基于相场方法的铁基合金高温氧化与生长应力分析

高温氧化性能是评价热防护材料的一项重要指标,然而由于氧化过程是一个含微结构演化的复杂过程,其定量计算分析一直是研究的难点．基于材料热力学理论,建立了能够考虑微结构演化的相场方法来模拟材料的高温氧化,从而解决了抗氧化性能与氧化生长应力定量计算分析的问题．采用所建立的相场方法,对Fe-Cr-Al-Y合金的高温扩散过程、氧化性能和生长应力演化进行了计算,数值计算结果与文献中的实验结果吻合良好,计算结果还揭示了最大生长应力和外界环境氧浓度之间的线性关系．所发展的相场方法为研究复杂环境下的高温氧化提供了一种有力的计算分析手段．     

具有初应力的1-3型压电复合材料的横向共振分析

1-3型压电复合材料在极化处理过程中会出现极化残余应力,基于线性压电理论,采用解析方法研究了极化残余应力对1-3型压电复合材料的横向共振模态的影响．首先建立含有初始应力的平面波波动方程,基于Bloch波函数理论构建了位移和电势函数,从而最终得到方程的解．数值结果表明初始残余应力的出现降低了复合材料的横向振动频率,而材料的压电性则使得横向振动频率提高．初始剪应力对对横向振动的频率影响较小,可以忽略．第一阶及第二阶振动频率将随着初始应力的大小呈线性变化．得出的结论对超声换能器的制作和研究将提供有意义的指导作用．     

多边形应力杂交单元的接触算法研究

针对单元较小的情况下,现有的非均匀模型难以得到精确应力场和应力集中现象的问题,采用直接约束法,提出了一种基于多边形应力杂交单元的优化接触算法.多边形应力杂交单元在应力函数的构造以及积分区域划分上的优势,使其能适应复杂的模型边界与材料边界,更易划分网格.根据上述理论研究成果编制了完整的计算程序,算例结果发现该方法能够得到粉末压制过程的宏观非线性力学响应、高精度的应力场以及明显的应力集中现象,为复杂优化问题的求解提供了有效手段.     

双材料接合半无限体三维矩形界面裂纹应力强度因子分析

基于体积力法,研究了双材料接合半无限体三维矩形界面裂纹的应力强度因子问题．在数值计算中,未知的体积力密度采用基本密度函数和多项式乘积的形式来近似,其中基本密度函数是根据界面裂纹应力的振荡奇异性来选取的．计算结果表明,基于本算法得到的数值结果其收敛精度和计算误差都是令人满意的．算例中,给出了应力强度因子随矩形形状及双材料参数的变化规律．     

加捻纤维复合材料三维残余应力分析

本文提供一种对于含有加捻纤维束的复合材料由于固化而产生的热残余应力的分析研究.纤维束中的纤维经过加捻产生了一种螺旋形状,这种形状所产生的三维热弹性力学问题可以利用能量法获得解答.这个问题的热残余应力场可以表示为纤维、基体材料的性质以及纤维束几何参数的函数.纤维/基体界面上的残余应力(包括环向和径向的应力)都可以从这些分析中得到.本文分析的结果表明:加捻纤维束构成的复合材料,由于纤维的适当加捻,可以减弱由于纤维与基体各具不同的热膨胀系数而产生的热固化残余应力.     

梯度材料平板弯拉耦合力学的精确化支配方程

基于非均匀材料弹性力学理论,采用算子谱分解和算子代数方法,对梯度材料平板结构弯曲与拉伸问题进行了研究.首次给出了指数梯度材料平板弯曲与拉伸的力学方程.研究结果表明:与各向同性平板结构弯曲和拉伸问题不同,在功能梯度平板中描述弯曲应力状态与描述拉伸应力状态的广义位移函数以及剪切函数都是耦合的.没有采用工程假设,推导得到的梯度材料平板结构力学方程是精确化的.通过分析可以认识和理解,分别对应于弯曲状态与拉伸状态的应力场耦合机理以及力学响应的构成等.给出的方程及其分析过程可望能够用于类平板形式热防护材料结构的应力分析与强度设计,推进热防护材料结构的轻型化.     

