THREE-DIMENSIONAL INTERACTIONS OF CIRCULAR CRACK IN TRANSVERSELY ISOTROPIC PIEZOELECTRIC SPACE WITH RESULTANT SOURCES

Exact solutions in form of elementary functions were derived for the stress and electric displacement intensity factors of a circular crack in a transversely isotropic piezoelectric space interacting with various stress and charge sources： force dipoles, electric dipoles, moments, force dilatation and rotation. The circular crack includes penny-shaped crack and external circular crack and the locations and orientations of these resultant sources with respect to the crack are arbitrary. Such stress and charge sources may model defects like vacancies, foreign particles, and dislocations. Numerical results are presented at last.

THE PROBLEM OF AN EXTERNAL CIRCULAR CRACK UNDER ASYMMETRIC LOADINGS

Using the boundary integral equation method, the problem of an external circular crack in a three-dimensional infinite elastic body under asymmetric loadings is investigated. The two-dimensional singular boundary integral equations of the problem were reduced to a system of Abel integral equations by means of Fourier series and hypergeometric functions. The exact solutions of stress intensity factors ore obtained for the problem of an external circular crack under asymmetric loadings, which are even more universal than the results obtained by the use of Hankel transform method. The results demonstrate that the boundary integral equation method has great potential as a new analytic method.

Torsion problem for elastic multilayered finite cylinder with circular crack

An axisymmetric tangent stress is applied to a lateral surface of a multilayered elastic finite cylinder with a fixed bottom face. The problem is solved for an arbitrary number of layers. The layers are coaxial, and the conditions of an ideal mechanical contact are fulfilled between them. A circular crack is situated parallel to the cylinder’s faces in the internal layer with branches free from stress. The upper face of the cylinder is also free from stress. Concretization of the problem is done on examples of two-and three-layered cylinders. An analysis of cylinders’ stress state is conducted and the stress intensity factor is evaluated depending on the crack’s geometry, its location and ratio of the shear modulus. Advantages of the proposed method include reduction of the solution constants’ number regardless of the number of layers, and presentation of the mechanical characteristics in a form of uniformly convergent series.

THE PROBLEM OF AN EXTERNAL CIRCULAR CRACK UNDER ASYMMETRIC LOADINGS

Using the boundary integral equation method, the problem of an external circular crack in a three_dimensional infinite elastic body under asymmetric loadings is investigated. The two_dimensional singular boundary integral equations of the problem were reduced to a system of Abel integral equations by means of Fourier series and hypergeometric functions. The exact solutions of stress intensity factors are obtained for the problem of an external circular crack under asymmetric loadings, which are even more universal than the results obtained by the use of Hankel transform method. The results demonstrate that the boundary integral equation method has great potential as a new analytic method.

NUMERICAL SOLUTIONS FOR A NEARLY CIRCULAR CRACK WITH DEVELOPING CUSPS UNDER SHEAR LOADING

In this paper, we study the behavior of the solution at the crack edges for a nearly circular crack with developing cusps subject to shear loading. The problem of finding the resulting force can be written in the form of a hypersingular integral equation. The equation is then trans-formed into a similar equation over a circular region using conformal mapping. The equation is solved numerically for the unknown coefficients, which will later be used in finding the stress intensity factors. The sliding and tearing mode stress intensity factors are evaluated for cracks and displayed graphically. Our results seem to agree with the existing asymptotic solution.

SCATTERING OF SH-WAVES BY AN INTERACTING INTERFACE LINEAR CRACK AND A CIRCULAR CAVITY NEAR BIMATERIAL INTERFACE

An analytical method is developed for scattering of SH-waves and dynamic stressconcentration by an interacting interface crack and a circular cavity near bimaterial interface.Asuitable Green’s function is contructed,which is the fundamental solution of the displacement fieldfor an elastic half space with a circular cavity impacted by an out-plane harmonic line source loadingat the horizontal surface.First,the bimaterial media is divided into two parts along the horizontalinterface,one is an elastic half space with a circular cavity and the other is a complete half space.Then the problem is solved according to the procedure of combination and by the Green’s functionmethod.The horizontal surfaces of the two half spaces are loaded with undetermined anti-plane forcesin order to satisfy continuity conditions at the linking section,or with some forces to recover cracks bymeans of crack-division technique.A series of Fredholm integral equations of first kind for determiningthe unknown forces can be set up through continuity conditions as expressed in terms of the Green’sfunction.Moreover,some expressions are given in this paper,such as dynamic stress intensity factor(DSIF)at the tip of the interface crack and dynamic stress concentration factor(DSCF)around thecircular cavity edge.Numerical examples are provided to show the influences of the wave numbers,the geometrical location of the interface crack and the circular cavity,and parameter combinations ofdifferent media upon DSIF and DSCF.

