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)     

An approach for prediction of the elasto-plastic behavior of particulate reinforced composites

A numerical approach is presented in this paper for the calculation of the elasto-plastic deformation behavior of particulate reinforced composites. The effect of shape and arrangement of particulate on the elastic modulus and tensile deformation behavior were estimated. The approach presented can consider the shape and arrangement effect of reinforcement particulate via a simple parameter called the geometrical factor (Gf). Elastic moduli and tensile deformation estimations for the particulate reinforced composites were studied. The results of proposed approach were in very good agreement with the results of finite element analysis.     

Nonlinear finite element analysis of shape memory alloy (SMA) wire reinforced hybrid laminate composite shells

This study introduces a non-linear finite element analysis approach to the procedure of modeling hybrid laminate composite shells with embedded shape memory alloy (SMA) wire subjected to coupled structural and thermal loading. Numerical analyses of SMA wire reinforced composite laminates were carried out by synergizing the non-linear laminate shell element with Brison's model of the SMA constitutive law. To verify the proposed procedure, the present illustrative applications involve rectangular laminated panels clamped along one side. Analysis results were compared with corresponding experimental results from a prior study. Several test cases that depend on the volume fraction of SMA, temperature, and ply angles are presented to illustrate the highly entangled thermo-mechanical behavior of shape memory alloy hybrid composites (SMAHCs). The results of the numerical analysis show the ability of the suggested procedure to compute the thermo-mechanical behavior of a SMAHC in accordance with the SMA's internal phase transformations induced by stress and temperature variation and demonstrate very good agreement with experimental results.     

Lifetime simulation of thermo-mechanically loaded components

The estimation of the lifetime of thermo-mechanically loaded components by testing is very costly and time-consuming, since the high temperature cycle time in practical application dominates the test duration. Common frequencies for TMF (thermo-mechanical fatigue) tests are at about 0.01 Hz compared to 10–100 Hz at HCF (high cycle fatigue) and about 0.1–1 Hz at isothermal LCF (low cycle fatigue) tests. Therefore, the simulation of fatigue life is an important design step in the fast moving and competitive automotive industry, where the steady rise of engine power and the demand for lightweight construction concurrent with enhanced reliability require an optimised dimensioning process. Methods and models are usually derived from results made on tests with specimens, since it is possible to systematically and exactly define loading parameters and measurement categories. After an extensive test programme (tensile tests, creep tests, low cycle fatigue tests and thermo-mechanical fatigue tests with different influences on specimens) it was possible to develop material models for the simulation of the time- and temperature dependent stress–strain hystereses and damage models for the simulation of the TMF lifetime. Based on this knowledge the whole simulation chain to determine the TMF life of a component is introduced: thermal calculation, mechanical calculation and lifetime calculation. Furthermore the transferability of specimen based simulation models to real components (an alternative test piece and a cylinder head) is investigated.     

SGBEM modeling of fatigue crack growth in particulate composites

The symmetric-Galerkin boundary element method (SGBEM) has previously been employed to model 2-D crack growth in particulate composites under quasi-static loading conditions. In this paper, an initial attempt is made in extending the simulation technique to analyze the interaction between a growing crack and clusters of perfectly bonded particles in a brittle matrix under cyclic loading conditions. To this end, linear elastic fracture mechanics and no hysteresis are assumed. Of particular interest is the role clusters of inclusions play on the fatigue life of particulate composites. The simulations employ a fatigue crack growth prediction tool based upon the SGBEM for multiregions, a modified quarter-point crack-tip element, the displacement correlation technique for evaluating stress intensity factors, a Paris law for fatigue crack growth rates, and the maximum principal stress criterion for crack-growth direction. The numerical results suggest that this fatigue crack growth prediction tool is as robust as the quasi-static crack growth prediction tool previously developed. The simulations also show a complex interplay between a propagating crack and an inclusion cluster of different densities when it comes to predicting the fatigue life of particulate composites with various volume fractions.     

