Anand模型采用有限元法模拟WLCSP器件Sn3.8Ag0.7Cu-X(Ce,Fe)无铅焊点在热循环载荷条件下的应力-应变响应,借助蠕变应变疲劳寿命预测模型Sn Ag Cu,Sn Ag Cu Ce,Sn Ag Cu Fe焊点疲劳寿命.结果表明,在服役器件整体器件出现明显的变形现象,...Anand模型采用有限元法模拟WLCSP器件Sn3.8Ag0.7Cu-X(Ce,Fe)无铅焊点在热循环载荷条件下的应力-应变响应,借助蠕变应变疲劳寿命预测模型Sn Ag Cu,Sn Ag Cu Ce,Sn Ag Cu Fe焊点疲劳寿命.结果表明,在服役器件整体器件出现明显的变形现象,电路板翘曲严重.从中心到拐角焊点变形-应力-应变逐渐增加,芯片下拐角焊点成为整个结构潜在的危险区域.通过计算WLCSP器件Sn Ag Cu、Sn Ag Cu Ce和Sn Ag Cu Fe三种焊点的疲劳寿命,证实了Sn Ag Cu Ce和Sn Ag Cu Fe焊点寿命明显高于Sn Ag Cu焊点,证明了在Sn Ag Cu中添加一定量的铈和铁可以显著提高Sn Ag Cu焊点的使用寿命,分析结果为新型无铅钎料的研发提供理论支撑.展开更多
Bi-modulus materials with different mechanical responses in tension and compression are often found in civil,composite, and biological engineering. Numerical analysis of bimodular materials is strongly nonlinear and c...Bi-modulus materials with different mechanical responses in tension and compression are often found in civil,composite, and biological engineering. Numerical analysis of bimodular materials is strongly nonlinear and convergence is usually a problem for traditional iterative schemes. This paper aims to develop a stabilized computational method for nonlinear analysis of 3D bimodular materials. Based on the parametric variational principle, a unified constitutive equation of 3D bimodular materials is proposed, which allows the eight principal stress states to be indicated by three parametric variables introduced in the principal stress directions.The original problem is transformed into a standard linear complementarity problem（LCP） by the parametric virtual work principle and a quadratic programming algorithm is developed by solving the LCP with the classic Lemke＇s algorithm. Update of elasticity and stiffness matrices is avoided and, thus, the proposed algorithm shows an excellent convergence behavior compared with traditional iterative schemes.Numerical examples show that the proposed method is valid and can accurately analyze mechanical responses of 3D bimodular materials. Also, stability of the algorithm is greatly improved.展开更多
文摘Anand模型采用有限元法模拟WLCSP器件Sn3.8Ag0.7Cu-X(Ce,Fe)无铅焊点在热循环载荷条件下的应力-应变响应,借助蠕变应变疲劳寿命预测模型Sn Ag Cu,Sn Ag Cu Ce,Sn Ag Cu Fe焊点疲劳寿命.结果表明,在服役器件整体器件出现明显的变形现象,电路板翘曲严重.从中心到拐角焊点变形-应力-应变逐渐增加,芯片下拐角焊点成为整个结构潜在的危险区域.通过计算WLCSP器件Sn Ag Cu、Sn Ag Cu Ce和Sn Ag Cu Fe三种焊点的疲劳寿命,证实了Sn Ag Cu Ce和Sn Ag Cu Fe焊点寿命明显高于Sn Ag Cu焊点,证明了在Sn Ag Cu中添加一定量的铈和铁可以显著提高Sn Ag Cu焊点的使用寿命,分析结果为新型无铅钎料的研发提供理论支撑.
基金supported by the National Natural Science Foundation of China (Grants 11232003, 91315302, 11502035)the Open Research Foundation (Grant GZ1404) of State Key Laboratory of Structural Analysis for Industrial Equipment at Dalian University of Technology
文摘Bi-modulus materials with different mechanical responses in tension and compression are often found in civil,composite, and biological engineering. Numerical analysis of bimodular materials is strongly nonlinear and convergence is usually a problem for traditional iterative schemes. This paper aims to develop a stabilized computational method for nonlinear analysis of 3D bimodular materials. Based on the parametric variational principle, a unified constitutive equation of 3D bimodular materials is proposed, which allows the eight principal stress states to be indicated by three parametric variables introduced in the principal stress directions.The original problem is transformed into a standard linear complementarity problem（LCP） by the parametric virtual work principle and a quadratic programming algorithm is developed by solving the LCP with the classic Lemke＇s algorithm. Update of elasticity and stiffness matrices is avoided and, thus, the proposed algorithm shows an excellent convergence behavior compared with traditional iterative schemes.Numerical examples show that the proposed method is valid and can accurately analyze mechanical responses of 3D bimodular materials. Also, stability of the algorithm is greatly improved.
