip. The complex form expressions of the stress field and the force field are divided. The critical stress intensity factors for the first dislocation emission are calculated. The influence of the disclination strength, the grain size (the quadrupole arms), the location of the disclinations and the angle between the crack plane and one of the quadrupole arms, as well as the crack length on the critical stress intensity factors is discussed in detail. And the results show that, the special rotational deformation has great influence on the dislocation emission from the crack tip.     

平行于功能梯度材料夹层的币型裂纹起裂条件

分析了功能梯度材料中币型裂纹的扩展问题．裂纹平行于无限域中功能梯度材料夹层,受有与裂纹面成任意角度的拉应力．假定功能梯度材料夹层与两个半无限域均匀介质完全粘合,其弹性模量沿厚度方向变化．采用基于层状材料广义Kelvin基本解的边界元方法分析裂纹问题,给出了均布正应力和剪应力作用下裂纹的应力强度因子、将应力强度因子耦合于应变能密度断裂判据,讨论了裂纹体在拉伸应力作用下的起裂条件．     

基于数字散斑相关方法测定Ⅰ型裂纹应力强度因子

提出了一种通过数字散斑相关方法测定金属材料Ⅰ型裂纹尖端位置和应力强度因子的实验方法.实验采用疲劳试验机对含Ⅰ型缺口的Cr12MoV钢试件预制裂纹,通过数字散斑相关方法测试试件在三点弯曲加载条件下裂纹的扩展过程及裂尖区域的位移场.将位移场数据代入裂尖位移场方程组,采用牛顿-拉普森方法求解含未知参量的裂尖非线性位移场方程组,计算裂尖位置和应力强度因子.实验结果表明,采用该方法可以准确地测定金属材料Ⅰ型裂纹应力强度因子、裂尖位置及裂纹扩展长度,解决了以往研究中因不能准确测定裂纹尖端位置,而无法准确计算Ⅰ型裂纹裂尖断裂参数的难题,揭示了金属材料裂纹扩展过程中应力强度因子演化特征.     

Torsion problems for a cylinder with a rectangular hole and a rectangular cylinder with a crack

Using the method of singular integral equation and the crack-cutting technique, the rigorous solutions are obtained for a cylinder with a rectangular hole and a rectangular cylinder with a crack, which exactly satisfy the boundary conditions and the conditions at the corner points. After that the torsional rigidities and the stress intensity factors at the crack tip are determined. Next, for the doubly connected circular cylinder with a rectangular hole the expressions for the singular stresses around the concave corner points are derived and the generalized stress intensity factors are then defined. Since the crack-cutting technique is used in this paper, the solution of the matching rectangular cylinder is also obtained and its numerical results coincide with those in references. Thus the method proposed here is verified. The project supported by National Natural Science Foundation of China     

一维六方准晶中平行螺型位错与有限长裂纹的相互作用

本文采用解析函数理论,利用Muskhelishvili著名的复变函数方法,给出了无限大一维六方准晶中多条平行螺型位错与有限长直裂纹相互作用的解析解,并得到了裂纹尖端的场强度因子和作用在位错上的像力.数值算例讨论了镜像力、场强度因子随位错位置的变化，及位错的位置与分布对广义应力场的影响．     

Stress intensity factors for interface crack in finite size specimen using a generalized variational approach

A generalized variational approach together with eigenfunction expansion is applied to determine the stress intensity factors for interface crack in finite size specimen. Application is also made of the complex potentials such that a complex stress intensity factor with components corresponding to the Mode I and II stress intensity factors can be identified with one of the leading coefficients in the eigenfunction expansion. Obtained are the numerical values of the stress intensity factors for an interface edge crack in a bimaterial rectangular specimen. The outside boundary is subjected to uniform stress normal and parallel to the crack. Solutions are also obtained for the same crack aand specimen geoinetry is subjected to a pair of equal and opposite concentrated forces along the open end away from the edge crack. The third example pertains to the case of three-point bending where the centre concentrated load is directed along the interface dividing the two materials. Numerical results are obtained for four different combinations of the bimaterial specimen with an interface edge crack.     

刚度微分法计算压电材料平面断裂问题

把计算应变能释放率的刚度微分法推广到压电材料平面断裂问题．在此基础上，利用压电材料平面断裂问题的有限元数值解作为真实场，用Ｓｏｓａ的平面问题裂端渐近解作为辅助场，由推广的交互Ｍ积分法求得了应力强度因子ＫＩ，ＫＩＩ和电位移强度因子ＫＩＶ．算例表明，计算结果与理论解符合得很好     

Asymptotic elastic solution for two straight cracks of arbitrary length and location

An infinite elastic plane containing two straight cracks of arbitrary length and location is analyzed within the framework of elastostatics. The mathematical formulation is based on the stress solution for a single crack and leads to a system of singular integral equations that govern the crack surface displacement densities. The solution series in terms of the reciprocal of the crack centre distance is not suitable for cracks that are spaced too closely. It is shown by way of examples that the method of asymptotic solution is convenient for developing approximation expressions of the stress and displacement field with certain characteristics. The formulas for the stress intensity factors and crack opening are given for the case of a constant tensile load. Graphical results are given for the variations of the stress intensity factors with parameters depending on the relative positions of the cracks.     

