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In this work, a computational model of rate dependent crystal plasticity is developed to simulate the stress-strain response of HSLA-50 steel in constant strain-rate tensile and fatigue tests. The plasticity model is based on the thermally activated theory for plastic flow and incorporates kinematic hardening and grain-size dependent hardening. This constitutive model for polycrystalline metals is implemented in ABAQUS using the user interface UMAT. A Genetic Algorithm (GA) based optimization method is utilized to identify the crystal plasticity parameters from experimental data. The simulations help in understanding the mechanisms of slip system activity, local hardening and local strain on the material behavior as well as the effects of grain-size and kinematic hardening on plastic strain ratcheting, even in the macroscopically elastic regime.