应变控制的热机械疲劳行为的数值模拟

根据高温合金材料的力学性能，以弹粘塑性本构模型为基础，用数值模拟方法研究材料的热机械疲劳循环特性，模型将应变分为弹性应变、温度应变和粘塑性应变三部分，认为材料在高温循环载荷下呈现明显的弹粘塑性特征，根据虚位移原理建立轴对称体的弹粘塑性计算有限元格式，对于循环机械载荷和循环温度载荷，程序中采用了增量法迭代求解，在非线性项中不仅考虑了机械载荷增量的影响，同时也考虑了温度增量的影响，根据应变控制热机械疲劳的特点，发展了应变增量法的有限元计算方法、通过数值模拟，得到材料在各种循环载荷下的应力—应变响应，数值模拟较好地反映了粘塑性变形过程以及温度变化的效应，所描述的不可逆系统在某一时刻的状态完全由当时的状态参数、内变量、承载时间及塑性应变累积量决定，对带缺口试件的模拟结果显示了程序对复杂轴对称结构进行热机械疲劳计算的有效性。     

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。     

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．     

多焊点情况下胶焊单搭接头的静力分析

以胶接分析为基础,将焊点视为大剪切弹性模量胶粘荆,假设被粘体切应力沿厚度线性分布,胶层和焊点切应力沿厚度方向不变,建立了多焊点情况下胶焊单搭拉剪接头的线弹性应力解析模型.计算结果表明:被粘体正应力和胶层切应力解析解与有限元模型吻合得较好.对焊距的参数研究表明:胶焊单搭拉剪接头连接区纵向正应力和切应力随焊距减少而分布更均匀,峰值切应力下降,与前人的试验结果一致.     

考虑材料循环塑性的疲劳裂纹扩展模拟

提出了一种考虑材料循环塑性性能的研究疲劳裂纹扩展与闭合行为的有限元模拟方法．对所选用的循环塑性本构关系进行了基本实验检验．探讨了在疲劳裂纹扩展有限元分析中网格尺寸的影响，给出了网格优化准则．研究了在循环硬化条件下考虑裂纹合效应时裂纹面张开廓形、裂纹尖端应力、应变场和正反向塑性区的演变规律．对于循环硬化和不同循环应力比Ｒ等因素对裂纹张开应力水平的影响也作了考察     

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     

循环硬化材料本构模型的隐式应力积分和有限元实现

针对新发展的、能够描述循环硬化行为应变幅值依赖性的粘塑性本构模型，讨论了它的数值实现方法。首先，为了能够对材料的循环棘轮行为（Ratcheting）和循环应力松弛现象进行描述，对已有的本构模型进行了改进；然后，在改进模型的基础上，建立了一个新的、全隐式应力积分算法，进而推导了相应的一致切线刚度（Consistent Tangent Modulus）矩阵的表达式；最后，通过ABAQUS用户材料子程序UMAT将上述本构模型进行了有限元实现，并通过一些算例对一些构件的循环变形行为进行了有限元数值模拟，讨论了该类本构模型有限元实现的必要性和合理性。     

电子封装元件的高阶层离散均匀化分析

将均匀化理论应用于具有非完全(单层内)周期性微结构的倒装焊底充胶电子封装元件，建立了高阶逐层离散层板模型，用解析法分析热载荷下结构的温度应力. 计算结果与有限元解的比较表明，该分析模型和方法是有效的，而且比较简便. 算例分析结果显示，胶层厚度、焊点密度、胶与焊点材料的模量比和体积比，对于焊点温度应力有明显影响.     

考虑塑性应变记忆恢复的循环棘轮本构模型研究

在统一粘塑性循环本构理论框架下，以Ohno-Abdel-Karim非线性随动硬化模型为基础，建立了一个循环本构模型。模型通过引入塑性应变幅值记忆效应，并在塑性应变记忆项中加入恢复系数，提高了对循环硬化材料单轴棘轮行为的预言能力。将模型应用于316L不锈钢单轴棘轮行为的描述中，模拟不同平均应力、应力幅值下的棘轮应变，均与实验数据吻合较好，证明本文改进的本构模型能合理地描述循环硬化材料的单轴棘轮行为。     

考虑空洞效应的共晶钎料合金粘塑性-损伤本构模型

在温度298K～398K和恒应变率10-5/s～10-3/s范围内进行一系列的拉伸实验,研究共晶焊料的力学行为,揭示空洞成核和生长变形机理的存在.提出一种考虑孔洞效应的粘塑性-损伤模型,基于Guron-Tvergaard-Needleman思想和正交法则,引入孔洞体积分数作为损伤变量以描述共晶钎料的力学特性.与实验数据比较,验证粘塑性-损伤模型对锡铅合金在恒应变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,该模型能够有效描述共晶焊料的本构行为:非线性、应变率敏感性、空洞损伤演化,并可用于分析电子封装中焊点的可靠性问题.     

Analytical elasto-creep model of interfacial thermal stresses and strains in trilayer assemblies

A two-dimensional model has been developed for thermal stresses, elastic strains, creep strains, and creep energy density at the interfaces of short and long trilayer assemblies under both plane stress and plane strain conditions. Both linear (viscous) and non-linear creep constitutive behavior under static and cyclic thermal loading can be modeled for all layers. Interfacial stresses and strains are approximated using a combination of exact elasticity solutions and elementary strength of materials theories. Partial differential equations are linearized through a simple finite difference discretization procedure. The approach is mathematically straightforward and can be extended to include plastic behavior and problems involving external loads and a variety of geometries. The model can provide input data for thermal fatigue life prediction in solder or adhesive joints. For a typical solder joint, it is demonstrated that the predicted cyclic stress–strain hysteresis shows shakedown and a rapid stabilization of the creep energy dissipation per cycle in agreement with the predictions of finite element analysis.     