Two scale damage model and related numerical issues for thermo-mechanical High Cycle Fatigue

On the idea that fatigue damage is localized at the microscopic scale, a scale smaller than the mesoscopic one of the Representative Volume Element (RVE), a three-dimensional two scale damage model has been proposed for High Cycle Fatigue applications. It is extended here to anisothermal cases and then to thermo-mechanical fatigue. The modeling consists in the micromechanics analysis of a weak micro-inclusion subjected to plasticity and damage embedded in an elastic meso-element (the RVE of continuum mechanics). The consideration of plasticity coupled with damage equations at microscale, altogether with Eshelby–Kröner localization law, allows to compute the value of microscopic damage up to failure for any kind of loading, 1D or 3D, cyclic or random, isothermal or anisothermal, mechanical, thermal or thermo-mechanical. A robust numerical scheme is proposed in order to make the computations fast. A post-processor for damage and fatigue (DAMAGE_2005) has been developed. It applies to complex thermo-mechanical loadings. Examples of the representation by the two scale damage model of physical phenomena related to High Cycle Fatigue are given such as the mean stress effect, the non-linear accumulation of damage. Examples of thermal and thermo-mechanical fatigue as well as complex applications on real size testing structure subjected to thermo-mechanical fatigue are detailed.     

Thermal fatigue crack networks: an computational study

Various components of nuclear reactors experience various thermo-mechanical loading. Thermal fatigue cracking has been clearly detected in reactor heat removal system (RHRS) of Pressurized Water Reactors (PWRs). The study presented here is focused on the AISI 304L stainless steel used in PWRs. The thermal fatigue behavior of this steel has been investigated using a specific thermal fatigue facility called “SPLASH test”. This test equipment allows the reproduction of multiple cracking networks similar to those detected during inspections. The present study deals with the modeling of cracking network development. It is structured in two parts: (i) experimental results and main characteristics of the crack networks, and (ii) numerical simulation on the multiple crack growth problem, using a modified stress intensity factor, and a generalized Paris’ law. In spite of simplified assumptions, the model predictions are in good agreement with observations, as far as the evolution of the mean and deepest cracks during cycling are concerned.     

Microstructure-dependent fatigue damage process in short fiber reinforced plastics

This paper proposes a numerical model of the fatigue damage process in short fiber-reinforced plastics. In the fatigue fracture of these composites, the microcracks in the polymer matrix increase with fatigue cycles and dominate the fatigue damage process. Therefore the matrix crack was modeled by the continuum damage mechanics approach while considering the microscopic fatigue damage process in the polymer matrix based on a Kachanov-type damage-evolution law. We applied the model to addressing the fatigue-cycle experiments of short glass-fiber reinforced polycarbonate conducted by Ha et al. The simulated results agreed well with the experimental results. Moreover, the simulation revealed that the dependence of the damage accumulation on the fiber orientation remarkably changes the fatigue life of the short glass-fiber reinforced plastics.     

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)     

Transformation-induced plasticity in high-temperature shape memory alloys: a one-dimensional continuum model

A constitutive model based on isotropic plasticity consideration ispresented in this work to model the thermo-mechanical behavior ofhigh-temperature shape memory alloys. In high-temperature shapememory alloys (HTSMAs), both martensitic transformation andrate-dependent plasticity (creep) occur simultaneously at hightemperatures. Furthermore, transformation-induced plasticity isanother deformation mechanism during martensitic transformation. Allthese phenomena are considered as dissipative processes to model themechanical behavior of HTSMAs in this study. The constitutive modelwas implemented for one-dimensional cases, and the results have beencompared with experimental data from thermal cycling test foractuator applications.     

增强颗粒对铝基复合材料摩擦学性能的影响

采用自制的摩擦磨损试验机考察了增强颗粒对铝基复合材料摩擦磨损性能的影响。结果表明：在基体合金、陶瓷颗粒尺寸和体积分数相同的条件下,SiC增强铝基复合材料的摩擦磨损性能优于Al2O3增强铝基复合材料;增大颗粒尺寸或增加颗粒体积分数均使得SiC颗粒增强铝基复合材料的平均摩擦系数略有降低,耐磨性能提高;在与半金属摩擦材料配副时,颗粒增强铝基复合材料的摩擦系数与基体合金的相近,耐磨性能提高了3个数量级。     

Constitutive relation of discontinuous reinforced metal-matrix composites

A micromechanical model is developed to simulate the mechanical behaviors of discontinuous reinforced composites. The analysis for a representative unit cell is based on the assumption of a periodic array of aligned reinforcements. The minimum energy principle is used to determine the unknown coefficients of the displacement field of the unit cell. The constitutive behavior of composites is studied to obtain the relationship between the main variables of matrix and reinforcements. It is concluded that the flow strength of composites is strongly influenced by volume fraction, aspect ratio of reinforcement, and the strain hardening exponent of matrix. An analytical constitutive relation of composites is obtained. The predicted results are in agreement with the existing experimental and numerical results. The project supported by the National Natural Science Foundation of China (19704100) and National Science Foundation of Chinese Academy of Sciences (KJ951-1-20)     

