SnPb钎料本构方程的建立与SMT焊点寿命预测
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摘要
有限元数值模拟是进行服役环境温度循环载荷下SMT焊点应力应变状态分析以及寿命预测的最有效方法之一。其中,钎料本构模式和寿命预测方法的选取直接决定着模拟结果的准确性,具有重要的理论研究价值。本文综合考虑钎料的应变硬化、蠕变变形和高温软化等特征,建立钎料的粘混合硬化本构关系,研究热循环加载下焊点内的应力应变场演变规律并进行寿命预测。
首先,采用混合硬化本构关系综合描述热循环加载下钎料的各向强化特征和循环加载的包申格效应,建立钎料的基于幂指数硬化模型的等向硬化增量本构关系和基于Ziegler双线性硬化模型的随动硬化增量本构关系,并利用MARC二次开发接口和Fortran语言开发用户子程序,实现了等向、随动、混合硬化三种本构关系的有限元计算。同时基于钎料的Darveaux蠕变方程,开发用户子程序定义钎料的粘性性质,得到了蠕变问题的有限元求解过程。
其次,在Darveaux焊点寿命预测模型的基础上,选取焊点整体的平均应变能密度作为主控力学参量对SMT焊点进行寿命预测,考虑了微小焊点的高约束度及网格密度对应力应变场的影响,利用二次开发接口提取单元应变能密度、单元体积等信息。
最后,研究钎料本构关系的选取及焊点形态对焊点力学行为和疲劳寿命的影响。焊点力学行为的模拟结果表明,元件与基板间隙高度处的焊根内侧产生应力集中,是焊点的薄弱部位;焊点内的应力应变分布具有温度历史相关性,但应变能密度分布基本不随时间变化,将其作为主控力学参量判断裂纹萌生及扩展位置具有代表意义。
焊点寿命预测结果表明,钎料本构关系的选取会对寿命预测结果产生重要影响。采用理想弹塑性本构关系的寿命预测结果最高;进一步考虑粘性时,非弹性变形增大,寿命略低;采用粘混合硬化钎料本构关系时,焊点具有明显的硬化特征,导致蠕变变形增大,进而使应变能密度显著增大,焊点寿命最低。由于粘混合硬化钎料本构关系考虑了钎料变形的多种影响因素,因此可将其寿命预测结果作为焊点可靠性设计的依据。随着焊点圆角形态从凹变凸,应力应变集中程度降低,焊点的寿命提高。
Numerical simulation is proved to be one of the best tools to analyze the stress and strain evolution in SnPb solder joint and predict its fatigue life under environment cycling temperature. In the simulation, the selection of constitutive model of SnPb and life prediction method determine the accuracy of finite element simulation results directly, so it needs deeply theoretic study. In this paper, a viscous-mixed hardening constitutive model of SnPb is established, which can describe the strain hardening, creep deformation and high temperature softening characteristics of SnPb.
Firstly, the mixed hardening constitutive equation has been used to describe the isotropic hardening characteristic and Bauschinger Effect under cyclic loading. The incremental constitutive relations are built based on Power Exponential hardening model and Ziegler bilinear hardening model, respectively. The three kinds of constitutive relations, including isotropic hardening equation,kinetic hardening equation and mixed hardening equation have been completed by users’subroutine of MARC written in Fortran. In addition, User’s subroutine has been compiled to define the creep deformation performance of SnPb based on Darveaux steady creeping equation. Afterward, FEM calculation process to solve creep deformation problem is given.
Then based on Darveaux life prediction model of solder joint, the average strain energy density of the whole solder joint is chosen as the dominant mechanical factor for fatigue life prediction of SMT solder joint. The high constraint of the tiny joint and the effect of meshing density on the stress-strain field have been considered, and information of unit such as strain energy density, volume is abstracted by subroutine program.
