Anand模型预测63Sn37Pb焊锡钎料的应力应变行为

通过在温度313K～398K、应变率10^-3％／s～10％／s内的一系列恒应变率拉伸实验，研究63Sn37Pb焊锡钎料的力学行为，发现该材料的应力应变关系与温度和应变率有很大的相关性。采用统一型Anand粘塑性本构方程对该材料在较大温度和应变率范围内的应力应变行为进行数值模拟。结果表明Anand粘塑性方程可以有效地描述63Sn37Pb焊锡钎料在10％应变下的温度和应变率相关粘塑性本构行为。     

极端温度环境Sn基焊点本构方程的研究进展

焊点在深空探测器的电子系统中承担机械支撑、电气连接和信号通道的作用,电子系统的失效也多由互连焊点的失效引起,这与钎料在不同温度载荷下力学行为和微观组织的变化有着重要的联系。目前焊点主要以Sn基钎料为主,且在-55～150℃温度范围内根据其力学性能构建黏塑性方程,如Anand、Garofalo-Arrheninus、Norton、Wiese模型等。但对小于-55℃温度环境下的钎料本构方程研究较少。通过对-55～150℃温度范围内现有的力学本构模型进行了综述,阐述在不同温度下力学性能和微观组织对焊点可靠性的影响,总结了目前面临的问题和挑战,最后对小于-55℃下Sn基钎料和焊点的力学本构模型研究进行了初步探索及展望。     

Sn60Pb40焊层在热循环过程中蠕变行为的仿真研究

文中采用ANAND焊点本构关系模型描述了Sn60Pb40焊层蠕变行为,通过MARC有限元软件模拟了电子封装器件Sn60Pb40焊层在热循环中的蠕变过程,研究了Sn60Pb40焊层的蠕变应变最大值出现的位置,分析了封装结构热失配和焊层厚度对Sn60Pb40焊层蠕变应变的影响。结果表明:焊层边角处最早发生蠕变断裂,降低封装结构热失配程度和优化焊层厚度均可减小Sn60Pb40焊层的蠕变变形。该研究结果不仅为封装结构的热匹配优化设计提供了新的思路,也为预测焊层蠕变断裂位置和优化工艺提供了技术支持。     

基于数值模拟的多圈QFN封装热疲劳可靠性试验设计方法

提出一种基于数值模拟的试验设计方法,研究材料属性和几何结构对多圈四边扁平无引脚(Quad flat no-lead,QFN)封装热疲劳寿命的影响,并进行最优因子的组合设计,以提升热疲劳可靠性。采用Anand黏塑性本构模型描述无铅钎料Sn3.0Ag0.5Cu的力学行为,建立三维有限元模型分析焊点在温度循环过程中的应力应变,采用Coffin-Manson寿命预测模型计算多圈QFN封装的热疲劳寿命。采用Taguchi试验设计(Design of experiment,DOE)方法建立L27(38)正交试验表进行最优因子的组合设计。采用有限元分析方法对最优因子组合设计结果进行验证。结果表明,印制电路板(Printed circuit board,PCB)的热膨胀系数、焊点的高度和塑封料的热膨胀系数对热疲劳寿命的影响最为显著;初始设计情况下多圈QFN封装的热疲劳寿命为767次;最优因子组合设计情况下的热疲劳寿命提高到4 165次,为初始设计情况下的5.43倍。     

63Sn-37Pb钎料合金耦合损伤时相关理论模型

在63Sn-37Pb钎料合金单轴时相关变形和失效行为研究的基础上,提出了耦合损伤时相关循环本构模型和疲劳失效模型;在模型中,引入了损伤演化方程,考虑了时相关效应;应用该理论模型对该钎料在不同应变率、不同应变幅值、不同保持时间及其历史下的变形行为及疲劳失效行为进行了模拟,并对疲劳寿命进行了预测。结果表明:该理论模型是合理有效的。     

