Experimental method of dynamic caustics and its application in fracture mechanics

The equation of static and dynamic caustics, and the formulae determining the position of crack tip and stress intensity factor are given. It is proven that for the case of low speed of crack propagation the static formula is applicable in calculation. A simple method to measure the static stress-optical constants is proposed. An Optical system which is suitable for the experiments of dynamic caustics was set-up and used to study the fracture in beam and rings with initial crack under impact loading. A series of dynamic caustics' photographs and curves showing the variations of corresponding crack lengths and dynamic stress intensity factors with time, are presented.     

Dynamic stress intensity factor K III and dynamic crack propagation characteristics of anisotropic materials

Based on the mechanics of anisotropic materials, the dynamic propagation problem of a mode Ⅲ crack in an infinite anisotropic body is investigated. Stress, strain and displacement around the crack tip are expressed as an analytical complex function, which can be represented in power series. Constant coefficients of series are determined by boundary conditions. Expressions of dynamic stress intensity factors for a mode Ⅲ crack are obtained. Components of dynamic stress, dynamic strain and dynamic displacement around the crack tip are derived. Crack propagation characteristics are represented by the mechanical properties of the anisotropic materials, i.e., crack propagation velocity M and the parameter ~. The faster the crack velocity is, the greater the maximums of stress components and dynamic displacement components around the crack tip are. In particular, the parameter α affects stress and dynamic displacement around the crack tip.     

Photoelastic experimental hybrid method for fracture mechanics of anisotropic materials

In this paper, the isotropic and anisotropic photoelastic experimental hybrid methods for fracture mechanics are developed. Using the photoelastic experimental hybrid method, it is demonstrated that one can precisely obtain stress intensity factors and separate the stress components of isotropic and anisotropic plate problems from the only isochromatics.     

反倾层状岩质边坡失稳的断裂力学分析

反倾层状岩质边坡的高危地质灾害承载体在自然界中普遍存在,为研究其失稳破坏机制,将反倾边坡岩层简化为一个带裂缝的悬臂梁,建立了由一组结构面控制边坡稳定性的断裂力学模型,推导了各岩层结构面等效应力强度因子和岩层及边坡稳定性判据。分析了岩层倾角、层厚、结构面长度、内摩擦角和粘聚力5个因素对边坡的稳定性影响。结果表明,随着岩层倾角和结构面长度的增加,边坡不稳定区域增加,坡脚处的抗滑稳定性减小;随着内摩擦角和粘聚力的增大,边坡不稳定区域减小,坡脚处的抗滑稳定性增大;随着岩层厚度的增大,不稳定岩层的范围基本保持不变,但是岩层的抗滑稳定区域随着厚度增加逐渐向坡脚移动,厚度越大,坡脚处的抗滑稳定性越大。实例分析验证了本文理论的合理与可行性,研究结论对工程实践具有一定指导意义。     

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给出了混流式转轮叶片与上冠(或下环)采用部分焊透裂纹尖端应力强 度因子的分析模型. 根据给出的模型，结合某电站转轮强度分析结果，通过实际算例，明 确了预留焊缝长度的确定方法. 该方法适用于所有混流式转轮叶片与上冠(或下环)之间 采用部分焊透预留焊缝长度的确定.     

节理岩体爆生裂纹扩展动态焦散线模型实验研究

应用动态焦散线测试系统,模拟含节理岩体断裂爆破过程,进行了PMMA模型透射式动态焦散线实验,着重研究了爆炸初始裂纹与节理面夹角不同的情况下,裂纹尖端动态强度因子的变化规律、裂纹穿过节理面的扩展规律、以及炮孔与节理距离不同时裂纹穿过节理扩展的规律。实验结果分析表明,爆生裂纹穿过节理面时,裂纹尖端的动态强度因子和裂纹扩展速度显著下降,穿过节理面后,强度因子又增强;裂纹穿过节理面时,裂纹会沿节理面偏离一段距离后沿原方向继续扩展。实验结果还表明,炮孔与节理间距适宜的情况下,裂纹才会穿过节理继续扩展,间距太小和过大都不利于裂纹的扩展。     

