Nonlinear Wear Modelling in Lubricated Pin-on-Disc Contacts Using the Archard–Bayer Law with FEM Validation for Sheet Metal Forming

Accurate prediction of wear in lubricated metal-to-metal contacts remains a critical challenge, as calibration parameters derived from laboratory tests often lack transferability to finite element method (FEM) simulations. While classical linear Archard models are widely applied, they fail to capture the nonlinear load-dependent wear behavior observed under varying operating conditions. This study addresses this limitation by developing and validating a nonlinear wear formulation based on the Archard–Bayer law within a coupled experimental–numerical framework. A comprehensive Pin-on-Disc test matrix was conducted under lubricated conditions using carbide–steel contacts across varying loads and cycle counts. Wear progression was quantified and analysed using outlier-corrected weighted regression, yielding a force exponent mexp=1.58±0.34 and cycle exponent nexp= 0.41 ± 0.17. The calibrated nonlinear model was implemented in a FEM environment and systematically evaluated across multiple loading scenarios. The nonlinear formulation demonstrates improved predictive capability compared to the classical linear Archard model, particularly under higher load conditions (15 N–20 N), where deviations between simulation and experiment remain below 11%. The FEM-calibrated exponent (m = 1.35) lies within the 95% confidence interval of the experimental value, indicating that numerical adjustments required for stability are statistically non-significant. The results show that nonlinear wear models provide a more accurate representation of load-dependent wear behavior but require constrained calibration ranges for reliable application. The proposed methodology enables robust transfer of experimentally derived wear parameters into FEM simulations and provides a practical basis for tool-life prediction, parameter tuning, and model deployment in sheet metal forming processes.