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When friction stress on a contact surface reaches material yield strength in shear, contact slippage can occur even if the slipping condition for Coulomb friction is not satisfied. In this paper, a three-dimensional (3-D) scratch model is proposed, which considers combined Coulomb and plastic friction. Influences of plastic friction are discussed for two continuous displacement loading steps: indentation and scratch. For indentation, initially the sliding on the contact surface can not take place and the complete cohesion condition should be employed; then as the indenter is further compressed down to the coating surface, plastic friction instead of Coulomb friction prevails in most of the contact region. For scratch, the previous complete cohesion at the initial indentation is substituted by plastic or Coulomb slipping, and the slippage becomes plastic-sliding governed for a slightly large indentation depth. The effects of the indentation depth and the Coulomb friction coefficient on the scratch friction coefficient are discussed in detail. Several experimental phenomena are interpreted, which include that with an increase of the normal loading, the scratch friction coefficient reduces for the soft coating but grows for the hard coating; and with the growth of hardness after heat treatment, the scratch friction coefficient increases due to weak plastic slippage. Obtained results help to elucidate tribological behaviors during scratch and are helpful for the interpretation of experimental phenomena and the improvement of numerical simulations for the scratch process.


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