Flattening of asperities during biaxial in-plane deformation – Full mapping of the strain space by numerical simulations

Friction in metal forming is primarily determined by the real contact area between the workpiece surface asperities and the comparably flat tool surface. Asperities flatten due to normal loading, and subsurface strains heavily influence the degree of flattening. This work employs a three-dimensional numerical model based on the irreducible finite element flow formulation to determine the flattening of one pyramidal asperity unit cell. The flattening is simulated under normal loading combined with different biaxial in-plane subsurface strains. The numerical model was validated against existing experimental data available for plane strain and balanced biaxial strain states. The results of real contact area ratios were subsequently expanded to other ratios of the in-plane principal strains to map the entire strain space typical of forming limit diagrams.