Finally, the influence of constitutive models of SnPb and shape of the solder joints on the mechanical behavior and fatigue life is studied. The simulated results of stress-strain field evolution in SMT solder joint show that the root of solder joint between the component and substrate gap is the weakest zone with a high stress concentration. The distribution of stress and strain within the solder joint under temperature cycling is dynamic and relative with the temperature history. As the strain energy density field remains about the same, it’s proved to be an appropriate dominant mechanical factor to judge the location where the crack begins and expands.
It shows that the constitutive model of SnPb has a great impact on the life prediction results of solder joint. When the ideal elastic-plastic constitutive model is used to define the mechanical behavior of SnPb, life of the solder joint is the longest. When creep deformation is taken into account, the nonlinear deformation is much larger. Accordingly, the calculated life of solder joint is slightly lower. When the viscous-mixed hardening constitutive model is used, the solder joint shows an obvious strain hardening characteristic and the improved stress leads to much larger creeping deformation. Synthetically the strain energy density increases significantly that life of the solder joint is comparatively the shortest. With most factors affecting SnPb deformation considered, the simulated result can be used as reference for reliability design of solder joint. With quantity of solder increasing and the shape changing from concave to convex, the average strain density gets lower and fatigue life increases.
首先,采用混合硬化本构关系综合描述热循环加载下钎料的各向强化特征和循环加载的包申格效应,建立钎料的基于幂指数硬化模型的等向硬化增量本构关系和基于Ziegler双线性硬化模型的随动硬化增量本构关系,并利用MARC二次开发接口和Fortran语言开发用户子程序,实现了等向、随动、混合硬化三种本构关系的有限元计算。同时基于钎料的Darveaux蠕变方程,开发用户子程序定义钎料的粘性性质,得到了蠕变问题的有限元求解过程。
其次,在Darveaux焊点寿命预测模型的基础上,选取焊点整体的平均应变能密度作为主控力学参量对SMT焊点进行寿命预测,考虑了微小焊点的高约束度及网格密度对应力应变场的影响,利用二次开发接口提取单元应变能密度、单元体积等信息。
最后,研究钎料本构关系的选取及焊点形态对焊点力学行为和疲劳寿命的影响。焊点力学行为的模拟结果表明,元件与基板间隙高度处的焊根内侧产生应力集中,是焊点的薄弱部位;焊点内的应力应变分布具有温度历史相关性,但应变能密度分布基本不随时间变化,将其作为主控力学参量判断裂纹萌生及扩展位置具有代表意义。
焊点寿命预测结果表明,钎料本构关系的选取会对寿命预测结果产生重要影响。采用理想弹塑性本构关系的寿命预测结果最高;进一步考虑粘性时,非弹性变形增大,寿命略低;采用粘混合硬化钎料本构关系时,焊点具有明显的硬化特征,导致蠕变变形增大,进而使应变能密度显著增大,焊点寿命最低。由于粘混合硬化钎料本构关系考虑了钎料变形的多种影响因素,因此可将其寿命预测结果作为焊点可靠性设计的依据。随着焊点圆角形态从凹变凸,应力应变集中程度降低,焊点的寿命提高。
Numerical simulation is proved to be one of the best tools to analyze the stress and strain evolution in SnPb solder joint and predict its fatigue life under environment cycling temperature. In the simulation, the selection of constitutive model of SnPb and life prediction method determine the accuracy of finite element simulation results directly, so it needs deeply theoretic study. In this paper, a viscous-mixed hardening constitutive model of SnPb is established, which can describe the strain hardening, creep deformation and high temperature softening characteristics of SnPb.
Firstly, the mixed hardening constitutive equation has been used to describe the isotropic hardening characteristic and Bauschinger Effect under cyclic loading. The incremental constitutive relations are built based on Power Exponential hardening model and Ziegler bilinear hardening model, respectively. The three kinds of constitutive relations, including isotropic hardening equation,kinetic hardening equation and mixed hardening equation have been completed by users’subroutine of MARC written in Fortran. In addition, User’s subroutine has been compiled to define the creep deformation performance of SnPb based on Darveaux steady creeping equation. Afterward, FEM calculation process to solve creep deformation problem is given.
