An analysis of a radial crack in a reinforced hollow cylinder

Using the Michell solution and the crack solution, the integral equation of a radial crack in a hollow cylinder reinforced on its outer boundary is derived. The effects of the reinforced membrane on the crack are analysed and several numerical results are presented herein.Projects is Supported by the Sceince Fund of the Chinese Academy of Sciences.This work was done while the author was a graduate student at the Depart. Math. and Mech., Lanzhou University.     

The propagation and arrest of an edge crack in anti-plane shear

The motion of an edge crack extending non-uniformly in an elastic half-space under conditions of anti-plane shear is investigated, taking the first reflected stress wave into account. An expression for the stress intensity factor at the crack tip is obtained, and an energy-balance crack propagation criterion is used to find the equation of motion of the tip. On solving this equation numerically, it is found that crack arrest occurs before the second reflected wave reaches the tip.     

An efficient numerical model for contact-induced crack propagation analysis

This paper presents an efficient boundary element formulation for the simulation of contact-induced crack propagation problems. The formulation combines a load-scaling boundary element technique for frictional contact analysis and a dual boundary element method for axisymmetric crack propagation. These previously developed contact and fracture mechanics algorithms are revisited and adapted for the proposed coupled formulation. The novelty of the present work is the development of an efficient algorithm capable of simulating contact-induced crack propagation, while keeping proper equilibrium conditions in the frictional contact area. An efficient combination of the two separate formulations is not straightforward, and possible approaches are explained. The algorithm is validated by comparing the results of several indentation tests with available experimental data and analytical expressions. Its efficiency is also verified in frictional, conforming and non-conforming, indentation simulations.     

岩石偏心圆孔单裂纹平台圆盘的动态裂纹扩展与止裂

针对平台圆环构型的优点, 提出偏心圆孔单裂纹平台圆盘(cracked eccentrically holed flattened disc, CEHFD), 该试样具有更长的断裂路径。利用霍普金森压杆加载系统, 径向冲击CEHFD试样, 完成Ⅰ型动态断裂实验。砂岩试样表面粘贴应变片和裂纹扩展计, 用于监测裂纹动态起裂、扩展和止裂的全过程。实验表明, 在整个断裂过程中, 裂纹非匀速扩展, 裂纹扩展速度在裂纹起裂后加速上升, 在裂纹止裂前有明显的减速, 与地震时断层的动态破裂全过程完全吻合。采用实验-数值-解析法得到动态应力强度因子, 其时间历程呈现先增大后减小的趋势。根据断裂过程不同时刻, 得到相应的动态起裂韧度、扩展韧度及止裂韧度。在动态断裂全过程中, 动态扩展韧度为速度的函数, 变化趋势与速度一致, 随着时间先增大后减小; 动态起裂韧度大于动态止裂韧度, 止裂韧度随着裂纹最大扩展速度的增大而降低, 并且有较大的离散性。

     

Multiple cracks in pressurized hollow cylinder

Presented is a particular solution of the hollow cylinder with one crack; it consists of two parts. The first corresponds to a pair of equal and opposite normal and tangential concentrated forces acting on a crack in an infinite plane region and the second to distributed tractions on both crack surfaces such that the sum of the first and second parts satisfies the prescribed traction boundary conditions on the cracks and cylinder surfaces. The particular solution can be expressed in terms of a density function for each crack giving rise to a system of Fredholm integral equations for the multiple crack system. Several numerical examples will be provided to illustrate the method of solution.     

Intersonic crack propagation along interfaces: Experimental observations and analysis

The isochromatic fringe patterns surrounding an intersonically propagating interface crack are developed and characterized using the recently developed stress field equations. A parametric investigation is conducted to study the influence of various parameters such as the crack-tip velocity and the contact coefficient on the isochromatic fringe patterns. It has been observed that the crack-tip velocity has a significant effect on the size and shape of isochromatic fringe patterns. The contact coefficient, on the other hand, does not affect the fringe pattern significantly. The paper also presents a numerical scheme to extract various parameters of interest such as the series coefficients of the stress field, the contact coefficient and the dissipation energy. The results show that the crack growth is highly unstable in the intersonic regime, and the energy dissipation decreases monotonically with increasing crack-tip velocity. The experimental data fit well with the recently proposed fracture criterion for intersonic interfacial fracture.     

