任意分布多个椭圆形刚性夹杂的反平面问题

对于硬夹杂与软基体的复合材料,考虑夹杂间的相互影响,采用坐标变换和复变函数的依次保角映射方法,构造任意分布且相互影响的多个椭圆形刚性夹杂模型的复应力函数,同时满足各个夹杂的边界条件,利用围线积分将求解方程化为线性代数方程,推导出了在无穷远双向均匀剪切,椭圆形刚性夹杂任意分布的界面应力解析表达式,算例分析给出了单夹杂模型与多夹杂模型的夹杂形状对界面应力最大值的影响规律,并进行了对比,描绘出了曲线。     

电磁材料中广义螺型位错与圆形界面刚性线夹杂的干涉效应

研究了广义螺型位错和圆形界面刚性导体线夹杂的磁电弹耦合干涉效应。采用Riemann-Schwarz对称原理并结合复势函数奇性主部分析,得到该问题的一般解答。当界面只含一条刚性线时,获得了封闭形式解。运用扰动技术,求解了位错点的扰动应力、电位移和磁感应强度场。由推广的Peach-Koehler公式求出了作用在位错上的位错力,讨论了圆弧形刚性线几何条件和材料失配对位错力的影响规律。解答不但可作为格林函数获得任意分布位错的相应解答,而且可以用于研究无穷远纵向剪切和面内电磁场作用下界面刚性线夹杂和任意形状裂纹的磁电弹耦合干涉效应问题。     

弹性模量比对界面迁移下夹杂演化的影响

集成电路的导线内不可避免存在夹杂等缺陷。在各种内在机制以及外界环境作用下夹杂会出现形态演化从而影响内连导线的各种性能。该文基于界面迁移机制下微结构演化理论,推导了应力诱发固-固界面迁移的单元控制方程,数值模拟了夹杂-基体弹性模量比对夹杂形态演化的影响。结果表明:不同模量比下夹杂的σσ_c、ββ_c或hh_c时,夹杂长大;反之收缩。随着模量比的增加,临界应力、临界形态比随之增大,而临界线宽会减小。并且,当夹杂与基体的弹性模量比α0.6时,模量比对于临界应力和临界形态比的影响可忽略。     

过渡层特性对金刚石涂层残余应力影响的有限元模拟

采用热．力耦合有限元方法对包含过渡层的金刚石涂层一硬质合金基体内的残余应力进行了数值模拟，重点研究了过渡层的特性（弹性模量和热膨胀系数）对金刚石涂层的各应力分量沿界面的最大值的影响。结果表明，随着过渡层弹性模量的增加，径向应力和轴向应力在界面处的最大值均减小，而剪应力的最大值则增大；随着过渡层热膨胀系数的增加，上述各应力分量在界面处的最大值均增大；受过渡层特性影响最敏感的是剪应力。     

压电螺型位错与椭圆夹杂界面导电刚性线的干涉效应

研究了无限大压电基体材料中压电螺型位错与含界面导电刚性线椭圆夹杂的电弹耦合干涉问题。运用求解复杂多连通域问题的复变函数方法,获得了椭圆夹杂和基体区域复势函数以及电弹性场的精确级数形式解答。利用广义Peach-Koehler公式导出作用于压电螺型位错上的位错力公式。主要讨论了刚性线几何尺寸和椭圆曲率对位错力的影响规律。分析结果表明:界面刚性线排斥基体中的位错,对靠近椭圆夹杂界面的螺型位错的运动和平衡位置有重要的影响。当刚性线的长度达到临界值,界面刚性线的存在会改变螺型位错与压电椭圆夹杂的干涉规律。椭圆夹杂的压缩系数变大,刚性线尺寸对位错力的影响也越大。     

