Effect of solder filler thickness on the mechanical stability of fiber-solder-ferrule joint under temperature cyclic loading

The base materials of package and ferrule are often gold-coated Kovar and Invar, they both have relatively low coefficient of thermal expansion (CTE). Solder 63Sn37Pb dissolves Au substantially and forms brittle AuSn₄, which may cause catastrophic failure in the fiber-solder-ferrule (FSF) joint in the long-term application. It is well known that thermal fatigue creep is one of the crucial factors affecting the life and reliability of a solder joint in electronic and optoelectronic assemblies. Therefore, it is important to understand the behavior of the FSF joint under thermal cyclic loading. In this study, four different thicknesses of solder filler in a FSF joint were examined. By using the finite element method (FEM), the equivalent creep strains of eutectic lead-tin solder were compared. The joints were subjected to 5 cycles of temperature cycling test, i.e., −65 to 150^∘C. It was found that the thicker solder filler is subjected to a larger equivalent creep strain than the thinner solder filler. It is discussed the vertical shift of the optical fiber, which is sensitive to temperature and has effects on the power loss coupling. Modeling and experimental results show that 0.5 mm is the best inner diameter of ferrule that provides the lowest displacement and, thus, the lowest power loss under temperature cycle.     

底充胶及其材料模型对倒装焊热循环可靠性的影响

对倒装焊电子封装可靠性进行了热循环实验和有限元模拟,结果表明,有底充胶（underfill)时,SnPb焊点的热循环寿命可提高约16倍,并确定了Coffin-Manson半经验方程的参数,采用3种底充胶材料模型,亦即定常弹性模型,温度相关弹性模型和粘弹性材料模型,描述了底充胶U8347－3的力学性能。模拟结果表明,材料模型影响计算得到的SnPb焊点的塑性应范围,封装形变以及底充胶／芯片界面应力,采用弹性材料模型可能过高估计了SnPb焊点的热循环寿命和界面应力。     

Large viscoplastic deformations of shells. Theory and finite element formulation

The paper is concerned with large viscoplastic deformations of shells when the constitutive model is based on the concept of unified evolution equations. Specifically the model due to Bodner and Partom is modified so as to fit in the frame of multiplicative viscoplasticity. Although the decomposition of the deformation gradient in elastic and inelastic parts is employed, no use is made of the concept of the intermediate configuration. A logarithmic elastic strain measure is used. An algorithm for the evaluation of the exponential map for nonsymmetric arguments as well as a closed form of the tangent operator are given. On the side of the shell theory itself, the shell model is chosen so as to allow for the application of a three-dimensional constitutive law. The shell theory, accordingly, allows for thickness change and is characterized by seven parameters. The constitutive law is evaluated pointwise over the shell thickness to allow for general cyclic loading. An enhanced strain finite element method is given and various examples of large shell deformations including loading-unloading cycles are presented.     

Topology optimization of finite strain viscoplastic systems under transient loads

A transient finite strain viscoplastic model is implemented in a gradient‐based topology optimization framework to design impact mitigating structures. The model's kinematics relies on the multiplicative split of the deformation gradient, and the constitutive response is based on isotropic hardening viscoplasticity. To solve the mechanical balance laws, the implicit Newmark‐beta method is used together with a total Lagrangian finite element formulation. The optimization problem is regularized using a partial differential equation filter and solved using the method of moving asymptotes. Sensitivities required to solve the optimization problem are derived using the adjoint method. To demonstrate the capability of the algorithm, several protective systems are designed, in which the absorbed viscoplastic energy is maximized. The numerical examples demonstrate that transient finite strain viscoplastic effects can successfully be combined with topology optimization.     

Experimental and numerical investigation on the reliability of leadfree solders

To assess the lifetime of leadfree solder joints, it is necessary to investigate their creep and failure behavior under cyclic thermo-mechanical loading. In connection with finite element analyses the use of an appropriate material model is necessary. The following paper reports on the implementation of a specific version of the viscoplastic constitutive model of Chaboche in the FEM-code ABAQUS, the experimental program for the identification of the material parameters of a Sn–Ag–Cu solder and a comparison of some numerical and experimental results.     