Then based on Darveaux life prediction model of solder joint, the average strain energy density of the whole solder joint is chosen as the dominant mechanical factor for fatigue life prediction of SMT solder joint. The high constraint of the tiny joint and the effect of meshing density on the stress-strain field have been considered, and information of unit such as strain energy density, volume is abstracted by subroutine program.
Finally, the influence of constitutive models of SnPb and shape of the solder joints on the mechanical behavior and fatigue life is studied. The simulated results of stress-strain field evolution in SMT solder joint show that the root of solder joint between the component and substrate gap is the weakest zone with a high stress concentration. The distribution of stress and strain within the solder joint under temperature cycling is dynamic and relative with the temperature history. As the strain energy density field remains about the same, it’s proved to be an appropriate dominant mechanical factor to judge the location where the crack begins and expands.
It shows that the constitutive model of SnPb has a great impact on the life prediction results of solder joint. When the ideal elastic-plastic constitutive model is used to define the mechanical behavior of SnPb, life of the solder joint is the longest. When creep deformation is taken into account, the nonlinear deformation is much larger. Accordingly, the calculated life of solder joint is slightly lower. When the viscous-mixed hardening constitutive model is used, the solder joint shows an obvious strain hardening characteristic and the improved stress leads to much larger creeping deformation. Synthetically the strain energy density increases significantly that life of the solder joint is comparatively the shortest. With most factors affecting SnPb deformation considered, the simulated result can be used as reference for reliability design of solder joint. With quantity of solder increasing and the shape changing from concave to convex, the average strain density gets lower and fatigue life increases.
引文
1郭强,赵玫,孟光.随机振动条件下SMT焊点半经验疲劳寿命累积模型.振动与冲击. 2005,24(2):24~26
2吕建刚.用云纹干涉法研究金属焊点的热变形问题.实验力学. 1997,12(2):242~247
3 A. J. Rafanell. Ramberg-Osgood Parameters for 63/37 Sn/Pb Solder. ASME J. Elect. Pack. 1992,114(2):234~238
4朱颖,方洪渊,王春青等. SMT焊点抗蠕变-疲劳技术研究现状.电子工艺技术. 1993,1:14~16
5 E. Pink, A. Marquez, A. Grinberg. A Note on Rate Sensitivities of Flow Stresses of Eutectic and Rutectoid Alloys. Scripta Metallurgica. 1981,15:191~194
6 W. Jung, J. H. Lau, Y. H. Pao. Nonlinear Analysis of Full-Matrix and Perimeter Plastic Ball Grid Array Solder Joints. ASME J. Elect. Pack. 1997,119(3):163~170
7 B. Wong, D. E. Hellling, R. W. Clark. A Creep-Rupture Model for Two-Phase Eutectic Solders. IEEE Trans. CHMT. 1988,11(3):284~290
8 S. Wiese, J. Wolter. Creep of the Thermally Aged SnAgCu Solder Joints. Microelectronics Reliability. 2007,47(2-3):223~232
