焊锡材料的应变率效应及其材料模型

采用分离式霍普金森压杆和拉杆实验,研究了含铅Sn37Pb、无铅Sn3.5Ag和Sn3.0Ag0.5Cu3种焊锡材料在600~2200s^{-1}应变率下的力学性能,得到了它们在不同应变率下的应力应变曲线. 根据实验数据建立了3种焊锡材料的应变率无关弹塑性材料模型和率相关Johnson-Cook材料模型,并用于模拟板级电子封装在跌落冲击载荷下焊锡接点的力学行为. 结果表明,高应变率下无铅焊料比含铅焊料对应变率更敏感,其抗拉强度为含铅焊料的1.5倍,其韧性也明显高于含铅焊料;在跌落冲击过程中,焊锡接点经历的应变率可达到1000s^{ -1}左右;给出的率相关Johnson-Cook材料模型能预测出比率无关的弹塑性模型更合理的应力应变结果.      

Anisotropic Mechanical Properties of SAC Solder Joints in Microelectronic Packaging and Prediction of Uniaxial Creep Using Nanoindentation Creep

In this paper, the mechanical properties and creep behavior of lead-free solder joints has been characterized by nano-mechanical testing of single grain SAC305 solder joints extracted from plastic ball grid array (PBGA) assemblies. The anisotropic mechanical properties characterized include the elastic modulus, hardness, and yield stress. An approach is suggested to predict tensile creep strain rates for low stress levels using nanoindentation creep data measured at very high compressive stress levels. The uniaxial creep rate measured on similarly prepared bulk (large) specimens was found to be of the same order-of-magnitude as the creep rate observed in single-grain BGA joints, with chararacteristically (slightly) higher creep strains measured during nanoindentation. This suggests that the same creep mechanism operates in both size domains. Electron backscattered diffraction (EBSD) and nanoindentation testing further showed that the modulus, hardness, and creep properties of solder joints are highly dependent on the crystal orientation.     

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。     

An analysis of ductile rupture in notched bars

Ductile fracture in axisymmetric and plane strain notched tensile specimens is analyzed numerically, based on a set of elastic-plastic constitutive relations that account for the nucleation and growth of microvoids. Final material failure by void coalescence is incorporated into the constitutive model via the dependence of the yield function on the void volume fraction. In the analyses the material has no voids initially; but as the voids nucleate and grow, the resultant dilatancy and pressure sensitivity of the macroscopic plastic flow influence the solution significantly. Considering both a blunt notch geometry and a sharp notch geometry in the computations permits a study of the relative roles of high strain and high triaxiality on failure. Comparison is made with published experimental results for notched tensile specimens of high-strength steels. All axisymmetric specimens analyzed fail at the center of the notched section, whereas failure initiation at the surface is found in plane strain specimens with sharp notches, in agreement with the experiments. The results for different specimens are used to investigate the circumstances under which fracture initiation can be represented by a single failure locus in a plot of stress triaxiality vs effective plastic strain.     

Electromigration induced strain field simulations for nanoelectronics lead-free solder joints

Electromigration is a major road block on the way to realization of nanoelectronics. Determination of plastic deformation under high current density is critical for prediction of electromigration failure. A new displacement–diffusion coupled model is proposed and implemented using finite element method. The model takes into account viscoplastic behavior of solder alloys, as a result, vacancy concentration evolution and electromigration process are accurately simulated. Finite element simulations were performed for lead-free solder joints under high current density and compared with experimental moiré interferometry measurements. The comparison validates the model.     