Nonlinear analysis of plastic ball grid array solder joints

A nonlinear finite element analysis was carried out to investigate the viscoplastic deformation of solder joints in a ball grid array (BGA) package under temperature cycling. The effects of constraint on printed circuit board (PCB) and stiffness of substrate on the deformation behavior of the solder joints were also studied. A relative damage stress was adopted to analyze the potential failure sites in the solder joints. The results indicated that high inelastic strain and strain energy density were developed in the joints close to the package center. On the other hand, high constraint and high relative damage stress were associated with the joint closest to the edge of the silicon chip which was regarded as the most susceptible failure site if cavitation instability is the dominant failure mechanism. Increasing the external constraint on PCB causes a slight increase in stress triaxiality and relative damage stress in the joint closest to the edge of the silicon die. The relative damage stress is not sensitive to the Young's modulus of the substrate.     

热循环条件下SnAgCu/Cu焊点金属间化合物生长及焊点失效行为

研究了热循环过程中SnAgCu/Cu焊点界面金属间化合物的生长规律及焊点疲劳失效行为。提出了热循环条件下金属间化合物生长的等效方程以及焊点界面区不均匀体模型,并用有限元模拟的方法分析了热循环条件下焊点界面区的应力应变场分布及焊点失效模式。研究结果表明:低温极限较低的热循环,对应焊点的寿命较低。焊点的失效表现为钎料与金属间化合物的界面失效,且金属间化合物厚度越大,焊点中的累加塑性功密度越大,焊点越容易失效。     

超声波振动激励下焊点失效分析与改进

为了解决管脚焊点在超声波焊接后出现的失效问题，研究用数值仿真的方法来进行建模分析，并提出改进方法。根据超声波能量转化形式，简化焊接系统模型，提出适合仿真的加载方法和边界条件，并根据热-力耦拿尊真尊温度场结果分析模型的可行性。针对具体的手机电池产品，建立超声波焊接系统整体三维有限元模型，利用仿真结果分析失效原因，提出减振措施并做实验验证。     

Design of solder joints for fundamental studies on the effects of electromigration

The continuous miniaturization of high performance electronic devices has reached a level at which current densities are large enough to make electromigration (EM) a significant issue affecting the electrical and mechanical reliability of solder joints. A new design of solder joints that controls the extent of regions experiencing relatively uniform current density, as well as regions with large current density gradient was developed. Current density distribution of this newly designed solder joint was calculated using finite element analysis (FEA), which was used to guide the characterization of EM of real solder joints. As a part of the effort in evaluating the suitability of the new joint configuration for evaluating the fundamental issues in EM, eutectic PbSn solder joints were fabricated using this design. EM effects due to applied current, current density distribution, and joint thickness of eutectic PbSn solder joints present in this joint configuration were investigated. Findings based on this new design can facilitate fundamental studies of EM issues that affect the reliability of solder joints.     

A review of mechanical properties of lead-free solders for electronic packaging

The characterization of lead-free solders, especially after isothermal aging, is very important in order to accurately predict the reliability of solder joints. However, due to lack of experimental testing standards and the high homologous temperature of solder alloys (T _h > 0.5T _m even at room temperature), there are very large discrepancies in both the tensile and creep properties provided in current databases for both lead-free and Sn–Pb solder alloys. Some recent researches show that the room temperature aging has significant effects on mechanical properties of solders. This paper is intended to review all available data in the field and give rise to the possible factors including room temperature effects which causes the large discrepancies of data. This review of the research literatures has documented the dramatic changes that occur in the constitutive and failure behavior of solder materials and solder joint interfaces during isothermal aging. However, these effects have been largely ignored in most previous studies involving solder material characterization or finite element predictions of solder joint reliability during thermal cycling. It is widely acknowledged that the large discrepancies in measured solder mechanical properties from one study to another arise due to differences in the microstructures of the tested samples. This problem is exacerbated by the aging issue, as it is clear that the microstructure and material behavior of the samples used in even a single investigation are moving targets that change rapidly even at room temperature. Furthermore, the effects of aging on solder behavior must be better understood so that more accurate viscoplastic constitutive equations can be developed for SnPb and SAC solders. Without such well-defined relationship, it is doubtful that finite element reliability predictions can ever reach their full potential.     

