Quasi-static normal indentation of an elasto-plastic substrate by a periodic array of elastic strip punches

The plane-strain, elasto-plastic, contact problem described in the title is treated for a substrate that is perfectly plastic post yield, and so simulates compression molding of some metals at elevated temperatures. The analysis uses finite elements and is verified with test problems and convergence checks. The key finding is that, in what might reasonably be viewed as a fully-plastic state, the molding pressure normalized by the yield stress is equal to a constant plus a term that increases linearly with the depth of indentation. This is in contrast to Tabor’s classical result for hardness testing that has the normalized pressure solely equal to a constant when response is fully plastic. The additional linear stiffening term found with the finite element analysis of the present configuration is confirmed experimentally. An explanation of the source of this stiffening term even with a perfectly-plastic substrate is offered. Contact stresses are also tracked as indentation proceeds. These stresses initially have high stress concentrations near the edges of the strip punches. However, these peak stresses abate rapidly with plastic flow and approach a nearly uniform distribution within the fully-plastic state. Implications for compression molding are discussed.