Analytical Solutions and a Numerical Approach for Diffusion-Induced Stresses in Intermetallic Compound Layers of Solder Joints

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
Tong An ◽  
Fei Qin ◽  
Guofeng Xia

Intermetallic compounds (IMC) play a key role in the mechanical reliability of solder joints. The present work investigates the diffusion-induced stress developed in the Cu pad/IMC/solder sandwich structure during a solid-state isothermal aging process. An analytical model and a numerical approach are proposed to predict the stress. The model consists of a Cu6Sn5 layer sandwiched between a Cu pad and a solder layer, and it is assumed that the diffusivity of the Cu atoms is much greater than that of the Sn atoms. We use the Laplace transformation method to obtain the distribution of the Cu atoms concentration. The diffusion-induced stress is determined analytically by the volumetric strain resulted from the effect of the atomic diffusion. It is found that the Cu6Sn5 layer is subjected to compressive stress due to the Cu atoms diffusion. As the diffusion time is long enough, the diffusion-induced stress shows a linear relationship with the thickness of the Cu6Sn5 layer. A finite element approach to calculate the diffusion-induced stress is proposed, and it is compared and validated by the analytical solution. The results show that the proposed approach can give a well estimation of the diffusion-induced stress in the Cu6Sn5 layer, and is also efficient in predicting the diffusion-induced stress in the structures with more complex geometry. The distribution of the Cu atoms concentration and the diffusion-induced stress in the model with a scallop-like or flat-like Cu6Sn5/solder interface are calculated by the numerical approach. The results show that the interfacial morphology of the Cu6Sn5/solder has great influence on the evolution of the Cu atoms concentration, and the diffusion-induced stress in the Cu6Sn5 layer with the scallop edge is less than that with the flat edge.

2015 ◽  
Vol 91 ◽  
pp. 351-362 ◽  
Author(s):  
Xing-yu Zhang ◽  
Feng Hao ◽  
Hao-sen Chen ◽  
Dai-ning Fang

Processes ◽  
2018 ◽  
Vol 6 (8) ◽  
pp. 104 ◽  
Author(s):  
Yulong Chen ◽  
Xuelong Li ◽  
Bo Li

Knowledge of the bedding plane properties of coal seams is essential for the coalbed gas production because of their great influence on the inner flow characteristics and sorption features of gas and water. In this study, an experimental study on the anisotropic gas adsorption–desorption and permeability of coal is presented. The results show that during the adsorption–desorption process, an increase in the bedding plane angle of the specimen expands the length and area of the contact surface, thereby increasing the speed and quantity of adsorption and desorption. With an increase in the bedding angle, the number of pores and cracks was found to increase together with the volumetric strain. The evolution of permeability of coal heavily depended on stress–strain stages. The permeability decreased with the increase of stress at the initial compaction and elastic deformation stages, while it increased with the increase of stress at the stages of strain-hardening, softening and residual strength. Initial permeability increased with increasing bedding angle.


Author(s):  
Y.-L. Shen ◽  
K. C. R. Abell ◽  
S. E. Garrett

Experiments on the eutectic tin-lead alloy were conducted to study the effects of grain boundary sliding on the deformation and damage processes at the microscopic level. The primary objective is to gain mechanistic understandings of solder joint reliability in microelectronic packaging. Bulk specimens were subject to relatively fast deformations of tension, compression and bending, for the purposes of examining the pure mechanical effect without the influence of diffusion related phenomena. Grain realignment and phase redistribution were characterized by microscopy and microhardness indentation. A micromechanical model is proposed to elucidate the observed microstructural changes and progressive damage. This study illustrates the significance of damage in the form of microscopic heterogeneity caused by grain boundary sliding. It also illustrates the possibility of mechanically induced phase coarsening in actual solder joints. High-frequency cyclic shear tests on tin-lead solder joints showed damage along the coarsened band after only a short time, in accord with the proposed effects. Boundary sliding without the influence of atomic diffusion plays an essential role in fatigue damage in solder.


Author(s):  
Cheng-Kai ChiuHuang ◽  
Hsiao-Ying Shadow Huang

The development of lithium-ion batteries plays an important role to stimulate electric vehicle (EV) and plug-in electric vehicle (PHEV) industries and it is one of many solutions to reduce US oil import dependence. To develop advanced vehicle technologies that use energy more efficiently, retaining the lithium-ion battery capacity is one of major challenges facing by the electrochemical community today. During electrochemical processes, lithium ions diffuse from and insert into nanoscaled cathode materials in which stresses are formed. It is considered that diffusion-induced stress is one of the factors causing electrode material capacity loss and failure. In this study, we present a model which is capable for describing diffusion mechanisms and stress formation in nano-platelike cathode materials, LiFePO4 (Lithium-iron-phosphate). We consider particle size >100 nm in this study since it has been suggested that very small nanoparticles (<100 nm) may not undergo phase separation during fast diffusion. To evaluate diffusion-induced stress accurately, factors such as the diffusivity and phase boundary movements are considered. Our result provides quantitative lithium concentrations inside LiFePO4 nanoparticles. The result could be used for evaluating stress formation and provides potential cues for precursors of capacity loss in lithium-ion batteries. This study contributes to the fundamental understanding of lithium ion diffusion in electrode materials, and results from this model help better electrode materials design in lithium-ion batteries.


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