Parameterized Anand constitutive model under a wide range of temperature and strain rate: experimental and theoretical studies

The inconsistency of constitutive parameters weakens the rationality and also impedes the application of the Anand model. In this paper, a modified framework of Anand model is proposed and the corresponding parameters are calibrated using two viscoplastic materials, that is, Sn-3.0Cu-0.5Ag and Sn37-Pb63 which are typical die-attach solder alloys in the electronic packaging industry. The stress–strain relationships under a wide range of temperature and strain rate are measured from the uniaxial tensile experiments for both materials by dog-bone specimens. The dependency on strain rate and temperature can be well described by reasonably parameterizing the proposed Anand model. Effects of strain rate and temperature on saturation stresses are emphasized. In order to highlight the necessity to account for strain rate and temperature effects, the plastic ball grid array packaging structures are adopted in the scenario of thermal cycling. Due to variation of strain rate and strain, different stresses are observed among different positions in the packaging structure under the applied cycled temperature field. The wide ranges of strain rate and temperature are satisfactorily described by the proposed Anand model with one set of parameters, rather than using multiple sets of parameters or even multiple types of constitutive models. Lastly, the accumulative plastic strain and stress of two materials are numerically predicted and discussed to reveal the relationship between strength, Young’s modulus and plastic deformation, which shows the proposed parameterized Anand model can be readily utilized for fatigue life estimations of packaging structures under thermal cycling.