EFFECT OF LOADING TYPE ON FATIGUE CRACK GROWTH BEHAVIOR OF SOLDER JOINT IN ELECTRONIC PACKAGING

Fatigue cracking tests of a solder joint were carried out using in-situ scanning electron microscopy （SEM） technology under tensile and bending cyclic loadings. The method for predicting the fatigue life is provided based on the fatigue crack growth rate of the solder joint. The results show that the effect of the loading type on the fatigue crack growth behavior of a solder joint cannot be ignored. In addition, the finite element analysis results help quantitatively estimate the response relationship between solder joint structures. The fatigue crack initiation life of a solder joint is in good agreement with the fatigue life （N50%） of a totally electronic board with 36 solder joints.     

Very high cycle fatigue behavior of bridge steel welded joint

Very high cycle fatigue (VHCF) behaviors of bridge steel (Q345) welded joints were investigated using an ultrasonic fatigue test system at room temperature with a stress ratio R = ?1. The results show that the fatigue strength of welded joints is dropped by an average of 60% comparing to the base metal and the fatigue failure still occurred beyond 10⁷ cycles. The fatigue fracture of welded joints in the low cycle regime generally occurred at the solder while at the heat-affected zone (HAZ) in the very high cycle regime. The fatigue fracture surface was analyzed with scanning electron microscopy (SEM), showing welding defects such as pore, micro-crack and inclusion were the main factors on decreasing the fatigue properties of welded joints. The effect of welding defects on the fatigue behaviors of welded joints was discussed in terms of experimental results and finite element simulations.     

Fatigue crack propagation life analysis of solder joints under thermal cyclic loading

Fatigue crack propagation life analysis of solder joints under thermal cyclic loadings was investigated by the strain energy release rate method using finite element analysis. A relationship between the crack-growth rate and the strain energy release rate was derived. Finite element simulations were carried out to investigate the effect of crack growth along the interface of solder and lead in a solder joint assembly. The crack propagation life of the solder joint with an interface crack was predicted from the derived relationship between crack growth rate and values of the strain energy release rate. It was found that crack propagation life is much higher than the crack initiation life.     

Quick assessment methodology for reliability of solder joints in ball grid array (BGA) assembly—Part II: Reliability experiment and numerical simulation

In the present study, a facility, i.e., a mechanical deflection system (MDS), was established and applied to assess the long-term reliability of the solder joints in plastic ball grid array (BGA) assembly. It was found that the MDS not only quickly assesses the long-term reliability of solder joints within days, but can also mimic similar failure mechanisms in accelerated thermal cycling (ATC) tests. Based on the MDS and ATC reliability experiments, the acceleration factors (AF) were obtained for different reliability testing conditions. Furthermore, by using the creep constitutive relation and fatigue life model developed in part I, a numerical approach was established for the purpose of virtual life prediction of solder joints. The simulation results were found to be in good agreement with the test results from the MDS. As a result, a new reliability assessment methodology was established as an alternative to ATC for the evaluation of long-term reliability of plastic BGA assembly. The project supported by the National Natural Science Foundation of China (59705008)     

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.     

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.     

基于实测数据的扁平钢箱温度梯度疲劳应力谱分析方法

为研究扁平钢箱梁温度疲劳应力谱,以南溪长江大桥悬索桥主梁为研究对象,基于温度传感器长期实测数据,筛选实测数据的日温度极值,运用广义极值模型描述季节极值概率分布并采用极值外推方法得到设计基准期极值模型。引入拉丁超立方抽样(LHS)法对极值模型进行抽样,得到日温度极值样本。结合日温度极值样本和正弦函数模型,构建服役期内关注点的温度时程曲线。基于有限元ANSYS软件平台,分析不同温度梯度下关注点的应力效应,回归温度梯度与疲劳应力的线性关系式,依据温度梯度时程曲线与线性关系式模型,采用雨流计数法得到钢箱梁温度梯度疲劳应力谱。研究表明,模拟抽样生成的温度样本数据符合温度场的季节变化特征,样本概率模型与实测数据概率模型相对吻合。关注点温度梯度疲劳应力谱能够为扁平钢箱梁疲劳寿命设计提供参考。     

基于内聚力模型法PBGA封装焊点/IMC界面的分层开裂研究

塑料球栅阵列封装PBGA的可靠性分析中,考虑封装过程中SnAgCu焊料与铜焊盘界面间产生的金属间化合物（Intermetallic compound,IMC）的影响,并引入内聚力模型（Cohesive zone model, CZM）,利用ANSYS对热循环作用下焊点/IMC界面的脱层开裂情况进行研究。结果表明：热循环作用下,在封装器件中焊点承受较大的应力应变,且远离中心的外侧焊点具有比内侧焊点更大的应力应变。IMC的存在极大的降低了焊点的可靠性。界面分层最先发生在最外侧的IMC/焊点界面的两端,随着热循环次数的增加,分层逐渐沿着界面两端向里扩展。在热循环的前几个阶段,各个界面的最大损伤值增大较快,随着热循环的继续加载,界面最大损伤值逐渐趋于稳定。整个过程中四号焊点界面的损伤值始终最大。