The work aims to study the influence of curvature radius of the asperity on the material wear by creating a micro-grinding model. Different variable curvatures of asperities were selected from asperities of abrasive tools and workpieces to create sliding grinding model I and II. By taking elastic/plastic deformation of materials and their fracture failure during the process of grinding into account, stress variation of embedded asperity and abrasive dust shedding during sliding were analyzed by using the finite element method. With the sliding grinding process, upper asperity on asperity contact pairs with smaller contact angle θ1≈19.4° was subject to wear fracture while the lower asperity on asperity contact pairs with larger contact angleθ2≈25.5° was subject to wear fracture. The maximum equivalent plastic strain of the wear asperity occured 1.5~2.0 μm beneath the subsurface. Abrasive dust is more likely to be present in smaller curvature radius of asperity provided that other influencing factors are the same during grinding of double-faced rough surface. The maximum equivalent plastic strain of the wear asperity occurs in certain depth of the subsurface. Stress triaxiality decreases with the increase of plastic deformation, leading to initiation of a micro crack and formation of abrasive dust.