多物理场下FCBGA焊点电迁移失效预测的数值模拟研究

随着微电子封装技术的快速发展, 焊点的电迁移失效问题日益受到关注. 基于有限元法并结合子模型技术对倒装芯片球栅阵列封装(flip chip ball grid array, FCBGA)进行电-热-结构多物理场耦合分析, 详细介绍了封装模型的简化处理方法, 重点分析了易失效关键焊点的电流密度分布、温度分布和应力分布, 发现电子流入口处易产生电流拥挤效应, 而整个焊点的温度梯度较小. 基于综合考虑“电子风力”、温度梯度、应力梯度和原子密度梯度四种电迁移驱动机制的原子密度积分法, 并结合空洞形成/扩散准则及失效判据, 分析FCBGA焊点在不同网格密度下的电迁移空洞演化过程, 发现原子密度积分算法稳定, 不依赖网格密度. 采用原子密度积分法模拟真实 工况下FCBGA关键焊点电迁移空洞形成位置和失效寿命, 重点研究了焊点材料和铜金属层结构对电迁移失效的影响. 结果表明, 电迁移失效寿命随激活能的增加呈指数级增加, 因此Sn3.5Ag焊点的电迁移失效寿命约为63Sn37Pb的2.5倍, 有效电荷数对电迁移寿命也有一定的影响;铜金属层结构的调整会改变电流的流向和焊点的应力分布, 进而影响焊点的电迁移失效寿命.      

多物理场下FCBGA焊点电迁移失效预测的数值模拟研究

随着微电子封装技术的快速发展,焊点的电迁移失效问题日益受到关注.基于有限元法并结合子模型技术对倒装芯片球栅阵列封装(flip chip ball grid array,FCBGA)进行电-热-结构多物理场耦合分析,详细介绍了封装模型的简化处理方法,重点分析了易失效关键焊点的电流密度分布、温度分布和应力分布,发现电子流入口处易产生电流拥挤效应,而整个焊点的温度梯度较小.基于综合考虑"电子风力"、温度梯度、应力梯度和原子密度梯度四种电迁移驱动机制的原子密度积分法,并结合空洞形成/扩散准则及失效判据,分析FCBGA焊点在不同网格密度下的电迁移空洞演化过程,发现原子密度积分算法稳定,不依赖网格密度.采用原子密度积分法模拟真实工况下FCBGA关键焊点电迁移空洞形成位置和失效寿命,重点研究了焊点材料和铜金属层结构对电迁移失效的影响.结果表明,电迁移失效寿命随激活能的增加呈指数级增加,因此Sn3.5Ag焊点的电迁移失效寿命约为63Sn37Pb的2.5倍,有效电荷数对电迁移寿命也有一定的影响;铜金属层结构的调整会改变电流的流向和焊点的应力分布,进而影响焊点的电迁移失效寿命.     

金属互连焊球的电迁移试验设计研究与灵敏度分析

综合考虑多种电迁移驱动机制, 基于ANSYS软件和FORTRAN程序提出电迁移失效算法, 导出了电迁移灵敏度分析方程, 并建立相应的数值算法. 在此基础上考虑设计变量为激活能、初始自扩散系数和材料力学性能参数等对金属互连焊球进行电迁移灵敏度分析, 同时基于三维有限元分析的全因子试验设计法对CSP封装结构的电迁移寿命进行仿真预测.     

电致失效力学

电致失效力学研究单调或交变电场载荷下由应力引起的失效行为,它包含了电致断裂、电致疲劳、电致迁移与电致损伤等新研究课题．本文概述了电致失效力学的领域与课题,并深入讨论了电致应变诱导断裂疲劳的机理及电迁移损伤的力电耦合过程．研究结果表明,电致失效力学可提供铁电陶瓷致动器和集成电路的若干关键设计参数．对铁电陶瓷多层共烧致动器,该分析提供其层厚、外加电场强度和交变电场循环周数．对集成电路内导线,该分析提供其允许电流密度和临界线长．      

考虑应变能密度的铜互连导线电迁移应力分析

铜互连导线导电后会产生由热扩散主导的电迁移现象,而根据广泛使用的一维电迁移引起的回流模型和原子通量散度的概念,可得到传统的线性应力演化方程.通过在表面晶体材料的表面自由能中计入应变能密度的影响,推导出适合铜导线的非线性应力演化方程.数值求解有界和半无界边界条件下铜导线中的瞬时应力分布.结果表明当考虑应变能密度影响后,导线中的拉应力演变较线性应力演化方程的解更缓趋于稳态,拉应力数值较线性方程应力解更小,而压应力则恰恰相反.同时还讨论了铜条的临界长度效应.计入应变能的影响后,导线内部的应力呈非对称分布,而这种趋势在导线长度减小时更加明显.文中的研究结果将为集成电路设计和铜互连材料的制备提供技术参考.     