Semi-analytical weight function method for center-cracked circular disk subjected to diametral compression

Büeckner Rice weight function method was used to analyse mixed mode fracture of center cracked circular disk subjected to uniaxial compression. Based on Wu Carlsson procedure semi analytical modes Ⅰ and Ⅱ weight functions were derived from corresponding reference displacement fields and stress intensity factors calculated by finite element method. Normalized mode Ⅰ and mode Ⅱ stress intensity factors, f Ⅰ, f Ⅱ , were derived from the obtained semi analytical weight functions. The results were then fitted into polynomials, the precision is within 0.5%. It is interesting to note that when the inclined angle θ of a crack is less than 15°, the f Ⅰvalues are positive. when θ =15°, the f Ⅰ values are positive for the crack length a varying from 0.1 to 0.7, but when a =0.8, the f Ⅰ takes the negative value -0.51. When θ >15°, all the f Ⅰ values become negative, which denotes that the compression shear mode is achieved at crack tips. These results are very useful in the investigation of mixed mode fracture of brittle materials.

Interaction between heat dipole and circular interfacial crack

The heat dipole consists of a heat source and a heat sink. The problem of an interracial crack of a composite containing a circular inclusion under a heat dipole is investigated by using the analytical extension technique, the generalized Liouville theorem, and the Muskhelishvili boundary value theory. Temperature and stress fields are formulated. The effects of the temperature field and the inhomogeneity on the interracial fracture axe analyzed. As a numerical illustration, the thermal stress intensity factors of the interfacial crack are presented for various material combinations and different positions of the heat dipole. The characteristics of the interfacial crack depend on the elasticity, the thermal property of the composite, and the condition of the dipole.

ANTIPLANE CIRCULAR INCLUSION WITH A CURVED CRACK CROSSING THE BOUNDARY

The weakly singular integral equation sued to solve the problem ofthe curved crack crossing the boundary of the antiplane circularinclusion is presented. Using the principal part analysis method ofthe Cauchy type integral equation, the singular stress index at theintersection and the singular stress of angular Regions near theintersection are obtained. By using the singular stress obtained, thestress intensity factor at The intersection is defined. After thenumerical solution of the integral equation, the stress intensityfactors at The end points of the crack and intersection areobtainable.

SAINT-VENANT’S TORSION PROBLEM FOR A COMPOSITE CIRCULAR CYLINDER WITH ANINTERNAL EDGE CRACK

In this paper the writer uses Muskhelishvili single-layer potential function solution and single crack solution for the torsion problem of a circular cylinder to discuss the torsion problem of a composite cylinder with an internal crack, and the problem is reduced to -a set of mixed-type integral equation with generalized Cauchy-kernel. Then, by using the integration formula of Gauss-Jacobi, the numerical method is established and several numerical examples are calculated. The torsional rigidity and the stress intensity factors are obtained. The results of these examples fit the results obtained by the previous papers better.

预应力钢丝绳加固空心混凝土桥墩试验研究

为加固桥墩竖向裂缝、抑制裂缝的发展和新裂缝的产生,开展了4组环形预应力钢丝绳加固空心混凝土桥墩试验,研究了钢丝绳拉力、混凝土径向压力、混凝土表面环向压应变的分布规律。试验结果表明:由于钢丝绳与混凝土桥墩表面摩阻力产生的预应力损失,钢丝绳拉力与对应的混凝土径向压力在张拉端最大,随着远离张拉端逐渐减小;混凝土表面环向压应变沿圆周随着远离张拉端逐渐减小,沿竖向随着远离钢丝绳逐渐减小。根据试验结果计算出摩擦系数为0.18,对应的最大预应力损失为43%。建立了相应的有限元模型,有限元计算结果与试验结果吻合良好。设定当混凝土表面环向压应变大于50×10^(-6)时为有效加固区域,结果表明在多根钢丝绳组合布置下,可建立范围较大的有效加固区域,验证了预应力钢丝绳的加固效果。

