Unified Constitutive Models For Lead-free Solders

In electronic packaging industry, with the rising of environment protection requirement and the appearance of more and more laws forbidding the use of lead-containing solder, it is a trend to replace the traditional lead-containing solder by lead-free solder. The reliability of solder joint greatly affects the reliability of IC packaging, even the performance of the circuit. However, because the lead-free solder is in its early stage of development, the research on mechanical properties of lead-free solders is relatively simple and little. Due to the situation mentioned above, it is necessary to perform experimental and theoretical research on mechanical properties of lead-free solders.Two types of lead-free solders, Sn-0.7Cu and Sn-3Ag-0.5Cu, which will be potential solders to be widely used in electronic packaging, are studied. Uniaxial tensile test, creep test, strain rate jump test, stress jump test, and complicated tests, such as uniaxial ratcheting test, uniaxial cyclic torsional test, multiaxial ratcheting test, multiaxial test with complex path, were conducted on the two types of lead-free solders under several conditions with different strain rates and temperatures. All the tests were carried out on a minitype tension-torsional testing machine, developed by ourself, which can provide complex loading tests on mini specimen.Anand model, Bodner-Partom model, SVBO model and McDowell model were adopted to simulate the uniaxial tensile tests of the lead-free solders, the applicability of the four models to lead-free solders were discussed based on the simulation results. Based on several uniaxial tensile tests with different strain rates and temperatures, the stress and strain were mormalized by saturation stress. The uniaxial tensile test curves showed unified stress-strain curves for all the tests. A unified constitutive model without back stress concept, model I was constructed.Loading/unloading asymmetry, which could not be explained by the four discussed models and model I, was observed in uniaxial ratcheting tests. A new unified model with back stress concept, model II was proposed. Two back stress components were employed by model II, just like the case of McDowell model. In addition, model II introduced a concept of"loading surface"similar with"yield surface". The model simulated the loading/unloading asymmetry phenomenon in uniaxial ratcheting tests successfully and presented good predictions to complex loading path tests. Model II kept the ability of model I to simulate uniaxial tensile tests.