SnPb钎料合金的粘塑性Anand本构方程

采用统一型粘塑性本构 Anand方程描述了电子封装焊点 Sn Pb钎料合金的非弹性变形行为 ,基于 Sn Pb 合金的弹塑性蠕变本构方程和实验数据 ,确定了6 2 Sn36 Pb2 Ag、6 0 Sn40 Pb、96 .5 Sn3.5 Ag和 97.5 Pb2 .5 Sn四种钎料合金 Anand方程的材料参数 ,验证了粘塑性 Anand本构方程对 Sn Pb合金在恒应变速率和稳态塑性流动条件下应力应变行为的预测能力。结果表明 ,Anand方程能有效描述 Sn Pb钎料的粘塑性本构行为 ,并可应用于电子封装 Sn Pb焊点的可靠性模拟和失效分析     

Constitutive and damage model for 63Sn37Pb solder under uniaxial and torsional cyclic loading

A constitutive model with Ohno–Wang kinematic hardening rule is developed and employed to simulate the isothermal cyclic behavior of Sn–Pb solder under uniaxial and torsional loading. An implicit constitutive integration scheme is presented for inelastic flow of solder. Then a modified low cycle fatigue life prediction model is put forward in which the sum of maximum shear strain range and normal strain range based on the critical plane concept is adopted to replace the uniaxial strain range used by Stolkarts et al. [Stolkarts, V., Keer, L.M., Fine, M.E., 1999. Damage evolution governed by microcrack nucleation with application to the fatigue of 63Sn–37Pb solder. J. Mech. Phys. Solids 47, 2451–2468]. Comparison of the experimental results and simulation verifies that the stress strain hysteresis loops and peak stress decline curve of solder can be reasonably modeled over a wide range of loading conditions with implement of damage coupled constitutive model, and the lifetime estimations of 63Sn37Pb solder based on the assumption of microcrack nucleation governed damage is effective to provide a conservative prediction.     

Nanoindentation of Pb/Sn solder alloys; experimental and finite element simulation results

A thermodynamics based damage mechanics coupled constitutive model is used to simulate the nanoindentation experiment on eutectic commercial Pb/Sn solder alloys. The study is aimed at explaining the apparent size dependent behavior observed at small indentation depths for this class of highly rate dependent materials. Interest is at small depths of indentation and a small-strains small-displacements theory is used. The study is motivated by the fact, that in the case of rate independent materials such a size dependence of the response is explained in terms of storage of the so-called geometrically necessary dislocations. Presently it is not clear if this is the source of size effects in a rate dependent material. Moreover, the storage of dislocations is difficult in eutectic solder alloys due to thermally activated diffusion processes that promote dislocation mobilization as opposed to storage. Therefore, a classical theory constitutive model should be able to capture such a size dependent feature of the response. The paper describes the constitutive model and its integration scheme. Simulations of the nanoindentation problem are performed at different temperatures and indentation strain rates and numerical results are compared with experiments.     

温度循环应力剖面对QFP焊点热疲劳寿命的影响

采用统一型粘塑性Anand本构方程描述了QFP(四方扁平封装)焊点的粘塑性力学行为,利用有限元分析软件建立组装在印制电路板上QFP的有限元模型,通过研究焊点内部总应变范围的变化进而研究温度循环应力剖面各个参数对焊点热疲劳寿命的影响,为设计合理的温度循环应力剖面提供了理论依据。     

锡铅钎料粘塑性行为及其本构描述

随着航天事业的发展，航天电子产品使用环境变得越来越复杂苛刻，对焊点可靠性要求日益提高，因此，研究焊点材料服役环境下的本构关系对于分析焊点性能、准确预测焊点可靠性具有重要意义．本文分析锡铅钎料Sn63Pb37在-45~150 ℃温度范围内和10-5~10-3/s应变率范围内的粘塑性行为，在此基础上，建立了修正的Anand本构模型．通过构建材料参数与温度的函数关系，提升Anand本构模型在不同环境温度尤其是低温环境下对材料应力-应变关系的预测能力，为航天电子产品可靠性设计提供技术支撑．     