63Sn-37Pb钎料合金耦合损伤时相关理论模型

在63Sn-37Pb钎料合金单轴时相关变形和失效行为研究的基础上,提出了耦合损伤时相关循环本构模型和疲劳失效模型;在模型中,引入了损伤演化方程,考虑了时相关效应;应用该理论模型对该钎料在不同应变率、不同应变幅值、不同保持时间及其历史下的变形行为及疲劳失效行为进行了模拟,并对疲劳寿命进行了预测。结果表明：该理论模型是合理有效的。     

正交各向异性有限变形下材料的粘塑性力学行为的研究

给出正交各向异性有限变形下的统一粘塑性理论中的 Walker模型的本构表达并成功地利用参数控制法(GPM方法 )对其进行数值计算 ,推导出 Walker模型的隐式应力积分过程。在计算的基础上 ,研究了温度、应变率对材料的应力应变关系的影响 ,以及蠕变 ,应力松弛 ,热恢复及循环塑性这些高温下材料的粘塑性力学行为。     

SMT软钎焊接头热循环力学行为研究

应用粘背景性理论分析研究了SMT软钎焊接头热循环力学行为,并用热膨胀模拟加载试样进行了试验验证。研究结果表明：SMT软钎焊接头在热循环过程中的应力由全部热循环的温度历史决定,时间效应（变温速率、保温时间等）对软钎焊接头在热循环中的力学行为具有显著影响。随热循环温度升高和保温时间延长,钎焊接头内将发生显著的应力松弛。     

中锰TRIP钢棘轮行为及其本构模拟分析

对中锰TRIP钢在室温下的单轴棘轮行为进行了实验研究,讨论了平均应力和应力幅值对材料棘轮行为的影响。在实验分析的基础上,建立了一个便于工程应用的循环塑性本构模型,对材料的单轴棘轮行为进行描述,并给出了模型参数的确定方法。将累积塑性应变和阶跃函数引入棘轮参数演化方程中,对本构模型中的背应力演化方程进行了改进。本构模型的预测结果与实验结果的对比表明,改进后的本构模型合理地描述了中锰TRIP钢的棘轮行为。     

残余应力对混合组装BGA热循环可靠性影响

研究混装球栅阵列(Ball grid array,BGA)回流焊后产生的残余应力对热循环寿命产生影响。根据Sn63Pb37/Sn3.0Ag0.5Cu均匀混装BGA封装实体,建立有铅和混装BGA封装体ANSYS有限元模型。通过加载不同峰值温度(220~265℃)和不同降温速度(1~6℃/s)的回流温度曲线后,得到BGA封装体焊点残余应力、应变。随后选取峰值温度243℃、降温速度3℃/s条件下的回流焊后BGA封装体模型施加热循环载荷,根据修正Coffin-Manson方程预测焊点寿命。研究结果表明:回流焊中降温速度对焊后应力占主导因素,应力降温速度的增加逐渐由27.9 MPa增加到32.5 MPa,而峰值温度对焊后应变影响明显;热循环分析中BGA焊球左上角区域始终处于高应力应变状态,均匀混装BGA寿命稍低于SnPb焊点BGA;回流焊工艺后进行热循环加载结果表明残余应力对Sn63Pb37/Sn3.0Ag0.5C均匀混装BGA寿命影响不大。     

Anand Parameters Determination for SnAgCu Solder Bearing Micro-amounts Rare Earth Ce

