复合材料层合板自由振动的薄板样条无网格解

无网格全局配点法分为多项式配点法和径向基函数配点法,国内外很多文献利用径向基函数配点法对复合材料层合板进行了分析。利用一阶剪切变形理论和基于薄板样条径向基函数的无网格配点法计算了复合材料层合板自由振动的固有频率和振型。研究了薄板样条径向基函数中形状参数的选取和本工作方法的收敛性。结果表明:形状参数m=3时收敛性最好,计算精度最高。将本工作计算结果与文献中的实验结果进行了对比,验证了本文方法的精度和效率。     

Characterization of the carbides and the martensite phase in powder-metallurgy high-speed steel

A microstructural characterization of the powder-metallurgy high-speed-steel S390 Microclean was performed based on an elemental distribution of the carbide phase as well as crystallographic analyses. The results showed that there were two types of carbides present: vanadium-rich carbides, which were not chemically homogeneous and exhibited a tungsten-enriched or tungsten-depleted central area; and chemically homogeneous tungsten-rich M₆C-type carbides. Despite the possibility of chemical inhomogenities, the crystallographic orientation of each of the carbides was shown to be uniform. Using electron backscatter diffraction the vanadium-rich carbides were determined to be either cubic VC or hexagonal V₆C₅, while the tungsten-rich carbides were M₆C. The electron backscatter diffraction results were also verified using X-ray diffraction. Several electron backscatter diffraction pattern maps were acquired in order to define the fraction of each carbide phase as well as the amount of martensite phase. The fraction of martensite was estimated using band-contrast images, while the fraction of carbides was calculated using the crystallographic data.     

求解任意四边形薄板动力问题的样条有限点法

本文将有限点法与等参元思想相结合形成了坐标变换下的样条有限点法，解决了任意四边形薄板的动力计算问题，为工程实际中薄板的静动力计算提供了一种简单、可靠、通用性强的有效方法。     

Thin plate spline radial basis function for the free vibration analysis of laminated composite shells

In this paper, the free vibration characteristics of laminated composite cylindrical and spherical shells are analyzed by the first-order shear deformation theory and a meshless global collocation method based on thin plate spline radial basis function. The singularity of thin plate spline radial basis function is eliminated by adding infinitesimal to the zero distance. Several numerical examples are used to show convergence of the present method and choose the proper shape parameter. It is found that the natural frequencies computed by thin plate spline radial basis function with shape parameter m = 4 converge most rapidly. In the comparison study, the present results are in good agreement with the results of Reddy and Liu [8] and Ferreira et al. [21].     

A procedure for indirect and automatic measurement of prior austenite grain size in bainite/martensite microstructures

An alternative procedure for indirect and automatic measurement of the prior austenite grain size (PAGS) in bainite/martensite is proposed in this work. It consists in the determination of an effective grain size by means of statistical post-processing of electron backscatter diffraction (EBSD) data. The algorithm developed for that purpose, which is available on-line, has been applied to simulated EBSD maps as well as to both nanocrystalline bainitic steel and commercial hot-rolled air-cooled steel with a granular bainitic microstructure. The new proposed method has been proven to be robust, and results are in good agreement with conventional PAGS measurements. The added value of the procedure comes from its simplicity, as no parent reconstruction is involved during the process, and its suitability for low-magnification EBSD maps, thus allowing a large step size and coverage of a substantially broader area of the sample than the previous methods reported.     

A new procedure for quantitative X-ray analysis with electron excitation

A method of quantitative x-ray analysis with electron excitation which eliminates the need to correct for absorption, fluorescence, and electron backscatter has been developed. This method consists of 1) analyzing an element using two or more different electron beam energies, 2) extrapolating the observed intensity ratios as a function of energy to an intensity ratio at the critical excitation potential, and 3) multiplying the result by an easily calculated factor to account for electron retardation effects. This method makes possible quantitative analyses of a single element in a multi-element assemblage without knowledge of the other elements. The procedure has been tested with a number of mineral and alloy specimens, and its accuracy is found to be at least as great as that obtained by conventional correction methods.     

任意四边形平面问题的样条有限元法

用三次B样条有限元通过坐标变换和变分法求解任意四边形区域上的平面问题,利用分区势能原理推广到由四边形组成的任意平面区域,推导出了具体的计算公式,为平面问题求解提供了一种高效的计算方法。与普通有限单元相比,该方法计算量小,而且计算结果具有对网格畸变不敏感,精度高等显著特点。     

On the microstructure and the origin of intermetallic phase seams in magnetic pulse welding of aluminum and steel

The microstructure of aluminum‐steel compounds fabricated by magnetic pulse welding are investigated. Electron backscatter diffraction, energy dispersive x‐ray spectroscopy and scanning electron microscopy revealed the existence of several different phases along the weld seam. While one layer could be identified as aluminum solid solution, a very thin layer close to the steel side of the compound eluded detailed characterization by scanning electron microscopy techniques. Transmission electron microscopy and selected area electron diffraction investigations of this layer revealed a mix of nanocrystalline and amorphous parts. When ambient pressure was reduced to 1 mbar during welding, no interlayers were observed in the samples. This suggests that the interlayers are precipitates of the jet that is formed during conventional impact welding.     

