The effects of material plasticity and local slip on the sliding inception of asperity are studied in the present work. Firstly, a semi-analytical solution is derived under the full-stick condition to analyze the effect of material plasticity on sliding friction. Then, a friction model with contact stiffness criterion is proposed to study the cases from partial-slip condition to full-stick condition. Finite element simulations with the provided model are used to present the friction map. The friction coefficient of full-stick interface converges at a stable value, approximately 0.3. Plasticity saturation appears as the normalized contact interference is larger than 3. A transition mechanism from slip-dominated to yield-dominated takes place in the sliding process. The simulation results are compared with the semi-analytical solution.