SnAgCu solder system with the addition of rare earth Ce,which has better thermo-mechanical properties compared to those of SnPb solder,is regarded as one of the promising candidates for electronic assembly.Moreover,the SnAgCuCe solder alloys can provide good quality joints with Cu substrates.However,there is few report of the constitutive model for SnAgCu solder beating micro-amounts rare earth Ce.In this paper,the unified viscoplastic constitutive model,Anand equations,is used to represent the inelastic deformation behavior for SnAgCu and SnAgCuCe solders.In order to obtain the acquired data for the fitting of the material parameters of this unified model,a series of experiments of constant strain rate test were conducted under isothermal conditions at different temperatures.The Anand parameters of the constitutive equations for SnAgCu and SnAgCuCe solder were determined from separated constitutive relations and experimental results.Nonlinear least-square fitting was selected to determine the model constants.And the simulated results were then compared with experimental measurements of the stress-inelastic strain curves:excellent agreement was found.The model accurately predicted the overall trend of steady-state stress-strain behavior of SnAgCu and SnAgCuCe solders for the temperature ranges from 25℃ to 150℃,and the strain rate ranges from 0.01 s-1 to 0.001 s-1.It is concluded that the Anand model can be applied for representing the inelastic deformation behavior of solders at high homologous temperature and can be recommended for finite element simulation of the stress-strain response of lead free soldered joints.Based on the Anand model,the investigations of thermo-mechanical of SnAgCu and SnAgCuCe soldered joints in fine pitch quad flat package by finite element code were done under thermal cyclic loading,it is found that the reliability of SnAgCu soldered joints can be improved remarkably with addition of rare earth Ce.The results may provide a theory guide for developing constitutive model for lead-free solders.     

MECHANICAL PROPERTIES OF FINE PITCH DEVICES SOLDERED JOINTS BASED ON CREEP MODEL

Nonlinear analyses of quad flat package （QFP） on printed circuit board （PCB） assemblies subjected to thermal cycling conditions are presented. Two different solders are considered, namely, Sn37Pb and Sn3.5Ag. The stress and strain response of fine pitch devices soldered joints was investigated by using finite element method based on Garofalo-Arrheninus model. The simulated results indicate creep distribution of soldered joints is not uniform, the heel and toe of soldered joints, the area between soldered joints and leads are the creep concentrated sites. The similar phenomena of stress curves simulated based on Garofalo-Arrheninus model and Anand equations is confirmed, and the creep strain value of Sn3.5Ag soldered joints is lower than that of Sn37Pb soldered joints. Thermal cycling results show that Sn3.5Ag strongly outperforms Sn37Pb for QFP devices under the studied test condition. This is well matched with the experimental outcome analyzed. In addition, the soldered devices were tested by micro-joints tester, the tensile strength of Sn3.5Ag soldered joints is found to be higher than that of Sn37Pb soldered joints. By analyzing the fracture microstructure of soldered joints, it is found that fracture mechanism of Sn3.5Ag soldered joints is toughness fracture, while fracture mechanism of Sn37Pb soldered joints includes brittle fracture and toughness fracture. The results of this study provide an important basis of understanding the mechanical properties of fine pitch devices with traditional Sn37Pb and Sn3.5Ag lead-free soldered joints.     

Board level reliability analysis of chip resistor assemblies under thermal cycling: A comparison study between SnPb and SnAgCu

Accelerated thermal cycling (ATC) tests are conducted for various chip resistor assemblies using the lead-based (SnPb) and lead-free (SnAgCu) solders. The corresponding life prediction models are developed by employing the well-established energy density approach. The life prediction model constants are obtained from the ATC test data. The models are utilized to predict the lifetimes of chip resistor assemblies under a mobile device field condition. The analysis indicates that the lead-free solder used in the chip resistor assembly would offer a longer lifetime under a field condition compared to the lead-based solder regardless of chip resistor types even when a reverse trend is observed in the ATC test results.     

Mechanical Properties of QFP Joints Soldered with SnAgCu and SnPb Solders

With the development of lead-free solder alloys, the investiagtion focusing on the relibility of lead-free solders are essential. Since the reliability database of lead-free solder joints needs to be further supplied, the creep behavior of SnAgCu soldered joints on Quad Flat Package (QFP) devices under thermo cycling load are studied in this paper, compared to conventional SnPb solder, by finite element simulation based on Garofalo-Arrhenius creep model. Meanwhile, the mechanical properties of SnAgCu and SnPb soldered joints in the pitches of QFP devices are also carried out by means of tensile test. The results indicate that the values of strain and stress of SnAgCu soldered joints were all smaller than those of SnPb under thermal cycling, and the tensile strength of the joints soldered with SnAgCu solder was higher than that of SnPb, which means the reliability of the joints soldered with SnAgCu solder is better than SnPb soldered joints. As the fracture surface morphology of the soldered joints compared, SnAgCu soldered joint presented ductile fracture, while the fracture mechanism of SnPb solder joints displayed both brittle and ductile fracture. Above all, the experimental results is in accord with that of simulation, which will provide guidance for reliability study and application of lead-free solders.     