不同集流方式下对称双阴极固体氧化物燃料电池的电-化-热-力数值模拟及失效分析

 本文围绕新型对称双阴极固体氧化物燃料电池电堆单元在不同集流位置下热应力分布情况和优化集流方式，建立了一个基于电-化-热-力多场耦合理论的三维SOFC 电堆单元数值模型．引入固体力学热-力学理论，结合Weibull 失效概率分析方法，讨论了不同集流方式对SOFC 内部应力分布及失效的影响．研究结果表明，双侧阴极同时开展电子集流方式下的电解质平均电流密度比单侧单一集流方式下高，改变阳极集流位置会改变电极高温区的分布；SOFC 电堆单元上电极结构处的最大主应力明显大于其他组件上的最大主应力；阳极集流位置设置在阳极气体入口处时电极结构上的最大主应力和失效概率大于集流位置设置在阳极气体出口处的最大主应力和失效概率．     

复合材料-金属毛化接头的失效预测模型

针对复合材料与金属连接的一种新型连接形式－毛化接头,建立了其在拉伸载荷作用下的失效模式与破坏载荷的宏－细观预测模型。首先根据毛刺的分布选择合适的代表体积元,建立毛刺层单胞模型,施加周期性边界条件,通过有限元分析得到毛刺层的平均刚度参数。其次,基于累积损伤理论预测毛刺层的单胞强度,分析毛刺层的失效机理。最后,将毛刺层的等效材料参数赋予接头整体模型,预测接头的抗拉强度及失效模式。预测结果与试验值吻合良好。分析结果表明,毛化接头的承载能力和失效模式与毛刺的密度高度、搭接面积等因素密切相关,通过参数设计可获得较高的承载能力。     

计算分析施工期大型混凝土基础底板的开裂

针对天都花园工程中出现的裂缝问题，研究建筑工程中大型基础底板施工中裂缝的产生，以及如何防止这类裂缝的产生. 用ANSYS有限元程 序，模拟工程施工期温度场，采用混凝土材料的开裂和压碎失效模型以及分布裂缝模型的处理方法, 计算混凝土结构的应力和开裂情况，获得一些结论.     

等截面金属弯钩极限承载力计算

研究等截面弯钩受力时的应力分布及承载极限问题,本文以弹性力学的曲梁问题为参考,建立了平面应力条件下的金属弯钩的力学模型,得出了弯钩应力分布解,并通过ANSYS数值模拟进行验证,得出其危险截面。基于极限变形原理、弹性极限设计原理与塑性极限设计原理,提出了等截面弯钩失效的三种准则,为工厂生产不同极限载荷下的弯钩提供了理论依据。     

微焊点电致损伤与断裂的实验及数值研究

本文制作了微焊点试件,并通过施加较大的电载荷使其发生了电迁移。对微焊点在电迁移过程中的微观组织形貌及其演化进行了观察。结果发现,高温和常温条件下的电致失效模式都是阴极处的界面断裂,但是低温条件下的迁移试件会在阳极处形成凸丘,而高温下则没有。此外,本文还测试了微焊点在电迁移过程中的电阻、温度场以及塑性变形,以期找到微焊点电致损伤的表征方法。实验表明,红外方法可以快速准确地发现焊点表面和内部的缺陷,而电阻值对微焊点的电致损伤并不敏感。最后本文采用有限元方法分析了微焊点的电致应力及空位浓度,较好地解释了微焊点电致失效的机制。     

Crystallographic failure analysis of film near cooling hole under temperature gradient of nickel-based single crystal superalloys

In this paper, a unit cell model with a film cooling hole has been set up to analyze the crystallographic stress characterization and failure behavior under temperature gradient of nickel-base single crystallographic superalloys (SC). The aim of this work is to study the failure behavior of SC blades with film cooling. The distribution of cooling air pressure on the hole side surface and the distribution of the temperature around the hole are obtained from the fluid analysis. The result of the temperature distribution is then transferred to the finite element model (cell model) by the interpolation method. The cell model is analyzed by the crystallographic rate dependent finite element method (FEM). Special attention is put on the influence of temperature gradient. The influence of the loading boundaries, i.e. displacement loading and stress loading, on the stress characterization around hole is also taken into consideration. The results show that temperature gradient hole has much influence on the stress characterization. Different types of loading boundaries result in different types of stress and strain distributions. There is clear stress concentration near the hole under displacement loading, while there is clear strain concentration under stress loading. The failure characterization has been studied by the strain energy density criterion. It is shown that the temperature gradient has influence on the failure behavior.     

