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.

Interaction of a circular cavity and a beeline crack in right-angle plane impacted by SH-wave

The problem of scattering of SH-wave by a circular cavity and an arbitrary beeline crack in right-angle plane was investigated using the methods of Green's function,complex variables and muti-polar coordinates.Firstly,we constructed a suitable Green's function,which is an essential solution to the displacement field for the elastic right-angle plane possessing a circular cavity while bearing out-of-plane harmonic line source load at arbitrary point.Secondly,based on the method of crack-division,integration for solution was established,then expressions of displacement and stress were obtained while crack and circular cavities were both in existence.Finally,the dynamic stress concentration factor around the circular cavity and the dynamic stress intensity factor at crack tip were discussed to the cases of different parameters in numerical examples.Calculation results show that the crack produces adverse engineering influence on both of the dynamic stress concentration factor and the dynamic stress intensity factor.

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.

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。

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

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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.

Experimental research on mechanical properties of prestressed truss concrete composite beam encased with circular steel tube

Tests of 4 simply supported unbonded prestressed truss concrete composite beams encased with circular steel tube were carried out. It is found that the ratio of the stress increment of the unbonded tendon to that of the tensile steel tube is 0.252 during the using stage,and the average crack space of beams depends on the ratio of the sum of the bottom chord steel tube's outside diameter and the secondary bottom chord steel tube's section area to the effective tensile concrete area. The coefficient of uneven crack distribution is 1.68 and the formula for the calculation of crack width is established. Test results indicate that the ultimate stress increment of unbonded tendon in the beams decreases in linearity with the increase of the composite reinforcement index β0. The pure bending region of beams accords with the plane section assumption from loading to failure. The calculation formula of ultimate stress increment of the unbonded tendon and the method to calculate the bearing capacity of normal section of beams have been presented. Besides,the method to calculate the stiffness of this sort of beams is brought forward as well.

圆弧形聚能装药结构爆破破岩效果数值模拟

为了研究不同圆弧形聚能装药结构下爆破参数最佳的爆破效果,以实现现有煤矿岩巷掘进高效破岩的需求。基于非线性动力模拟软件ANSYS/LS-DYNA建立了圆弧形聚能装药爆破几何模型,研究了炮孔直径42 mm时,聚能圆弧半径10 mm,圆弧边缘至炮孔中心距离分别为6、8、10、12 mm下的聚能爆破破岩效果,通过添加失效关键字得到各个工况的裂纹发展情况,对比分析了不同工况下的聚能过程和距炮孔中心聚能和非聚能方向的有效应力时程曲线;展现了聚能装药情况下的岩体损伤演化历程。研究结果表明:4个工况都出现了不同的聚能效果,对裂纹的发展起到一定的导向作用;随着聚能穴内边缘至管中心距离的增大,有效应力峰值先减小后增大,其中聚能穴内边缘至管中心距离12 mm,单位装药量为10.47 cm^(3)时有效应力峰值最大;聚能穴内边缘至管中心距离12 mm在距炮孔15 cm处最先达到完全损伤破坏,说明聚能穴内边缘至管中心距离12 mm的装药结构参数聚能效果最佳。

数字图像散斑技术的玄武岩纤维沥青混合料长期抗裂性能分析

针对传统的测试方法难以对纤维沥青混合料长期抗裂性能评价的问题,将两种类型纤维(木质素纤维和玄武岩纤维)干法掺入SMA-13沥青混合料中,制备不同老化程度的纤维增强沥青混合料试件。通过半圆弯拉试验对纤维沥青混合料的抗裂性能进行测试,同时采用数字图像散斑技术分别计算实时裂纹扩展长度和平均裂纹扩展速率参数,评价纤维类型对沥青混合料抗裂性能的影响。通过扫描电子显微镜试验分析纤维在混合料中的强化机制。研究结果表明:不同老化程度下,玄武岩纤维沥青混合料的抗裂性能优于木质素纤维沥青混合料;玄武岩纤维加入混合料中可以显著减缓裂纹扩展速率,延长了试件断裂时间;玄武岩纤维在混合料中形成固定的三维网状结构,有助于混合料的强化。在未老化、短期老化和长期老化阶段,BFSMA-13的V值分别为LFSMA-13的V值的53.53%、48.35%和53.94%。同时,V值与FI指数的相关性较好,两者的线性相关系数R达到了0.9。