EBSD imaging of orientation relationships and variant groupings in different martensitic alloys and Widmanstätten iron meteorites

An automatic method to colorize and quantify the classical Pitsch, Kurdjumov–Sachs, Greninger–Troiano and Nishiyama–Wasserman orientation relationships in the electron backscatter diffraction maps of martensitic/bainitic steels is detailed. Automatic analysis of variant grouping is also presented. The method was applied to low and high carbon steels, and to iron–nickel Widmanstätten meteorites. Many results of recent literature are confirmed. In low carbon steels the individual laths exhibit continuous orientation gradients between the classical orientation relationships, and the laths tend to be grouped by close-packed plane (morphological) packets. A crystallographic scenario describing the formation of the packets is proposed on the base of the one-step model. When the carbon content increases, the orientation spreading is reduced; and martensite tends to form plate groups and burst configurations. In iron–nickel meteorites, the centimeter long Widmanstätten laths do not exhibit continuous orientation gradients but are constituted of subgrains with uniform orientation relationship; the kamacite grains in the plessite regions are grouped into Bain zones, probably due to a recrystallization during the slow cooling of the meteorites.     

Microstructure at friction stir lap joint interface of pure titanium and steel

A commercially pure titanium plate was lap joined to a structural steel plate via friction stir welding, and the microstructures at the lap joint interface were intensively examined by means of electron backscatter diffraction analysis and transmission electron microscopy. Swirling-like macro- and micro-intermixing zones of titanium and steel are formed along the interface, where tiny Fe-Ti intermetallic particles are dispersed and mixed with β titanium in layers. The lap joint has high shear tensile strength, which is supposed to result from the dispersion of tiny Fe-Ti intermetallic particles and the formation of β titanium at the joint interface.     

A two-dimensional adaptive nodes technique in irregular regions applied to meshless-type methods

We propose a two-dimensional (2D) adaptive nodes technique for irregular regions. The method is based on equi-distribution principle and dimension reduction. The mesh generation is carried out by first producing some adaptive nodes in a rectangle based on equi-distribution along the coordinate axes and then transforming the generated nodes to the physical domain. Since the produced mesh is applied to the meshless-type methods, the connectivity of the points is not used and only the grid points are important, though the grid lines are utilized in the adapting process. The performance of the adaptive points is examined by considering a collocation meshless method which is based on interpolation in terms of a set of radial basis functions. A generalized thin plate spline with sufficient smoothness is used as a basis function and the arc-length is employed as a monitor in the equi-distribution process. Some experimental results will be presented to illustrate the effectiveness of the proposed method.     

样条函数在激光跟踪仪测距补偿中的应用

激光跟踪仪测距精度取决于激光干涉仪(IFM)和激光绝对测距仪(ADM)的精度,就目前技术水平而言,IFM测距精度远高于ADM测距精度,因此需要对ADM测距误差进行修正。本文采用三次样条函数对激光跟踪仪全程ADM测距误差进行修正,并与线性误差修正方法进行了对比,结果显示三次样条函数能够更好地拟合误差曲线,改善修正后残余误差的均方差,均方差为0.007 mm,优于最小二乘直线拟合,从而提高激光跟踪仪测距精度和空间测量精度。     

金属电子背散射衍射试样的制备技术

电子背散射衍射样品的制备质量对其成像效果的影响至关重要,着重介绍了几种有效的样品制备方法.试验证实,与其他方法相比,机械-化学抛光法具有设备简单、易操作及效果明显等优点.     

Mapping microstructure inhomogeneity using electron backscatter diffraction in 316L stainless steel subjected to hot plane strain compression tests

Abstract

The microstructure inhomogeneity in 316L stainless steel subjected to hot plane strain compression tests has been assessed using electron backscatter diffraction (EBSD). Two variables were investigated: the effect of strain rate and the effect of friction at the tool/specimen interface. Tests were performed isothermally at 950°C at nominal equivalent tensile strain rates of 0·01 and 1 s^?1. Low and high friction conditions have been simulated by applying both a glass based lubricant and a boron nitride spray respectively. Results suggest that friction causes a variation in microstructure from the surface to the midplane of the deformed specimen. Several methods used to quantify and represent this inhomogeneity are presented in the present paper. Electron backscatter diffraction measurement issues are discussed. A grain size mapping method using a two-dimensional moving average has been developed to overcome the difficulties associated with the visualisation of measurement results over large areas on EBSD maps. It has proved to be a powerful tool for the spatial statistics of large quantity data obtained by EBSD.     