9 F. Garofalo. An Empirical Relation Defining the Stress Dependence of Minimum Creep Rate in Metals. Trans J. of Applied Mechanics. 1963:227~231
10 R. Darveaux, K. Banerji. Constitutive Relation for Tin-based Solder Joints. IEEE Transactions on Components. Hybrid and Manufaturing Technology. 1992,15(6):1013~1019
11周文凡,田艳红,王春青. BGA焊点的形态预测及可靠性优化设计.电子工艺技术. 2005,26(4):187~191
12李晓延,王志升.倒装芯片结构中SnAgCu焊点热疲劳寿命预测方法研究.机械强度. 2006,28(6):893~898
13上官东恺.无铅焊料互联及可靠性.刘建影,孙鹏译.电子工业出版社. 2008:158
14 F. X. Chen, H. L. J. Pang. Thermal Fatigue Reliability Analysis for PBGA with Sn3.8Ag0.7Cu Solder Joints. 54th Electronic Packaging Technology Conference. 2004:210~212
15 S. Knecht, L. R. Fox. Constitutive Relation and Creep-Fatigue Life Model for Eutectic Tin-Lead Solder. IEEE Trans. CHMT. 1990,13(2):424~433
16 V. Sarihan. Temperature Dependent Viscoplastic Simulation of Controlled Collapse Solder Joint under Thermal Cycling. ASME J. Elect. Pack. 1993,115(3):16~21
17 K. Iwasaki, Y. H. Pao. Fatigue-Creep Crack Propagation Path in Solder Joints under Thermal Cycling. Advances in Electronic Packaging. ASME EEP. 1997,19(2):1058~1064
18 H. L. J. Pang, C. W. Seetoh, Z. P. Wang. CBGA Solder Joint Reliability Evaluation Based on Elastic-Plastic-Creep Analysis. ASME J. Elect. Pack. 2000,122:255~261
19 E. P. Busso, M. Kitano. A Visco-Plastic Constitutive Model for 60/40 Tin-Lead Solder Used in IC Package Joints. ASME J. Engineering Materials and Technology. 1992,114:331~337
20 S. R. Bodner, Y. Partom. Constitutive Equations for Elastic-Viscoplastic Strain Hardening Materials. ASME J. Applied Mech. 1975,42:385~389
21马鑫,王莉,方洪渊等. Sn-Pb共晶钎料合金的Bonder-Partom本构方程.应用力学学报. 1998,15(2):87~90
22 R. Zaera, J. Fernandez. An Implicit Consistent Algorithm for the Integration of Thermoviscoplastic Constitutive Equations in Adiabatic Conditions and Finite Deformations. International Journal of Solids and Structures. 2006,43:1594~1612
23张莉,陈旭, H. Nose, et al. Anand模型预测63Sn37Pb焊锡钎料的应力应变行为.机械强度. 2004,26(4):447~450
24 X. D. HU, D. Y. JU. Application of Anand's Constitutive Model on Twin Roll Casting Process of AZ31 Magnesium Alloy. Trans. Nonferrous Met. SOC. China. 2006,16:586~590
25 Ning Bai, Xu Chen, Hong Gao. Simulation of Uniaxial Tensile Properties for Lead-free Solders with Modified Anand Model. Materials and Design. 2009,30:122~128
26王莉,方洪渊,钱乙余等. 60Sn40Pb钎料合金的具有蠕变和塑性边界的粘塑性本构方程.应用力学学报. 2001,18(3):130~133
27 E. P. Busso, M. Kitano, T. Kumazawa. Modeling Complex Inelastic Deformation Processes in IC Packages' Solder Joints. ASME Journal ofElectronic Packaging. 1994,116(1):6~15
28罗艳.电子封装钎料合金耦合损伤时相关多轴本构模型及疲劳失效模型研究.西南交通大学博士学位论文. 2008:4~6
29 Jaroslav Polak. Plastic Strain-controlled Short Crack Growth and Fatigue Life. International Journal of Fatigue. 2005,27:1192~1201
30肖小清,何小琦,恩云飞等.倒装芯片焊点可靠性的有限元模拟法探讨.电子工艺技术. 2006,27(4):201~204
31 L. F. Coffin. A Study of the Effects of Cyclic Thermal Stresses on a Ductile Metal. Transaction of ASME. 1954,76:931~950
32 S. S. Manson. Experimental Mechanics. 1965,5(7):193~196
