Isothermic formation of spherulitic boundaries with equidistant time marks in a foil of polypropylene

In a foil of polypropylene two circularly growing spherulites which touch each other and finally form a common grain boundary are regarded. Another grain boundary is formed by one circularly growing spherulite which makes contact with a growing band and with the growing interior of a circular ring. All possible grain boundary formations are systemized. This is done theoretically using analytical planar curves geometry, and is done in most cases, experimentally with equidistant time marks.     

Rayleigh wave interaction with inhomogeneities—Part 1: Near surface cavity and inclusion

The interaction of a Rayleigh pulse with a circular cavity and circular inclusion has been examined employing dynamic photoelasticity. The explosively generated R-pulse travels along the free boundary and is trapped in the ligament between the cavity and the free boundary with little energy propagating around the cavity. For cavities and inclusions at shallow depth below the free surface failure of the ligament occurs and most of the energy associated with the incident R-wave is converted by diffraction into body and surface waves. The existence of a shadow zone on the downstream side of the circular cavity provides a means of identifying the location of the cavity which is nearly tangent to the surface by e.g. ultrasonic inspection.     

A hybrid finite element method for heterogeneous materials with randomly dispersed rigid inclusions

A hybrid finite element approach is proposed for the mechanical response of two-dimensional heterogeneous materials with linearly elastic matrix and randomly dispersed rigid circular inclusions of arbitrary sizes. In conventional finite element methods, many elements must be used to represent one inclusion. In this work, each inclusion is embedded inside a polygonal element and only one element is required to represent one inclusion. In numerically approximating stress and displacement distributions around the inclusion, classical elasticity solutions for a multiply-connected region are employed. A modified hybrid functional is used as the basis of the element formulation where the displacement boundary conditions of the element are automatically considered in a variational sense. The accuracy and efficiency of the proposed method are demonstrated by two boundary value problems. In one example, the results based on the proposed method with only 64 hybrid elements (450 degrees of freedom) are shown to be almost identical to those based on the traditional method with 2928 conventional elements (5526 degrees of freedom).     

求解三维物体波浪荷载的边界元模型

建立了求解规则波中任意形状三维物体绕射问题的边界元模型。设置辐射面将流场分为内、外场,外场中的绕射势用特征函数展开式解析表达,内场则由边界积分方程求解,所取的Green 函数为简单的1/r 形式。内场边界采用四边形面元和轴对称面元混合布置的划分方式,轴对称面元上奇点强度沿周向为Fourier 级数展开的高次分布,提高了求解三维绕射问题的精度和效率。经与直立圆柱绕射的线性理论解比较,验证了数值方法的可靠性。利用谱分析原理,将规则波中的结果拓展,得到多向不规则波中绕射物体所受波浪力的统计特性。     

Transverse electric scattering by a dielectric biconvex cylinder loaded with a shallow circular trough in a ground plane

The scattering problem of transverse electric wave from a dielectric biconvex cylinder buried in a shallow circular trough of a ground plane is investigated and a rigorous series solution is also derived. Based on the region-matching method, the analysed region is decomposed into two subregions by introducing a semi-circular auxiliary boundary. The magnetic field of each subregion is expressed in terms of cylindrical wave functions with unknown expansion coefficients. After imposing the matching conditions and the boundary condition on the trough surface with the aid of Graf's addition theorem, the unknown coefficients are determined. Comparisons with published data for a dielectric circular cylinder case show very good agreement. Visible effects of depth-to-half-width ratios of a dielectric biconvex cylinder on echo width, far- field pattern and near-field distribution are illustrated in graphical form.     

Effect of the electric discharge on nonstationary processes during supersonic air and methane jet flow over a flat obstacle

The features of supersonic air and methane jet flows over a flat obstacle, accompanied by an electric discharge, were studied. The flow under consideration is characterized by a number of unsteady effects appearing as oscillations of shock-wave fronts with various amplitudes and frequencies depending on the nozzle-obstacle system configuration and jet gas-dynamic parameters. The oscillation frequency of the bow shock wave increases as the obstacle becomes closer to the nozzle edge and the relative obstacle diameter and the supersonic jet stagnation pressure increase. Initiation of the energy release region at the supersonic jet edge causes a change in the oscillation frequency of the bow shock wave; under certain conditions, it causes a change in the entire shock-wave flow pattern.     

