A rate and temperature dependent unified creep-plasticity model for high strength steel and solder alloys

Temperature has profound effects on viscoplastic deformation of materials. The rate sensitivity of metallic materials is complicated by the change of temperature and the concern of material behavior. In the current research, a constitutive framework based on unified creep-plasticity theory is developed. The change of material rate sensitivity and temperature is investigated. The curve of rate sensitivity versus temperature is divided into several segments to ensure that each individual part is monotonically changing. The deformation behavior corresponding to each part is described by hyperbolic tangent and cotangent functions. The flow functions of segments are integrated into a common flow rule by utilizing the property of the hyperbolic tangent function, in which the value remains equal to one when the independent variable is large enough. Considering that the rate-dependent behavior of different materials vary drastically, the proposed constitutive framework incorporates the drag stress evolution, temperature function and the adjustment equations. The developed model is validated by comparing with experiments of two representative materials: high strength steel and Sn-3.0Ag-0.5Cu solder alloy under different loading rates and temperatures.