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.     

预测纳米纤维复合材料有效弹性性能的界面模型和界面相模型北大核心CSCD

基于广义自洽法,同时采用Gurtin-Murdoch界面模型和界面相模型研究了纳米纤维复合材料的有效弹性性能,获得了两种模型下有效体积模量的封闭解析解和计算有效面内剪切模量数值解的全部公式.基于界面模型的解答,讨论了有效体积模量和有效面内剪切模量的界面效应.证明了界面模型的解答可由界面相模型的解答退化得到,其中有效体积模量可以实现解析退化,有效面内剪切模量则可以数值退化.以含纳米孔洞的金属铝为例,比较了两种模型计算结果的差异.结果表明,当纳米孔洞半径较小时,两个模型的结果存在很大差异,而当半径较大时两个模型的结果差别不大.     

空心球复合材料热弹性性质的一些精确结果

本文基于所提出的基体均匀场方法研究了空心球增强复合材料的热弹性性质·导出了均匀边界条件激发的局部热场和力学场量的关系，并进而得到了复合材料等效热弹性性质之间的精确关系·对于具有某种特定内外径比的空心球所构成的宏观各向同性复合材料，如果基体和空心球的热膨胀系数相同，可以证明其等效体积模量和线膨胀系可以精确地确定·     

高体积百分比颗粒增强聚合物材料的有效粘弹性性质

聚合物材料通常表现为粘弹性性质．为了改进聚合物材料的力学性能,通常将某种无机材料以颗粒或纤维的形式填充到聚合物中,从而得到增强、增韧的聚合物基复合材料．提出了一个新的细观力学模型,用于预测颗粒增强聚合物复合材料的有效粘弹性性质,尤其针对高体积百分比的颗粒夹杂复合材料,该方法基于Laplace变换和双夹杂相互作用的弹性模型．计算了玻璃微珠/ED-6复合材料的有效松弛模量以及恒应变率下的应力应变关系．计算结果表明在高体积百分比下该文方法比基于Mori Tanaka方法预测的粘弹性效应明显减弱．     

复合材料弹性结构的高精度多尺度算法与数值模拟

１．引言 由于复合材料结构物理参数的非均匀各向异性以及细部几何构形的复杂性,在计算它的位移场、应力、应变场时,传统的有限元法因网格生成困难和计算规模太大而难以实现．７０年代初,Ｉ．Ｂａｂｕｓｋａ,Ｊ．Ｌ．Ｌｉｏｎｓ等人针对复合材料弹性结构提出了均匀化方法,见文［１］,数值实验表明,均匀化方法对描述复合材料弹性结构的有效材料常数及刚度性质是有效的,但它不能刻画应力和应变场的局部变化,因而作为复合材料强度理论的判断依据,均匀化理论显然是不够的．为此,Ｊ．Ｌ．Ｌｉｏｎｓ,Ｏ．Ａ．Ｏｌｅｉｎｉｋ等分别就…     

颗粒增强复合材料热应力分析的双层嵌套模型

建立了一个把增强颗粒球和基体空心球嵌入等效复合介质空腔中的“双层嵌套模型”,研究了颗粒增强材料自高温冷却下来时,不同相中热应力的分布特点。推出了热应力在弹性和弹塑性状态的各种表达式。研究表明,随着温度降低,增强体受到压应力,基体材料中存在的静水应力为拉应力。温度继续下降,将出现自增强颗粒与基体界面向外扩展的屈服区。随增强相体积分数增大,增强颗粒受到的压应力和基体中的静水拉应力减小,增强颗粒与基体界面屈服的起始温差增大,而基体材料全面屈服的温差却减小。     

含涂层空心球复合泡沫塑料的模量预测及讨论

利用Mori-Tanaka平均应力的概念和Eshelby等效夹杂的原理,研究了含涂层空心球复合泡沫塑料的弹性性质,从理论上导出了这类复合材料的有效模量预测公式．此外,基于这些理论公式,讨论了涂层厚度和泊松比变化对复合泡沫塑料有效模量性质的影响．     

热弹性波在偶应力固体界面上的反射和透射

基于广义热弹性无能量耗散的G-N理论,研究了两种不同偶应力固体界面上弹性波的反射和透射.首先,建立偶应力弹性固体中的运动方程和边界条件.然后,根据非传统界面条件推导出弹性波反射和透射的振幅比.最后,用法向能量守恒验证了数值计算结果,根据数值计算结果,讨论了微结构参数和热力学参数对弹性波反射和透射的影响.结果显示,偶应力热弹性固体界面处存在三种体波和一种表面波;微结构参数对所有波的传播都有影响,而热力学参数只对热波的影响显著.     