Light extinction technique for void fraction measurements in bubbly flow

 The analysis of the scattering induced by a dispersion of gas bubbles in a liquid medium on a collimated, monochromatic light beam, traversing the two-phase flow, allows for the direct measurement of the 2-D distribution of the line-average of the interfacial area density. The 2-D distribution of the line-average of the void fraction is deduced from that of the interfacial area density through an image processing algorithm. To demonstrate the technique, experiments are performed in a pool of water injected with air and illuminated with a CW argon ion laser. Since the bubble diameters range from a fraction of a millimeter to a few millimeters, the scattering processes are entirely in the Mie range. The limits of applicability of the technique and the measurement uncertainty are discussed. The results compare favorably with level-swell based measurements used as a reference. Received: 14 February 1997/Accepted: 4 February 1998     

纤维增强复合材料风机叶片宏细观一体化有限元分析An unified FEM for macroscopic and mesoscopic analysis of fiber reinforced composite fan blades

为了建立纤维增强复合材料风机叶片宏观性能和细观组分的直接关联,得到一般有限元分析时无法获得的细观参量值,利用FORTRAN程序把细观力学的失效／损伤分析模块,嵌入到有限元软件ABAQUS中的USD‐FLD 用户子程序中,建立了风机叶片宏细观一体化模型。该模型能够实现基于细观组分级损伤／失效判据的宏细观渐进损伤分析和强度预报功能。该模型计算结果与文献中的试验结果有较好的一致性。     

Relating cellular structure of open solid food foams to their Young’s modulus: Finite element calculation

This paper investigates the role of structure on Young’s modulus of open cell materials of relative densities between 0.1 and 0.3. The cellular solid is obtained by generating mixture size of spherical voids using the Random Sequential Addition – RSA algorithm. The relative density of the material is controlled by increasing void number and overlap. Structural effects consider mainly a Gaussian distribution of spherical void size of varying width, distribution centre and void overlap distance. Finite element method is used to calculate effective Young’s modulus using a regular meshing scheme of 3D typical cellular solids and Conjugate Gradient solver. It is found that sphere overlap has the largest effect compared to sphere distribution width for a given density. A large scatter in the wall thickness distribution is predicted when overlapping is increased or when the width of sphere size distribution is decreased. Increased rigidity is found to be correlated to particular arrangement of mixture size spheres which is pointed out using the Pair Correlation Function. Experimental evidence of the role of void overlapping is treated in the case of bread crumbs structures determined using X-ray tomography. The scatter of effective Young’s modulus for a given relative density is sensitive to void overlapping.     

砂土初始孔隙比空间变异性对其力学特性及破坏模式的影响分析

现有研究大多采用简单的摩尔库伦模型针对土的空间变异性对边坡或基础的安全系数或失效概率做计算分析.事实上临界状态本构模型,如SIMSAND,能更准确地反映土的应力-应变关系.为此,本文采用SIM-SAND模型,针对砂土初始孔隙比的空间变异性对其力学特性及破坏模式的影响做详细分析,算例采用简单的室内平面应变双轴试验,分为松砂排水、密砂排水、松砂不排水和密砂不排水四种情况.每一种情况均采用蒙特卡罗方法进行初始孔隙比的随机分布生成,并做大量计算,以此来分析初始孔隙比的不均匀性对剪切带生成和破坏模式和竖向承载力发展及其概率密度分布的影响.     

Prediction of liquid level distribution in horizontal gas-liquid stratified flows with interfacial level gradient

A one-dimensional momentum equation has been derived based on a two-fluid model and used to predict the axial distribution of liquid level or void fraction in steady, cocurrent, gas-liquid stratified flows in horizontal circular pipes and rectangular channels. The equation is carefully formulated to incorporate the effect of interfacial level gradient. Two different critical liquid levels are found from the momentum equation and are adopted as a boundary condition to calculate the liquid level or void fraction distribution upstream of the channel exit. The predicted void fraction distributions are compared with the experimental data obtained in a rectangular channel in this work and other data reported for large-diameter pipes. Good agreement is shown for air-kerosene, air-water and stream-water stratified flows with a smooth gas-liquid interface.     

A void nucleation and growth based damage framework to model failure initiation ahead of a sharp notch in irradiated bcc materials

A continuum damage framework is developed and coupled with an existing crystal plasticity framework, to model failure initiation in irradiated bcc polycrystalline materials at intermediate temperatures. Constitutive equations for vacancy generation due to inelastic deformation, void nucleation due to vacancy condensation, and diffusion-assisted void growth are developed. The framework is used to simulate failure initiation at dislocation channel interfaces and grain boundaries ahead of a sharp notch. Evolution of the microstructure is considered in terms of the evolution of inelastic deformation, vacancy concentration, and void number density and radius. Evolution of the damage, i.e., volume fraction of the voids, is studied as a function of applied deformation. Effects of strain rate and temperature on failure initiation are also studied. The framework is used to compute the fracture toughness of irradiated specimens for various loading histories and notch geometries. Crack growth resistance of the irradiated specimens are computed and compared to that of virgin specimens. Results are compared to available experimental data.