复合材料中压电螺型位错与含刚性核夹杂的电弹干涉

为了研究压电复合材料中位于基体的压电螺型位错与含共焦椭圆导电刚性核椭圆夹杂的电弹相互作用, 基于复变函数方法, 获得了基体和夹杂区域的精确级数形式解析解。运用广义Peach-Koehler公式, 导出了作用在位错上像力的解析表达式。在此基础上讨论了椭圆刚性核和材料电弹特性对位错像力以及位错平衡位置的影响规律, 同时讨论了压电夹杂和弹性基体的复合情况。结果表明: 椭圆刚性核对位错有着明显的排斥作用, 可以增强硬夹杂对位错的排斥, 减弱软夹杂对位错的吸引; 对于软夹杂, 在界面附近位错存在一个不稳定的平衡位置; 在基体和夹杂的界面上, 像力迅速增大; 当夹杂的剪切模量远小于基体时, 界面附近不会出现位错的平衡位置。     

压电材料中螺型位错与含界面刚性线圆形涂层夹杂的干涉

研究了压电材料中位于基体的螺型位错与含界面刚性线圆形涂层夹杂的电弹耦合干涉问题。运用复变函数方法,获得了基体、涂层和夹杂中复势函数的精确级数形式解答。基于广义Peach-Koehler公式,计算了作用在位错上的像力。讨论了刚性线几何条件、界面层厚度和材料电弹特性对位错力和位错平衡位置的影响规律。结果表明:对于软夹杂和软涂层的情况,刚性线长度存在一个临界值改变像力的方向。螺型位错先被吸引后被排斥,在夹杂附近有一个稳定的平衡点。对于硬夹杂和硬涂层的情况,位错一直被排斥,刚性线对位错力的影响较小。     

碳酸饮料瓶爪瓣式瓶底结构力学性能研究

目的研究碳酸饮料瓶爪瓣瓶底几何形状参数对瓶底应力开裂现象的影响规律。方法通过加速应力开裂测试观察瓶底的应力开裂现象;通过单因素试验分别分析凹槽底部圆弧直径、凹槽侧壁张角、凹槽深度以及爪瓣数量对最大主应力最大值的影响规律;通过全因素实验研究对比4个几何参数对最大主应力最大值影响的显著性。结果通过单因素试验,发现随着凹槽侧壁张角、凹槽底部圆弧直径以及爪瓣数量的增大,最大主应力的最大值均呈现下降的态势,而表示凹槽深度4个数据的分析结果则呈现虽深度增加但最大主应力的最大值均增加的态势。全因素实验证实这4个参数中只有槽底圆弧直径、凹槽数量以及凹槽深度对瓶底最大主应力的最大值有显著的影响。另外,凹槽深度、凹槽数量分别与槽底圆弧直径的交互效应呈现出显著影响。最后拟合了瓶底最大主应力的最大值与影响显著的几何参数之间的回归方程。结论在厚度均匀的前提下研究了几何结构的相关参数对应力开裂的影响及规律,厚度变化及厚度分布的变化对应力开裂的影响还需进一步研究。     

螺型位错偶极子与界面刚性线的弹性干涉

研究了晶体材料中螺型位错偶极子和界面刚性线夹杂的弹性干涉作用。利用复变函数方法,得到了该问题的复势函数以及应力场的封闭形式解答。求出了作用在螺型位错偶极子中心的像力和力偶矩,并分析了界面刚性线几何条件和不同材料特征组合对位错偶极子平衡位置的影响规律。研究结果表明:当位错偶极子不断靠近刚性线时,刚性线对螺型位错偶极子的运动有很强的排斥作用。当刚性线的长度和材料剪切模量比达到临界值时,可以改变偶极子和界面之间的干涉机理。同时,偶极子偶臂的方向对其自身的平衡也有很大的影响。     

