Method of caustics for the study of cracked plates made of viscoelastic materials

The optical method of caustics was used for the evaluation of the stress intensity factor at the crack tip in a viscoelastic plate made of polycarbonate of bisphenol A and containing a single external crack under conditions of generalized plane stress. It was assumed that the crack developed in a linear viscoelastic material. The reflected rays from both lateral faces, as well as the transmitted rays of a normally incident light beam were significantly dispersed at the close neighborhood of the crack tip because of the excessive lateral constraint and the strong variation of the refractive index, and concentrated along singular curves (caustics) at some distances from the plate. The reflected caustics formed two branches. While the internal branch, which was formed by reflections from the front face, depended only on the elastic modulus (E) and Poisson's ratio (v) of the material, the external branch, formed by reflections from the rear face, depended on E and v, as well as on the refractive index of the material (n). The transmitted rays formed the same type of caustic as that which was formed by reflections from the rear face, but with a different size.

By studying the relative position and shape of the two reflected branches and their variation with time, information was derived concerning the viscoelastic state of the material at fracture. The transmitted light caustic was used as a check on the results.

A series of viscoelastic tests in pure tension at various stress and strain levels yielded the variation of the mechanical (E, v) and optical (n, c_r, c_f) properties of the material with applied stress and strain. The values of these quantities at each stress level allowed the plotting of the relative positions of the two branches of the reflected caustics. Comparison of the actual position of the caustics at the crack tip with the caustic nomogram yielded the viscoelastic behavior of the material during the progress of loading. It was shown that by increasing the loading mode a strong viscoelastic behaviour was apparent which influenced considerably the fracture mode of the plate.     

带有两个共线裂纹载流薄板的温度场及热应力强度因子

采用复变函数的方法,给出带有两个等长度共线穿透裂纹的无限大载流薄板在瞬间电流作用下,裂纹尖端附近产生的温度场的表达式,得到温度在裂纹尖端的奇异特征.在通入垂直于裂纹的均匀电流作用下,由于裂纹的存在,裂纹尖端出现绕流现象,产生焦耳热,瞬时高温形成点热源.通过点热源在金属薄板内形成的温度场,可以导出裂纹尖端产生的热应力强度因子表达式.将其与外载荷产生的应力强度因子叠加,可建立通电状态下的断裂判据.算例分析表明,点热源在裂纹尖端附近产生的热应力强度因子为负值,可以部分抵消无穷远处施加的拉应力产生的应力强度因子的作用,进而达到止裂的目的.文中建立带有两个等长度共线穿透裂纹载流薄板的热应力强度因子的概念.其研究结果对工程结构实施电磁热效应裂纹止裂具有理论意义和实用价值.     

Ductile fracture in glassy polymers

The optical method of caustics was used to study the highly deformed region at the crack tip of a tension plate made of polycarbonate (PCBA) up to fracture. This polymer was selected for its typical quasi-plastic behaviour. The modified Dugdale-Barenblatt (D-B) model was used in order to take into account the influence of the non-linear region of quasi-plastic behaviour of PCBA. Furthermore, it has also been observed that the tensile specimens of PCBA were curved significantly before fracture and this phenomenon is typical of all ductile materials. Comparison of the caustics formed from reflected and transmitted rays allowed the accurate evaluation of the curvature of the cracked plate during loading. The influence of curvature being excluded, the remaining parts of the caustics were related to the stress distribution at the crack tip. The size and the dimensions of the caustics were fitted into one of the six typical stress configurations in the plastic zones studied by the modified Dugdale-Barenblatt model and the form of stress distribution in the plastic zone for each loading step was determined. It was shown that the modified D-B model is capable of describing the plastic behaviour in cracked plates made of ductile materials. Furthermore, the method of caustics was capable of evaluating the influence of curvature of the cracked plate during loading.     

