The in-plane loading of rigid disc inclusion embedded in a crack

The paper examines the in-plane loading of a disc shaped rigid disc inclusion which is embedded in bonded contact with the plane surfaces of a penny-shaped crack. The mixed boundary value problem governing the elastostatic problem is reduced to the solution of a system of coupled integral equations, which are solved numerically to determine results of engineering interest. These results include the in-plane stiffness of the disc inclusion and the crack opening mode stress intensity factor at the boundary of the penny-shaped crack.     

Indentation of a spherical cavity in an elastic body by a rigid spherical inclusion: influence of non-classical interface conditions

This paper examines the indentation of an elastic body by a rigid spherical inclusion. In contrast to conventional treatments where the contact between a rigid inclusion and the elastic medium is regarded as being perfectly bonded, we examine the influence of non-classical interface conditions including frictionless bilateral contact, separation and Coulomb friction on the load–displacement behaviour of the spherical rigid inclusion. Both analytical methods and boundary element techniques are used to examine the inclusion/elastic medium interaction problems. This paper also provides a comprehensive review of non-classical interface conditions between inclusions and the surrounding elastic media.     

Discrete modeling of crack bridging by a discontinuous platelet with a controlled interface

Crack bridging by discontinuous fibers can make brittle materials tougher by transferring stresses from the crack tip to elsewhere in the matrix material. One important aspect of crack bridging is the nature of the interface between the fibers and the matrix material. In this paper, a two-dimensional numerical model of bridging a Mode I loaded crack by linear elastic discontinuous platelets is developed for two different types of interfaces. The first type is a perfectly bonded interface. The second type is an imperfect interface described as a stick–slip interface. A shear-lag model to predict platelet pullout is developed in detail to verify the numerical implementation of the stick–slip interface. An example of a crack tip bridged by a platelet is examined for both interfaces. The perfectly bonded interface will reduce the Stress Intensity Factor (SIF) of the crack greatly but introduces new stress concentrations at the platelet ends. The stick–slip interface can be tailored to also reduce the SIF while not introducing new stress concentrations.     

Thermal stress analysis of a three-dimensional anticrack in a transversely isotropic solid

A three-dimensional analysis is performed for an infinite transversely isotropic elastic body containing an insulated rigid sheet-like inclusion (an anticrack) in the isotropy plane under a remote perpendicularly uniform heat flow. A general solution scheme is presented for the resulting boundary-value problems. Accurate results are obtained by constructing suitable potential solutions and reducing the thermal problem to a mechanical analog for the corresponding isotropic problem. The governing boundary integral equation for a planar anticrack of arbitrary shape is obtained in terms of a normal stress discontinuity. As an illustration, a complete solution for a rigid circular inclusion is obtained in terms of elementary functions and analyzed. This solution is compared with that corresponding to a penny-shaped crack problem.     

Effects of interfacial friction on flaw tolerant adhesion between two dissimilar elastic solids

Flaw tolerance refers to a state in which a pre-existing crack-like flaw does not propagate even as the material is stretched to failure near its theoretical strength. Such an optimal scenario can be achieved when the characteristic length scale is reduced to below a critical value. So far, the critical conditions to achieve flaw tolerance have been discussed mostly for homogeneous materials or for two dissimilar materials in frictionless or perfectly bonded adhesion. In this paper, we consider the role of friction in flaw tolerant adhesion between two dissimilar elastic solids. We adopt a frictional contact model in which slip is allowed wherever the shear stress along the interface reaches a threshold value defined as the friction strength. The critical length scale for flaw tolerance is derived analytically for a penny-shaped crack and for an external circular crack. Compared to the cases of frictionless contact, we find that interfacial friction can reduce the critical length scales for flaw tolerance by up to 12.5%.     

Exact solution for elliptical inclusion in magnetoelectroelastic materials

This paper considers the magneto-electro-mechanical coupling between an inclusion and matrix, which are both of magnetoelectroelastic materials. The general cases including the mode I, mode II and mode III are studied. Analytical solutions for an elliptical cylinder inclusion inside an infinite magnetoelectroelastic medium under combined mechanical–electrical–magnetic loadings are formulated via the Stroh formalism. Crack problem is also investigated and the stress, electric and magnetic fields in the vicinity of the crack tip are determined by a complex vector of intensity factors. Various special cases, including an impermeable inclusion, a permeable crack, a rigid and permeable inclusion, a rigid and permeable line inclusion, a permeable cavity, and an impermeable cavity are discussed.     

Internally indented penny-shaped cracks: A comparison of analytical and boundary integral equation estimates

The problem of the axisymmetric internal indentation of a penny-shaped crack by a rigid circular inclusion is discussed. The paper presents a comparison of analytical and boundary integral equation results for the stress intensity factor at the boundary of the penny-shaped crack indented by a smooth inclusion. Numerical results presented in the paper examines the influence of features such as adhesion at the inclusion-elastic medium interface and finite geometry of the elastic solid containing the penny shaped crack.     

