Determination and modification of unified inelastic constitutive model in predicting 95.5Sn-4.0Ag-0.5Cu solder material response

Accurately forecasting the mechanical properties of materials is crucial in the field of materials science and engineering. The Anand model, a renowned constitutive model for inelasticity, has proven to be valuable in describing the intricate deformation characteristics of materials. Nevertheless, it has been observed that the parameters of the Anand model may ineffectively represent the strain rate and temperature-dependent characteristics exhibited by certain materials, leading to discrepancies between the model's predictions and experimental findings. Literature study reveals that researchers have calculated varying values for the Anand model parameters when describing different SAC solders. Using Anand's inelastic constitutive model for SAC405 (95.5Sn-4.0Ag-0.5Cu) lead-free solder, the theoretical equations for the solder's uniaxial stress-strain response were obtained in this paper. The steps to obtain the parameters of Anand model using stress-strain were also determined. Nonlinear least squares fitting was employed to optimize the Anand parameters based on the experimental data. Data on uniaxial stress and strain at various temperatures (T = 298 K (25 °C), 323 K (50 °C), 348 K (75 °C), 373 K (100 °C), and 398 K (125 °C)) and strain rates ( ̇ɛ = 0.001 sec-1, 0.0001 sec-1, and 0.00001 sec-1) was used to calculate the Anand parameters. The effects of temperature and strain rate on the model's predictions were thoroughly analysed, demonstrating their significant influence on the model's accuracy. To increase the capability of the model, 4 material parameters are screened to determine if the parameters are significantly affected by temperature and strain rate. The refined Anand model's accurateness (goodness of fit) with the modified parameters was assessed by comparing the model's findings to the original model and the observed stress-strain data. The modified Anand model consistently generated good predictions of the empirical data in all cases, across a wide range of temperatures and stress-strain levels. The goodness of fit values obtained were 99.38%, 98.67% and 98.40% for strain rate 0.001 sec-1, 0.0001 sec-1 and 0.00001 sec-1 respectively.