穿过界面的刚性线夹杂对SH波的散射

利用两个联结半平面中简谐集中力的格林函数,得出了穿过界面刚性线的散射场。刚性线的散射场可分解为有界部分和奇异部分。利用散射场的有界部分和奇异部分得出了刚性线的在SH波作用下的Cauchy型奇异积分方程。根据所得奇异积分方程和Cauchy型积分的端点性质,得出了确定刚性线和界面交点处奇异性阶数的特征方程。根据刚性线和界面交点处的奇性应力定义了交点处的应力奇异因子。对所得Cauchy型奇异积分方程的数值求解,可得刚性线端点和交点处的应力奇异因子。     

Scattering of elastic waves by a diamond shaped inclusion with cracks

This paper studies the scattering of in-plane compressional and shear waves by a diamond shaped inclusion with cracks using the boundary element method. The special case that the shape of the diamond becomes square is also considered. Numerical calculations are carried out for the limited cases of diamond shaped hole and rigid inclusions, and the effects of frequency and inclusion shape on the scattering cross section and dynamic stress intensity factor are shown in graphical form. The results where the elastic properties of the inclusion are the same as those of the matrix are also discussed.     

Crack–inclusion problem for a long rectangular slab of superconductor under an electromagnetic force

The interaction between a crack and an inclusion in a type-II superconductor is investigated in this paper. Using the finite element method, the crack–inclusion problem can be solved. Numerical results are presented to illustrate fracture behavior of superconductor under electromagnetic force. The magnetic behavior of the superconductor is described by the critical-state Bean model. The stress intensity factors at the crack tip are obtained and discussed for decreasing field after zero-field cooling. Numerical results show that the stress intensity factors at crack tip are always larger with an elastic inclusion than for a rigid inclusion. Because of the barrier effect of the rigid inclusion, the values of the stress intensity factors decrease when the crack approaches the inclusion. Relative to rigid inclusion and no inclusion cases, elastic inclusion leads to the largest value of the stress intensity factor at crack tip. Thus, the crack propagation is easier near an elastic inclusion and the rigid inclusion is helpful for crack arrest.     

Eigenfunction expansion solutions for three-dimensional rigid planar inclusion problems

An eigenfunction expansion method is presented to obtain three-dimensional asymptotic stress fields in the vicinity of the front of a semi-infinite infinitely rigid inclusion, subjected to the far-field antiplane shear and extension/bending loadings. Four different rigid inclusion side-surface boundary conditions are considered: (i) anticrack or perfectly bonded rigid inclusion, (ii) transversely rigid inclusion (longitudinal slip permitted), (iii) rigid inclusion in part perfectly bonded, the remainder with slip, (iv) rigid inclusion located alongside a crack. The computed stress singularity for an anticrack is the same as its plane strain counterpart, while the expression for the stress intensity factor varies in the thickness direction.     

Determination of stress intensity factors for bimaterial interface stationary rigid line inclusions by boundary element method

The stress intensity factors for a rigid line inclusion lying along a bimaterial interface are calculated by the boundary element method with the multiregion and the discontinuous traction singular elements. The relationships between the stress intensity factors and the inclusion surface stresses are derived. The numerically computed stress intensity factors for the bimaterial interface rigid line inclusion in the infinite body are proved to be in good agreement within 3% when compared with the previous exact solutions. In the finite bimaterial models, the stress intensity factors for the center and edge rigid line inclusions at the interface are computed with the variation of the rigid line inclusion length and the shear modulus ratio under the uniaxial and biaxial loading conditions.     

Stress analysis of a kinked crack initiating from a rigid line inclusion. Part 1: Formulation

The problem of a kinked crack which has initiated from the tip of a rigid line inclusion is analyzed as a mixed boudary value problem. The stress distribution, stress intensity factors, singularity at the inclusion tip, and the resultant moment on the rigid line inclusion are investigated for various angles of the kinked crack and crack lengths. The rotation of the rigid line inclusion, when loaded by a uniform farfield stress, is calculated. The cases in which the inclusion is free to rotate or is fixed are separately considered.     