Modified Burzynski criterion with non-associated flow rule for anisotropic asymmetric metals in plane stress problems

The Burzynski criterion is developed for anisotropic asymmetric metals with the non-associated flow rule (NAFR) for plane stress problems. The presented pressure depending on the yield criterion can be calibrated with ten experimental data, i.e., the tensile yield stresses at 0°, 45°, and 90°, the compressive yield stresses at 0°, 15°, 30°, 45°, 75°, and 90° from the rolling direction, and the biaxial tensile yield stress. The corresponding pressure independent plastic potential function can be calibrated with six experimental data, i.e., the tensile R-values at 0°, 15°, 45°, 75°, and 90° from the rolling direction and the tensile biaxial R-value. The downhill simplex method is used to solve these ten and six high nonlinear equations for the yield and plastic potential functions, re- spectively. The results show that the presented new criterion is appropriate for anisotropic asymmetric metals.     

A viscoplastic constitutive model with effect of aging

It is recognized experimentally that differences in plastic flow stress due to the change in strain rate of SUS304 stainless steel are found to decrease after cyclic preloadings, but minimal change is observed in relaxation properties. Therefore, viscosity function based on tensile stress–strain properties differs from that obtained from relaxation behavior. For such case, the existing visco-plastic constitutive concept, such as the so-called overstress model where only viscosity is taken into consideration, has a poor capability in predicting the time-dependent mechanical properties systematically. A new viscoplastic constitutive concept is presented to analyze the phenomenon. In the constitutive concept, the dynamic strain aging even at room temperature, as well as viscosity, are introduced as the dominant factors of the time-dependent plastic deformation. An experimental technique is proposed and some experimental results are presented to estimate the effects of aging and viscosity separately on the time-dependency of a SCM435 low alloyed steel under tensile loading. The proposed constitutive model with aging is verified for the systematical predictions of both plastic flow properties and relaxation behavior of the SCM435 low alloyed steel.     

A FLUID–STRUCTURE MODEL FOR FAST BRITTLE FRACTURE IN PLASTIC PIPES

This paper presents an intermediate stage in the development of a unified computational model based on finite volume (FV) discretization, for coupled fluid–structure analysis of rapid crack propagation fluid-pressurized plastic pipes. The pressure profile behind the crack tip, which is the main source of the crack driving force, is computed by combining a one-dimensional (1-D) gas flow analysis with FV stress analysis of the pipe. The coupled model is then validated against experimental results and used to determine the dependence of crack driving force on crack speed and to study the effect of various physical parameters on crack driving force.     

6061-T6铝合金动态拉伸本构关系及失效行为

采用HMH-206高速材料试验机开展了6061-T6铝合金在0.001～100 s-1应变率范围内的静、动态拉伸力学性能实验,分析了其应力-应变响应特征和应变率敏感性,讨论了应变率对6061-T6铝合金流动应力和应变率敏感性指数的影响,并基于实验结果对Johnson-Cook本构模型进行了修正。结合缺口试件的实验结果和模拟数据,得到了材料的Johnson-Cook失效模型参数,并对模型的准确性和适用性进行了验证。结果表明,在拉伸载荷作用下,6061-T6铝合金表现出明显的应变硬化特征和应变率敏感性,其流动应力随应变率的升高而提高,修正的Johnson-Cook本构模型可以描述材料的动态塑性流动行为,建立的Johnson-Cook失效模型能够表征材料的断裂失效行为。     

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)     

Numerical study of the plastic behaviour in tension of welds in high strength steels

The influence of the mismatch between material properties and constraint on the plastic deformation behaviour of the heat affected zone of welds in high strength steels is investigated in this study, using finite element simulations. An elastoplastic implicit three-dimensional finite element code (EPIM3D) was used in the analysis. The paper presents the mechanical model of the code and the methodology used for the numerical simulation of the tensile test of welded joints. Numerical results of the tensile test of welded samples with different hypothetical widths for the Heat Affected Zone and various material mismatch levels are shown. The analysis concerns the overall strength and ductility of the joint and in relation to the plastic behaviour of the heat affected zone. The influence of the yield stress, tensile strength and constraint on the stress and plastic strain distribution in the soft heat affected zone is also discussed.     