Analysis of shadow and direct-feed radiation mutual coupling in paraboloid antennas

By considering the shadow region of diffracted rays and direct-feed radiation, the calculation of the power coupling between skew paraboloid antennas is modified. The skew configuration means there is an angle between the axes of two antennas, and the two antennas are placed in the back of half-space of each other. It is illustrated by considering the coupling between two identical front-fed symmetric paraboloid antennas, each of which is fed by a TE11 mode circular waveguide. The result can be used as guidance for the installation disposition of multiple antennas.     

Two-dimensional scattering from an impenetrable cylindrical obstacle in an acoustic quarterspace

The problem of sound scattering by an infinitely long hard or soft circular cylindrical obstacle suspended near a rigid corner is investigated. The separation of variables technique, the appropriate wave field expansions and the method of images along with the translational addition theorem for cylindrical wave functions are used to derive a closed-form analytical solution in form of infinite series. The analytical results are illustrated with a numerical example in which the cylindrical obstacle is positioned near the rigid boundary of a water-filled acoustic quarter-space. The backscattering form function amplitude and spatial distribution of the total acoustic pressure are evaluated and discussed for representative values of the parameters characterizing the system. The effects of incident wave frequency, angle of incidence and proximity of the cylinder to the rigid boundary are examined. Limiting case involving an infinite cylinder in an acoustic halfspace is considered and fair agreement with a well-known solution is established.     

The development of fatigue damage around fastener holes in thick graphite/epoxy composite laminates

This paper discusses the mechanisms by which damage develops and grows around countersunk fastener holes in composite laminates under fatigue loading conditions. Experiments have shown that the erosion of material between ply layers nucleates delaminations which then grow through the laminate under the action of the fatigue loads. The damage at the hole bore surface produces sites for the nucleation of delaminations. The morphology of the delaminations and ply cracking was mapped extensively and from these maps it was found that the volume of material around the fastener hole, damaged by the fatigue loading, adopted a characteristic shape; the volume of damaged laminate increased towards the faying surface of the laminate and (metal) fixture. This characteristic damage volume was generated by the fastener rocking under the fatigue loads. Growth of the delaminations has been shown to be preceded by intraply cracking and, as fatigue loading proceeded, more delaminations were generated at the hole bore surface. The interfacial region between the composite laminate and the fixture also provided the nucleation site for fatigue cracks in the fasteners. The effects of initial fastener-hole clearances on damage nucleation and growth did not appear to follow any clear pattern. However, coupons with excessive initial hole clearances did appear to exhibit greater than expected damage growth after only one sequence block.Several techniques for the measurement of damage growth (development) were investigated. Stiffness measurements of the test system were found to show only small changes with hole wear and fastener rocking (using shadow moire techniques) also showed only small changes with hole wear. Ultrasonic C-scanning methods were used to map the extent of damage around the fastener holes with fatigue loading.The experimental work has shown that damage development around fastener holes is a complex process, usually producing several delaminations in the region of the fastener hole which grow and may ultimately lead to the failure of the coupon.     

热交联处理对聚苯硫醚结晶行为的影响

采用热台偏光显微镜和差示扫描量热法,研究了直链型低分子量聚苯硫醚(PPS)热交联处理后的等温结晶行为,考察了热处理时间对PPS球晶生长速率与晶体形态的影响.结果表明:球晶的生长速率随热交联时间的延长呈先升高后降低的趋势,20min时结晶速率达到最大值;经过一定时间的热交联处理后,PPS的晶体形态更趋完善.当热交联时间超过60min后,球晶超结构基本消失.     