考虑裂纹面摩擦的有限多裂纹板的应力强度因子解析与数值方法

对在双轴压缩作用下,考虑裂纹面间摩擦力的无限大板中双裂纹与单裂纹的应力强度因子解析解进行对比分析。结果表明,裂纹面间的摩擦力对多裂纹应力强度因子的修正系数是没有影响的,只对有效剪应力产生影响。以无限板周期裂纹的解为例,将该解析解作为有限板共线多裂纹应力强度因子的近似理论解,运用有限元数值计算有限板共线双裂纹的应力强度因子,并将其结果与近似理论解进行对比分析。计算结果表明,有限板共线双裂纹应力强度因子的近似理论解与通过有限元法计算得到的数值解基本吻合,验证裂纹面间摩擦力对应力强度因子的修正系数没有影响,裂纹面间无摩擦力时多裂纹相互影响引起的修正系数可以作为考虑裂纹面间摩擦力时的修正系数。     

板结构裂纹兰姆波阵列复合成像方法研究

针对板结构中裂纹方向识别及定量检测问题,提出了一种板结构兰姆波阵列复合成像方法。利用超声阵列采集的单模态兰姆波全矩阵数据,分别提取其幅值信息和极性信息,进行全聚焦成像和极性一致成像,并利用极性一致成像对全聚焦成像进行了加权处理;对全阵列进行子阵列划分,计算出各子阵列的特征矢量,并进行加权合成,得到矢量全聚焦成像;利用全聚焦成像的强度信息和矢量全聚焦成像的方向信息,综合得到兰姆波阵列的复合成像,并从中提取出缺陷的方向及空间分布范围等信息。实验结果表明,提出的兰姆波阵列复合成像方法可以很好地实现板中多个裂纹方向识别,其角度测量误差在20%以内。本文工作为裂纹缺陷识别及定量检测做了有益探索。     

Symmetric bending of cracked plates studied by caustics

The optical method of reflected caustics was applied to the study of singularities in the stress field appearing at the crack tip of symmetric plates containing a symmetric crack and submitted to bending loads. The method of caustics was used in connection with the most effective plate theories, that is the theories of Kirchhoff-Williams and Reissner-Sih as they apply to problems of cracked plates.     

Investigation of Behavior of Stress-Corrosion Cracks in a Pipes under Internal Pressure

Corrosion induced by ambient conditions causes generation of longitudinal cracks on outside surfaces of gas pipelines, and this can lead to breaks in main pipelines. The paper presents experimental data on behavior of cracks in sections of pipelines with aws under constant and cyclically varied (45 cycles) hydrostatic pressure, the pressure magnitude corresponding to operational parameters. Crack parameters (increasing depths and openings of cracks) were monitored by sensors of magnetic induction placed on pipes immediately over cracks. The data indicated that cracks with depths of up to 30–35% of the wall thickness did not show residual changes (in their depths and openings) after tests. Residual changes were detected in deeper cracks, which manifested as critical ows of metal near the crack edge and growth of cracks to their critical dimensions. Photographs of fractured surfaces showed that crack depths started to increase long before the ultimate fracture of a pipeline. Thus, tests conducted by applying high pressure to operating gas pipelines can lead to increases in crack dimensions without detecting them. This effect is actually detrimental to the tested pipeline's safety. The absence of residual changes in cracks with depths of up to 30–35% of the wall thickness indicates that, possibly, new limits on aw dimensions should be established for decommissioning unsafe sections of pipelines, and these limits should take account of the hazard due to stress-corrosion cracks, depending on their dimensions and inside gas pressure.     

Fracture of an elastic strip containing a pair of collinear cracks perpendicular to the edges of the strip: Theory and experiment

A theoretical and experimental study is made on the fracture of an infinitely long strip containing a pair of collinear cracks perpendicular to the edges of the strip. In the theoretical investigation, the surfaces of the cracks are loaded by an arbitrary opening pressure, while the edges of the strip are free from tractions. By the use of the Fourier transforms and the finite Hilbert transform, the problem is reduced to the solution of the Fredholm integral equations of the second kind. In the case of uniform opening pressure, the exact expressions for the stress intensity factors at the inner tip and the outer tip of the cracks and the shape of the deformed crack are derived. Numerical calculations are carried out to study the interaction between the cracks and the effect of the edge free boundary. A series of tensile tests of PMMA strips containing a pair of collinear cracks of equal length is carried out to study the correlation between the experimental data and the values predicted from the equations obtained in this investigation.     

