Stress intensity factor analysis of a three-dimensional interfacial corner between anisotropic bimaterials under thermal stress

A numerical method using a path-independent H-integral based on the conservation integral was developed to analyze the singular stress field of a three-dimensional interfacial corner between anisotropic bimaterials under thermal stress. In the present method, the shape of the corner front is smooth. According to the theory of linear elasticity, asymptotic stress near the tip of a sharp interfacial corner is generally singular as a result of a mismatch of the materials’ elastic constants. The eigenvalues and the eigenfunctions are obtained using the Williams eigenfunction method, which depends on the anisotropic materials’ properties and the geometry of an interfacial corner. The order of the singularity related to the eigenvalue is real, complex or power-logarithmic. The amplitudes of the singular stress terms can be calculated using the H-integral. The stress and displacement around an interfacial corner for the H-integral are obtained using finite element analysis. In this study, a proposed definition of the stress intensity factors of an interfacial corner, which includes those of an interfacial crack and a homogeneous crack, is used to evaluate the singular stress fields. Asymptotic solutions of stress and displacement around an interfacial corner front are uniquely obtained using these stress intensity factors. To prove the accuracy of the present method, several different kinds of examples are shown such as interfacial corners or cracks in three-dimensional structures.     

复合材料中矩形夹杂角端部力学行为分析

提出了一种分析矩形夹杂角端部奇异应力场的新型杂交有限元方法,该方法在分析矩形夹杂角端部奇异应力场时,需要在夹杂端部构造一个超级单元。超级单元的刚度矩阵可以通过夹杂端部特征问题数值解建立。我们用这种方法计算了单向载荷作用下无限大均质板中单个矩形夹杂角端部奇异应力场,并与现有的数值解进行了比较。比较结果表明:本文提出的方法是可行的、有效的,而且数值结果精度高。为说明本文方法适用范围更广,文章最后讨论了各向异性弹性材料和横观各向同性压电材料中矩形夹杂角端部电弹性场行为。     

A novel hybrid finite element analysis of inplane singular elastic field around inclusion corners in elastic media

This paper deals with the inplane singular elastic field problems of inclusion corners in elastic media by an ad hoc hybrid-stress finite element method. A one-dimensional finite element method-based eigenanalysis is first applied to determine the order of singularity and the angular dependence of the stress and displacement field, which reflects elastic behavior around an inclusion corner. These numerical eigensolutions are subsequently used to develop a super element that simulates the elastic behavior around the inclusion corner. The super element is finally incorporated with standard four-node hybrid-stress elements to constitute an ad hoc hybrid-stress finite element method for the analysis of local singular stress fields arising from inclusion corners. The singular stress field is expressed by generalized stress intensity factors defined at the inclusion corner. The ad hoc finite element method is used to investigate the problem of a single rectangular or diamond inclusion in isotropic materials under longitudinal tension. Comparison with available numerical results shows the present method is an efficient mesh reducer and yields accurate stress distribution in the near-field region. As applications, the present ad hoc finite element method is extended to discuss the inplane singular elastic field problems of a single rectangular or diamond inclusion in anisotropic materials and of two interacting rectangular inclusions in isotropic materials. In the numerical analysis, the generalized stress intensity factors at the inclusion corner are systematically calculated for various material type, stiffness ratio, shape and spacing position of one or two inclusions in a plate subjected to tension and shear loadings.     

夹杂角端部奇异应力场分析

提出一种分析夹杂角端部奇异应力场的新型杂交有限元方法.构造了一个角端部奇异单元,该单元刚度建立不依赖数学解析解.用这种方法计算了单向载荷作用下无限大板含单个方形夹杂和菱形夹杂角端部奇异应力场,并与现有的数值解进行了比较,结果表明:目前的数值方法是可行的、有效的、数值结果精度高,适用范围广.作为应用讨论了双方形夹杂刚度和位置对夹杂角端部奇异应力场的影响.     