基于微结构演化的V5Cr5Ti合金塑性本构模型

为合理描述V5Cr5Ti合金的塑性变形行为,本文建立了基于微结构演化的塑性本构模型。首先,采用小尺寸试样开展了V5Cr5Ti合金单轴拉伸试验,并对其在不同应变程度下的微结构演化特征进行了分析。研究发现,影响V5Cr5Ti合金塑性变形行为的主要因素是位错密度演化以及团簇状和弥散析出相。据此建立了位错密度演化方程、组分相含量体积分量演化方程,并考虑团簇状和弥散状第二相对V5Cr5Ti合金流动应力的影响,进一步建立了包括非热应力、热激活应力和弥散相强化应力的流动应力关系式。最后,根据隐式应力更新算法对新模型进行了有限元实现,并与实验结果进行比较,验证了新模型的合理性和预测精度。     

金属材料在复杂应力状态下的塑性流动特性及本构模型

工程应用中,金属材料和结构往往处于复杂应力状态。材料的塑性行为会受到应力状态的影响,要精确描述材料在复杂应力状态下的塑性流动行为,必须在本构模型中考虑应力状态效应的影响。然而,由于在动态加载下材料的应变率效应和应力状态效应相互耦合、难以分离,给应力状态效应的研究和模型的建立造成很大困难。通过对Ti-6Al-4V钛合金材料开展不同加载条件下的力学性能测试,提出了一个包含应力三轴度和罗德角参数影响的新型本构模型,并通过VUMAT用户子程序嵌入ABAQUS/Explicit软件。分别采用新提出的塑性模型和Johnson-Cook模型对压剪复合试样的动态实验进行了数值模拟。结果表明,新模型不仅在对材料本构曲线的拟合方面具有较强的优势,而且由该模型所得到的透射脉冲和载荷-位移曲线均更加准确。因此,该模型能够更精确地描述和预测金属材料在复杂应力状态下的塑性流变行为。     

基于微结构演化的V5Cr5Ti合金塑性本构模型

为合理描述V5Cr5Ti合金的塑性变形行为,本文建立了基于微结构演化的塑性本构模型。首先,采用小尺寸试样开展了V5Cr5Ti合金单轴拉伸试验,并对其在不同应变程度下的微结构演化特征进行了分析。研究发现,影响V5Cr5Ti合金塑性变形行为的主要因素是位错密度演化以及团簇状和弥散析出相。据此建立了位错密度演化方程、组分相含量体积分量演化方程,并考虑团簇状和弥散状第二相对V5Cr5Ti合金流动应力的影响,进一步建立了包括非热应力、热激活应力和弥散相强化应力的流动应力关系式。最后,根据隐式应力更新算法对新模型进行了有限元实现,并与实验结果进行比较,验证了新模型的合理性和预测精度。     

Study of Pressure Sensitive Plastic Flow Behaviour of Gasket Materials

The mechanical behaviour of the materials used as compressible gasket in the ultra high pressure apparatus is investigated. Materials such as pyrophyllite and talc, showing a pressure sensitive plastic flow behaviour were considered and a testing configuration was set up for studying the dependence of their plastic response on the hydrostatic component of the stress tensor, according to the Drucker-Prager criterion. A Finite Element modelling of the test was performed to evaluate the specimen response and the local stress condition, during loading. The Finite Element results were validated by comparison with those of a specific experimental characterisation. A parametric analysis was then carried out, by varying the materials constitutive behaviour, in order to build up a data base of representative curves. In this way an algorithm was developed, with the aim of determining the material constitutive behaviours by the analysis of the experimental data. The proposed procedure was then used to study the mechanical response of different gasket materials.     