Solution of the second-order one-dimensional hyperbolic telegraph equation by using the dual reciprocity boundary integral equation (DRBIE) method

In this paper, we use a numerical method based on the boundary integral equation (BIE) and an application of the dual reciprocity method (DRM) to solve the second-order one space-dimensional hyperbolic telegraph equation. Also the time stepping scheme is employed to deal with the time derivative. In this study, we have used three different types of radial basis functions (cubic, thin plate spline and linear RBFs), to approximate functions in the dual reciprocity method (DRM). To confirm the accuracy of the new approach and to show the performance of each of the RBFs, several examples are presented. The convergence of the DRBIE method is studied numerically by comparison with the exact solutions of the problems.     

大变形复合材料薄板多体系统动力学建模

本文对大变形复合材料薄板的多体系统动力学建模方法进行研究。基于Kirchhoff假设,法线与中面保持垂直,从格林应变的表达式出发,建立了面内应变和曲率与绝对位置坐标和斜率的关系,在此基础上推导了广义弹性力阵和弹性力阵对广义坐标的导数阵,用绝对节点坐标方法建立了大变形复合材料薄板多体系统的动力学方程,用广义法和和牛顿迭代法求解微分-代数混合方程。对外载荷作用下的复合材料薄板进行数值仿真,通过与ANSYS的仿真结果进行对比,验证了本文建模方法的准确性和快速收敛性。最后,将建模方法应用于复合材料太阳帆板展开机构的数值仿真,分析了不同铺层情况下驱动力和约束力的振动特性。     

Theoretical prediction of welding distortion in large and complex structures

Welding technology is widely used to assemble large thin plate structures such as ships, automobiles, and passenger trains because of its high productivity. However, it is impossible to avoid welding-induced distortion during the assembly process. Welding distortion not only reduces the fabrication accuracy of a weldment, but also decreases the productivity due to correction work. If welding distortion can be predicted using a practical method beforehand, the prediction will be useful for taking appropriate measures to control the dimensional accuracy to an acceptable limit. In this study, a two-step computational approach, which is a combination of a thermoelastic-plastic finite element method (FEM) and an elastic finite element with consideration for large deformation, is developed to estimate welding distortion for large and complex welded structures. Welding distortions in several representative large complex structures, which are often used in shipbuilding, are simulated using the proposed method. By comparing the predictions and the measurements, the effectiveness of the two-step computational approach is verified.     

Five‐Parameter Grain Boundary Analysis by 3D EBSD of an Ultra Fine Grained CuZr Alloy Processed by Equal Channel Angular Pressing

The 3D grain boundary character distribution (GBCD) of a sample subjected to equal channel angular pressing (ECAP) after eight passes and successive annealing at 650 °C for about 10 min is analyzed. The experiments are conducted using a dual beam system, which is a combination of a focused ion beam and a scanning electron microscope to collect a series of electron backscatter diffraction (EBSD) maps of the microstructure (3D EBSD). The data set was aligned and reconstructed to a 3D microstructure. The crystallographic character of the grain boundary planes was determined using three different methods, namely, the line segment method, the stereological method, and the triangular surface mesh method. The line segment and triangular surface mesh methods produce consistent data sets, both yielding approximately a 7% area fraction of coherent twins. These results starkly contrast that of the statistical stereological method, which produced a 44% area fraction of coherent twins.     

Theoretical prediction of welding distortion in large and complex structures

Welding technology is widely used to assemble large thin plate structures such as ships, automobiles, and passenger trains because of its high productivity. However, it is impossible to avoid welding-induced distortion during the assembly process. Welding distortion not only reduces the fabrication accuracy of a weldment, but also decreases the productivity due to correction work. If welding distortion can be predicted using a practical method beforehand, the prediction will be useful for taking appropriate measures to control the dimensional accuracy to an acceptable limit. In this study, a two-step computational approach, which is a combination of a thermo-elastic-plastic finite element method (FEM) and an elastic finite element with consideration for large deformation, is developed to estimate welding distortion for large and complex welded structures. Welding distortions in several representative large complex structures, which are often used in shipbuilding, are simulated using the proposed method. By comparing the predictions and the measurements, the effectiveness of the two-step computational approach is verified.     

Bending analysis of functionally graded annular sector plates by extended Kantorovich method

The small deflection equation for isotropic and non-homogenous thin annular sector subject to transverse loading is derived in polar coordinate. The Poisson’s ratio of the plate is assumed to be constant, but the Young’s modulus varies continuously through the radial direction according to the power-law function. A closed-form solution with fast convergence rate is obtained using the extended Kantorovich method and the classical theory of thin plates (Kirchhoff theory). The validity and accuracy of results are examined by resolving the problem using commercial finite element code ABAQUS and a good agreement between them is obtained for either deflection or stress resultants.