Viscoplastic Constitutive Model for Lead-Free Solder Including Effects of Silver Content, Solidification Profile, and Severe Aging
Authors: Basit Munshi , Motalab Mohammad , Suhling Jeffrey C. , Lall Pradeep 
Published: November 2015

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 viscoplastic 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. In addition, we have performed tensile testing on reflowed specimens subjected to 6 months of aging at 100 C. After this level of aging, any further changes in the mechanical response and properties will be rather small. Thus, the results for these tests can be regarded as approaching the highest level of mechanical behavior degradation possible for a “severely aged” lead free solder material.
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. 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 relatively small, significant differences are present for the yield and ultimate tensile stresses of all four SAC alloys.
The changes in the Anand model parameters after severe aging (6 months at 100 °C) were significant. The measured experimental results have been used to illustrate the range of values possible for Anand parameters for the SACN05 alloys. The upper extreme was the water quenched limit, where the materials have extremely fine microstructures and high mechanical properties. The lower extreme was the severely aged limit, where the materials have extremely coarsened microstructures and highly degraded mechanical properties. While further degradations are certainly possible with even further aging, the limiting values found for a severely aged SAC alloy can be used by designers as a conservative set of constitutive parameters representing the lower end of the material properties for that alloy.
After deriving the Anand parameters for each alloy and microstructure, the stress-strain curves have been calculated for various conditions, and excellent agreement was found between the predicted results and experimental stress-strain curves.