Quick assessment methodology for reliability of solder joints in ball grid array (BGA) assembly—Part I: Creep constitutive relation and fatigue model

In this study, a new unified creep constitutive relation and a modified energy-based fatigue model have been established respectively to describe the creep flow and predict the fatigue life of Sn−Pb solders. It is found that the relation successfully elucidates the creep mechanism related to current constitutive relations. The model can be used to describe the temperature and frequency dependent low cycle fatigue behavior of the solder. The relation and the model are further employed in part II to develop the numerical simulation approach for the long-term reliability assessment of the plastic ball grid array (BGA) assembly. The project supported by the National Natural Science Foundation of China (59705008)     

跌落冲击载荷下焊锡接点金属间化合物层的动态开裂

跌落冲击载荷作用下,含铅焊锡接点与无铅焊锡接点的破坏模式明显不同,而导致这种差异的原因目前尚不明朗。本文提出了一种可用于模拟焊锡接点在跌落冲击载荷下破坏行为的有限元模型,此模型中,金属间化合物（IMC）与焊料间的界面采用粘性区模型（CZM）来模拟其损伤开裂过程,而IMC层内的破坏程度则通过计算其能量释放率来判断。通过对板级封装跌落冲击过程的数值模拟发现,与无铅焊锡接点（Sn3.5Ag）相比,含铅焊锡接点（Sn37Pb）与IMC间的CZM层更容易发生损伤破坏,而该层的开裂会减小IMC层的应力,即降低了其内部的裂纹驱动力,从而缓解了IMC层裂纹的起始和扩展。     

Isothermal low-cycle fatigue testing of microscale solder interconnections

A series of isothermal low-cycle fatigue studies of small to extremely small-volume solder joints has been conducted. These solder microjoints were designed and fabricated using processing which duplicates the microelectronics interconnection structures that might be used in high density, highly integrated flip-chip packaging and all fatigue tests were conducted in fully reversed simple shear both with and without dwells at maximum strain. Results of low-cycle fatigue tests of both single and double-bump 95/5 Pb/Sn solder microjoints in the form of Manson-Coffin (plastic strain amplitude versus fatigue life) plots and post-test failure mode analysis (FMA) carried out using scanning electron microscope (SEM) fractography are presented and evaluated. Paper was presented at the 1991 SEM Spring Conference on Experimental Mechanics held in Milwaukee, WI on June 9–12.     

Integrated numerical–experimental analysis of interfacial fatigue fracture in SnAgCu solder joints

In ball grid array (BGA) packages, solder balls are exposed to cyclic thermo-mechanical strains arising from the thermal mismatch between package components. Thermo-mechanical fatigue crack propagation in solder balls is almost always observed at the chip side of the bump/pad junction. The objective of the experimental part of this study is to characterize the bump/pad interface under fatigue loading. Fatigue specimens are prepared by reflowing Sn3.8Ag0.5Cu lead-free solder alloy on Ni/Au substrates. Obtained results show that fatigue damage evolution strongly depends on the microstructure. Applied strain and solder volume both have an influence on the fatigue damage mechanism. In the numerical part of the study, fatigue experiments are modeled using the finite element technique. A cohesive zone approach is used to predict the fatigue damage evolution in soldered connections. Crack propagation is simulated by an irreversible linear traction–separation cohesive zone law accompanied by a non-linear damage parameter. Cohesive zone elements are placed where failure is experimentally observed. Damage evolution parameters for normal and tangential interaction are scrutinized through dedicated fatigue tests in pure tensile and shear directions. The proposed cohesive zone model is quantitatively capable of describing fatigue failure in soldered joints, which can be further extended to a numerical life-time prediction tool in microelectronic packages.     