Numerical analysis of viscoplastic axisymmetric shells based on a hybrid strain finite element

The viscoplastic deformation behavior of the shell is governed by any of the more recently proposed unified constitutive models with internal state variables and with the assumption that the total strain rate tensor can be decomposed additively into an elastic and an inelastic part. For the numerical analysis of viscoplastically deformed shells we use a hybrid strain finite element based on a geometrically linear theory of inelastic shells proposed by Kollmann and Mukherjee (1985). This theory gives the reduction of a two-field variational principle originally proposed by Oden and Reddy (1974) for elastic shells to the shell midsurface. It contains strain and displacement rates as variables to be independently varied. The shell formulation of this variational principle is the basis for the present work. First, a general hybrid finite element model is derived in which the shape functions for the strain and displacement rates can be polynomials of different order. Here we use the term hybrid in the sense of Pian (1988), i.e. in our two-field finite element the strain rates are condensed statically on the element level, leaving nodal displacements as the only unknowns in the final matrix equation. Then the finite element model is specialized for an axisymmetrically loaded conical shell with linear approximation of the strain rate field and quadratic interpolation of the displacement rates. Special emphasis is given to the derivation of the inelastic pseudo-forces and pseudo-moments. Numerical results for elastically and viscoplastically deformed shells are presented, where viscoplastic deformations are described by Hart's (1976) constitutive model.     

The viscoplastic crack growth behavior of a compact tension specimen using the Bodner-Partom flow law

Creep crack growth in IN-100 was studied using a hybrid experimental-numerical procedure (HEN). This procedure couples displacement data generated during creep crack growth tests to a finite element model of the test specimen. A standard compact tension specimen geometry was used in all cases.The computer program used herein is a 2-dimensional plane stress/plane strain code that uses constant strain triangular elements and has the ability to release fixed nodes to simulate crack growth. This procedure is facilitated by using a Gauss-Seidel iterative solution technique that allows appropriate terms in the stiffness matrix to be changed between timesteps to accommodate changing boundary conditions due to crack growth. A variable timestep algorithm maximizes the timestep size during the analysis while maintaining good accuracy.Constitutive equations proposed by Bodner and Partom were used to account for the nonlinear, viscoplastic material behavior exhibited by IN-100 at high temperatures. These equations were integrated through time by a linear Euler extrapolation technique.Crack growth estimates generated with the HEN procedure were within 20% of the actual crack growth in the test specimens after times ranging from 5–14 hr. Additionally, a critical stress and an accumulated stress history criterion for crack growth were both found to show promise. Both of these criteria merit further investigation.     

Temperature rise in a viscoplastic material during dynamic crack growth

Dynamic steady-state crack growth has been analyzed under mode I plane stress, small-scale yielding conditions using a finite element procedure. A Perzyna type viscoplastic constitutive equation has been employed in this analysis. The viscoplastic work rate is converted into heat input and the temperature distribution is determined by solving the governing conduction/convection equation also by a finite element method. The Stream-line Upwinding Petrov-Galerkin formulation has been employed for this purpose because of the high Péclet number that results in such a type of analysis. The effect of strain rate sensitivity and crack speed on the temperature distribution near the crack tip is examined.     

A nonlinear viscoelastic–viscoplastic model for adhesives

We consider the nonlinear viscoelastic–viscoplastic behavior of adhesives. We develop a one-dimensional nonlinear model by combining Schapery’s nonlinear single integral model and Perzyna’s viscoplastic model. The viscoplastic strain was solved iteratively using the von Mises yield criterion and nonlinear kinematic hardening. The combined viscoelastic–viscoplastic model was solved using Newton’s iteration and implemented into a finite element model. The model was calibrated using creep-recovery data from bulk adhesives and verified from the cyclic behavior of the bulk adhesives. The finite element model results agreed with experimental creep and cyclic responses, including recoverable and permanent strain after load removal. Although the contribution of the viscoplastic strain was small, both viscoplastic and viscoelastic components of strain response were required to describe the adhesive creep and cyclic response.

