Depth-dependent stress–strain relation for friction prediction

• Depth-dependent stress–strain relation based on the indentation size effect model is presented.
• The effect of surface roughness size effect on friction is studied.
• Tribometer experiment showed good agreement with strain gradient dependent friction simulation.

The effect of strain gradient on the mechanical property of a material is implemented through a depth-dependent stress strain relation model in conventional finite element simulations for use in friction prediction. For the incorporation of a strain gradient effect, contact simulation involving asperities was developed with the assumption that the deformation pattern created by asperities from the tool surface in microforming is comparable to the deformation created by the indenter in a hardness test. Consequently, a depth-dependent stress–strain relation was derived from the indentation size effect model and this stress–strain relation was used in a simulation to show the effect of strain gradient on friction behaviour in microforming at different surface roughness levels. An experiment was conducted alongside the simulation and the results showed that with asperity ploughing considered as the major contributor to friction in microforming at room temperature, the simulation involving depth-dependent material properties is able to better predict the friction behaviour as compared to its continuum simulation counterpart.

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