瓷修复体界面断裂行为的模拟实验研究

本文利用云纹干涉法和云纹干涉－－有限元混合法，对瓷修复体的模拟双材料模型界面断裂问题进行了实验研究。用云纹干涉和数字错位云纹干涉法测量带边裂纹的双材料四点简支梁在剪切作用下界面表面的剪应变分布及界面两侧局部表面的位移场，实验表明，由于界面两两侧材料力学性质不同，表现出界面剪切断裂问题的非称性和裂尖附近复合型断裂的特点；用云纹干涉法和有限元法相结合的混合法对粘接界面角点应力奇异性进行研究，并对角点附近应力应变场作了分析，得到了应力奇异指数与边界楔角，载荷的关系，证明了用界面应力强度因子Kf来描述界面端部区域应力分布的公式，并得到了双材料界面端部区域的应力应变分布情况。本文的实验结果为进一步研究口腔金瓷修复体界面的优化设计提供了基础，同时也说明云纹干涉法对于双材料界面断裂行为的研究是有效的。     

THERMAL SHOCK PROTECTION BASED ON MICROTUBE AND MICROPOST ARRAY SURFACE

针对核电站核泵主轴、管道系统等高温环境下工作的部件受冷却水热冲击而容易出现裂纹的问题,提出通过表面微结构设计,利用水低热扩散率的特性,在被热冲击表面产生隔热水膜,从而降低瞬态热冲击过程中表层结构的热应力,防止结构热疲劳损伤. 针对这一设想,采用有限元与无限元相结合的办法,解决热应力分析的多尺度问题. 利用COMSOL多场耦合分析软件,对瞬态热冲击条件下,表面微结构的温度场与热应力分布进行分析,研究了冲击时间、微结构几何参数和流体黏性底层厚度等对微结构表面热冲击防护能力的影响. 研究发现,表面微柱或微管结构对降低短时间冷水冲击产生的表面热应力具有显著效果,同时在微结构与基底之间存在最优过渡曲面使表面热应力最小化.     

Adiabatic shear localization in the dynamic punch test,part II: numerical simulations

The behavior of 1018 steel, 6061-T6 aluminum, and titanium 6%Al–4%V alloy during the dynamic punch test is investigated using the finite element method. Specifically, the possibility and effects of adiabatic shear localization and its role in burr formation are examined, and comparisons to experimental tests in the first part of this two part study are made. A maximum stress criterion involving strain and strain rate hardening and thermal softening is used to determine the occurrence of shear localization in the simulations. It is observed that adiabatic shear localization occurs in the simulations of the titanium alloy. This material exhibits narrow regions of concentrated shear strain during the deformation, and the shear localization criterion is satisfied in these regions. The strain is more widely distributed in the other two metals, and the same criterion is not satisfied. In the calculations of the shear localization criterion it is seen that strain rate hardening has a significant effect when compared to strain hardening and thermal softening. Also, contact between specimen and punch is lost around the center of the punch during operation. This loss of contact is important as it leads to higher stress concentrations at the punch corner and dishing of the blank.     

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     

尖锐夹杂角端部局部应力场杂交有限元分析

本文首先利用作者曾提出的一维有限元特征分析方法计算所得到的尖锐夹杂角端部应力奇异指数和奇异应力场、位移场角分布函数,并依据Hellinger-Reissner原理,开发出了一个特殊的、能够反映夹杂角端部局部弹性现象的n结点多边形超级角端部单元,然后将该超级单元与标准的4结点杂交应力单元耦合在一起构建了一种分析异形夹杂角端部奇异弹性场的新型特殊杂交应力有限元方法.文中给出了两个应用算例,算例结果表明:本文方法不仅使用单元少、计算结果精度高,而且适用范围广,可拓展应用于分析复合材料微结构组织与力学行为关系.     

Centered simple waves for the two-dimensional pseudo-steady isothermal ?ow around a convex corner

The two-dimensional(2D) pseudo-steady isothermal flow, which is isentropic and irrotational, around a convex corner is studied. The self-similar solutions for the supersonic flow around the convex corner are constructed, where the properties of the centered simple wave are used for the 2D isentropic irrotational pseudo-steady Euler equations. The geometric procedures of the center simple waves are given. It is proven that the supersonic flow turns the convex corner by an incomplete centered expansion wave or an incomplete centered compression wave, depending on the conditions of the downstream state.     