Dynamic fracture mechanics analysis for composite material with material non-homogeneity in thickness direction

The problem considered here is the response of a non-homogeneous composite material containing some cracks subjected to dynamic loading. It is assumed that the composite material is orthotropic and all the material properties depend only on the coordinatey (along the thickness direction). In the analysis, the elastic region is divided into a number of plies of infinite length. The material properties are taken to be constants for each ply. By utilizing the Laplace transform and Fourier transform technique, the general solutions for plies are derived. The singular integral equations of the entire elastic region are obtained and solved by the virtual displacement principle. Attention is focused on the time-dependent full field solutions of stress intensity factor(SIF) and strain energy release rate. As a numerical illustration, the dynamic stress intensity factor of a substrate/functionally graded film structure with two cracks under suddenly applied forces on cracks face are presented for various material non-homogeneity parameters.     

三维断裂分析软件FRANC3D

介绍了三维断裂分析软件FRANC3D(FRacture ANalysis Codein 3 Dimensions),它和立体对象建模器OSM(Object Solid Modeler)以及边界元系统BES(Boundary Element System)一起构成一套完整的断裂分析系统。该软件可以进行复杂裂纹的应力强度因子计算、自适应裂纹扩展,具有友好的图形用户界面和强大的前后处理功能。本文还给出了两个应用该软件的实例,证明分析是成功的。     

横观各向同性材料的三维断裂力学问题

从三维横观各向同性材料弹性力学理论出发, 使用Hadamard有限部积分概念, 导出了三维状态下单位位移间断(位错)集度的基 本解. 在此基础上, 进一步运用极限理论, 将任意载荷作用下, 三维无限大横观各向 同性材料弹性体中, 含有一个位于弹性对称面内的任意形状的片状裂纹问题, 归结为求 解一组超奇异积分方程的问题. 通过二维超奇异积分的主部分析方法, 精确地求得了裂纹前沿光滑点附近的应力奇异指数和奇异应力场, 从而找到了以裂纹表面位移间断表示的应力强度因子表达式及裂纹局部扩展所提供 的能量释放率. 作为以上理论的实际应用,最后给出了一个圆形片状裂纹问题 的精确解例和一个正方形片状裂纹问题的数值解例. 对受轴对称法向均布载荷作用下圆形片状裂纹问题, 讨论了超奇异积分方程的精确求解方法, 并获得了位移间断和应力强度因子的封闭解, 此结果与现有理论解完全一致.     

动、静裂纹作用偏置效应的动焦散冲击实验

为了研究冲击荷载作用下脆性材料中运动裂纹与静止裂纹的相互作用,选取动态载荷下断裂行为与岩石材料类似且本身光学特性较好的有机玻璃（PMMA）作为实验材料,试件尺寸为220 mm×50 mm×5 mm,采用激光切割制作长度5 mm的预制裂纹和长度10 mm的静止裂纹,预制裂纹位于试件的底部边缘中心,静止裂纹的中心位于试件水平轴线。将静止裂纹偏置距离作为单一变量,采用数字激光动态焦散实验系统对含不同缺陷的PMMA进行三点弯曲实验,并结合几何分形理论研究不同偏置距离下运动裂纹的分形规律。实验结果表明：存在预制裂纹与静止裂纹的临界偏置距离（6 mm）,该条件下裂纹轨迹对应的分形维数值最大,裂纹轨迹的规则程度最低,裂纹破坏形态最复杂。当预制裂纹与静止裂纹的偏置距离在0～6 mm时,裂纹Ⅰ起裂后垂直向上扩展一段距离,与静止裂纹交汇,并停滞一段时间后发生二次起裂,直至贯穿试件,偏置距离和交汇点竖向坐标值呈近似线性函数关系。偏置距离的存在不会影响裂纹Ⅰ的起裂时间和应力强度因子,但会显著减小裂纹Ⅱ的动态应力强度因子,且停滞时长随偏置距离的增大而逐渐缩短。当偏置距离大于临界偏置距离时,运动裂纹不再与静止裂纹交汇而是呈拱状向试件上边缘扩展直至贯穿,裂纹的起偏时间、起偏位置也会出现明显的滞后现象。