Effect of crack on the impact response of plates by the extended finite element method (X-FEM)

The dynamic response of cracked isotropic plates subjected to impact loading is studied in this paper. The impact properties of cracked plate are compared with the virgin ones to predict the eventual presence of discontinuities in plates. The extended finite element method (X-FEM) is employed in the mathematical modeling of the impact problem, wherein the effects of shear deformation is considered. Conventional finite element without any discontinuity is initially conducted in the numerical implementation. Enriched functions are then added to the nodal displacement field for element nodes that contain cracks. The effects of crack length and crack position on contact force and on plate deflection are analyzed. Results show that the maximal contact force decreases as the deflection increases with increasing crack length a. The effect of crack position on the dynamic response is less pronounced when the crack is near the fixed end.     

Fatigue Resistance and Failure Behavior of Penetration and Non-Penetration Laser Welded Lap Joints

Penetration and non-penetration lap laser welding is the joining method for assembling side facade panels of railway passenger cars,while their fatigue performances and the difference between them are not completely understood.In this study,the fatigue resistance and failure behavior of penetration 1.5+0.8-P and non-penetration 0.8+1.5-N laser welded lap joints prepared with 0.8 mm and 1.5 mm cold-rolled 301L plates were investigated.The weld beads showed a solidification microstructure of primary ferrite with good thermal cracking resistance,and their hardness was lower than that of the plates.The 1.5+0.8-P joint exhibited better fatigue resistance to low stress amplitudes,whereas the 0.8+1.5-N joint showed greater resistance to high stress amplitudes.The failure modes of 0.8+1.5-N and 1.5+0.8-P joints were 1.5 mm and 0.8 mm lower lap plate fracture,respectively,and the primary cracks were initiated at welding fusion lines on the lap surface.There were long plastic ribs on the penetration plate fracture,but not on the non-penetration plate fracture.The fatigue resistance stresses in the crack initiation area of the penetration and non-penetration plates calculated based on the mean fatigue limits are 408 MPa and 326 MPa,respectively,which can be used as reference stress for the fatigue design of the laser welded structures.The main reason for the difference in fatigue performance between the two laser welded joints was that the asymmetrical heating in the non-penetration plate thickness resulted in higher residual stress near the welding fusion line.     

Characteristic Vibrational Modes of Piezoceramic Plates with Variable Thicknesses

The paper considers characteristic oscillations of finite round piezoceramic plates of variable thicknesses, with convex and concave surfaces. Characteristic oscillation spectra of these plates were studied in the regimes of resonance and antiresonance, and the dynamic coefficient of electro-mechanical coupling was calculated as a function of plate dimensions and displacement distribution over the surface. Improvements in the characteristics of thickness oscillations in the plates (the possibility of increasing the coefficient of electro-mechanical coupling and smoothing the distribution of the normal displacement component over the plate surface) owing to variable thicknesses of piezoceramic plates have been analyzed. This can be achieved only in plates with convex conical surfaces, whereas concave conical surfaces of plates lead to inferior characteristics of thickness oscillations. Improvements in characteristics of thickness oscillations in piezoelectric plates fabricated from ceramics with various compositions will be discussed.     

Fracture behavior of two non-symmetrical collinear cracks emanating from an elliptical hole in a piezoelectric material

Based on the Stroh-type formalism and the technique of conformal mapping, the problem of two non-symmetrical collinear cracks emanating from an elliptical hole in a piezoelectric solid is investigated under remotely uniform in-plane electric loading and anti-plane mechanical loading, which allowed us to take the electric field inside the hole and cracks into account. The analytical solutions of the field intensity factors and the energy release rate are presented in closed-form, which includes the extreme cases for an impermeable crack and a permeable crack. Numerical results are then presented to reveal the effects of geometrical parameters, crack permeability and combined mechanical and electric loadings on the energy release rate.     

基于模糊神经网络的薄板不同指标裂纹诊断

将采用模糊神经网络的故障诊断技术和诊断模型,利用改进的BP算法对模糊神经网络进行训练,并利用训练好的网络,对悬臂薄铝板仿真裂纹进行了诊断。对悬臂薄铝板裂纹的诊断方法是:首先得到完好板结构和各种仿真裂纹板结构的振型和固有频率,在此基础上提取各种裂纹损伤情况下的五种裂纹诊断指标。将五种诊断指标分成三组,构成三个模糊神经网络,对模糊神经网络进行训练之后,利用训练好的网络对悬臂铝板裂纹进行了故障诊断,将裂纹的诊断结果与实际情况进行了比较,得到了不同诊断指标组合下,不同神经网络的诊断结果。并对不同组别裂纹诊断指标的诊断结果与实际裂纹情况进行了比较。     