A rigid inclusion in an elastic space under the action of a uniform heat flow in the inclusion plane

A solution is presented for the three dimensional static thermoelastic problem of an absolutely rigid inclusion (anticrack) in the case when a uniform heat flow is directed along the inclusion plane. By using the potential method and the Fourier transform technique, the problem is reduced to a system of coupled two-dimensional singular integral equations for the shear stress jumps across the inclusion. As an illustration, a typical application to the circular anticrack is presented. Explicit expressions for the thermal stresses in the inclusion plane are obtained and discussed from the point of view of material failure.     

An axisymmetric problem of an embedded crack in a graded layer bonded to a homogeneous half-space

In an attempt to simulate non-uniform coating delamination, the elasto-static problem of a penny shaped axisymmetric crack embedded in a functionally graded coating bonded to a homogeneous substrate subjected to crack surface tractions is considered. The coating’s material gradient is parallel to the axisymmetric direction and is orthogonal to the crack plane. The graded coating is modeled as a non-homogeneous medium with an isotropic constitutive law. Using Hankel transform, the governing equations are converted into coupled singular integral equations, which are solved numerically to yield the crack tip stress intensity factors. The Finite Element Method was additionally used to model the crack problem. The main objective of this paper is to study the influence of the material non-homogeneity and the crack position on the stress intensity factors for the purpose of gaining better understanding on the behavior of graded coatings.     

A penny shaped crack in a transversely isotropic material under non-axisymmetric impact loads

A solution is given for problems involving non-axisymmetric dynamic impact loading of a penny shaped crack in a transversely isotropic medium. Laplace and Hankel transforms are used to reduce the equations of elasticity to integral equations, and solutions are obtained for the three modes of fracture. The stress intensity factors are determined for a penny shaped crack loaded by concentrated normal impact forces and concentrated radial shear impact forces. The integral equations are solved by numerical methods, and the results are plotted showing how the dynamic stress intensity factors are influenced by the asymmetric loading.     

Thermal stresses in an elastic space with a perfectly rigid flat inclusion under perpendicular heat flow

This paper examines the three-dimensional problem of finding thermal stresses due to an insulated rigid sheet-like inclusion (anticrack) in an elastic space under a uniform perpendicular heat flow. By using appropriate harmonic potentials, a general method of solving this problem is presented. The resulting boundary-value problems are reduced to classical mixed problems of potential theory. For the purpose of illustration, a complete solution in terms of elementary functions for a rigid circularly shaped inclusion is given and discussed from the point of view of material failure.     

无限均质弹性体中圆片裂纹受均布载荷时的超奇异积分方程封闭解

本文运用一种特殊技巧将一个受均布压力作用的圆片裂纹超奇异积分方程化为Ａｂｅｌ积分形式，从而可获得超奇异积分方程中未知位移间断的封闭解。再利用这个封闭解和应力强度因子的定义，得到了一个无限弹性体中受均布载荷分布时圆片裂纹前沿Ｉ型应力强度因子的精确表达式。所得到的结果与现有解完全相同。     

平行于功能梯度材料夹层的币型裂纹起裂条件

分析了功能梯度材料中币型裂纹的扩展问题．裂纹平行于无限域中功能梯度材料夹层,受有与裂纹面成任意角度的拉应力．假定功能梯度材料夹层与两个半无限域均匀介质完全粘合,其弹性模量沿厚度方向变化．采用基于层状材料广义Kelvin基本解的边界元方法分析裂纹问题,给出了均布正应力和剪应力作用下裂纹的应力强度因子、将应力强度因子耦合于应变能密度断裂判据,讨论了裂纹体在拉伸应力作用下的起裂条件．     

双材料界面断裂力学模型与实验方法

纤维增强聚合物(FRP)质轻、高强, 可提高结构的刚度、强度、抗震性能和耐久性, 近年来在结构加固及工程改造中得到广泛应用. FRP与传统复合材料之间形成双材料黏结界面, 界面断裂特性是决定双材料结构性能的关键因素. 对双材料界面裂纹尖端应力场理论、界面裂纹模型、黏结界面I型、II型及混合型断裂试验及理论研究现状进行综合评述和分析. 界面模型主要有经典梁/板理论和刚性节点模型、考虑剪切变形的双亚层理论和半刚性节点模型、基于双亚层理论的柔性节点模型、考虑剪切变形的多层亚层理论和多亚层柔性节点模型、弹性地基梁模型以及黏聚模型. 还介绍了双材料界面断裂力学在FRP-混凝土研究中的应用.      

