Load–displacement behavior during sharp indentation of viscous–elastic–plastic materials

A model is developed that describes the sharp indentation behavior of time-dependent materials. The model constitutive equation is constructed from a series of quadratic mechanical elements, with independent viscous (dashpot), elastic (spring), and plastic (slider) responses. Solutions to this equation describe features observed under load-controlled indentation of polymers, including creep, negative unloading tangents, and loading-rate dependence. The model describes a full range of viscous–elastic–plastic responses and includes as bounding behaviors time-independent elastic–plastic indentation (appropriate to metals and ceramics) and time-dependent viscous–elastic indentation (appropriate to elastomers). Experimental indentation traces for a range of olymers with different material properties (elastic modulus, hardness, viscosity) are econvoluted and ranked by calculated time constant. Material properties for these polymers, deconvoluted from single load–unload cycles, are used to predict the indentation load–displacement behavior at loading rates three times slower and faster, as well as the steady-state creep rate under fixed load.