     

压应力场中爆生裂纹分布与扩展特征实验分析

采用动静组合加载实验装置和数字激光焦散线实验系统,进行了0、3、6、9 MPa等4种压应力场中PMMA试件的爆破致裂实验,分析了沿静态主应力方向扩展的裂纹运动学和力学行为。实验结果表明:首先,静态竖向载荷在预制炮孔周围产生应力集中,在炮孔壁上下端部处出现最大拉应力;随后,在动态爆炸载荷的叠加作用下,裂纹优先在炮孔壁上最大拉应力位置处起裂,并沿最大主应力方向扩展;裂纹扩展过程中,静态竖向载荷越大,裂纹扩展速度越大,且裂纹尖端应力强度因子值越大。     

切槽孔爆破动态力学特征的动焦散线实验

应用爆炸加载的透射式动焦散线测试系统,分析了有机玻璃切槽孔爆破模型的裂纹动态特征变化规律。比较了不同切槽角度、切槽深度的定向断裂裂纹尖端的扩展长度、扩展速度和动态应力强度因子。初步探讨了切槽爆破的动态效应,研究表明切槽孔爆破早期裂纹破坏模式为爆炸拉应力波作用下的I型快速扩展裂纹,裂纹尖端拉应力集中积聚的较大应变能维持了爆炸裂纹进一步扩展,裂纹尖端扩展后期表现为P波、S波共同作用下的复合型扩展特征。切槽角为60时获得的定向断裂效果最好,合理切槽深度为炮孔半径的1/4～1/2。     

Experimental investigation of dynamic punch tests on isotropic and composite materials

An experimental investigation is conducted on the two-dimensional punch problem for isotropic materials and unidirectional fiber-reinforced composite materials under quasi-static and impact loading. Singular stresses are generated in the specimen near the punch corners, and the stress intensity factorK _Iis introduced to describe the singular stress field. Laser interferometry is used to measure in-plane stresses (transmission mode) and out-of-plane displacements (reflection mode) and then estimate the stress intensity factor. In the dynamic case, a high-speed photography technique was employed to capture the transient response of the specimen and measureK(t) just after the impact. In all the cases, a good agreement between the measurements ofK and theoretical predictions was found.     

三维计算断裂力学

断裂力学理论从1921年Griffith研究玻璃的脆性断裂问题开始,经历了从线弹性体系到弹塑性以及蠕变理论体系、从单参数到多参数体系和从理想的二维平面理论到实际三维含裂纹结构的三维断裂理论的发展历程。针对应力强度因子K和J积分以及C(t)积分的计算方法从理想化模型的理论计算发展到实际复杂工程结构裂纹体计算的各种商业软件平台以及专业的断裂理论分析平台。尤其是随着计算机技术的发展,对三维含裂结构的静态和扩展裂纹的计算模拟已经能够融入计算机辅助设计。结合本研究组近30年来在三维疲劳断裂理论和应用研究方面的体会,简述了三维计算断裂力学从裂纹体应力应变分析和断裂参数计算到三维蠕变断裂和疲劳裂纹扩展模拟的国内外进展,并对涉及的计算方法,包括原子尺度和跨尺度的计算模拟,以及目前面临的挑战性问题作了简要介绍和分析。     

Sensitivity of probabilistic fracture mechanics analysis to variations in statistical parameters

Probability of failure (p_f) of a structure is usually calculated for a specified set of statistical parameters (mean, standard deviation, and probability distribution) that characterize random variables. This approach may not be efficient in cases where one would like to know the effect of variations in statistical parameters on the probability of failure. A method based on generating and analyzing randomly selected statistical parameters is proposed. The method consists of generating databases of mean and coefficient of variation (COV = mean/standard deviation) values of relevant fracture mechanics variables through a random process. The method was applied to surface cracks in a flat wide plate loaded under elastic conditions. Probability of failure was calculated for each database record using the first-order reliability method (FORM). Multiple linear regression analyses of the database records were performed with p_f as dependent variable and statistical parameters as independent variables. The predicted p_f values were in very good agreement with the directly calculated p_f values for the specified variations of statistical parameters (±10%, ±15%, and ±20%), except those for fracture toughness and tensile stress, where variations should be limited to ±10% and ±15% ranges.     

