Time-Dependent Contact Behaviour of ZDDP-Derived Tribofilms: A Viscoelastic Layered Model Approach.

The ZDDP-derived tribofilm was recently reported to be viscoelastic based on a creep experiment, where a Burgers material model mathematically represents its creep compliance. This study develops a contact model for layered materials by extending a previously established viscoelastic half-space contact model. The approach involves converting analytical frequency response functions into influence coefficients, enabling the investigation of the viscoelastic behaviour of ZDDP-derived tribofilms. The results reveal that the tribofilm exhibits a highly fluid-like response when modelled as a half-space body being in contact with a carbon steel ball during indentation or sliding. When bonded to an elastic substrate in its typical thin-film form (on the nanometre scale), the contact behaviour can still exhibit time-dependent characteristics, depending on the operating conditions. Creep and stress relaxation are observed during indentation, particularly under low loads, while high loads result in a more pronounced viscoelastic response in extremely slow-speed contacts. However, under moderate sliding speeds ranging from millimetres to meters per second, time-dependent effects become negligible, regardless of the applied load. These findings indicate that although ZDDP-derived tribofilms exhibit significant viscoelasticity, their behaviour in practical applications generally resembles that of a soft elastic layer, as typical sliding speeds fall outside the range where pronounced time-dependent effects occur. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1007/s11249-025-01990-5.