Twin-roll thin strip casting process combines casting and hot rolling into a single process, in which thermal stress and thermal mechanical stress were involved. Considering the high temperature gradient, the existing...Twin-roll thin strip casting process combines casting and hot rolling into a single process, in which thermal stress and thermal mechanical stress were involved. Considering the high temperature gradient, the existing of liquid and solid regions and rolling deformation, suitable constitutive model is the key to describe the process. Anand's model is a temperature-dependent, rate-dependent and unified of creep and plasticity model and the Jaumann derivative was employed in Anand's model which makes the constitutive model frame-indifferent or objective, therefore the highly nonlinearities behavior in the twin-roll casting process can be simulated. The parameters of the Anand's model were regressed based on the compression tests of AZ31 magnesium alloy. The simulation results reveal that the Anand's model can well describe the deformation characteristics of twin-roll casting process. Based on the simulation results, the form of evolution equations in Anand's model was discussed.展开更多
SnAgCu solder system with the addition of rare earth Ce,which has better thermo-mechanical properties compared to those of SnPb solder,is regarded as one of the promising candidates for electronic assembly.Moreover,th...SnAgCu solder system with the addition of rare earth Ce,which has better thermo-mechanical properties compared to those of SnPb solder,is regarded as one of the promising candidates for electronic assembly.Moreover,the SnAgCuCe solder alloys can provide good quality joints with Cu substrates.However,there is few report of the constitutive model for SnAgCu solder bearing micro-amounts rare earth Ce.In this paper,the unified viscoplastic constitutive model,Anand equations,is used to represent the inelastic deformation behavior for SnAgCu and SnAgCuCe solders.In order to obtain the acquired data for the fitting of the material parameters of this unified model,a series of experiments of constant strain rate test were conducted under isothermal conditions at different temperatures.The Anand parameters of the constitutive equations for SnAgCu and SnAgCuCe solder were determined from separated constitutive relations and experimental results.Nonlinear least-square fitting was selected to determine the model constants.And the simulated results were then compared with experimental measurements of the stress-inelastic strain curves:excellent agreement was found.The model accurately predicted the overall trend of steady-state stress-strain behavior of SnAgCu and SnAgCuCe solders for the temperature ranges from 25℃to 150℃,and the strain rate ranges from 0.01 s^-1 to 0.001 s^-1.It is concluded that the Anand model can be applied for representing the inelastic deformation behavior of solders at high homologous temperature and can be recommended for finite element simulation of the stress-strain response of lead free soldered joints.Based on the Anand model,the investigations of thermo-mechanical of SnAgCu and SnAgCuCe soldered joints in fine pitch quad flat package by finite element code were done under thermal cyclic loading,it is found that the reliability of SnAgCu soldered joints can be improved remarkably with addition of rare earth Ce.The results may provide a theory guide for developing constitutive model for lead-free solders.展开更多
文摘Twin-roll thin strip casting process combines casting and hot rolling into a single process, in which thermal stress and thermal mechanical stress were involved. Considering the high temperature gradient, the existing of liquid and solid regions and rolling deformation, suitable constitutive model is the key to describe the process. Anand's model is a temperature-dependent, rate-dependent and unified of creep and plasticity model and the Jaumann derivative was employed in Anand's model which makes the constitutive model frame-indifferent or objective, therefore the highly nonlinearities behavior in the twin-roll casting process can be simulated. The parameters of the Anand's model were regressed based on the compression tests of AZ31 magnesium alloy. The simulation results reveal that the Anand's model can well describe the deformation characteristics of twin-roll casting process. Based on the simulation results, the form of evolution equations in Anand's model was discussed.
基金supported by Doctoral Dissertation Innovation and Excellence Producing Foundation of Nanjing University of Aeronautics and Astronautics,China(Grant No.BCXJ09-07)Jiangsu Provincial Six Kind Skilled Personnel Project of China(Grant No.06-E-020)Jiangsu General Colleges and Universities Postgraduate Scientific Research Innovative Plan of China(Grant No.CX09B_074Z)
文摘SnAgCu solder system with the addition of rare earth Ce,which has better thermo-mechanical properties compared to those of SnPb solder,is regarded as one of the promising candidates for electronic assembly.Moreover,the SnAgCuCe solder alloys can provide good quality joints with Cu substrates.However,there is few report of the constitutive model for SnAgCu solder bearing micro-amounts rare earth Ce.In this paper,the unified viscoplastic constitutive model,Anand equations,is used to represent the inelastic deformation behavior for SnAgCu and SnAgCuCe solders.In order to obtain the acquired data for the fitting of the material parameters of this unified model,a series of experiments of constant strain rate test were conducted under isothermal conditions at different temperatures.The Anand parameters of the constitutive equations for SnAgCu and SnAgCuCe solder were determined from separated constitutive relations and experimental results.Nonlinear least-square fitting was selected to determine the model constants.And the simulated results were then compared with experimental measurements of the stress-inelastic strain curves:excellent agreement was found.The model accurately predicted the overall trend of steady-state stress-strain behavior of SnAgCu and SnAgCuCe solders for the temperature ranges from 25℃to 150℃,and the strain rate ranges from 0.01 s^-1 to 0.001 s^-1.It is concluded that the Anand model can be applied for representing the inelastic deformation behavior of solders at high homologous temperature and can be recommended for finite element simulation of the stress-strain response of lead free soldered joints.Based on the Anand model,the investigations of thermo-mechanical of SnAgCu and SnAgCuCe soldered joints in fine pitch quad flat package by finite element code were done under thermal cyclic loading,it is found that the reliability of SnAgCu soldered joints can be improved remarkably with addition of rare earth Ce.The results may provide a theory guide for developing constitutive model for lead-free solders.
