The paper considers 3D movable cellular automata (MCA) models of contact interactions involved in nanoindentation, sclerometry, and tribospectroscopy. The system under study is a titanium substrate with a hardening coating. The substrate and coating materials are both described in the elastoplastic approximation. It is shown that the MCA method of numerical simulation provides correct description of the contact interaction of elastoplastic materials under different types of loads with explicit account for fracture. The possibility to detect damages in material surface layers from friction force estimates is assessed.