压电薄板板边导电裂纹尖端的力电场分析

采用有限元方法，分析了压电薄板板边不同长度导电裂纹尖端的力电场分布规律，发现导电裂纹尖端的应力场和电场强度存在明显的集中和奇异现象，集中和奇异的程度与裂纹长度有关。而且，在裂纹延长线上分别存在两点，这里的应力和电场对裂纹长度不太敏感，总等于无裂纹时薄板的均匀应力和均匀电场强度；同时，还研究了导电裂纹尖端的应力强度因子和电场强度因子对裂纹长度的依赖关系，发现在线性本构的前提下，导电裂纹尖端的应力强度因子与电场强度因子之间具有近似的线性关系。     

International conference on role of fracture mechanics in modern technology : Fukuoka, Japan, June 2–6, 1986

An infinite elastic plane containing two straight cracks of arbitrary length and location is analyzed within the framework of elastostatics. The mathematical formulation is based on the stress solution for a single crack and leads to a system of singular integral equations that govern the crack surface displacement densities. The solution series in terms of the reciprocal of the crack centre distance is not suitable for cracks that are spaced too closely. It is shown by way of examples that the method of asymptotic solution is convenient for developing approximation expressions of the stress and displacement field with certain characteristics. The formulas for the stress intensity factors and crack opening are given for the case of a constant tensile load. Graphical results are given for the variations of the stress intensity factors with parameters depending on the relative positions of the cracks.     

Time-harmonic P-waves engulfing a rectangular limited-permeable crack in piezoelectric medium: Energy density and energy release

The dynamic behavior of a limited-permeable rectangular crack in a transversely isotropic piezoelectric material is impinged by to a P-wave. The generalized Almansi theorem and the Schmidt method are used to determine the stress intensity factor and energy density factor as the primary fracture criterion of failure. The mixed boundary value problem entails the evaluation of the appropriate crack edge stress singularities that are characteristics of the fundamental functions. The stress and electric displacement intensity factors are also used to find the energy release rate that can be computed numerically and compared with the results corresponding to those of the stress intensity factor, and energy density factor. Graphical presentation shows that the energy release rate is always negative for the boundary conditions considered while the energy density factors always remain positive. Under certain conditions, the stress and electric displacement intensity factors can be negative and subject to physical limitations. Piezoelectric material boundary value problem solutions should therefore be qualified by the application of failure criteria by fracture of otherwise, particularly when the mechanical and electrical energy can release by creating free surface at the macroscopic and microscopic scales. Negative energy release rate found for the piezoelectric medium in this work can be a case in point.Positive definiteness of the energy density factor can be applied to mutliscale fracture. This is not true for the stress intensity factor nor the energy release rate. Hence, crack initiation behavior for the permittivity of a rectangular crack due to the wave propagation effects may be studied. In particular, the initiation of micro-cracks may be identified with certain critical stress wave frequency band. Negative stress intensity factor may not enhance macrocracking but it does not exclude microcrack initiation.     

Interface crack problems for mode Ⅱ of double dissimilar orthotropic composite materials

The fracture problems near the interface crack tip for mode Ⅱ of double dissimilar orthotropic composite materials are studied. The mechanical models of interface crack for mode Ⅱ are given. By translating the governing equations into the generalized bi-harmonic equations,the stress functions containing two stress singularity exponents are derived with the help of a complex function method. Based on the boundary conditions,a system of non-homogeneous linear equations is found. Two real stress singularity exponents are determined be solving this system under appropriate conditions about himaterial engineering parameters. According to the uniqueness theorem of limit,both the formulae of stress intensity factors and theoretical solutions of stress field near the interface crack tip are derived. When the two orthotropic materials are the same,the stress singularity exponents,stress intensity factors and stresses for mode Ⅱ crack of the orthotropic single material are obtained.     

裂纹在冲击载荷作用下起裂的临界载荷面

采用有限元方法研究裂纹在I型短脉冲载荷作用下应力强度因子随时间的变化 ,用应力强度因子的初始上升时间Tr 对时间坐标无量纲化 ,对应力强度因子初始上升段进行曲线拟合 ,得到了上升段的曲线表达式。运用简单弹性梁理论和Lagrangian运动方程 ,获得载荷与时间对裂纹作用的关系式 ,结合有限元的结果 ,得到了上升时间Tr 的计算表达式 ,并进一步推出了裂纹在冲击载荷作用下起裂的临界载荷面。     

Stress intensity factors for an oblique edge crack in a coating/substrate system with a graded interfacial zone under antiplane shear

This paper investigates the edge crack problem for a coating/substrate system with a functionally graded interfacial zone under the condition of antiplane deformation. With the interfacial zone being modeled by a nonhomogeneous interlayer having the continuously varying shear modulus between the dissimilar, homogeneous phases of the coated medium, the coating is assumed to contain an edge crack at an arbitrary angle to the interfacial zone. The Fourier integral transform method is used in conjunction with the coordinate transformations of basic field variables. Formulation of the proposed crack problem is then reduced to solving a singular integral equation with a generalized Cauchy kernel. The mode III stress intensity factors are defined and evaluated in terms of the solution to the integral equation. In the numerical results, the values of the stress intensity factors are plotted, illustrating the effects of the crack orientation angle for various material and geometric combinations of the coating/substrate system with the graded interfacial zone.     

Interactions of multiple parallel symmetric permeable mode-III cracks in a piezoelectric material plane

In this paper, the interactions of multiple parallel symmetric and permeable finite length cracks in a piezoelectric material plane subjected to anti-plane shear stress loading were studied by the Schmidt method. The problem was formulated through Fourier transform into dual integral equations, in which the unknown variables are the jumps of displacements across the crack surfaces. To solve the dual integral equations, the jumps of displacements across the crack surfaces were directly expanded as a series of Jacobi polynomials. Finally, the relation between the electric field and the stress field near the crack tips was obtained. The results show that the stress and the electric displacement intensity factors at the crack tips depend on the lengths and spacing of the cracks. It is also revealed that the crack shielding effect presents in piezoelectric materials.