33 K. C. Norris, A. H. Landzberg. Reliability of Controlled Collapse Interconnections. IBM Journal Research & Development. 1969,13:266~271
34 A. Syed. Solder Joint Life Prediction Model and Application to Ball Grid Array Design Optimization. Proc. of the International Congress on Experimental/Numerical Mechanics in Electronic Packaging. Nashville, TN, USA, June 10~13. 1996,l:136~144
35 N. H. Paydar, Y. Tong, H. U. Akay. A Finite Element Study of Factors Affecting Fatigue Life of Solder Joints. ASME Journal of Electronic Packaging. 1994,116(2):265~273
36 R. Darveaux. Solder Joint Fatigue Life Model in Design and Reliability of Solders and Solder Interconnections. The Minerals, Metals and Material Society. 1997:213~218
37林健,雷永平. SMT中焊点形状对焊点可靠性的影响.电子元件与材料, 2008,27(2):60~64
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45黄春跃,周德俭,李春泉. CCGA焊点热循环加载条件下应力应变有限元分析.桂林电子工业学院学报. 2001,21(3):22~28
46朱颖.锡铅稀土钎料SMT焊点热循环失效机制研究.哈尔滨工业大学博士论文. 1996:27~30
47 B. Z. Hong, L. G. Burrell. Nonlinear Finite Element Simulation of Thermo-viscoplastic Deformation of C4 Solder Joints in High Density Packaging under Thermal Cycling. IEEE Trans. CPMT. 1995,18(3):585~591
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49马鑫.微电子表面组装焊点失效的相关力学及金属学因素分析.哈尔滨工业大学博士论文. 2006:32~33
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51 E. Nicewaner. Historical Failure Distibution and Significant Factors Affecting Surface Mount Solder Joint Fatigue Life. Soldering & Surface Mount Technology. 2007,17:22~29
2吕建刚.用云纹干涉法研究金属焊点的热变形问题.实验力学. 1997,12(2):242~247
3 A. J. Rafanell. Ramberg-Osgood Parameters for 63/37 Sn/Pb Solder. ASME J. Elect. Pack. 1992,114(2):234~238
4朱颖,方洪渊,王春青等. SMT焊点抗蠕变-疲劳技术研究现状.电子工艺技术. 1993,1:14~16
5 E. Pink, A. Marquez, A. Grinberg. A Note on Rate Sensitivities of Flow Stresses of Eutectic and Rutectoid Alloys. Scripta Metallurgica. 1981,15:191~194
6 W. Jung, J. H. Lau, Y. H. Pao. Nonlinear Analysis of Full-Matrix and Perimeter Plastic Ball Grid Array Solder Joints. ASME J. Elect. Pack. 1997,119(3):163~170
7 B. Wong, D. E. Hellling, R. W. Clark. A Creep-Rupture Model for Two-Phase Eutectic Solders. IEEE Trans. CHMT. 1988,11(3):284~290
8 S. Wiese, J. Wolter. Creep of the Thermally Aged SnAgCu Solder Joints. Microelectronics Reliability. 2007,47(2-3):223~232
9 F. Garofalo. An Empirical Relation Defining the Stress Dependence of Minimum Creep Rate in Metals. Trans J. of Applied Mechanics. 1963:227~231
10 R. Darveaux, K. Banerji. Constitutive Relation for Tin-based Solder Joints. IEEE Transactions on Components. Hybrid and Manufaturing Technology. 1992,15(6):1013~1019
11周文凡,田艳红,王春青. BGA焊点的形态预测及可靠性优化设计.电子工艺技术. 2005,26(4):187~191
12李晓延,王志升.倒装芯片结构中SnAgCu焊点热疲劳寿命预测方法研究.机械强度. 2006,28(6):893~898
13上官东恺.无铅焊料互联及可靠性.刘建影,孙鹏译.电子工业出版社. 2008:158
14 F. X. Chen, H. L. J. Pang. Thermal Fatigue Reliability Analysis for PBGA with Sn3.8Ag0.7Cu Solder Joints. 54th Electronic Packaging Technology Conference. 2004:210~212
15 S. Knecht, L. R. Fox. Constitutive Relation and Creep-Fatigue Life Model for Eutectic Tin-Lead Solder. IEEE Trans. CHMT. 1990,13(2):424~433
