A new unified constitutive model with short- and long-range back stress for lead-free solders of Sn–3Ag–0.5Cu and Sn–0.7Cu

A series of tensile tests of Sn–3Ag–0.5Cu and Sn–0.7Cu lead-free solders were investigated at various strain rates from 1 × 10−4 s−1 to 1 × 10−2 s−1 and over a wide temperature range from 25 oC to 150 oC. Two-step strain rate jump tests, three-step short term creep tests with stress jump, and uniaxial ratcheting tests were also conducted. Based on the test data, a new constitutive model was proposed with a simple formulation and only eight material constants which can be easily obtained. The model employs two carefully defined back stress components to simulate the loading/unloading asymmetry phenomenon in uniaxial ratcheting tests. Different evolution rules of short-range back stress were given for loading and unloading stage, which provides the model ability to simulate the asymmetry in hysteresis loops. The proposed model presents good simulation of uniaxial tensile tests, strain rate jump tests, short term creep tests with stress jump, and uniaxial ratcheting tests.