A hybrid model for computationally efficient fatigue fracture simulations at microelectronic assembly interfaces

Modern microelectronic assemblies are heterogeneous, layered structures joined by interconnects made of solder alloys with low homologous temperatures. The solder interconnections join devices to circuit boards and they fail by thermal fatigue fracture at their interfaces either to the device or to the circuit board. Predicting the fatigue fracture of the solder interconnections is a challenge due to the fact that they undergo large inelastic deformations during temperature cycling tests. In this paper we develop a hybrid approach inspired by cohesive zone fracture mechanics and the Disturbed State Concept to predict the crack trajectory and fatigue life of a solder interconnection subjected to both isothermal temperature cycling and anisothermal temperature cycling conditions (representing the two common accelerated test conditions for microelectronic products). A hybrid computational approach is used in which a first order approximation of the disturbance is used to estimate incremental cycles to criticality and thereby propagate the crack. The modeled crack fronts and the fatigue lives are validated through a comparison to results from the two types of accelerated tests. Overall, the model is shown to predict the fatigue life of the critical interconnection in the assembly to within 20% of the experimentally determined life. More importantly, the predicted crack trajectory is demonstrated to agree very well with the experimentally observed trajectory. Strikingly, the microscopically observed microstructural changes during crack propagation from that corresponding to creep fatigue to that of shear overload were found to be excellently correlated with the rate of change of the disturbance calculated in the model.     

用云纹干涉法研究金属焊点的热变形问题

本文采用现代光测力学的云纹干涉法，对铜－可伐焊接件热应变问题进行了实验研究，确定了焊层的热应变特征，结果表明：由于热膨胀系数不匹配、焊层存在复杂的应力状态，它不仅受到焊板材料对它的剪切作用，而且受到纵向拉伸、挤压作用。这对于认识微电子封装芯片焊层的热疲劳失效机理有重要意义     

Computational modeling of phase separation and coarsening in solder alloys

Solders represent highly versatile and useful materials. They provide a broad range of technical applications such as soldering in automotive processing, microelectromechanical systems (MEMS) and solar panels. Due to the fascinating variety of microstructural changes solder materials underlie, their micromorphological dynamics have been extensively studied in the past decades by experimental, analytical and numerical approaches. The evolved microstructure exerts a significant effect, in particular, in very small components such as solder joints in microelectronic packages. In order to capture the essence of the microstructural evolution in solder alloys with a diffusion theory of heterogeneous solid mixtures we employ an extended Cahn–Hilliard phase-field model. In our contribution we introduce different numerical schemes to treat Cahn–Hilliard equation. Here we focus on the innovative isogeometric finite element approach and outline its considerable benefits in comparison to the other methods. To this end we present numerical simulations of phase decomposition and coarsening controlled by diffusion for eutectic binary solders Sn–Pb and Ag–Cu illustrating the versatility of this approach. A concluding computational study of a three-dimensional phase separation event within a solder ball geometry will corroborate the quality of our model.     

基于纳米压入法Sn-Ag-Cu无铅焊料高温力学性能的研究

无铅化和微型化已经成为电子封装的发展趋势,温度对无铅焊点的可靠性产生了不可忽视的影响。本文对Sn96.5Ag3Cu0.5无铅焊料进行回流处理,采用纳米压入法研究其在实际工况下的高温力学性能。结果表明,温度对焊料试样的力学性能影响显著。随着温度的升高,弹性模量和硬度逐渐降低,焊料发生软化;较高温度下的蠕变应力指数较小,焊料的蠕变抗力降低,其相应的蠕变激活能为76kJ/mol。由此可知,随温度的升高,焊料的蠕变机制由位错攀移逐渐转变为晶界滑移。     

Fatigue damage modeling in solder interconnects using a cohesive zone approach

The objective of this work is to model the fatigue damage process in a solder bump subjected to cyclic loading conditions. Fatigue damage is simulated using the cohesive zone methodology. Damage is assumed to occur at interfaces modeled through cohesive zones in the material, while the bulk material is assumed to be linear elastic. The state of damage at a cohesive zone is incorporated into the cohesive zone constitutive law by a elasticity-based damage variable. The gradual degradation of the solder material and the corresponding damage accumulation throughout the cycling process is accounted for by a damage evolution law which captures the main damage characteristics. The model prediction of the solder bump life-time is shown to be in good agreement with one of the commonly used empirical life-time prediction laws.     