Equilibrium of a pressurized plastic fluid in a wellbore crack

This paper investigates equilibrium of a pressurized plastic fluid invading a tensile wellbore crack in a linear elastic, permeable rock. The crack is initially filled by pore fluid at ambient pressure, that is immiscibly displaced by the plastic fluid invading from the wellbore. The plastic fluid comes to rest to form a “plug” within the elastically deformed crack when the limit equilibrium between the shear stresses generated at the fracture walls and the pressure drop between the wellbore wall and the crack tip is reached. The model assumes that the leak-off of the plastic fluid into the rock is negligible, while the displaced pore fluid in the crack tip region is freely exchanged with the surrounding permeable rock to maintain the ambient pressure level. When the crack length ? is small or large compared to the wellbore radius R, the problem reduces to that of a pressurized edge or Griffith’s crack, respectively, subjected to a uniform far-field confining stress. In these two end-member cases, the normalized solution for the net pressure distribution, the plug length, and the stress intensity factor at the crack tip is obtained as a function of two numbers – the normalized net fluid pressure at the crack inlet and at the crack tip (partial plugs only) – that embody the solution’s dependence on the wellbore and the far field loading, the fluid yield strength, and the rock modulus. In the general case of an intermediate crack length (? ～ R), the normalized solution is a function of two additional parameters, the length-to-radius ratio and a normalized measure of the far field stress anisotropy, respectively, which accurate approximation is devised from an end-member solution using a rescaling argument. The equilibrium plug solutions are used to evaluate the breakdown pressure, the critical wellbore pressure at which the crack propagation condition is first met, and to analyze the stability of the ensuing crack propagation.     

Elasto-plastic analysis of an internally pressurized thick-walled cylinder using a strain gradient plasticity theory

An analytical solution for the stress, strain and displacement fields in an internally pressurized thick-walled cylinder of an elastic strain-hardening plastic material in the plane strain state is presented. A strain gradient plasticity theory is used to describe the constitutive behavior of the material undergoing plastic deformations, whereas the generalized Hooke’s law is invoked to represent the material response in the elastic region. The solution gives explicit expressions for the stress, strain and displacement components. The inner radius of the cylinder enters these expressions not only in non-dimensional forms but also with its own dimensional identity, unlike classical plasticity-based solutions. As a result, the current solution can capture the size (strengthening) effect at the micron scale. The classical plasticity-based solution of the same problem is shown to be a special case of the present solution. Numerical results for the maximum effective stress in the cylinder wall are also provided to illustrate applications of the newly derived solution.     

海洋平台K型管节点的疲劳裂纹扩展分析Ⅱ:数值分析

对于已含初始裂纹平台管节点的寿命预测很大程度上依靠应力强度因子的精确值,而复杂载荷条件下的节点应力强度因子的计算尚无参数方程直接确定.本文提出了一种含表面裂纹的K节点的有限元网格产生方法,即把整个K节点划分为几个子区域,每个子区域的网格具有不同类型的单元和不同的密度.这种方法在控制网格密度,尤其是控制沿着裂纹边缘单元的边长比方面有其独特的优越性,当所有子区域的网格自动产生后,容易得到整个结构的有限元模型.同时用J积分和位移外推插值法分别计算了一个K型节点沿着裂纹前缘的应力强度因子值,发现:试验得到的应力强度因子值和提出的模型计算结果非常吻合,证明了所提有限元模型的准确性.     

海洋平台K型管节点的疲劳裂纹扩展分析 II:数值分析

对于已含初始裂纹平台管节点的寿命预测很大程度上依靠应力强度因子的精确值,而复杂载荷条件下的节点应力强度因子的计算尚无参数方程直接确定。本文提出了一种含表面裂纹的K节点的有限元网格产生方法,即把整个K节点划分为几个子区域,每个子区域的网格具有不同类型的单元和不同的密度。这种方法在控制网格密度,尤其是控制沿着裂纹边缘单元的边长比方面有其独特的优越性,当所有子区域的网格自动产生后,容易得到整个结构的有限元模型。同时用J积分和位移外推插值法分别计算了一个K型节点沿着裂纹前缘的应力强度因子值,发现:试验得到的应力强度因子值和提出的模型计算结果非常吻合,证明了所提有限元模型的准确性。     

Dynamic crack propagation in a viscoelastic strip

The dynamic propagation of a semi-infinite crack in a finite linear viscoelastic strip subjected to Mode I loading is investigated. Through the use of integral transforms the problem is reduced to solving a Wiener-Hopf equation. The asymptotic properties of the transforms are exploited to establish the stress intensity factor. Plane-stress and plane-strain stress intensity factors as a function of crack speed for both fully-clamped and shear-free lateral boundaries are presented for the standard linear viscoelastic solid. Comparisons are made with previously obtained asymptotic stress intensity factors and with stress intensity factors for the equivalent elastic strips.     