     

Viscoplastic response of multiphase composites using a strain-compatible volume-averaging method

The strain-compatible volume-averaging method, a recently developed micromechanical method for the analysis of multi-phase composites, is extended here to deal with viscoplastic behavior. Specifically, the method is applied to the problem of finding the viscoplastic response of a boron–aluminum unidirectional composite. A unified Bodner–Partom viscoplasticity model is used to model the inelastic behavior of the aluminum matrix of the composite. The inelastic response is obtained for different loading conditions and for several different fiber architectures. The influence of the loading orientation on the viscoplastic response of the composite is investigated using the strain-compatible volume-averaging method and the widely utilized generalized method of cells. It is shown that the response predictions of the strain-compatible volume-averaging method are invariant with respect to coordinate transformations while those of the generalized method of cells are not. This is due to the fact that the new method accurately models shear-coupling, a feature that is absent in the generalized method of cells. The results obtained with the new method are also compared with those of the finite element method. As far as the effective response of the composite is concerned, it is found that the results of the strain-compatible volume-averaging method are in good agreement with those of the other two methods. It is found however, that the computational cost of each of the three methods is proportional to the accuracy of the microstress field as might be expected.     

板壳非线性分析的新理论新方法

提出了板壳非线性分析的新理论新方法。首先建立了下列几个新的本构关系:塑性应变向量增量与总应变向量增量的新关系,热塑性应变向量增量与总应变向量增量及温度应变向量增量的新关系,粘塑性应变向量增量与总应变向量增量的新关系,热粘塑性应变向量增量与总应变向量增量及温度应变向量增量的新关系。这些关系分别称为弹塑性应变增量理论、热弹塑性应变增量理论、弹粘塑性应变增量理论及热弹粘塑性应变增量理论,避开了屈服曲面、加载曲面、流动法则及复杂的非线性应力应变关系。其次建立了非线性样条无网格法,这种方法是以新的本构关系、几何非线性理论、变分原理、广义变分原理、加权残数法及样条离散化为基础建立的,避免了经典本构关系及有限元法带来的巨大困难及缺陷,不仅计算简便,而且精度高,收敛速度很快。建立了板壳非线性分析的统一格式,对板壳的几何非线性分析、材料非线性分析及双重非线性分析都适用。     

Prediction of welding buckling distortion in a thin wall aluminum T joint

In this paper, local and global welding buckling distortion of a thin wall aluminum T joint is investigated. A thermo-elastic–viscoplastic model is employed to determine longitudinal residual stresses; analysis of thermal model and elastic–viscoplastic (Anand) model are uncoupled. Molten puddle motion (speed of welding) is modeled by using time dependent birth and death element method. Three dimensional nonlinear-transient heat flow analysis has been used to obtain the temperature distribution, and then by applying thermal results and using three dimensional Anand elastic–viscoplastic model, stress and deformation distributions are obtained during welding and after cooling. Local buckling is investigated by analyzing the history of stress and strain relations. Local buckling is assumed to occur at a point if a small change in the magnitude of stress causes large deformation during of the welding process. By applying residual stresses on a structural model and using eigenvalue methods, global buckling instability of the welded structure is determined.     

Low cycle fatigue behavior of a eutectic 80Au/20Sn solder alloy

The eutectic 80Au/20Sn solder alloy is widely used in high power electronics and optoelectronics packaging. In this study, low cycle fatigue behavior of a eutectic 80Au/20Sn solder alloy is reported. The 80Au/20Sn solder shows a quasi-static fracture characteristic at high strain rates, and then gradually transforms from a transgranular fracture (dominated by fatigue damage) to intergranular fracture (dominated by creep damage) at low strain rates with increasing temperature. Coffin-Manson and Morrow models are proposed to evaluate the low cycle fatigue behavior of the 80Au/20Sn solder. Besides, the 80Au/20Sn solder has enhanced fatigue resistance compared to the 63Sn/37Pb solder.