非完美界面弹性复合材料中的微分几何方法

首次用微分几何方法计算了含一般旋转椭球体嵌入相的非完美界面弹性复合材料的有效模量·用内蕴几何量表出了能量泛函中的全部界面积分项，由此得到了这种统一嵌入相模型的复合材料有效模量的上下界限·在三种极限情况，即球、盘和针状嵌入相下，本文的结果将退化到Ｈａｓｈｉｎ（１９９２）的结果·     

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．     

Elastic fields in two imperfectly bonded half-planes with a thermal inclusion of arbitrary shape

A general method is presented for the rigorous solution of Eshelby’s problem concerned with an arbitrary shaped inclusion embedded within one of two dissimilar elastic half-planes in plane elasticity. The bonding between the half-planes is considered to be imperfect with the assumption that the interface imperfections are uniform. Using analytic continuation, the basic boundary value problem is reduced to a set of two coupled nonhomogeneous first-order differential equations for two analytic functions defined in the lower half-plane which is free of the thermal inclusion. Using diagonalization, the two coupled differential equations are decoupled into two independent nonhomogeneous first-order differential equations for two newly defined analytic functions. The resulting closed-form solutions are given in terms of the constant imperfect interface parameters and the auxiliary function constructed from the conformal mapping which maps the exterior of the inclusion onto the exterior of the unit circle. The method is illustrated using several examples of an imperfect interface. In particular, when the same degree of imperfection is realized in both the normal and tangential directions between the two half-planes, a thermal inclusion of arbitrary shape in the upper half-plane does not cause any mean stress to develop in the lower half-plane. Alternatively, when the imperfect interface parameters are not equal, then a nonzero mean stress will be induced in the lower half-plane by the thermal inclusion of arbitrary shape in the upper half-plane. Detailed results are presented for the mean stress and the interfacial normal and shear stresses caused by a circular and elliptical thermal inclusion, respectively. Results from these calculations reveal that the imperfect bonding condition has a significant effect on the internal stress field induced within the inclusion as well as on the interfacial normal and shear stresses existing between the two half-planes especially when the inclusion is near the imperfect interface.     

Crack – interface crack interactions in functionally graded/homogeneous composite bimaterials subjected to a heat flux

A bimaterial containing an interface crack and consisting of a homogeneous material and a functionally graded material (FGM) with a system of small internal cracks is considered. The thermal fracture of the biomaterial under the action of a heat flux applied to it at infinity is investigated. The problem is studied in the case where the interface crack is much larger than the internal ones. It is assumed that the thermal properties of the FGM are continuous functions of the thickness coordinate. Asymptotic analytical formulas for the thermal stress intensity factors (TSIFs) at the tips of the interface crack are obtained as series in a small parameter (the ratio between sizes of the internal and interface cracks). Then, the critical heat fluxes and the angles of propagation direction of the interface crack are calculated using the criterion of maximum circumferential stress. A parametric analysis shows that the propagation direction of the interface crack depends on the location and orientation of the system of internal cracks. The parameters of inhomogeneity of the FGM affect the value of TSIFs and, hence, the deflection angle of the interface crack.     

具有初始层间压力的层合圆筒的热冲击研究

采用一种解析方法求解具有初始层间压力的双层层合圆筒内的动态热应力的瞬态响应·　首先,将由自紧装配双层层合圆筒引起的初始层间压力考虑作为热弹性动力学方程的初始条件·　其次,利用一个简便的数学变换方法求解具有初始应力场的单层圆筒的热弹性动力学解,然后利用层合圆筒的边界条件和连接条件,得到具有初始层间压力的双层层合圆筒的热冲击解·     

四段式有限元法分析热耦合的流体-固体相互作用问题

给出了一种流(体)-热-结构综合的分析方法,固体中的热传导耦合了粘性流体中的热对流,因而在固体中产生热应力.应用四段式有限元法和流线逆风Petrov-Galerkin法分析热粘性流动,应用Galerkin法分析固体中的热传导和热应力.应用二阶半隐式Crank-Nicolson格式对时间积分,提高了非线性方程线性化后的计算效率.为了简化所有有限元公式,采用3节点的三角形单元,对所有的变量:流体的速度分量、压力、温度和固体的位移,使用同阶次的插值函数.这样做的主要优点是,使流体-固体介面处的热传导连接成一体.数个测试问题的结果表明,这种有限元法是有效的,且能加深对流(体)-热-结构相互作用现象的理解.     