16 V. Sarihan. Temperature Dependent Viscoplastic Simulation of Controlled Collapse Solder Joint under Thermal Cycling. ASME J. Elect. Pack. 1993,115(3):16~21
17 K. Iwasaki, Y. H. Pao. Fatigue-Creep Crack Propagation Path in Solder Joints under Thermal Cycling. Advances in Electronic Packaging. ASME EEP. 1997,19(2):1058~1064
18 H. L. J. Pang, C. W. Seetoh, Z. P. Wang. CBGA Solder Joint Reliability Evaluation Based on Elastic-Plastic-Creep Analysis. ASME J. Elect. Pack. 2000,122:255~261
19 E. P. Busso, M. Kitano. A Visco-Plastic Constitutive Model for 60/40 Tin-Lead Solder Used in IC Package Joints. ASME J. Engineering Materials and Technology. 1992,114:331~337
20 S. R. Bodner, Y. Partom. Constitutive Equations for Elastic-Viscoplastic Strain Hardening Materials. ASME J. Applied Mech. 1975,42:385~389
21马鑫,王莉,方洪渊等. Sn-Pb共晶钎料合金的Bonder-Partom本构方程.应用力学学报. 1998,15(2):87~90
22 R. Zaera, J. Fernandez. An Implicit Consistent Algorithm for the Integration of Thermoviscoplastic Constitutive Equations in Adiabatic Conditions and Finite Deformations. International Journal of Solids and Structures. 2006,43:1594~1612
23张莉,陈旭, H. Nose, et al. Anand模型预测63Sn37Pb焊锡钎料的应力应变行为.机械强度. 2004,26(4):447~450
24 X. D. HU, D. Y. JU. Application of Anand's Constitutive Model on Twin Roll Casting Process of AZ31 Magnesium Alloy. Trans. Nonferrous Met. SOC. China. 2006,16:586~590
25 Ning Bai, Xu Chen, Hong Gao. Simulation of Uniaxial Tensile Properties for Lead-free Solders with Modified Anand Model. Materials and Design. 2009,30:122~128
26王莉,方洪渊,钱乙余等. 60Sn40Pb钎料合金的具有蠕变和塑性边界的粘塑性本构方程.应用力学学报. 2001,18(3):130~133
27 E. P. Busso, M. Kitano, T. Kumazawa. Modeling Complex Inelastic Deformation Processes in IC Packages' Solder Joints. ASME Journal ofElectronic Packaging. 1994,116(1):6~15
28罗艳.电子封装钎料合金耦合损伤时相关多轴本构模型及疲劳失效模型研究.西南交通大学博士学位论文. 2008:4~6
29 Jaroslav Polak. Plastic Strain-controlled Short Crack Growth and Fatigue Life. International Journal of Fatigue. 2005,27:1192~1201
30肖小清,何小琦,恩云飞等.倒装芯片焊点可靠性的有限元模拟法探讨.电子工艺技术. 2006,27(4):201~204
31 L. F. Coffin. A Study of the Effects of Cyclic Thermal Stresses on a Ductile Metal. Transaction of ASME. 1954,76:931~950
32 S. S. Manson. Experimental Mechanics. 1965,5(7):193~196
33 K. C. Norris, A. H. Landzberg. Reliability of Controlled Collapse Interconnections. IBM Journal Research & Development. 1969,13:266~271
34 A. Syed. Solder Joint Life Prediction Model and Application to Ball Grid Array Design Optimization. Proc. of the International Congress on Experimental/Numerical Mechanics in Electronic Packaging. Nashville, TN, USA, June 10~13. 1996,l:136~144
35 N. H. Paydar, Y. Tong, H. U. Akay. A Finite Element Study of Factors Affecting Fatigue Life of Solder Joints. ASME Journal of Electronic Packaging. 1994,116(2):265~273
36 R. Darveaux. Solder Joint Fatigue Life Model in Design and Reliability of Solders and Solder Interconnections. The Minerals, Metals and Material Society. 1997:213~218
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