Stress intensity factors for curvilinear cracks loaded under anti-plane strain (mode III) conditions

A general solution to the elastic and thermoelastic problems with a rigid circular-arc inclusion is presented. The proposed analysis is based upon the complex variable theory dealing with sectionally holomorphic functions which is reduced to the solution of the Hilbert problem. It is indicated that both the stress and thermal stress fields near the inclusion tip possess a square-root singularity similar to that for the corresponding crack problem. In analogy to the stress intensity factors defined for crack problem, stress singularity coefficients are introduced in this paper to characterize the near tip fields. Complete stress fields and the corresponding stress singularity coefficients as the circular-arc inclusion are under uniform remote load, concentrated force and uniform heat flux are given. Failure initiation of an infinite plate embedded with a rigid arc inclusion under different loading conditions is also discussed.     

Electroelastic fields and effective moduli of a medium containing cavities or rigid inclusions of arbitrary shape under anti-plane mechanical and in-plane electric fields

Summary We examine the two-dimensional problem of an infinite piezoelectric medium containing a solitary cavity or rigid inclusion of arbitrary shape, subjected to a coupled anti-plane mechanical and in-plane electric load at the remote boundary of the matrix. Conformal mapping techniques are employed to analyze the boundary value problems. Specific results are given for elliptical, polygonal and star-shape inclusions. Local fields of this type are used to estimate the overall moduli of a medium containing voids or rigid inclusions. This is accomplished with the help of an extension of Eshelby's formula which evaluates the total electric enthalpy by a particular line integral. Explicit estimates of the effective moduli are derived for dilute as well as for moderate area fractions of inclusions. The formulae depend solely on the cross area of the inclusion, area fraction and one particular coefficient of the mapping function. In addition, the stress and electric displacement singularities around the sharp corners of the inclusion are examined. The existence of uniform fields inside the inclusion is also envisaged. The present results, with appropriate modifications, apply equally well to those of thermoelectric and magnetoelectric effects.     

Bending of a thin plate containing a rigid inclusion and a crack

The bending of a thin infinite plate with a line crack and an arbitrarily shaped rigid inclusion is analyzed. The superposition principle is used to reduce the original formulation to two subsidiary problems. A distribution of dislocation is assumed along the crack line. The solution is obtained in an integral form by using the Green function of a point dislocation. The stress functions for both subsidiary problems are obtained by employing the rational mapping function technique. The stress intensity factors are obtained in terms of the dislocation density function. Numerical results are demonstrated for the plate containing a square rigid inclusion and a line crack.     

On three-dimensional singular stress/residual stress fields at the front of a crack/anticrack in an orthotropic/orthorhombic plate under anti-plane shear loading

A novel eigenfunction expansion technique, based in part on separation of the thickness-variable, is developed to derive three-dimensional asymptotic stress field in the vicinity of the front of a semi-infinite through-thickness crack/anticrack weakening/reinforcing an infinite orthotropic/orthorhombic plate, of finite thickness and subjected to far-field anti-plane shear loading. Crack/anticrack-face boundary conditions and those that are prescribed on the top and bottom (free, fixed and lubricated) surfaces of the orthotropic plate are exactly satisfied. Five different through-thickness crack/anticrack-face boundary conditions are considered: (i) slit crack, (ii) anticrack or perfectly bonded rigid inclusion, (iii) transversely rigid inclusion (longitudinal slip permitted), (iv) rigid inclusion in part perfectly bonded, the remainder with slip, and (v) rigid inclusion located alongside a crack. Explicit expressions for the singular stress fields in the vicinity of the fronts of the through-thickness cracks, anticracks or mixed crack–anticrack type discontinuities, weakening/reinforcing orthotropic/orthorhombic plates, subjected to far-field anti-plane shear (mode III) loadings, are presented. In addition, singular residual stress fields in the vicinity of the fronts of these cracks, anticracks and similar discontinuities are also discussed.