残余界面应力对粒子填充热弹性纳米复合材料有效热膨胀系数的影响

根据黄筑平等人提出的基于“3个构形”的表/界面能理论,研究了热弹性纳米复合材料的有效性质,重点讨论了残余界面应力对纳米尺度夹杂填充的热弹性复合材料有效热膨胀系数的影响．首先,给出了由第一类Piola-Kirchhoff界面应力表示的热弹性界面本构关系和Lagrange描述下的Young-Laplace方程;其次,采用Hashin复合球作为代表性体积单元,推导了在参考构形下复合球内部由残余界面应力诱导的残余弹性场,并进一步计算了从参考构形到当前构形的变形场;最后,基于以上计算得到了热弹性复合材料有效体积模量和有效热膨胀系数的解析表达式．研究表明,残余表/界面应力对复合材料的热膨胀系数有重要影响．     

人体动脉瘤生成与破裂的力学分析

在大变形超弹性理论框架下研究了内压、轴向拉伸和扭转联合作用下人体动脉壁的力学响应,应用结构不稳定性理论对动脉瘤生成的可能性进行了解释,应用材料强度理论对动脉瘤破裂的可能性进行了分析．考虑动脉壁中残余应力和平滑肌主动作用的影响,用纤维加强各向异性不可压超弹性复合材料两层厚壁圆筒模型来模拟动脉壁的力学特性．给出了正常和几种非正常状态下动脉壁的变形曲线和应力分布．变形和稳定性分析结果表明该文模型可以模拟正常状态下动脉壁的均匀变形,还可以模拟在动脉壁中弹性蛋白纤维和胶原蛋白纤维强度降低的非正常状态下动脉瘤生成的可能性及动脉瘤的增长．应力和强度分析结果表明该文模型可以模拟当动脉瘤中的最大应力超过管壁的强度时动脉瘤破裂的可能性．     

任意形状孔口单边裂纹问题的边界配位解法

本文提出了一组复应力函数,采用边界配位方法对不同形状孔口(包括圆、椭圆、矩形及菱形孔口)的单边裂纹平板的应力强度因子进行了计算.计算结果表明,对长度和宽度远大于孔口和裂纹几何尺寸的试件,配位法与用其他方法所得的无限大板含圆或椭圆孔边裂纹问题的解符合得很好.同时,对其他孔口问题,特别是有限大板情形,本文给出了一系列计算结果.本文所提出的函数及计算过程可以应用于任意形状孔口单边裂纹平板的计算.     

基于孔洞分布理论的多孔材料板振动分析

主要研究了不规则几何结构多孔材料制备的板材的振动分析．基于Gibson-Ashby等效模量计算,引入了分布因子加以改进原有的理论．对于材料的孔洞分布情况,提出了Burr分布的概率密度拟合,获得了Burr分布的3个自变量参数并用实际的孔洞几何参数进行了比对与描述．基于平板振动理论和等效模量理论,计算出了随着孔洞分布情况变化下的平板固有振动频率,并分析了孔洞尺寸与频率间的关系．之后引入了尺度因子来量化描述平均孔洞尺寸对多孔平板的频率影响．结论证明了改进的等效理论能够有效地体现孔洞的分布对平板力学性能的改变,论述了孔洞尺寸范围,孔洞离散度以及平均孔洞尺寸对多孔方板结构固有频率的影响．这种影响将会对多孔材料结构的优化设计起指导作用．     

Determination of the residual stresses in the welded joints of glass structures

We propose a computational model for determining the residual stresses in a welded glass structure taking account of the properties of the formation of residual stresses in glass. The problem is solved in displacements using Galerkin's method in conjunction with a finite-element model. A numerical solution is obtained for the axisymmetric case. Translated fromMatematichni Metodi ta Fiziko-mekhanichni Polya, Vol. 39, No. 1, 1996, pp. 131–134.     

Experimental study of the effect of technological parameters on the residual stresses in thin-walled coiled parts

The effect of the parameters of heat treatment and programmed winding under tension on the residual stresses in thin-walled coiled parts made from glass plastic by the "dry" winding of a heated glass strip on an unheated mandrel is studied experimentally. The effect of the thickness of the parts on the maximum radial residual stresses is considered. A method is proposed for regulating the residual stresses in parts with very thick walls.Translated from Mekhanika Polimerov, No. 1, pp. 75–80, January–February, 1972.     

Delamination of Grain-Interfaces in Silicon Nitride

Intergranular cracking due to delamination of grain interfaces along with the development of bridging grains is the most important mechanism for the high fracture toughness of silicon nitride. In this line, an interface behavior, which is extending the Coulomb friction concept into the tensile domain has been implemented into a thermodynamical consistent frame work of Helmholtz free energy and dissipation. The model is used to describe the fracture process in a simple model geometry with a β-Si₃N₄ grain embedded into a precracked matrix of oxynitride glass. The material model considers the thermoelastic anisotropy of the grain and the thermal residual stresses, which evolve during the cooling of the model from the glass transition temperature to room temperature. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Sensitivity of Residual Stresses of Cross-Ply Laminates to Manufacturing and Material Parameters

By using a finite-element model elaborated, the sensitivity of residual stresses of polyester/glass cross-ply laminates to manufacturing and material parameters is investigated. The development of residual stresses in the laminates and the significance of the parameters for the problem are discussed. It is found that the main attention in calculating residual stresses should be focused on the properties of resin, which must be measured with care. The most important parameters related to the resin are, of course, its stiffness, thermal expansion, and chemical shrinkage, while the properties of fibers can be obtained from material handbooks with a sufficient accuracy. In curing a thin laminate in an autoclave, the simulation of chemical reactions and the parameters needed in thermal analysis are quite insignificant, because, in practice, the autoclave temperature and the properties of the mold determine the laminate temperature history.     