Solutions of multiple crack problems of a circular region with free or fixed boundary condition in antiplane elasticity

Four cases of multiple crack problems in antiplane elasticity, circular region or an infinite region exterior to a circle with free or fixed boundary condition, are considered in this paper. For all these cases, the presented elementary solution is a particular solution of the circular region containing one crack. The solution consists of two parts and satisfies the following conditions: (a) The first part corresponds to a pair of longitudinal forces acting at a prescribed point on both edges of a single crack; (b) The second part corresponds to some distributed forces along both edges of the crack; (c) The elementary solution, i.e. the sum of the first and second parts, satisfies the above mentioned boundary value conditions along the circular boundary. As we have done in [1–3], the system of Fredholm integral equations for the undetermined densities of the elementary solutions can be easily estabished and the stress intensity factors at crack tips can also be evaluated.     

聚苯硫醚及其纤维增强复合材料的等温结晶形态

采用热台偏光显微镜技术观察了聚苯硫醚(PPS)及其玻璃纤维、 炭纤维及芳纶纤维增强复合材料等温结晶过程中球晶结构形态的变化。研究了等温结晶温度对PPS的晶体形态及球晶生长速率的影响。结果表明, 结晶温度对PPS的结晶影响非常明显。在235~265℃, 随着等温结晶温度的升高, 聚苯硫醚球晶形态发生了从细小而具有部分束状结构到大而完善再到细小而不完善的变化过程, 球晶的生长速率随着结晶温度的增大呈非线性下降。而纤维的存在使PPS的结晶形态发生了从球晶结构到横穿晶的变化, 且不同纤维诱导形成横穿晶的程度有所不同。其中玻璃纤维和芳纶纤维可以诱导形成较为明显的横穿晶形态, 而炭纤维则不能诱导形成明显的横穿晶。      

The effect of spherulite size on the fracture morphology of polypropylene

Tensile tests show that for isotactic polypropylene the graph of yield stress versus spherulite size goes through a maximum at a critical spherulite size. Scanning electron and transmission optical microscopy indicate that this represents a change-over from spherulite yield to boundary yield, caused by an increased segregation of impurities at the boundaries coupled with voidage owing to contraction of the spherulites on cooling.     

SH波对覆盖层下浅埋圆孔和圆夹杂的散射

利用复变函数法和波函数展开法给出了具有地表覆盖层的弹性半空间内圆形孔洞和圆柱形夹杂在稳态SH波作用下动应力集中问题的解。根据SH波散射的衰减特性,该问题采用大圆弧假定法求解,利用半径很大的圆来拟合地表覆盖层的直边界,将具有地表覆盖层的半空间直边界问题转化为曲面边界问题。借助Helmholtz定理预先写出问题波函数的一般形式解,再利用边界条件并借助复数Fourier-Hankel级数展开把问题化为求解波函数中未知系数的无穷线性代数方程组,截断该无穷代数方程组可求得该问题的近似解析解。最后,通过算例讨论了地表覆盖层及圆孔对浅埋圆柱形夹杂动应力集中的影响。结果表明,覆盖层刚度和厚度的变化及圆孔的存在可显著改变圆夹杂周边动应力集中的分布。     

Elastic anisotropy effect on indentation-induced thin film interfacial delamination

Effect of elastic anisotropy on indentation-induced thin film interfacial delamination, especially, at the initiation and early growth stage, is examined. The indentation load is modeled as a constant pressure over an expanding semi-spherical cavity. The delamination process is approached by a cohesive zone model. The rest of the problem is formulated within the general anisotropic elasticity theory, and solved numerically by the boundary element method employing a special Green’s function for multilayers. The material system of a Cu(0 0 1) film on a Si(0 0 1) substrate is studied as an example. The interfacial damage initiation and crack development under indentation are captured in the simulation. By comparing the predictions with the materials being modeled as isotropic and as anisotropic (of the cubic symmetry as they are), it is shown that the elastic anisotropy of the copper film plays a significant role in determining the delamination pattern. In the isotropic model, the delamination crack fronts are circular reflecting the problem axisymmetry. In contrast, crack fronts are square with rounded corners in the anisotropic case. This significant difference necessitates a three-dimensional anisotropic stress analysis of the indentation-induced delamination of strongly anisotropic films.     

