颗粒缺陷相互作用下复合材料的细观损伤模型

含尖角的非椭球颗粒附近应力集中较大,诱导缺陷形成裂纹是材料损伤的重要来源.对于强界面颗粒,大刚度颗粒诱导裂纹向基体中扩展形成近似平面片状裂纹,认为诱导裂纹受颗粒应力附近应力场控制,基于有效自洽理论建立了材料细观损伤模型,得到了单向拉伸下的损伤演化,并分析了颗粒形状、尺寸、颗粒性能以及颗粒与初始缺陷相对位置等因素对材料损伤的影响.结果表明,非椭球颗粒更易诱发裂纹,同样外载应力下,损伤程度更大,含非椭球颗粒材料强度更低;含扁平型的颗粒材料裂纹损伤过程更加明显并且材料强度更大;提高颗粒刚度和含量能够增大材料强度.材料中存在尺寸过大或过小的初始裂纹时材料损伤过程不明显.     

冲击荷载作用下混凝土材料的细观本构模型

将混凝土材料看成是水泥砂浆基体和粗骨料颗粒组成的2相复合材料,假设水泥砂浆基体和粗骨料颗粒均为弹性、均匀、各向同性的,粗骨料颗粒为球形。基于Mori-Tanaka理论和Eshelby 等效夹杂理论推出了混凝土材料弹性模量的计算公式。在Horii和Nemat-Nasser提出的脆性材料在双轴向压应力作用下破坏的滑移裂纹模型基础上,运用细观力学方法推导了微裂纹对材料弹性模量的弱化作用以及微裂纹的损伤演化方程。建立了混凝土材料在冲击荷载作用下的一维动态本构模型,模拟曲线与实验曲线符合良好,因而可以用该模型模拟混凝土材料在冲击荷载下的动态特性。     

含随机分布微裂纹的相变颗粒增韧陶瓷材料的强度和刚度预报

本文针对相变颗粒增韧陶瓷基复合材料中存在大量微裂的现象，分析了微裂纹产生的原因，利用作者改进的等效平杂理论，研究了相变陶瓷中微裂纹对材料强度与刚度的影响，通过与Ａｌ２Ｏ３／ＺｒＯ２陶瓷的三点弯曲实验结果的比较表明，理论与实验结果十分接近，说明本文理论模型是合理的，同时也证明了微裂纹对相变陶恣材料的重要影响。     

2124 Al/SiC_p复合材料的动态变形行为及微结构效应

研究了在动态压缩时２１２４Ａｌ／ＳｉＣｐ复合材料的变形行为与微结构效应．分析结果表明，对于给定材料，复合材料的流动应力主要取决于微结构尺度效应．若增强相尺寸，基体晶粒尺寸以及增强相间距三者大小相当，则复合材料的流动应力取决于增强相的分散程度和位错密度；若增强相尺寸及其间距大小相当，但比基体晶粒大得多，那复合材料的流动应力主要取决于增强相的分散度．微观观测发现在同样加载条件下，变形局部化更容易在含较小碳化硅颗粒的复合材料内形成；变形区内的微损伤几乎都是基体与粒子界面脱粘和粒子角点邻近的微裂纹．对于所研究的这类复合材料，弹性模量及应变硬化几乎不受增强颗粒尺寸影响．     

晶须增韧陶瓷基复合材料中微裂纹演化规律的描述

本文利用作者改进的等效夹杂理论和内容量理论，研究了晶须增韧陶瓷基复合材料中随机分布微裂纹的演化规律及其对材料力学性能的影响，同时考虑了热残余应变、晶须含量及长径比的影响，预报了材料的模量、非线性起始点、材料强度及非线性本构关系，给出了许多有意义的结论。     

含旋转椭球形夹杂复合材料的弹塑性本构关系

在体胞模型的基础之上应用解析方法分析了颗粒或短纤维增强复合材料的本构行为，结合数值计算给出了表征材料本构关系的解析表达式，提出了一种新的正交椭球坐标变换以简化推导过程，在计算中，将真实位移场分为两部分：基本场的扰动场，然后通过摄动方法将原来的非线性问题转化为一组线性方程组的求解，计算了当基体材料和夹杂的特征参数取不同值时的应力应变曲线，并与已有的实验和分析结果进行了比较，符合得较好，通过对数值计算结果的拟合，提出了一个颗粒或短纤维增强复合材料的弹塑性本构关系的解析表达式。     