SIMULATION OF THE IN-PILE BEHAVIORS EVOLUTION IN NUCLEAR FUEL RODS WITH THE IRRADIATION DAMAGE EFFECTS

Based on the commercial computational software, a three-dimensional finite ele- ment model to simulate the thermo-mechanical behaviors in a nuclear fuel rod is established; By taking into consideration irradiation-swelling of the pellet and the irradiation damage effects in the cladding together with the coupling effects between the temperature field and the mechanical field, the user subroutines to define the special material performance and boundary conditions have been developed independently and validated. Three-dimensional numerical simulation of the thermo-mechanical coupling behaviors in a nuclear fuel rod is carried out, and the evolution rules of the important thermal and mechanical variables are obtained and analyzed. The research re- sults indicate that： （i） the fuel pellets will be in contact with the cladding at high burnup, which will induce a strong mechanical interaction between them; （2） the irradiation creep effect plays an important role in the mechanical behavior evolution in the nuclear fuel rod.     

高温环境下纤维复合材料蠕变损伤的细观机理研究

首先利用复合材料纤维断裂单胞模型，编制蠕变损伤子程序，对单胞模型进行蠕变损伤分析。分析了纤维／基体弹性模量比对蠕变变形、蠕变损伤以及应力场的影响。从计算结果发现，蠕变损伤首先在纤维断裂尖端起始，然后沿着一定的角度向基体外围延伸，直至完全损伤，而且纤维／基体模量比对高温环境下的复合材料蠕变损伤产生很大的影响；纤维与基体的模量相差越大，复合材料越容易变形，抵抗蠕变变形的能力就越小，蠕变损伤越严重。经过对不同韧性的基体材料进行研究，发现基体韧性低的复合材料蠕变损伤明显高于高韧性基体复合材料，表明低韧性基体复合材料抵抗蠕变破坏的能力较低。     

Influence of fiber architecture on the inelastic response of metal matrix composites

This three-part paper focuses on the effect of fiber architecture (i.e. shape and distribution) on the elastic and inelastic response of unidirectionally reinforced metal matrix composites (MMCs). The first part provides an annotated survey of the literature; it is presented as an historical perspective dealing with the effects of fiber shape and distribution on the response of advanced polymeric matrix composites and MMCs. A summary of the state of teh art will assist in defining new directions in this quickly reviving area of research. The second part outlines a recently developed analytical micromechanics model that is particularly well suited for studying the influence of these effects on the response of MMCs. This micromechanics model, referred to as the generalized method of cells (GMC), can predict the overall inelastic behavior of unidirectional, multiphase composites, given the properties of the constituents. The model is also general enough to predict the response of unidirectional composites that are reinforced by either continuous or discontinuous fibers, with different inclusion shapes and spatial arrangements, in the presence of either perfect or imperfect interfaces and/or interfacial layers. Recent developments on this promising model, as well as directions for future enhancements of the model's predictive capability, are included. Finally, the third part provides qualitative results generated by using GMC for a representative titanium matrix composite system, SCS-6/TIMETAL 21S. The results presented correctly demonstrate the relative effects of fiber arrangement and shape on the longitudinal and transverse stress-strain and creep behavior of MMCs, with both strong and weak fiber/matrix interfacial bonds. Fiber arrangements included square, square-diagonal, hexagonal and rectangular periodic arrays, as well as a random array. The fiber shapes were circular, square, and cross-shaped cross-sections. The effect of fiber volume fraction on the stress-strain response is also discussed, as is the thus-far poorly documented strain rate sensitivity effect. In addition to the well-documented features of the architecture-dependent behavior of continuously reinforced two-phase MMCs, new results are presented about continuous multiphase internal architectures. Specifically, the stress-strain and creep responses of composites with different size fibers and different internal arrangements and bond strengths are investigated; the aim was to determine the feasibility of using this approach to enhance the transverse toughness and creep resistance of titanium matrix composites (TMCs).     