热障涂层界面微区域热蠕变应力演化分析

热障涂层热循环载荷下不同界面层蠕变特性是影响界面微区域残余应力变化的关键因素,探究热障涂层蠕变与残余应力的关系有助于提高热障涂层的稳定性。以热弹塑蠕变理论为依据,采用Norton蠕变模型,建立陶瓷层、氧化层、粘接层和基体四层几何分析模型,考虑不同层蠕变和蠕变程度因素,研究热循环载荷作用下涂层界面微区域应力演化规律。结果表明,蠕变参数和蠕变层数的变化影响热障涂层界面残余应力的大小和分布,这对预测热障涂层失效具有指导意义。     

刚性夹杂角点处奇异场的数值分析及双夹杂间的相互影响

本文采用编制的有限元程序求解了无限大板中含有单个具有角点的刚性夹杂在无限远处均布外载作用下夹杂角点附近的位移场，并结合Ｉｎｓｈｉｋａｗａ的工作，求得了相应的应力强度因子。在此基础上，着重分析了两个刚性夹杂间的相互作用，得到了双夹杂左右角点附近的ＫⅠ，Ⅱ值随夹寻间距离改变而变化的规律。     

Residual stress analysis of joints of ceramics and metals

Development of reliable bonding techniques for ceramics and metals is considered to be very important for more useful applications of ceramics to machinery parts. However, a high thermal stress concentration occurs at the corner of bonded interface in ceramics during the bonding process. This occurs because of the difference in thermal properties of the bond materials and reduces the strength of the bonded joint considerably.The authors have been investigating various methods for effectively decreasing this stress concentration. In this paper, they present theoretical and experimental evidence that the stress concentration can be successfully diminished by varying the apex angle of joints. It is found that the tensile strength of joints increases as the apex angle of metals decreases from 90 deg to 45 deg. It also increases with increasing the apex angle of metals. Numerical calculations confirm these experimental results and the proposed procedure may be useful in the design and manufacture dissimilar joints.Paper was presented at the 1992 SEM Spring Conference on Experimental Mechanics held in Las Vegas, NV on June 8–11.     

Wedge corner stress behaviour of bonded dissimilar materials

A contour integral, based on Betti’s reciprocal theorem, is used in conjunction with the finite element method to evaluate the magnitude of the wedge corner stress intensities associated with the higher order terms of the singular stress field near the interface corner of a bi-material joint. It is shown that using a different auxiliary field can eliminate the dependence of the wedge corner stress intensity on the integration path observed by [W.C. Carpenter, Int. J. Fracture 73 (1995) 93–108]. Finite element analysis of a typical joint geometry is used to demonstrate the path-independence of the magnitude of the stress intensities evaluated using the proposed method, and to show the effects of higher order terms on the stress state near the interface corner.     

Corner stress singularities in an FGM thin plate

Describing the behaviors of stress singularities correctly is essential for obtaining accurate numerical solutions of complicated problems with stress singularities. This analysis derives asymptotic solutions for functionally graded material (FGM) thin plates with geometrically induced stress singularities. The classical thin plate theory is used to establish the equilibrium equations for FGM thin plates. It is assumed that the Young’s modulus varies along the thickness and Poisson’s ratio is constant. The eigenfunction expansion method is employed to the equilibrium equations in terms of displacement components for an asymptotic analysis in the vicinity of a sharp corner. The characteristic equations for determining the stress singularity order at the corner vertex and the corresponding corner functions are explicitly given for different combinations of boundary conditions along the radial edges forming the sharp corner. The non-homogeneous elasticity properties are present only in the characteristic equations corresponding to boundary conditions involving simple support. Finally, the effects of material non-homogeneity following a power law on the stress singularity orders are thoroughly examined by showing the minimum real values of the roots of the characteristic equations varying with the material properties and vertex angle.     

锚固体红外温度场与应力场特性研究

为了研究锚固体力-热耦合机制,分别对不同类型的锚固体加载变形破坏过程进行试验研究。应用红外热像技术,获得红外温度场,同时对锚固体进行应力场数值分析。结果显示:中心位置布置单根锚杆的锚固体;应力峰值前,随着荷载的增加,红外温度场呈现整体均匀性升温变化;应力峰值后,在锚杆周围形成一个由多条不同等温线组成的区域,其形状是以锚杆为中心的近似圆形区域,由内向外,温度逐步降低;有锚杆一侧围岩红外温度高于无锚杆一侧,锚杆周围形成一个近似"喇叭"状的等温线图,高温等温线对应高应力区,低温等温线对应低应力区,红外温度场与应力场之间存在空间分布对应关系。     