Dynamic strain aging and related instabilities: experimental,theoretical and numerical aspects

Experimental data from uniaxial tensile tests on smooth and notched specimens of aluminium alloy 5083-H116 show that the material exhibits negative strain-rate sensitivity for strain rates within a certain range. The negative strain-rate dependence, which is attributed to dynamic strain aging, leads to serrated stress–strain curves, discontinuous plastic flow and propagating deformation bands during plastic straining (also denoted as the Portevin–Le Chatelier effect). Band analysis and linear perturbation analysis are performed using simple elastic-viscoplastic constitutive equations that include negative strain-rate sensitivity in a simplified manner. The negative strain-rate sensitivity allows for jumps in the plastic strain rate, which in turn permits the existence of localisation bands for the elastic-viscoplastic model. The simple elastic-viscoplastic constitutive model has been implemented in LS-DYNA, and non-linear finite element simulations of smooth and notched tensile test specimens are performed, allowing more detailed investigations into the effects of the negative strain-rate sensitivity on the material's behaviour.     

A simple plasticity model for prediction of non-coaxial flow of sand

A bounding surface plasticity model for non-coaxiality, another aspect of anisotropic behavior of sands under rotation of principal stress axes; is developed in the critical state framework. Numerous experimental evidences exist that corroborate dependence of plastic shear strain rate direction on inherent fabric anisotropy. At first, general expressions for plastic strain rate with respect to possible emerge of non-coaxial flow are obtained. Consequently, using an anisotropy state parameter that is specially developed for this model and accounts for the interaction between imposed loading and soil fabric; effect of anisotropy on plastic flow direction is taken into account. Besides, novel circumstances are proposed for plastic modulus and dilatancy under rotation of principal stress axes. Finally, it is shown that the model is able to simulate successfully the non-coaxial behavior of sands subjected to principal stress axes rotation.     

爆炸载荷下飞机典型加筋结构毁伤特性

为了探讨爆炸载荷下飞机典型加筋结构的响应规律,开展了爆炸实验,获得了飞机典型结构表面的反射超压历程,加筋结构的应变、位移等结构响应数据。并结合实验结果建立了高置信度的有限元模型,研究了所选结构的变形分布规律和塑性毁伤特性。结果表明,对于本文中选取的飞机加筋结构,塑性变形除了会开始于常见的加强筋中点外,还会开始于加强筋与加强筋联结处、加强筋与外框联结处。这主要是受加筋板的双向拉伸变形和应力集中的影响。进一步总结了随冲击波正压时间增长,能够引发加筋结构塑性变形的有效冲量和反射超压峰值阈值。研究结果对飞机气动外形、抗爆能力设计具有重要意义。     

Thermomechanical instability associated with heat release during plastic flow

The effect of heat generation accompanying plastic deformation on instability of uniform plastic flow is considered. Linear stability analysis is performed taking into account both classical necking (geometrical effect) and thermomechanical coupling. Two types of conditions imposed in tensile testing are considered: those of constant (time and coordinate independent) imposed load and constant imposed cross-head velocity. A central issue in the paper is instability of plastic flow at extremely low temperatures (4.2 K to 10 K). Instability conditions are formulated, taking into account the temperature dependence of the thermal parameters. An example of tensile deformation of a thin Al-Mg rod is considered in some detail. Available experimental data are explained on the basis of stability analysis.     

A modified model for simulating latent hardening during the plastic deformation of rate-dependent FCC polycrystals

A strain hardening model for the plastic deformation of rate-dependent FCC crystals is proposed based on experimental observations previously reported for single crystals. This model, which is an extension of that employed by et al. [1983], includes both the self-hardening and latent hardening of the slip systems. The differential hardening of the latent systems is assumed to arise from the interaction between glide dislocations and forests. With this hardening model and a rate-sensitive crystal plasticity theory, the deformation behavior of FCC polycrystals can be predicted from the deformation response of the constituent single crystals. As examples, the uniaxial tensile behaviour of pure aluminum and copper polycrystals is simulated using the extended model, and the results are compared with published experimental data. The effects of latent hardening on polycrystal deformation, especially on flow stress and the formation of tensile textures, are discussed.