Friction, lubrication, and wear are responsible for significant energy losses across transportation, industrial, and utility sectors. In metal forming, controlling friction is essential both for reducing energy consumption and for improving the manufacturability of challenging components. For example, in deep drawing, a widely used sheet metal forming process where the punch gradually pulls a blank sheet into the die cavity, friction must not be too high, to allow material flow, but also not too low, to prevent defects such as wrinkling. Achieving optimal friction not only enhances formability but also extends tool life and reduces production costs. Since friction arises at the contact interface, understanding the tribological behavior in such interfaces is crucial for optimizing forming processes.
However, investigating tribology in this context is particularly challenging, as it constitutes a multiscale and multiphysics problem. Real surfaces are rough, and contact occurs only at the asperity summits at smaller scales. Moreover, when considering mixed lubrication regimes, commonly used in sheet metal forming, and wear particles generated during the process, the situation becomes even more complex due to the interplay between surface roughness, lubricant availability, and wear debris. While empirical approaches have enabled a certain degree of process optimization, their predictive capability remains limited, and experiments alone are costly. This motivates the development of robust multiscale, physics-based numerical tools that can capture the frictional behavior during the forming process while accounting for the relevant mesoscale physics.
This thesis develops a hierarchical multiscale numerical framework to model the friction coefficient. At the macroscale, a one-dimensional finite-element strip-draw model is used to predict the global frictional response of the deformable sheet during sliding, while the local friction at the contact interface is informed by mesoscale simulation results. At the mesoscale, a coupled discrete-element and boundary-element approach resolves the load sharing between rough surfaces and rigid oblate-spheroidal wear particles, while also capturing the evolution of the deformable surface during sliding. Another mesoscale model is developed to account for the effects of discrete lubricant droplets and trapped lubricant pockets. Using these models, the local friction coefficient at the mesoscale can be determined as a function of macroscopic normal pressure, sliding velocity, and surface topography. In this way, the framework effectively closes the loop between scales.
The proposed model accurately reproduces experimental strip-draw tests on aluminum sheets provided by Novelis, capturing key trends such as the decrease of friction with increasing normal pressure and the influence of tool-pad geometry. This framework establishes a predictive methodology for friction in mixed-lubrication regimes, offering both theoret