圆盘状裂纹前缘塑性区尺寸及张开位移估计

将Ｄｕｇｄａｌｅ模型推广到三维裂纹问题计算了圆盘状裂纹前缘塑性区尺寸,并结合断裂力学中的Ｂａｒｅｎｂｌａｔｔ－Ｄｕｇｄａｌｅ裂纹模型和三维Ｊ－积分原理计算了圆盘状裂纹前缘张开位移,得到了Ｊ－积分与裂纹张开位移的关系,最后用非线性有限元方法对圆盘状裂纹的前缘塑性区尺寸作了数值分析,确定了公式中的未知常数,并对其正确性作了数值验证,本文的工作推广了Ｄｕｇｄａｌｅ模型的应用范围。     

Photoelastic investigation of crack-inclusion interaction

An experimental procedure is presented for determining the mode I stress-intensity factor of an edge crack with a nearby rigid elliptical inclusion in a finite plate loaded in uniform tension. The rigid inclusion was modeled by bonding two identical steel inclusions on to the faces of a thin plate of polycarbonate. Models were constructed with edge cracks and various inclusion geometries so that the effect of parameters such as inclusion shape, orientation, and cracktip position on the stress-intensity factors of the crack could be determined. Photoelasticity experiments were used for this investigation and the results were compared to the results of a similar theoretical analysis of the interaction between a crack and an inclusion in an infinite plate. A good correlation was found between the experimental and theoretical models indicating that the results may help provide a better understanding of the toughening mechanisms in materials such as short-fiber-reinforced composites and ceramics. This experimental method is relatively easy to use making it an attractive candidate to be applied to similar problems involving cracks and inhomogeneities.     

二氧化碳在砂岩透镜体中充注封存的盖层岩石抗断裂性能分析

把CO2这一主要的温室气体注入到地下深处具有适当封闭条件的地层中进行封存和隔离,已被公认为是有效减少CO2排放量的一种比较安全的技术途径。砂岩透镜体油气藏具有良好的圈闭构造和储层物性,油气濒临枯竭的砂岩透镜体是较理想的CO2地质封存箱。基于币形裂纹模型和水力致裂原理,将纵向厚度和横向展布长度均远小于盖层岩石尺度的水平产状砂岩透镜体简化为盖层岩石中的I型币形裂纹,从岩石断裂力学角度分析封存箱盖层岩石的抗断裂性能。采用叠加原理给出了盖层岩石币形裂纹尖端（砂岩透镜体尖灭部位）应力强度因子的计算公式,在此基础上提出了断裂力学判别准则（K=KIC）和临界有效压应力判别准则（P=PC）,从岩石断裂力学角度为砂岩透镜体封存箱盖层岩石抗断裂性能分析和评价提供了一种新的研究思路。     

Interaction between rigid-disc inclusion and penny-shaped crack under elastic time-harmonic wave incidence

Influence of a rigid-disc massive inclusion on a neighboring penny-shaped crack induced by the time-harmonic wave propagation in an infinite elastic matrix is investigated by the numerical solution of associated 3D elastodynamic problem. No restrictions on the mutual orientation of interacting objects and direction of wave incidence are assumed. The inclusion is perfectly bonded with a matrix and supposes the translations and rotations, the crack faces are load-free. Frequency-domain problem is reduced to a system of boundary integral equations (BIEs) relative to the interfacial stress jumps (ISJs) on the inclusion and the crack opening displacements (CODs). The subtraction technique in conjunction with mapping technique, under taking into account the structure of solution at the fronts of inclusion and crack, is applied for regularization of BIEs obtained. A discrete analogue of equations is constructed by using the collocation scheme. Numerical calculations are carried out for the grazing incidence of a plane P-wave on the crack, where the interacting inclusion is coplanar and perpendicular to the crack, and has the same radius. The shielding and amplification effects of inclusion are assessed by the analysis of mode-I stress intensity factor (SIF) in the crack vicinity depending on the wave number, incident wave direction, position of the crack front point, inclusion mass, crack-inclusion orientation and distance.     

T应力对光弹性条纹影响的理论分析

以裂尖弹性应力场的多参数模型为基础,研究I型、II型以及I/II混合型裂纹参数对光弹性条纹的影响. T应力的存在和符号影响着等色线条纹环的半径大小和旋转方向,对于纯I型或II型裂纹而言,条纹环的旋转角度只与T应力有关;而对于I/II混合型裂纹,条纹环旋转角度与K_{\rm I}, K_{\rm II}和T应力有关. T应力的存在使得I型裂纹在裂尖±π/3方向上出现2个各向同性点(T应力为正时),使得II型裂纹在裂尖后的裂纹面上出现1个各向同性点. 对于I/II混合型裂纹而言,当T应力为正时等倾线出现距裂尖半径不等的3个各向同性点;反之, T应力为负时在裂尖后只存在1个各向同性点,这些各向同性点分别与I型和II型裂纹情况具有相同的规律.      

The axisymmetrical elastic field of an ellipsoidal inclusion with a slipping interface

This paper is concerned with the axisymmetrical elastic fields caused by an ellipsoidal inclusion with a slipping interface which undergoes a uniform eigenstrain. The problem is solved under a revolving ellipsoidal coordinate with the aid of Papkovich-Neuber general dipacement formula. In contrast to the perfectly bonded interface, when the interface between the inclusion and the matrix cannot sustain shear stress, and is free to slip, the solution cannot be expressed in closed form and involves infinite series. Therefore, the results are illustrated by numerical examples.