Modeling and numerical study of thermal-compression bonding in the packaging process using NCA

Packaging technology used in liquid crystal displays (LCDs) faces the critical issues such as high density interconnects, thinner packaging size, and environmental safety. In order to reduce the packaging size, driver integrated circuit (IC) chips are directly attached to LCD panels using flip chip technology with adhesives, which is called chip on glass (COG) packaging processes. To investigate the effects of the bonding force and bonding temperature on the flip chip thermal-compression packaging, this study established a compression model to analyze the flip chip packaging processes with non-conductive adhesives (NCAs). The plastic deformation of bumps and the NCA flow dynamics between chip and substrate were taken into account in this model. The gap height, bump deformation, bump contact area, and residual stresses after bonding can be estimated with this model.According to the simulation in this work, the best tactic for the flip chip packaging process using NCA is bonded at a lower temperature. This reduces the maximum warpage and only slightly decreases the average compressive residual stress in the bottom of bumps. A larger bonding force results in a larger bump contact area with the substrate, but has a lower compressive residual stress at the contact areas. The bonding force during the flip chip thermal bonding process will affect the contact resistance and reliability of packaging at the same time.     

Residual stresses in plastic rings reinforced with glass and manufactured with consolidation of the various layers

The residual stresses in thin-wall plastic rings reinforced with glass and prepared by the method of consolidating the layers in combination with various winding regimes have been studied experimentally. It is shown that variation of the winding regime from one layer to another can change the distribution of the stresses through the thickness of the ring.Moscow Energy Institute. Translated from Mekhanika Polimerov, No. 1, pp. 174–176, January–February, 1972.     

Microsopic Simulation of Thermally-Induced 2nd Order Eigenstresses in AlSi-Alloys

Due to the different coefficients of thermal expansion of aluminium and silicon, high residual stresses of second order occur in Al-Si alloys depending on the cooling rate during the molding process. In products as for example crank cases made of Al-Si alloys these residual stresses may cause microcracks. In the work at hand measurements of the eigenstresses in the single phases (i.e. residual stresses of second kind) performed via neutron diffractometry are compared to numerical simulations for a specific cooling rate. To this end a three-phase model is presented, which considers the α aluminium, the eutectic aluminium, and the silicon particles. The presented model is able to predict the residual stresses in the single phases within an elastoplastic framework. The simulation of tensile loadings of these structures are compared to experiments. The numerical computations are carried on stochastic geometry models by using a fast solver [1] for the Lippmann-Schwinger integral equation, which is based on the fast Fourier transformation. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Calculation of the residual stresses and strains in wound reinforced-plastic products

A method is proposed for determining the residual stresses and strains in wound glass-reinforced plastic products. The fabrication process is divided into five stages: winding, heating polymerization, cooling, and removal from the mandrel. The initial stresses that develop during winding and the subsequent stress increment associated with heating are taken into account. Polymerization is treated as a process during which the mechanical and thermophysical properties of the material change. Chemical shrinkage of the resin and its filtration through the fiberglass are disregarded. Equations are derived for the residual radial and peripheral stresses in the finished product, for the residual change in inside diameter, and for the temperature at which the product is released from the mandrel during the cooling process. The experimental data relating to two types of wound products are discussed. The results of a computation of the residual stresses and the residual changes in inside diameter are compared with the experimental data.Moscow Power Engineering Institute. Translated from Mekhanika Polimerov, Vol. 5, No. 1, pp. 134–139, January–February, 1969.     

Lamb Problem for a Half-Space Covered with a Two-Axially Prestretched Layer

Within the framework of a piecewise homogeneous body model, with the use of the three-dimensional linearized theory of elastic waves in initially stressed bodies, an approach for investigating the Lamb problem for a half-space covered with a layer is developed. It is assumed that the half-space and the cover layer have two-axial initial stresses operating parallel to the layer plane. To the free face of the layer, a normal point force changing harmonically with time is applied. For solving the corresponding boundary value problems, the double-exponential Fourier transformation is employed. An algorithm for obtaining numerical results is proposed, which is examined in particular cases. Numerical results for the influence of prestretching the cover layer on the interfacial stresses are presented.