The effects of silver content and solidification profile on the Anand constitutive model for SAC lead free solders

In the electronic packaging industry, it is important to be able to make accurate predictions of board level solder joint reliability during thermal cycling exposures. The Anand viscoelastic constitutive model is often used to represent the material behavior of the solder in finite element simulations. This model is defined using nine material parameters, and the reliability prediction results are often highly sensitive to the Anand parameters. In this work, an investigation on the Anand constitutive model and its application to SAC solders of various Ag contents (i.e. SACN05, with N = 1, 2, 3, 4) has been performed. For each alloy, both water quenched (WQ) and reflowed (RF) solidification profiles were utilized to establish two unique specimen microstructures, and the same reflow profile was used for all four of the SAC alloys so that the results could be compared and the effects of Ag content could be studied systematically. The nine Anand parameters were determined for each unique solder alloy and microstructure from a set of stress-strain tests performed at several strain rates and temperatures. Testing conditions included strain rates of 0.001, 0.0001, and 0.00001 (sec-1), and temperatures of 25, 50, 75, 100, and 125 C. The Anand parameters were calculated from each set of stress-strain data using an established procedure that is described in detail in the paper. Using the calculated results for the various SAC alloys and microstructures, a set of empirical models have been established to describe the effects of SAC alloy Ag content on the Anand model parameters. As expected, the mechanical properties (modulus and strength) increase with the percentage of Ag content, and these changes strongly affect the Anand parameters. The sensitivity of the mechanical properties and Anand parameters to silver content is higher at lower silver percentages (1-2%). Also, the observed mechanical properties of water quenched samples were better (higher in magnitude) than the corresponding mechanical properties of the reflowed samples. Although the differences in elastic modulus between the water quenched and reflowed samples are small, significant differences are present for the yield and ultimate tensile stresses of all four SAC alloys. After deriving the Anand parameters for each alloy, the stress-strain curves have been calculated for various conditions, and excellent agreement was found between the predicted results and experimental stress-strain curves.