近片层γ-TiAl基合金宏观屈服的微观表征

将近片层-γTiAl基合金视为以等轴γ颗粒为基体,PST颗粒为夹杂的两相复合材料,基于细观力学自洽理论,对合金的有效弹性模量及基体和夹杂中的应力和应变场进行了解析分析计算,并结合细观力学的宏细观关联方法,确定了近片层-γTiAl基合金的宏观屈服的微观表征.结果表明:夹杂颗粒中的应力和应变场与外载及夹杂的体积分数f和椭球长细比ρ有关,软取向PST夹杂颗粒的微变形屈服导致近片层-γTiAl基合金材料的整体宏观屈服.     

粉末冶金材料各向异性连续型损伤模型研究

在采用微裂纹扩展区描述脆性材料损伤状态的基础上,通过引入颗粒度大小和微裂纹概率分布密度函数来研究粉末冶金材料特征体积单元的损伤演化.同时结合Hill自洽模型采用空间混合平均的方法,可考虑粉末冶金材料的微结构特征及微裂纹间相互作用的影响,可描述粉末冶金类材料的各向异性连续型损伤.     

动载荷作用下微裂纹的增韧分析

在实验研究的基础上，将细观统计力学应用于材料的动态增韧分析中，探索性的研究了在动态载荷作用下微裂纹的增韧机理，并进行了相应的有限元分析计算，得出在动载荷作用下，微裂纹增韧主要表现在微裂纹的快速成核。如果要提高材料在动态情况下的增韧幅值，必须提高增韧颗粒的特征尺寸。     

陶瓷颗粒增强金属基复合材料的细观强度分析

陶瓷颗粒增强金属基复合材料的失效主要有界面脱粘、增强粒子开裂等新的细观结构损伤机制。为了减小这些不足并对细观失效过程有一个清晰的了解,近来人们对金属基复合材料进行了大量研究,在此基础上,本文用细观力学的方法和损伤模型研究了陶瓷颗粒增强金属基复合材料的强度和损伤失效。为了计算方便,陶瓷颗粒简化为在复合材料中随机分布的椭球形粒子,然后以二相胞元模型计算分析了金属基体、颗粒中的应力应变分布情况,结果表明,基体中应力极不均匀,界面区存在应力集中,并计算了界面弧形裂纹扩展时的能量。最后分别提出了基体,颗粒和界面的失效强度准则,本文结果对于颗粒增强金属基复合材料具有普遍的实用性。     

细长椭球体在水中自由下落的运动特性实验研究

固体颗粒在液体中的运动现象在日常生活和工业应用领域广泛存在, 其中因蕴含着丰富的流体力学现象而受到学者们的广泛关注. 本文通过实验研究了细长椭球体在水中受浮力影响的下落特性. 实验中采用带有两台相互垂直的高速摄像机和光源组成的运动跟踪平台并结合荧光染色技术对细长椭球体下落过程中的运动轨迹和尾涡结构进行研究. 文中选用的细长椭球体与环境流体的密度比为1.2, 其长短轴比范围为2$\sim $10, 相应的阿基米德数范围为400$\sim$1400, 对应实现的终态雷诺数范围为120$\sim$1350. 实验过程中我们观察到细长椭球体在水中下落过程中产生的5种典型路径, 分别为: 小振幅不规则运动、小振幅高频振荡运动、大振幅低频振荡运动、高度非线性运动以及直线运动, 并得到了对应的速度振荡以及倾斜角的演化规律. 进一步地, 分析了细长椭球体运动过程中受到的阻力系数与雷诺数之间的关系. 随后采用荧光可视化技术清晰获得了颗粒下落过程中的尾涡结构特性, 并结合颗粒的运动状态详细分析了涡脱落过程对颗粒运动状态转捩的影响. 最后, 通过对比前人关于圆柱体下落的运动特性的相关结果, 获得了细长椭球体和细长圆柱体运动特性之间的异同点以及其潜在的物理机理.      