Identification of Behavior of Linearly Viscoelastic Materials from Experiments on Relaxation with Initial Area of Increasing Strain

The problem of the determination of the relaxation functions of linearly viscoelastic materials is studied in experiments with a double-step strain process (ramp test); strain increases at the first stage and is constant at the second stage. The experimental data on the dependency of stresses on time are analyzed in three ways with a subsequent comparison of results. The first method requires fulfillment of the 10 rule and uses the backward recurrence method; the second is based on the formulas of approximate integration. In the third, it is immediately assumed that the relaxation function can be represented by a truncated Prony series. For the Maxwell linear model, the 10 rule was analyzed analytically.     

Evaluation of thermal deformation in electronic packages

Thermal deformation in an electronic package due to thermal strain mismatch is investigated. The warpage and the in-plane deformation of the package after encapsulation is analyzed using the laminated plate theory. An exact solution for the thermal deformation of an electronic package with circular shape is derived. Theoretical results are presented on the effects of the layer geometries and material properties on the thermal deformation. Several applications of the exact solution to electronic packaging product development are illustrated. The applications include lead on chip package, encapsulated chip on board and chip on substrate.     

A modelling of cutting for viscoplastic materials

A model is presented of stationary shearing produced during the chip formation in orthogonal cutting. The work material is supposed to be a thermal sensitive viscoplastic rigid material. The effects of material parameters, of heat conductivity and of inertia on the distribution of strain rate and of temperature in the primary shear zone are analysed. The cutting forces are calculated for a large range of cutting speeds including high speed machining. The results are obtained by developing a simple one-dimensional modelling of the primary shear zone. Experimental measurements are compared with the theoretical results.     

基于蒙特卡罗法和有限元法分析封装焊点中微孔洞对应力的影响

将蒙特卡罗法和有限元方法用于分析球珊阵列封装(BGA封装)焊点中微孔洞缺陷对焊点应力的影响。先用X射线断层扫描方法测定焊点中孔洞大小及其分布规律,然后利用Abaqus有限元分析软件建立BGA封装有限元模型,采用Anand本构方程描述焊点的应力应变响应,分析BGA封装焊点应力分布情况;并针对关键焊点即应力最大的焊点,建立了含孔洞大小和位置呈随机分布的焊点参数化有限元模型,结合试验结果,分析了孔洞直径和位置对焊点应力分布的影响。结果表明:微孔洞直径越小,越接近于焊点的表面,焊点中的应力越大。     

有限元粘弹计算中松弛模量的确定

在对粘弹材料进行有限元分析时需要确定材料Maxwell松弛模量。但很难用直接法获得相应的材料参数。本文以粘弹理论为基础,提出了线性方程求解和非线性单纯形最优解两种方法,通过材料的松弛模量KWW函数对松弛模量Maxwell函数拟合,得出了用于粘弹有限元分析的Maxwell模型粘弹参数的计算方法及其表达式。     

Analytical Solution of the General Linear Viscoelastic Radial Load Equation for Rotary Shaft Seals

The viscoelastic radial load equation for a cylindrical shell representing the seal was derived from the static solution by the correspondence principle and from first principles. The equation decoupled in space and time by a normal mode analysis was solved both by conventional methods with an impact initial condition and rather more efficiently by the Laplace transform method, for a general linear Maxwell body in plane stress. The solution was in the form of a recurrence relation, allowing representation of material properties by any number of Maxwell elements. When subjected to the standard creep test, step radial load, the seal responded with an impact displacement, followed by transient and finally steady creep. The equation was also solved by the finite element method with the semidiscrete approximation. The solution for stress relaxation and oscillatory strain are given in the Appendix.