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对于连续截面直梁平面横力弯曲情形, 分析了剪切变形引起横截面翘曲的影响. 基于位移模式假定, 用材料力学方法得到相应的正应力与切应力表达式, 并以均布力作用的矩形截面简支梁为例说明截面翘曲对于应力的影响. 该分析方法及其结果适用于材料力学教学.     

Transient thermal shock fracture analysis of functionally graded piezoelectric materials by the extended finite element method

Transient thermal dynamic analysis of stationary cracks in functionally graded piezoelectric materials (FGPMs) based on the extended finite element method (X-FEM) is presented. Both heating and cooling shocks are considered. The material properties are supposed to vary exponentially along specific direction while the crack-faces are assumed to be adiabatic and electrically impermeable. A dynamic X-FEM model is developed in which both Crank–Nicolson and Newmark time integration methods are used for calculating transient responses of thermal and electromechanical fields respectively. The generalized dynamic intensity factors for the thermal stresses and electrical displacements are extracted by using the interaction integral. The accuracy of the developed approach is verified numerically by comparing the calculated results with reference solutions. Numerical examples with mixed-mode crack problems are analyzed. The effects of the crack-length, poling direction, material gradation, etc. on the dynamic intensity factors are investigated. It shows that the transient dynamic crack behaviors under the cooling shock differ from those under the heating shock. The influence of the thermal shock loading on the dynamic intensity factors is significant.     

On study of nonclassical problems of fracture and failure mechanics and related mechanisms

Nonclassical problems of fracture and failure mechanics that have been analyzed by the author and his collaborators at the S. P. Timoshenko Institute of Mechanics (Kiev, National Academy of Sciences of Ukraine) during the past forty years are considered in brief. The results of the analysis are presented in a form that would be quite informative for the majority of experts interested in various fundamental and applied aspects of fracture and failure problems including the identification of related mechanisms. This paper was prepared on invitation of the Editorial Board of the journal “Annals. The European Academy of Sciences” and may be considered as an Extended Pascal Medal Lecture (The 2007 Blaise Pascal Medal in Materials Sciences of the EAS) This is an updated edition of the author’s lecture prepared at the invitation of the Annals—The European Academy of Sciences Magazine on the occasion of awarding him the 2007 Blaise Pascal Medal in Materials Sciences by the EAS. The author’s speech at the award ceremony at the General Assembly of the Academy has already been published in International Applied Mechanics [75]. The electronic version of the paper in Annals has been prepared; this issue of Annals is to be published as a book. The paper includes an additional section and extended list of references [41–99]. Published in Prikladnaya Mekhanika, Vol. 45, No. 1, pp. 3–40, January 2009.     

Coupled solution for anisotropic piezoelectric materials with cracks

The coupled elastic and electric fields for anisotropic piezoelectric materials with electrically permeable cracks are analyzed by using Stroh formula in anisotropic elasticity. It is shown from the solution that the tangent component of the electric field strength and the normal component of the electric displacement along the faces of cracks are all constants, and the electric field intensity and electric displacement have the singularity of type (1/2) at the crack tip. The energy release rate for crack propagation depends on both the stress intensity factor and material constants. The electric field intensity and electric displacement inside electrically permeable cracks are all constants.     

围压与径向荷载共同作用下巴西盘裂纹应力强度因子的解析解

利用权函数法推导了围压和径向荷载共同作用下,考虑裂纹面摩擦的预制裂纹巴西盘应力强度因子计算公式,从理论上分析了围压、径向荷载和裂纹面摩擦对巴西盘应力强度因子的影响。结果表明,围压对I型应力强度因子有很大影响,I型应力强度因子随围压的增大而减小。当裂纹面闭合后围压和摩擦系数对II型应力强度因子同样具有显著影响,考虑裂纹面有效剪应力的权函数法理论解与有限元数值解相吻合,表明理论分析的正确性。