带有任意边缘裂纹的自由圆板流固耦合动力特性

提出一种基于Rayleigh-Ritz法,分析带有任意深度、任意角度边缘裂纹的自由圆板流固耦合动力特性的方法,其中,圆板被置于无限大障板中并与单面无限大水域相临。采用同时包含对称和反对称模态振型函数的位移基函数表达带有任意边缘裂纹圆板自由振动的位移;在水体无旋、无粘、不可压假设的基础上,根据Green函数法获得水体的附加质量密度,并基于Ritz过程获得裂纹圆板湿模态对应的固有频率和振型。在与ANSYS数值仿真结果进行对比并验证方法的有效性和精度后,分析水体对带有不同深度和不同角度边缘裂纹的自由圆板动力特性的影响。计算结果表明:水体引起的固有频率降低率整体上随模态阶数的增加而减小,而裂纹深度与角度对固有频率降低率的影响较小;裂纹的出现会增大干、湿振型的差别,某些高阶模态的干、湿振型差别较大。     

Fracture development in solid perspex spheres with short cylindrical projections (bosses) due to point explosive loading

Fracture and void development in Perspex spheres with bosses (i.e. with cylindrical projections) due to point explosive loading by a detonator have been examined using high speed photography. The order in time, at which cracks or voids occur and their respective locations is discussed by reference to ray reflection from the free boundary. The different natures of the voids created is shown and an explanation of resulting terminal fracture patterns is offered.     

Buckling of unsymmetrical, cross-ply laminates with matrix cracks

The effect of matrix cracks on the buckling of unsymmetrical, cross-ply laminates is investigated. The cracks are modelled as aligned slit cracks across the ply thickness and transverse to the laminate plane. The distribution of cracks is assumed to be statistically homogeneous corresponding to an average crack density. The results are given for antisymmetrically- and unsymmetrically-laminated plates with a given density of matrix cracks. The effect of reduction in the laminate stiffness is studied by plotting the ratio of the buckling loads of cracked and uncracked laminates against the aspect ratio, crack density and relative layer thicknesses. It is observed that the amount of reduction in the buckling load depends on the stacking sequence as well as on the relative thicknesses of layers. This reduction is found to be substantially less than the reduction in the affected elastic moduli of the material.     

Detection for transverse corner cracks of steel plates’ surface using wavelet

An algorithm is presented for detecting transverse corner cracks at a steel plate surface using wavelet transform. According to characteristics of transverse corner crack images, the wavelet transform is used for the multi-scale analysis of detecting the image edges and disintegrating the image into four directions at the same time. The proper threshold value is chosen to segment the image into vertical components to obtain the final detection result. The experiment shows that transverse corner cracks of steel plates can be more effectively extracted by the proposed method than the other two common methods.     

Detection for transverse corner cracks of steel plates’ surface using wavelet

An algorithm is presented for detecting transverse corner cracks at a steel plate surface using wavelet transform. According to characteristics of transverse corner crack images, the wavelet transform is used for the multi-scale analysis of detecting the image edges and disintegrating the image into four directions at the same time. The proper threshold value is chosen to segment the image into vertical components to obtain the final detection result. The experiment shows that transverse corner cracks of steel plates can be more effectively extracted by the proposed method than the other two common methods.     

用有限元研究金属构件裂纹的修补参数

金属结构的裂纹可以用加补强板的方法修补 ,但有限元程序计算表明 :选择补强板的参数应按照最大限度降低裂纹尖端应力的原则。笔者用实例说明修补裂纹只能延缓裂纹的扩展速度而不能根除裂纹的存在     

A waveguide method for the investigation of the elastic wave action on a newly formed crack

A technique for studying the processes of mechanical action on a newly formed crack and a device with a movable waveguide used to form fixed cracks in a rock sample in laboratory conditions are described. Analyzing the features of acoustic pulses, one can relate them to the dimensions and rate of the crack propagation, as well as control the sample destruction process. Characteristic time intervals in the sample destruction process are observed and resolved. Experimental results on the destruction of a marble plate with the use of the waveguide method are presented.