Nonlinear thermoelastic analysis of layered structures

The nonlinear thermoelastic behavior of orthotropic layered slabs and cylinders including radiation boundaries, temperature-dependent material properties, and stress-dependent layer interface conditions is investigated. A one-dimensional finite element formulation employing quadratic layer and linear interface elements is used to perform the analyses. The transient heat conduction portion of the program is temporally discretized via an implicit linear time interpolation algorithm which includes Crank-Nicolson, Galerkin, and Euler backward differencing. The nonlinear heat conduction equations are iteratively evaluated using a modified Newton-Raphson scheme. Direct iteration between heat conduction and stress analysis is employed when stress-dependent interface thermal resistance coefficients are utilized. Verification problems are presented to demonstrate the accuracy of the finite element code.     

On the structure of the stresses inside an ellipsoidal irregularity in thermoelastic problems

We study the structure of the stresses inside an ellipsoidal irregularity. We obtain a result that generalizes the theorem on polynomial conservation for thermoelastic problems under homogeneous and linear external stress and temperature fields when there is perfect thermal and mechanical contact on the phase interface. We show by a specific example how significantly the stress structure inside the irregularity changes when the form of interaction on the boundary surface changes.Translated fromVychislitel'naya i Prikladnaya Matematika, Issue 71, 1990, pp. 70–77.     

Thermo-mechanical description of material diffusion during an ultrasonic wire bonding process

The volume diffusion during an ultrasonic wire bonding process leads to a material transport between the wire and the material of the substrate and thus creates an intermetallic phase between them. In order to investigate this process, the thermal and mechanical mechanisms occurring during wire bonding should be studied. For this purpose, finite element simulations based on coupled thermo-mechanical equations are performed to study the temperature and stress distribution in and around the interface. The final objective of the model is to develop a growth law for the intermetallic phases by considering the mechanical work applied to the wire in addition to the temperature increase at the interface. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Reflection and refraction of P-, SV- and thermal wave,at an initially stressed solid–liquid interface in generalized thermoelasticity

We have investigated the problem of reflection and refraction of thermoelastic wave at a solid–liquid interface in presence of initial stress. Using the theory of generalized thermoelasticity the problem has been solved in the context of various linear theories of thermoelasticity namely Lord–Shulmon, Green–Lindsay and coupled thermoelasticity. The appropriate expressions to find the amplitude ratios for all the three cases of P-wave incidence, SV-wave incidence and thermal wave incidence have been developed. However the ratios of amplitudes of reflected and refracted waves to that of incident wave are computed numerically for earth’s crust-water interface, for incident P-wave only, considering the initial stress to be tensile as well as compressional both. The results obtained are discussed and compared in the three models of thermoelasticity. The variations of the amplitude ratios with initial stress in G–L model have also been shown.     

垂直于双材料非完美界面Ⅱ型裂纹的断裂分析

研究了垂直于双材料非完美界面的Ⅱ型裂纹问题,采用线性弹簧模型模拟非完美界面．然后用Fourier积分变换方法把边值问题转化为求解具有Cauchy核的奇异积分方程,获得了裂纹两端应力强度因子的数值解．详细研究了问题的几种特例,并用数值实例分析了界面的非完美性对应力强度因子的影响．结果表明应力强度因子与界面参量有关并在完美界面和分离界面所对应的结果中变化．     

An atomic-continuum multiscale modeling approach for interfacial thermal behavior between materials

The aim of this paper is to provide a systematic method to perform interfacial thermal behavior between materials. A multiscale modeling method is proposed to investigate the interfacial thermal properties about copper nano interface structure. The interface stress element (ISE) method is set as a coupling button to a span-scale model combined with molecular dynamics (MD) and finite element (FE) methods. The handshake regions can simulate the structure transfer properties between the transition with MD and ISE, ISE and FE. The multiscale model is used to calculate the interfacial thermal characters under different temperatures. Some examples about numerical experiments with copper materials demonstrate the performance of MD–ISE–FE multiscale model is more successful compared with the approach applying MD–FE model. The results indicate that the accuracy of the MD–ISE–FE model is higher than that of MD–FE mode. This investigation implies a potential possibility of multiscale analysis from atomic to continuum scales.