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 polymers with different material properties (elastic modulus, hardness, 'Viscosity) are deconvoluted 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.