基于归一化RGB色彩模型的阴影处理方法

通过分析影像上阴影区域的属性，提出了一种基于阴影属性的高分辨率遥感影像阴影检测和去除算法。利用阴影区域蓝色分量偏高的特性，对归一化B分量和原始B分量进行阈值检测，并结合小区域去除和数学形态学处理，得到较精确的阴影区域；然后，分别在RGB空间和HSI空间对各个独立的阴影区域与其邻近的非阴影区域进行匹配，完成阴影去除操作；最后沿着阴影边界做一次中值滤波以减轻边缘效应。仿真结果验证了算法的有效性，并且显示在HSI空间获得了更好的补偿效果。     

A mixed boundary problem for a finite internally cracked plate

A displacements and resultant forces model (see eqns 2–5, 13 and 17) for a finite internally cracked plate is proposed. This model satisfies: (a) The equilibrium and compatibility condition in the region occupied by cracked plate; (b) Stress free condition on the surface of crack; (c) Single value condition of displacements around the crack. In this model, some undetermined coefficients are contained, these coefficients are derived from outer boundary condition.

It is proved that, this model is convenient not only for the displacements or resultant forces boundary problem, but also for the mixed boundary problem. Besides this, if the boundary problem is solved, to find the value of displacements of any points in cracked body is also convenient.

Two mixed boundary problems, one for the square cracked plate (see Fig. 3), and another for circular cracked plate (see Fig. 5), are solved. The numerical results obtained are shown in Tables 1 and 2 and Figs. 4 and 6 respectively. These results can explain how the constraint affects the values of the stress intensity factor on the crack tips.     

A non-axisymmetric cylindrical contact problem

The contact problem under investigation is one whereby a solid circular elastic cylinder of infinite length is rigidly indented by a two piece collar of finite length, each piece being diametrically opposed and extending only partially around one half of the circumference. This case is practically significant in relation to the axisymmetric cylindrical contact problem since in many cases attachment of a component to a cylindrical shaft is achieved by means of a two piece clamp.Shear stresses on the contact interface are taken zero and a radial displacement influence coefficient technique is used to model the integral equation governing this contact problem. Adopting the Papkovich-Neuber solution for the non-axisymmetric cylindrical coordinate case and substituting the appropriate boundary conditions leads to a combined Fourier series, Fourier integral representation for the desired displacements. Convergence of this series—integral is studied and results of interference contact pressure are presented for an illustrative range of the various parameters involved.     

“Causal” shape functions in the time domain boundary element method

Since failing to respect the causality condition has been identified as one of the main sources of inaccuracies in the time domain boundary element method for elastodynamics and scalar wave propagation problems, in this contribution new shape functions are investigated, which permit a more accurate simulation of the continuous propagation of wave fronts. The performance of these shape functions in 2D scalar wave propagation problems is tested both for the potential (displacement) and for the time gradient (velocity) equations. Analytical time integrations are developed and numerical results are presented.     

An algorithm to generate quadrilateral or triangular element surface meshes in arbitrary domains with applications to crack propagation

A new hybrid algorithm for automatically generating either an all-quadrilateral or an all-triangular element mesh within an arbitrarily shaped domain is described. The input consists of one or more closed loops of straight-line segments that bound the domain. Internal mesh density is inferred from the boundary density using a recursive spatial decomposition (quadtree) procedure. All-triangular element meshes are generated using a boundary contraction procedure. All-quadrilateral element meshes are generated by modifying the boundary contraction procedure to produce a mixed element mesh at half the density of the final mesh and then applying a polygon-splitting procedure. The final meshes exhibit good transitioning properties and are compatible with the given boundary segments which are not altered. The algorithm can support discrete crack growth simulation wherein each step of crack growth results in an arbitrarily shaped region of elements deleted about each crack tip. The algorithm is described and examples of the generated meshes are provided for a representative selection of cracked and uncracked structures.