高温合金材料循环相关和时间相关热机械疲劳循环性能模拟

从平衡热力学不可逆系统出发，用非线性粘弹塑性运动强化莱模拟高温合金材料的应变控制热机械疲劳循环特性。讨论了温度变化和应变循环的相位关系，循环相关和时间相关热机械疲劳损伤机制，蠕变和疲劳间的相互作用。在建立本构关系和状态方程时，均考虑了温度变化所产生的影响。     

Measurement and modeling of back stress at intermediate to high homologous temperatures

Unified creep-plasticity models often require a number of internal state variables to accurately capture the path dependence of rate- and temperature-dependent alloys especially at intermediate to high homologous temperatures. However, it is impossible to fully measure the internal state variables directly. Consequently, assumptions on the relative importance of the various state variables must be made when determining the material parameters and their evolution must be inferred. Any enhancements designed to better capture the evolution of the state variables are dependent on these assumptions and are generally limited. The strain transient dip test and the rapid load/unload test are two indirect experimental methods used to obtain an approximate measure of the evolutionary nature of the back stress in 60Sn–40Pb, a common rate- and temperature-dependent solder alloy. The rapid load/unload test gives a better measure of back stress because there is less time for the internal state to evolve during data acquisition. Modifications to the back stress evolution equations in the McDowell unified creep-plasticity model are proposed using these new measurements as guidance. The modified model can better capture the transients under cyclic loading and following strain-rate jumps.     

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.      

热循环加载条件下空洞对EBGA焊点可靠性的影响

空洞是球栅阵列(BGA：Ball Grid Array)器件在装配过程中形成的主要缺陷之一,本文以增强性BGA(EBGA：Enhanced BGA)为研究对象,采用统一型粘塑性Anand本构方程描述Sn63Pb37的粘塑性力学行为,应用非线性有限元的方法分析了不同位置和大小的空洞对焊点疲劳寿命的影响,为制定装配后的BGA焊点接收标准提供理论参考。     

高密度封装倒装焊的新简化模型及疲劳寿命分析

高密度封装结构中存在大量焊球,在进行有限元建模时,考虑到焊球数量多且尺寸小的特点,需简化焊球层模型．本文针对高密度封装结构中倒装焊及底填胶,提出了一种新的简化模型,采用非重点部位简化和材料均匀化相结合的方法,将内部焊球层和底填胶简化为均匀层,只保留外圈几层焊球．通过建立代表性体积单元,计算得到均匀化层的材料参数．讨论了外层焊球圈数对焊球层危险点应力的影响,发现保留外圈两层焊球就能得到非常精确的结果．利用新简化模型计算了高密度封装结构的疲劳寿命,所获得的结果与未均匀化模型结果误差在0.3%以内．     

几种铝锡硅铜合金的摩擦磨损特性

采用环－块摩擦磨损试验机，考察了含Ｓｉ质量分数为１％～５％的Ａｌ－２０Ｓｎ－Ｓｉ－１Ｃｕ合金及传统的Ａｌ－２０Ｓｎ－１Ｃｕ合金的摩擦磨损性能．结果表明：几种Ａｌ－２０Ｓｎ－Ｓｉ－１Ｃｕ合金的磨损率低于Ａｌ－２０Ｓｎ－１Ｃｕ合金的磨损率，并且随Ｓｉ含量的增加而降低．干摩擦时，摩擦因数随Ｓｉ含量的增加无明显变化；油润滑时摩擦因数则随Ｓｉ含量的增加而略微减小．两类合金的摩擦因数均随滑动速度的增加而减小，随摩擦时间的增加先增加后减小并趋于稳定．磨损表面的ＳＥＭ分析表明：Ａｌ－２０Ｓｎ－Ｓｉ－１Ｃｕ合金在干摩擦下的磨损机制主要是磨粒磨损和氧化磨损，而Ａｌ－２０Ｓｎ－１Ｃｕ合金则包括粘着、疲劳及磨粒磨损等多种形式．在油润滑下，两者的磨损机理则分别为犁削作用和疲劳磨损及分层磨损．