A three-dimensional (3D) scratch model is proposed to investigate the effects of yield strength of\nboth coatings and substrates. With the help of combined Coulomb and plastic friction, the obtained results\ncomprehensively interpret the experimental phenomena in most metals that with the growth of hardness after\nheat treatment the scratch friction coefficient (SFC) increases. This interpretation could not be done before.\nScratch tests on the surface with or without the coating are discussed. Without the coating the SFC increases\ndue to the decrease of the area with plastic slippage and/or the increase of friction stress during the increase of\nthe yield strength in the material. With a softer substrate the friction stress decreases but the SFC increases,\nwhich is caused by the growth of the entire contact area and surface deformation. Conversely, with a stronger\nsubstrate the SFC decreases due to an intensified plastic slippage. The obtained results pave a new way to\nunderstanding the effects of yield strength on scratch tests, interpret experimental phenomena, and should be\nhelpful for an optimum design in experiments.
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