Multiscale modeling of the anisotropic transient creep response of heterogeneous single crystal SnAgCu solder
Multiscale modeling of the anisotropic transient creep response of heterogeneous single crystal SnAgCu solder
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DOI：
10.1016/j.ijplas.2015.10.011
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发表时间：
2016-03-01
影响因子：
9.8
通讯作者：
Bieler, T. R.
中科院分区：
文献类型：
--
作者：
Mukherjee, S.;Zhou, B.;Bieler, T. R.
功能SnAgCu（SAC）焊点由于其粗晶粒的微观结构，结合单晶Sn所表现出的严重各向异性，缺乏统计均匀性，使得每个接头在机械行为方面都是独特的。在这项研究中，提出了一个机制的多尺度建模框架，预测成分和微观结构对单晶SnAgCu（SAC）焊料的各向异性瞬态蠕变响应的影响。第I层由单晶共晶Sn-Ag合金组成，纳米级Ag 3Sn颗粒嵌入单晶Sn基质中。第II层由单晶SAC焊料组成，其由第I层的共晶Sn-Ag相包围的Sn枝晶组成。第一层各向异性瞬态蠕变模型是基于位错力学。Tier II模型使用Tier I的结果作为输入，并基于各向异性复合材料微观力学。在Tier I中，蠕变变形由纳米级Ag 3Sn颗粒的位错阻碍和回复控制，回复是速率控制机制。位错攀移和位错脱离的Ag 3Sn颗粒提出的竞争率控制恢复机制。根据体心四面体（BCT）Sn的弹性晶体各向异性，估算了Sn单晶主导滑移系中位错的线张力和迁移率。然后，使用上述输入和在蠕变的瞬态阶段期间针对主导滑移系统计算的演变位错密度，对第I层的共晶Sn-Ag相的各向异性瞬态蠕变速率进行建模。主要滑移系是根据位错的迁移率和晶体主轴与加载方向之间的取向角确定的。共晶相（从第1层）的蠕变响应相结合的Sn瓣在第2层的蠕变响应，使用各向异性的Mod-Tanaka均匀化理论，获得的瞬态蠕变响应的SAC 305单晶沿着全球试样方向。该模型已被校准使用实验获得的瞬态蠕变响应的SAC 305单晶试样。然后使用上述多尺度校准模型来预测（i）另一个SAC 305单晶样品的瞬态蠕变响应和（ii）取向（通过改变欧拉角之一）对SAC 305单晶的瞬态蠕变响应的影响。利用取向图像映射法确定了上述两个SAC单晶试样的晶粒取向（相对于加载方向），并将其用于模型中，以估计沿主导滑移方向沿着的解析剪切应力。参数研究也进行了预测的体积分数，纵横比，和取向的椭圆形锡夹杂物的SAC单晶的各向异性瞬态蠕变响应的影响。(C)2015爱思唯尔有限公司版权所有。
The lack of statistical homogeneity in functional SnAgCu (SAC) solder joints due to their coarse grained microstructure, in conjunction with the severe anisotropy exhibited by single crystal Sn, renders each joint unique in terms of mechanical behavior. A mechanistic multi-scale modeling framework is proposed in this study to predict the influence of composition and microstructure on the anisotropic transient creep response of single crystal SnAgCu (SAC) solder. Tier I consist of single-crystal eutectic Sn-Ag alloy, with nanoscale Ag3Sn particles embedded in a single-crystal Sn matrix. Tier II consists of single crystal SAC solder which is composed of Sn dendrites surrounded by the eutectic Sn-Ag phase of Tier I. The Tier I anisotropic transient creep model is based on dislocation mechanics. The Tier II model uses the results of Tier I as an input and is based on anisotropic composite micro-mechanics.In Tier I, creep deformation is governed by dislocation impediment and recovery at nanoscale Ag3Sn particles, with recovery being the rate controlling mechanism. Dislocation climb and dislocation detachment at the Ag3Sn particles are proposed to be the competing rate controlling recovery mechanisms. Line tension and mobility of dislocations in dominant slip systems of single crystal Sn are estimated based on the elastic crystal anisotropy of body centered tetragonal (BCT) Sn. The anisotropic transient creep rate of the eutectic Sn-Ag phase of Tier I is then modeled using above inputs and the evolving dislocation density calculated for dominant glide systems during the transient stage of creep. The dominant slip systems are determined based on the dislocation mobility and on the orientation angle between the crystal principal axes and the loading direction. The creep response of the eutectic phase (from Tier 1) is combined with the creep response of Sn lobes at Tier 2, using the anisotropic Mod-Tanaka homogenization theory, to obtain the transient creep response of a SAC305 single crystal along global specimen directions. This model has been calibrated using experimentally obtained transient creep response of a SAC305 single crystal specimen. The above multiscale calibrated model is then used to predict (i) the transient creep response of another SAC305 single crystal specimen and (ii) the effect of orientation (by changing one of the Euler angles) on the transient creep response of SAC305 single crystal. The grain orientation of above two SAC single crystal specimens (with respect to loading direction) were identified with orientation image mapping and then utilized in the model to estimate the resolved shear stress along the dominant slip directions. Parametric studies have also been conducted to predict the effects of the volume fraction, aspect ratio, and orientation of ellipsoidal Sn inclusions on the anisotropic transient creep response of SAC single crystals. (C) 2015 Elsevier Ltd. All rights reserved.