SMA短纤维增强复合材料在热载下的相交特性

在形状记忆合金（ＳＭＡ）复合材料研究中,相变特性的研究是一个主要的工作．基于Ｅｓｈｅｌｂｙ的等效夹杂模型和Ｍｏｒｉ和Ｔａｎａｋａ的场平均法,考虑到ＳＭＡ材料的强物理非线性,发展了增量型的等效夹杂模型（ＩｎｃｒｅｍｅｎｔａｌＥｑｕｉｖａｌｅｎｔＩｎｃｌｕｓｉｏｎＭｏｄｅｌ）．考虑在某一温度循环条件下讨论形状记忆合金短纤维增强的铝基复合材料在热载下的相变行为．特别研究了ＳＭＡ短纤维复合材料在变温过程中纤维几何尺寸、体积分数等参数对ＳＭＡ复合材料的相变行为和ＳＭＡ内残余应力等的影响．这些工作对于指导材料设计和了解ＳＭＡ复合材料热机械特性是颇有意义的．     

Model for Elastic Modulus of Multi-Constituent Particulate Composites

In this paper, a methodology has been developed to accurately predict the elastic properties of multi-constituent particulate composites by accounting for irreversible effects, such as energy loss that arises due to internal friction. The complex dependence on loading density and particle properties (i.e., size, shape, morphology, etc.) is investigated in terms of their effects on the effective elastic modulus of the composite. Confirmed by experimental data from the compression loading of individual Ni and Al particles dispersed in an epoxy matrix, it is believed that this approach captures the effects of internal friction, consequently providing a more accurate and comprehensive representation for predicting and understanding the material behavior of multi-constituent particulate reinforced composites. The present methodology provides a model to directly compare the elastic modulus from an uncomplicated test, such as dual-cantilever beam loading in dynamic mechanical analysis (DMA), to the modulus obtained by other more complex experimental methods such as quasi-static compression. The model illustrates an efficient method to incorporate input data from DMA to represent realistic elastic moduli, hence promising for the characterization and design of particulate composites.     

Micromechanics-based thermoelastic model for functionally graded particulate materials with particle interactions

Thermoelastic behavior of functionally graded particulate materials is investigated with a micromechanical approach. Based on a special representative volume element constructed to represent the graded microstructure of a macroscopic material point, the relation between the averaged strains of the particle and matrix phases is derived with pair-wise particle interactions, and a set of governing equations for the thermoelastic behavior of functionally graded materials is presented. The effective coefficient of thermal expansion at a material point is solved through the overall averaged strain of two phases induced by temperature change under the stress-free condition, and is shown to exhibit a weak anisotropy due to the particle interactions within the graded microstructure. When the material gradient is eliminated, the proposed model predicts the effective coefficient of thermal expansion for uniform composites as expected. If the particle interactions are disregarded, the proposed model recovers the Kerner model. The proposed semi-analytical scheme is consistent and general, and can handle any thermal loading variation. As examples, the thermal stress distributions of graded thermal barrier coatings are solved for two types of thermal loading: uniform temperature change and steady-state heat conduction in the gradation direction.     

航空涡轮盘多轴蠕变-疲劳寿命预测及对比研究

针对几种经典和新发展的蠕变-疲劳寿命模型开展综述介绍,并建立预测航空涡轮盘在循环热-机蠕变-疲劳载荷谱下蠕变-疲劳行为的数值流程,对某型航空涡轮盘的蠕变-疲劳损伤和寿命进行预测和对比．结果表明：等效应变法与临界平面法得出的疲劳损伤差距较小,等效应变法由于数值计算简单,工程适用性更强．寿命-时间分数(TF)法由于无法考虑应力松弛效应,给出了最为保守的蠕变损伤预测,其对盘体应力三轴度引起的损伤不敏感;延性耗竭法(DE)法仅以蠕变应变率作为损伤因素,虽考虑多轴蠕变因子的影响,但是给出的蠕变损伤过小;修正应变能密度耗竭(MSEDE)法综合考虑蠕变应变与应力松弛,并且考虑多轴蠕变因子与弹性跟随效应的影响,结合疲劳损伤模型可以给出合理的蠕变、疲劳损伤比例,其预测结果更加合理．     

对二维编织复合材料弹性、热、强度及失效分析模型的评论

纺织结构作为聚合物复合材料的增强相在许多工业应用中变得非常重要,例如在航海与航空 领域中,由于其刚度及强度与其重量的高比值而倍受欢迎.由于工业及工程应用的需求, 研究纺织复合材料的弹性性质及失效行为变得非常重要.这篇文章重点评论了关于二维编织复合材料弹性、热、强度及失效分析的数值及解析模型,给出了主要的建模技术及方法. 同时也简单给出了编织复合材料从最初的一维模型到最近三维模型的发展.本文的目的不是对所 论模型的数学方法进行详细分析,而是告知研究者关于先前工作的主要思想. 这篇评论总共引用了122篇文献.