实时测算阻尼比研究转动惯量

以``长摆线三线摆'为物理动力学模型, 采用拉格朗日第二类方程研究阻尼对工件 转动惯量测量的影响, 针对``振幅测量法'中很难测准摆幅幅值等实际问题,提出 一种``等弧--时间比法', 即通过计算悬盘在不同周期内、在相同位 置摆过相等圆弧所用时间比来计算系统阻尼比$\zeta$的方法, 提高外形尺寸较大 工件的转动惯量测量精度.     

Stresses in an elastic circular cylinder with a prolate spheroidal cavity under torsion

This paper contains an exact solution for the stresses arising from torsion of an elastic circular cylinder with a prolate spheroidal cavity. The solution, which is represented as a combination of a solution that is regular outside the cavity and a solution regular in the solid infinite circular cylinder, is deduced with the aid of a harmonic displacement potential. The two harmonic functions needed are given by simple expressions referred to cylindrical and prolate spheroidal coordinates. The boundary conditions on the surfaces of the cylinder and of the cavity are satisfied by using the relations between cylindrical and prolate spheroidal harmonics. Numerical results are presented for different shapes and sizes of the cavity, and the ensuing stress distribution in the neighborhood of the cavity is illustrated graphically.     

绕椭球的低速流动研究

理解和预测绕椭球的流动对指导飞行器和潜艇等交通工具的设计具有很强的工程意义. 近年来, 针对椭球绕流开展了大量的实验和数值模拟研究. 对有攻角下椭球绕流分离的定性描述和定量研究, 促进了对三维分离的辨识和拓扑研究. 文章对流场特性进行了分析, 介绍了分离对气动力、噪声、尾迹的影响, 以及实验条件对流动的影响. 上述定常流动与非定常机动过程之间存在明显差异, 非定常机动过程不能作为定常或准定常问题处理, 在机动过程中, 分离出现明显延迟, 气动力出现明显变化. 随后介绍了数值模拟在求解绕椭球流动中的进展, 当前求解雷诺平均的N-S方程湍流模式仍然是解决绕椭球大范围分离流动的主要工程方法, 大涡模拟和分离涡模拟等也逐渐得到了广泛应用. 受限于计算能力, 直接数据模拟只能用于较低雷诺数, 在高雷诺数流动中还不适用. 非定常机动过程的数值模拟较定常状态, 与实验结果的差距要大一些. 最后, 介绍了对椭球绕流场转捩的研究进展, 对T-S转捩与横流转捩的机理和辨识已经较为准确, 数值模拟结果与实验结果基本相符, 但对再附转捩的认识还不够清晰, 尤其是迎风面, 因此椭球绕流转捩的研究还需要依靠实验.      

The stokes flow of an arbitrary prolate axisymmetric body towards an infinite plane wall

By distributing continuously the image Sampsonlets with respect to the plane and by applying the constant density, the linear and the parabolic approximation, the analytic expressions in closed form for flow field are obtained. The drag factor of the prolate spheroid and the Cassini oval are calculated for different slender ratios and different distances between the body and the plane. It is demonstrated that the proposed method is satisfactory both in convergence and accuracy. Comparison with existing results in the case of prolate spheroid shows that the coincidence is quite good.     

Void-shape effects on strength properties of nanoporous materials

In this paper, strength properties of nanoporous materials with spheroidal nanocavities are investigated via a Molecular Dynamics approach applied to a nanovoided aluminium single crystal, in the case of a fixed porosity level, and for prolate, oblate and spherical void shapes. Estimates of the effective strength domain are provided, by considering several mechanical loadings including axisymmetric and shear strain-rate states. Void-shape effects are quantified for different values of the void aspect ratio, mainly resulting in an overall weakening of the sample as the spheroidal nanovoid assumes either an oblate or a prolate shape, in comparison to the case of a spherical void. Finally, it is observed that the computed strength profiles exhibit the following specific features: (i) a strong dependence on the hydrostatic, second-order and third-order deviatoric stress invariants, (ii) more significant void-shape effects for triaxial-expansion stress states with a small hydrostatic component, and (iii) a more pronounced influence of the spheroid shape, as the aspect ratio is varied, in the presence of an oblate nanovoid rather than of a prolate one.     