初始和边界不同恒温时二维梯度板瞬态温度场

为了研究二维功能梯度板的平面瞬态温度场及影响因素,假设热导率和容积比热容在板的高和宽方向为同一类型指数函数分布,基于该板的瞬态热传导基本方程,采用分离变量法,导出在初始和边界不同恒温时该板平面瞬态温度场的级数解析解。通过两种方法的对比,验证了本文研究结果的正确性。结果表明：方板内的等温线,在梯度参数ALFA=BETA时,对称于板的450对角线分布,在ALFA=BETA=0时,对称于板的中心分布;在ALFA不等于BETA时,板的等温线不具对称性;随着冷却时间的增加,非均匀板的等温线向左下（或右上）角移动,右上（或左下）角等温线间距变宽,左下（或右上）角等温线间距变窄,且矩形板的冷却过程比方板更快。因此,可选择适合的梯度参数和几何形状来满足设计、应用和热应力分析的需要,该解析解可作为检验其他近似方法的参考标准。     

The laminar boundary layer near a body corner point

A method is developed for calculating the characteristics of a laminar boundary layer near a body contour corner point, in the vicinity of which the outer supersonic stream passes through a rarefaction flow. In the study we use the asymptotic solution of the Navier-Stokes equations in the region with large longitudinal gradients of the flow functions for large values of the Reynolds number, the general form of which was used in [1].The pressure, heat flux, and friction distributions along the body surface are obtained. For small pressure differentials near the corner the solution of the corresponding equations for small disturbances is obtained in analytic form.The conventional method for studying viscous gas flow near body surfaces for large values of the Reynolds number is the use of the Prandtl boundary layer theory. Far from the body the asymptotic solution of the Navier-Stokes equations in the first approximation reduces to the solution of the Euler equations, while near the body it reduces to the solution of the Prandtl boundary layer equations. The characteristic feature of the boundary layer region is the small variation of the flow functions in the longitudinal direction in comparison with their variation in the transverse direction. However, in many cases this condition is violated.The necessity arises for constructing additional asymptotic expansions for the region in which the longitudinal and transverse variations of the flow functions are quantities of the same order. The general method for constructing asymptotic solutions for such flows with the use of the known method of outer and inner expansions is presented in [1].In the following we consider the flow in a laminar boundary layer for the case of a viscous supersonic gas stream in the vicinity of a body corner point. Behind the corner the flow separates from the body surface and flows around a stagnant zone, in which the pressure differs by a specified amount from the pressure in the undisturbed flow ahead of the point of separation. A pressure (rarefaction) disturbance propagates in the subsonic portion of the boundary layer upstream for a distance which in order of magnitude is equal to several boundary layer thicknesses. In the disturbed region of the boundary layer the longitudinal and transverse pressure and velocity disturbances are quantities of the same order. In this study we construct additional asymptotic expansions in the first approximation and calculate the distributions of the pressure, friction stress, and thermal flux along the body surface.     

十次对称二维准晶中的热应力分析

推导了当考虑热效应时十次对称二维准晶体平面应变问题的通解表示．作为应用，采用所获得的通解首先得到了十次对称二维准晶体中的一个点热源所引起的声子场和相位子场，给出了点热源所引起的声子场和相位子场应力分量的解析表达式；接着获得了在均匀热流作用下十次对称二维准晶体中-绝缘椭圆孔洞所引起的热应力问题的弹性解答，给出了沿椭圆边界环向应力分布的解析表达式；当椭圆的短轴趋于零时，则获得了裂纹问题的解答，给出了应力强度因子、裂纹表面张开位移及能量释放率的解析表达式；推导了在任意热载荷作用下裂尖附近的渐近场．     

Stress singularities at crack corners

In this paper the stress and displacement fields near an embedded crack corner in a linear elastic medium are analytically computed. The conical-spherical coordinate system is introduced to solve this problem. It is observed that the strength of the stress singularity depends on the angle of the crack corner. The singularity becomes weaker, varying from r ^-1 to r ⁰, as the angle of the crack corner varies from 360° to 0°. Both symmetric and skew-symmetric loadings give the same variation of the behavior of the stress singularity. It is also found that the order of the singularity is independent of the Poisson's ratio, unlike the corner cracks at a free surface where Poisson's ratio affects the results.