Constitutive Description Of Tin-Lead Solder 63Sn-37Pb Under Multiaxial Loading

Fatigue tests under uniaxial, torsional, multiaxial proportional and non-proportional loading, in addition with some uniaxial and multiaxial ratcheting tests are carried out on tin-lead solder 63Sn-37Pb at room temperature. It can be concluded that the materials exhibit non-additional cyclic hardening effect under non-proportional loading compared with proportional loading. With same equivalent strain amplitude, the descending curve of peak stress with cycle under non-proportional loading is declining faster than that under proportional loading, and the fatigue lives of solder under non-proportional loading are reduced by a factor of 3 in comparison with those under proportional loading. Even low second stress can cause high ratcheting strain. The trend of shakedown doesn't take place when the ratcheting strain is large. Loading history and its sequence have no clear influence on the subsequent ratcheting behavior. The axial ratcheting strain rate is found to be strongly dependent on applied shear strain rates in axial/torsional ratcheting experiments, the ratcheting strain rate under strain rate of 10-4/s is approximately five times as large as that under strain rate of 10-2/s.The Euler backward method is implemented to update the stress. The diagram of algorithm and the general form of algorithm modulus for rate-independent and rate-dependent constitutive model is derived and presented. Features of integration algorithm such as accuracy, robustness, efficiency and stability are verified by numerical examples.A 3-Dimensional finite element model of tin-lead round solid specimen is established and the validity of shear stress approximation on the surface of solid specimen under proportional and non-proportional loading is verified. On this basis, a constitutive model with Ohno-Wang kinematic hardening rule and an implicit constitutive integration scheme is employed to simulate the isothermal cyclic behavior of Sn-Pb solder under various loading conditions.With the consideration of fatigue damage specifications of tin-lead solder 63Sn-37Pb, a modified low-cycle fatigue life prediction model, KBM-Stolkarts model, is put forward in which the sum of maximum shear strain range and normal strain range based on the critical plane concept is adopted to replace the original damage parameter used by Stolkarts et al. The reasonable substitution of damage parameter is capable of explaining the difference of damage evolution procedure of eutectic tin-lead solder under proportional and nonproportional loading.Comparison of experimental and predicted results verifies that the stress strain hysteresis loops and peak stress decline curve of solder can be reasonably modeled over a wide range of loading conditions with implement of damage coupled Ohno-Wang constitutive model, and the lifetime estimations of 63Sn-37Pb solder based on the assumption of microcrack nucleation governed damage is effective to provide a conservative prediction.The influence of axial stress, shear strain amplitude, loading history and its sequence on multiaxial ratcheting behavior of 63Sn-37Pb can be simulated reasonably by a modified rate-dependent AF-OW model. In addition, the modified model not only can be used to describe the stress strain response at different strain rates very well, but also can be applied to predict the highly rate dependent multiaxial ratcheting behavior of eutectic tin-lead solder.