磁电弹性材料中圆弧形裂纹的反平面断裂问题

利用广义复变函数理论和保角映射技术,研究磁电弹性复合材料中圆弧形裂纹在无穷远处受到沿磁电极化方向的磁/电载荷和反平面机械载荷的共同作用下的反平面问题,给出应力场及位移场的精确解析解,并获得在磁电全非渗透及全渗透边界条件下圆弧裂纹尖端场强度因子和能量释放率的解析解。基于数值解进行数值分析,由数值结果表明:控制圆弧形裂纹半弦长与弓高比值的减少,可以提高材料的可靠性能;在两种边界条件下,机械载荷的不断增加最终会促进裂纹的扩展;在磁电全渗透边界条件下,裂纹扩展不受磁/电载荷的影响,但与材料常数和机械载荷的大小水平有关;在磁电全非渗透边界条件下,正(负)磁/电载荷的增加会阻碍裂纹扩展。

基于RA-AF特征的橡胶自密实混凝土裂缝扩展研究

为探究橡胶自密实混凝土断裂扩展模式,结合声发射RA-AF特征和高斯混合模型(GMM),利用带预制裂缝的半圆盘弯曲试件进行三点弯曲试验,选取橡胶掺量(0%、10%、20%、30%)及跨径比(0.45、0.54、0.72)为试验变量,分析橡胶自密实混凝土裂缝开展种类及变化规律。结果表明:橡胶掺量为20%时,橡胶自密实混凝土表现出较好的工作性能;橡胶掺量增加,拉伸断裂声发射事件占比增大,说明裂缝向Ⅰ型拉伸裂缝发展,并且裂缝发展具有连续的特点;增大跨径比会导致试件承载能力下降,但相同加载阶段其损伤程度逐渐降低,试件内部的断裂模式发生变化,跨径比为0.54时试件表现出较好的工作性能;GMM法显示,拉伸裂缝与剪切裂缝并非简单地以直线作为分界,而是在某些区域内共同存在,GMM法能更为合理地表述不同工况下拉伸断裂事件与剪切断裂事件发生比例的变化规律。

基于循环孔洞扩张模型的X型圆管节点超低周疲劳寿命预测

海洋工程钢结构在服役过程中,受风、浪、流或地震等极端循环载荷的影响,易发生超低周疲劳断裂破坏,造成人员伤亡及财产损失,因此超低周疲劳断裂分析及寿命预测对于海工结构安全性评估至关重要。然而,现阶段基于累积损伤理论提出的多种超低周疲劳寿命预测模型无法对多尺度节点实现统一预测,造成了实际工程应用的不便。因此文中基于循环孔洞扩张模型开展X型圆管节点超低周疲劳寿命预测。首先,开发了基于循环孔洞扩张模型的VUSDFLD程序,实现ABAQUS与FORTRAN子程序联合应用,利用有限元分析验证循环孔洞扩张模型在X型圆管节点超低周疲劳断裂分析中的有效性;其次,根据多组X型圆管节点超低周疲劳断裂有限元分析结果,在宏观层面提出了一种基于Manson-Coffin公式的超低周疲劳寿命预测公式;最后,依据Miner理论,将适用于等幅加载的超低周疲劳寿命公式扩展至变幅加载情况,验证了多种节点尺寸下超低周疲劳公式的适用性,为工程应用提供了理论依据。

基于黏聚区模型的沥青路面反射裂缝数值模拟

为研究半刚性基层沥青路面反射裂缝的扩展规律,结合ABAQUS有限元软件,采用双线性黏聚区模型模拟了半圆弯曲试验断裂过程,将模拟得到的荷载-线位移曲线与试验结果进行对比以验证黏聚区模型在开裂分析中的适用性,其次使用弹簧单元模拟Winker地基,同时将黏聚区模型应用在沥青路面有限元模型中,研究沥青面层反射裂缝扩展规律。结果表明,双线性黏聚区模型在沥青混凝土开裂过程具有良好适用性;在加载过程中半圆弯曲试件经历了弹性、损伤和断裂3个阶段,荷载峰值为试件达到初始损伤点的7.39倍;损伤单元主要集中在轮印正下方,随着加载位移的不断增加,损伤单元向四周扩展,单元逐步失效形成宏观裂缝;路面结构参数中,基层模量、地基反应模量的增加对面层阻止反射裂缝扩展有利,而面层模量的增加则不利于面层阻止反射裂缝扩展。