The linear approximation of the line continuous distribution method of singularities in creeping motion

The linear approximation of the line continuous distribution method of singularities is proposed to treat the creeping motion of the arbitrary prolate axisymmetrical body. The analytic expressions in closed form for the flow field are obtained. The numerical results for the proiate spheroid and Cassini oval demonstrate that the convergence and the accuracy of the proposen method are better that the constant density approximation. Furthermore, it can be applied to greater slender ratio. In this paper the example is yielded to show that the linear approximation of the singularities for the density on the partitioned segments can be utilized to consider the creeping motion of the arhitrary pointed prolate axisymmetrical body.     

The orientation dynamics of small prolate and oblate spheroids in linear shear flows

The present work deals with the stable orientation of oblate and prolate spheroids in general steady linear flows and with the mode of convergence to these stable orientations. The orientation dynamics is governed by the Jeffery equation. The stable orientations are either fixed points or limit cycles in the orientation space. The type of stable orientation depends on whether the eigenvalues of the linear part of Jeffery equation are real or complex. We define prolate and oblate spheroids to be equivalent if the aspect ratio of one is the reciprocal of the other. We show that, in a given flow, equivalent oblate and prolate spheroids possess the same number of fixed points and limit cycles of which only one is stable. If they possess only fixed points, then their corresponding stable fixed points are orthogonal. If they possess one fixed point and one limit cycle each, then the stable fixed point of one is orthogonal to the plane of the limit cycle of the other. The rate of convergence to these attractors is important to consideration of the orientations in time-space varying flow fields. We show that non-normal growth (NNG) of the distance to these attractors may delay the convergence by several characteristic shear time scales. We derive conditions for occurrence of NNG and explicit expressions for the maximal duration of the growth. We consider a specific case of which the vorticity is a stable orientation of prolate spheroids. We analyze the conditions that imply monotonic or, conversely, non-monotonic convergence to this orientation due to NNG. We thereby find the corresponding conditions for convergence of the equivalent oblate spheroids to their attractors, normal to the vorticity. We show that the convergence is monotonic if the vorticity is parallel to the strain tensor’s largest eigenvector, but that NNG occurs if the vorticity is parallel to the strain tensor’s intermediate eigenvector. The NNG duration decreases with increasing vorticity-strain ratio and with the strain intermediate eigenvalue approaching the largest eigenvalue.     

Particle shape effect on hydrodynamics and heat transfer in spouted bed: A CFD–DEM study

Spouted bed has drawn much attention due to its good heat and mass transfer efficiency in many chemical units. Investigating the flow patterns and heat and mass transfer inside a spouted bed can help optimize the spouting process. Therefore, in this study, the effects of particle shape on the hydrodynamics and heat transfer in a spouted bed are investigated. This is done by using a validated computational fluid dynamics–discrete element method (CFD–DEM) model, considering volume–equivalent spheres and oblate and prolate spheroids. The results are analysed in detail in terms of the flow pattern, microstructure, and heat transfer characteristics. The numerical results show that the prolate spheroids (Ar = 2.4) form the largest bubble from the beginning of the spouting process and rise the highest because the fluid drag forces can overcome the interlocking and particle–particle frictional forces. Compared with spherical particles, ellipsoidal spheroids have better mobility because of the stronger rotational kinetic energy resulting from the rough surfaces and nonuniform torques. In addition, the oblate spheroid system exhibits better heat transfer performance benefiting from the larger surface area, while prolate spheroids have poor heat transfer efficiency because of their orientation distribution. These findings can serve as a reference for optimizing the design and operation of complex spouted beds.     

COUPLING EFFECTS OF VOID SHAPE AND VOID SIZE ON THE GROWTH OF AN ELLIPTIC VOID IN A FIBER-REINFORCED HYPER-ELASTIC THIN PLATE

The growth of a prolate or oblate elliptic micro-void in a fiber reinforced anisotropic incompressible hyper-elastic rectangular thin plate subjected to uniaxial extensions is studied within the framework of finite elasticity. Coupling effects of void shape and void size on the growth of the void are paid special attention to. The deformation function of the plate with an isolated elliptic void is given, which is expressed by two parameters to solve the differential equation. The solution is approximately obtained from the minimum potential energy principle. Deformation curves for the void with a wide range of void aspect ratios and the stress distributions on the surface of the void have been obtained by numerical computation. The growth behavior of the void and the characteristics of stress distributions on the surface of the void are captured. The combined effects of void size and void shape on the growth of the void in the thin plate are discussed. The maximum stresses for the void with different sizes and different void aspect ratios are compared.