Determination of Anand constants for SAC solders using stress-strain or creep data

Abstract

The Anand viscoplastic constitutive model is often used to represent the deformation behavior of solders in electronic assemblies. In the Anand model, plasticity and creep are unified and described by the same set of flow and evolution relations. The nine parameters of the Anand constitutive model are typically determined from uniaxial stress-strain tests at several strain rates and temperatures using a standard multistep model parameter determination procedure. Conversely, creep data are often measured for solders, but typically are not used to determine Anand model constants. In this study, the theoretical equations for the uniaxial stress-strain response (constant strain rate) and for the creep response of solder have been derived from the Anand viscoplastic model. Procedures for extracting the Anand model constants from experimental stress-strain and creep data were also established. The two developed methods were then applied to find the Anand constants for SAC305 (Sn3.0Ag-0.5Cu) lead free solder using two completely different sets of experimental test data. The first set of Anand parameters were extracted from uniaxial stress strain data measured over a wide range of strain rates (ε = 0.001, 0.0001, and 0.00001 1/sec) and temperatures (T = 25, 50, 75, 100, and 125 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</sup> C). The second set of Anand parameters were calculated from creep test data measured at several stress levels ( = 10, 12 and 15 MPa and temperatures (T = 25, 50, 75, 100, and 125 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</sup> C). The two sets of Anand model constants derived from the stress-strain and creep data have been compared and found to be numerically very similar in magnitude. In addition, the accuracy (goodness of fit) of the Anand model using the extracted material constants has been evaluated by comparing the responses calculated from the Anand model with the measured stress-strain and creep data. In all cases, the Anand model was shown to represent the observed data very well over a wide range of temperatures and stress/strain levels.