A photoelastic and FEM analysis of interfacial crack propagation

The linear elastic solution for the bimaterial interface crack is applied to determine the direction of crack propagation during surface-layer removal by scraping. The direction of the load which must be applied to the free end of the surface layer for continued interfacial crack propagation is determined using photoelasticity and finite elements, and results are found to be in good agreement.Paper was presented at the 1990 SEM Spring Conference on Experimental Mechanics held in Albuquerque, NM on June 3–6.     

Bending of a circular cylinder containing a crack

The study of bending of cracked circular cylinders is of more significance. The bending of cylinders containing radical crack or cracks was discussed by refs. [1]–[4] and that of concentrically craked circular cylinders was studied by [5]. Continuing [6] and using complex variable methods in elasticity, this paper deals with the bending problems of a circular cylinder, containing an internal linear crack at any position under an acting force perpendicular to the crack. The general forms of displacements, stresses, and stressintensity factors, expressed in terms of series, are obtained and to this bending problems with small Ah are presented good approximate formulas for the stress-intensity factors whose variations with the center of the crack are analysed. Finally, the twist angle per unit length and the center of bending for the radically cracked circular cylinder, one of whose crack-tips is located at the origin, have been computed and the results are almost the same as that calculated in [1].     

Intersonic crack propagation in homogeneous media under shear-dominated loading: theoretical analysis

The mechanics of cohesive failure under mixed-mode loading is investigated for the case of a steadily propagating subsonic and intersonic dynamic crack subjected to a follower tensile and shear distributed load. The cohesive failure model chosen in this study is rate independent but accounts for the coupling between normal and tangential damage. Special emphasis is placed here on mixed-mode cases with predominantly shear loading. The analysis shows that the size of the mixed-mode cohesive zone is smaller than that obtained in the pure shear case. The relative extent of the shear and tensile cohesive damage zones depends on the crack speed and the mode mixity. In the intersonic regime, the failure process takes place exclusively in shear, even under remote mixed-mode loading conditions.     

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     

Fracture analysis on the arc-shaped interfacial crack between a homogeneous cylinder and its coating

The mechanical model is established for a mode I arc-shaped crack along the interface between a functionally graded layer and a homogeneous cylinder. The displacement and stress fields are expressed in the form of infinite series by the method of variable separation. By introducing two dislocation density functions, the mixed boundary conditions of the crack are recast into a system of Cauchy singular integral equations, which are then solved numerically. Parametric studies on the stress intensity factors (SIFs) yield two aspects of guidelines for engineering designs. (a) The SIFs depend on the ratio between the outer and inner radii rather than their respective values, and 1.5 seems to be an optimal value for this ratio. (b) The outer graded layer should be stiffer than the inner homogeneous cylinder and large non-homogeneity parameter is beneficial to SIF reduction.     

Numerical analysis of fast fracture and crack arrest in a sheet of elastic perfectly-plastic material

The dynamic fields for acceleration, deceleration and arrest of a crack tip have been investigated numerically. We consider cracks which start to extend rapidly under brittle conditions. The crack-tips then enter regions of elasto-plastic constitutive behavior and they are subsequently arrested. Results have been obtained for a symmetrically expanding central crack and for an edge crack, both in thin sheets. The elasto-plastic behavior has been described by J₂ flow theory, with the von Mises yield criterion and a bilinear relation between effective stress and effective strain. Numerical results are presented for stress and strain components at a short distance ahead of the propagating and arresting crack tips.     

Stress intensity factors of a crack in a composedcircular cylinder

A composed circular cylinder, formed by a core circular cylinder, containing a crackand enclosed by a layered hollow circular cylinder, is investigated in regard to the evaluation ofstress intensity factors. Analytic solutions to the problem are provided, with which the upper andlower bounds of stress intensity factors in a cracked circular cylinder, the stress distribution in alayered hollow circular cylinder, and the stress intensity factors for a crack in the composedcircular cylinder can precisely be determined. Numerical materials, demonstrating the discretevalues of the stress intensity factors, as well as the general pattern according to which the stressintensity factors vary with the material and geometric constants, are presented. The solutions aredeveloped based on a simplified and modified solution to the Hilbert problem, and the matrixpresentation and manipulation of functions and variables, used in the circuit theory.     

海洋平台K型管节点的疲劳裂纹扩展分析I:试验测试

对承受疲劳载荷的海洋平台K型管节点首先进行了静力测试,确定了沿着焊缝的热应力区的应力分布及热应力区最大应力点的位置,从而判断裂纹产生的位置;然后通过专用测试设备提供循环疲劳载荷,用ACPD(Alternating Current Potential Drop,即交流电流势能落差法)技术检测裂纹的产生和增长过程,得到裂纹最深点,用S-N曲线估算其疲劳寿命.对已有裂纹的K型管节点,用应力强度因子估计其剩余寿命.同时用测试的结果验证了S-N的准确性和可靠性.