弯曲试件上边缘裂缝和砂浆-砂浆界面间的影响研究

研究分析了边缘裂缝(缺口)与砂浆–砂浆界面的相互作用对半圆形弯曲(SCB)试件力学性能的影响。在实验中,对不同砂浆–砂浆界面角度和不同接缝长度的SCB试件进行了实验测量。在0.004mm/min的受力速率下,制备出了直径为10cm且有不同长度边缘裂缝的SCB样品,并在实验室进行了试验,界面抗拉强度为0.15MPa,接头抗拉断裂韧性为0.28MPa√m。上述实验表明,裂缝(缺口)长度和界面角度(与加载方向相关)在很大程度上决定了SCB试件的破坏和破裂过程。同时,利用PFC2D中的粒子折叠码(颗粒流代码)对实验测试的SCB试样进行了模拟。

Fracture evolution characteristics of sandstone containing double fissures and a single circular hole under uniaxial compression

The uniaxial compression experiments on the sandstone samples containing double fissures and a single circular hole were carried out by using electro-hydraulic servo universal testing machine to investigate the effect of rock bridge angle β and fissure angle α on mechanical properties and evolution characteristics of cracks.The results show that the peak strength,peak strain and elastic modulus of defected specimens decrease comparing with those for intact sample,and show a decreased trend firstly and then increase with β changing from 0° to 90°.The peak strength and elastic modulus achieve the minimum value as the rock bridge angle is 60°,while the peak strain reaches the minimum value with the rock bridge angle of 45°.The crack initiation of tested rock samples occurs firstly in stress concentration areas at tips of prefabricated fissures under uniaxial compression,and then propagates constantly and coalescences with the prefabricated hole.Some secondary cracks initiate and propagate as well until buckling failure happens.The rock bridge angle has a great influence on crack initiation,coalescence,final failure mode,crack initiation stress and transfixion stress.The peak strength varies significantly,while the elastic modulus and peak strain change slightly,and the failure modes are also different due to the influence of fissure angle.

STUDY ON DYNAMIC STRESS INTENSITY FACTORS OF DISK WITH A RADIAL EDGE CRACK SUBJECTED TO EXTERNAL IMPULSIVE PRESSURE

A dynamic weight function method is presented for dynamic stress intensity factors of circular disk with a radial edge crack under external impulsive pressure. The dynamic stresses in a circular disk are solved under abrupt step external pressure using the eigenfunction method. The solution consists of a quasi-static solution satisfying inhomogeneous boundary conditions and a dynamic solution satisfying homogeneous boundary conditions. By making use of Fourier- Bessel series expansion, the history and distribution of dynamic stresses in the circular disk are derived. Furthermore, the equation for stress intensity factors under uniform pressure is used as the reference case, the weight function equation for the circular disk containing an edge crack is worked out, and the dynamic stress intensity factor equation for the circular disk containing a radial edge crack can be given. The results indicate that the stress intensity factors under sudden step external pressure vary periodically with time, and the ratio of the maximum value of dynamic stress intensity factors to the corresponding static value is about 2.0.

ANTIPLANE MULTIPLE CURVED CRACK PROBLEM IN CIR-CULAR INCLUSION AND MATRIX MATERIAL

Antiplane multiple curved crack problem in circular inclusion and matrix material is considered. In order to solve the proposed problem, two kinds of elementary solutions corresponding to a point screw dislocation in inclusion and matrix material respectively are presented. Utilizing the elementary solutions and taking the density of dislocation along cracks surfaces as unknown functions, by the principle of superposition, a group of weakly singular integral equations with log kernels can be obtained. After the numerical solution of the integral equations, the discrete values of dislocation density are obtainable. So stress intensity factors at the cracks tips can be calculated, and several numerical examples are given.

AN ANALYSIS OF AXISYMMETRIC BUCKLING AND GROWTH OF CIRCULAR-SHAPED DELAMINATION

The buckling and post-buckling of clamped circular plate subjected to distributed radial compressed load is presented by using the high-order perturbation analysis and shooting method. The sixth-order solution shows good agreement with the FEM results in [11]. The results in this paper are applied to investigate the buckling and growth of pressed thin film delamination in the film/substrate system. Under a certain residual pressure in the thin film, two characteristic blister radii R(c) and R(g), the critical radius and growing radius respectively, are obtained. The numerical result shows that the growth criterion of delamination in [9,10] is not perfect. In variant residual stress or interface toughness, the conditions of no growth, stable growth and unstable growth of the delamination are obtained by comparing the driving force at the interface crack tip with the interface toughness.