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.      

冲击加载下铝中孔洞长大的微观机理分析

 利用扫描电镜和透射电镜观测了冲击加载后高纯铝损伤状态孔洞的分布,发现在冲击波加载后,高纯铝中出现了大量的孔洞,孔洞大小多集中在百纳米尺度,分布不均匀,且呈现出带状形貌,局部区域的孔洞在冲击波作用下优先发展,孔洞长大,形成微米级的大孔洞。进一步的观测发现,在孔洞周围出现了大量的位错发射,发射方向位于{111}晶面上,是面心立方金属的密排面。运用分子动力学模拟进行了对比研究,验证了位错发射方向与观测结果是一致的。     

一个新的损伤演化方程及其在层裂中的应用

 采用统计细观损伤力学方法,基于延性金属断裂过程的孔洞演化机理,提出一个新的损伤演化方程,该方程在一定的条件下与由空心球体胞模型导出的损伤方程形式相同。在此基础上,将新的损伤演化方程编入一维Lagrange有限差分动力学程序,对OFHC铜的平板对称正碰撞层裂实验进行了数值模拟,计算结果与实验吻合得较好。     

Improving the accuracy of the capacitance method for void fraction measurement

Void fraction measurements were made using capacitance method. Five capacitor configurations were manufactured and tested; parallel, strip-type plates, ring-type plates, unidirectional, and double-helix. The void fraction was simulated by nonflow air-paraffin wax, air-glass, air-wood, and air-Freon 113 systems. The relative statistical error in void fraction measurement was minimized by taking into account the spacing between the ends of the two electrodes.     

Collapsing void in a spatially flat Robertson-Walker universe

We consider here a model of the spherical void (or its precursor) containing low density conducting fluid surrounded by a thick spherical shell of radiation embedded in a RobertsonWalker (RW) universe with flat space sections. The underdense region has a metric which is the special case of a solution given by Maiti [1] surrounded by Vaidya metric. We also assume the RW universe to be filled with a perfect fluid with a linear equation of state. The matching conditions indicate that if the time coordinate in each region is future directed then the underdense region appears to go on contracting to a comoving observer in the universe as the latter expands until it disappears. However, if the pressure in the RW universe vanishes, (approximately the present day condition), the underdense region remains static. We have also extended the space-time coordinates of Vaidya metric to the interior of the underdense region as well as the RW universe. It remains to be seen if the region having Vaidya metric disappears earlier than the interior or vice versa.     

垂直加热管内下降两相流瞬态空泡率的数学模型研究

本文提出瞬态垂直下降流动管内两相流空泡率的数学模型和其计算方法，可用来计算介质流量瞬变和加热负荷瞬变时管内各处的空泡率．为了验证模型计算的精确性，在R－12实验台架上进行了空泡率的测量，同样工况下，测量与计算结果相当一致．流量瞬变时的最大平均偏差小于13％，热负荷瞬变时小于15％．由此可认为本模型方法，可用于工程计算，尤其适用于棒束之类的复杂流道．     

Morphological evolution during diffusive healing of internal cracks within grains of α-iron

Micron-sized internal cracks were introduced into rounded bars of pure iron by low cycle fatigue, and the cracks had irregular penny-shaped morphology with the critical diameter of about 30μm and the thickness of 0.5–1.5μm. The initiation and propagation of the cracks were investigated quantitatively as well as their location and geometry. After vacuum annealing of the samples fatigued, the morphology in a two-dimensional longitudinal section of cracks within grains had evolved from initially elliptical one into arrays of spherical voids controlled by surface diffusion. Furthermore, a typical morphology for a broken crack with a center spherical void surrounded by outer doughnut-like cavities was observed along a perpendicular section of the specimen. Subsequently the spherical voids shrink and diminish gradually dominated by bulk diffusion. A physical model to heal an internal microcrack was proposed, in particular for the various healing stages controlled by the related dominant diffusion mechanism and their dependencies upon the morphology and geometry of an original micro-crack in materials. The project supported by the National Outstanding Young Investigator Grant of China (59925104) and the National Natural Science Foundation of China (59889101)     

冲击加载下孔洞诱导相变形核分析

用分子动力学方法模拟了冲击加载(沿［001］向)下单晶Fe中孔洞诱导相变形核及生长过程,并分析了初始温度对这一生长过程的影响.数值模拟显示：1) 相变形核首先出现在孔洞周围的(110)和(110)面上,并分别沿［110］,［110］向和［110］,［110］向生长成片状,之后核的生长方向则变为沿〈111〉向,形成“V”形板条状新相颗粒;2) 在相同冲击压力下,初始温度为300 K时在新相晶核边缘出现许多核胚,生成的新相颗粒比60 K时明显减小.这些现象表明,孔洞诱导相变形核及生长过程沿着特定晶向进行,而初 关键词： 相变 孔洞 分子动力学     

Spatial distribution of void fraction within a liquid slug and some other related slug parameters

The structure of vertical upward slug flow in a pipe is studied. The distribution of the phases in the Taylor bubble zone and the liquid slug zone is investigated by simultaneous measurements with two optical fiber probes. In the Taylor bubble zone the shape of the Taylor bubble and the distribution of the bubble length is reported. In the liquid slug region, the distribution of the void fraction is obtained over a dense grid in both the axial and radial directions. These experimental results shed some light on the hydrodynamics of the two-phase slug flow, in particular regarding the production of the dispersed bubbles and their distribution along the liquid slug.     

子通道内空泡份额的实验研究

本文以低压空气－水为介质，对子通道内的空泡份额分布进行了实验研究，使用电导探针测量系统测定了子通道内的空泡份额分布。通过实验数据的整理，得到了截面平均空泡份额，并将实验结果与已有的计算截面平均空泡份额的方法进行了比较，在此基础上，讨论了子通道内截面平均空泡份额的计算方法。