This work addresses numerical modeling of a sliding contact problem where rigid, spherical indenters slide across two-layered time-dependent materials. A nano-indentation technique was used to obtain the material properties, and a finite element method was used for numerical simulations. While most of the previous work in this area assumes polymers to be pure visco-elastic materials, this current analysis proposes a unified constitutive equation which considers both visco-elastic and plastic behaviors in the simulations. Although the nano-indentation technique normally adopts Sneddon’s elastic solution to measure Young’s modulus derived from the slope of unloading curve, it is not applicable for certain polymeric materials since the unloading curve is affected by visco-elastic properties as well as modulus. Therefore, an iterative method, a combination of experimental data with numerical simulation, is proposed to determine material properties.

With two-layered media, the influence of four parameters (normal load, indenter radius, friction coefficient, and sliding velocity) on the stresses in the substrate is investigated for verification and comparison. If the material is brittle, the friction coefficient may be the most important factor for explaining material failure such as ring cracking. If the material is ductile, normal load and indenter radius have a major influence on microcracking and wear with an increase in von Mises stress. The results of three polymeric structures obtained from the unified equation implies that the visco-elastic effect is larger than the plastic effect, as in most polymeric materials. While visco-elastic properties have the effect of decreasing the pressure and stresses in normal indentation, it is also likely to enhance material failure when sliding occurs.

Based on the study of parameter estimation, the finite element model (FEM) results were compared to experimental scratch test results in order to predict tensile (ring cracking) stress by using an analogy between 2-D and 3-D Hertzian contact. For each of the structures, the tensile stresses at the trailing edge determined from three different indenter sizes were reasonably consistent. This implies that the (consistent) tensile stress computed, when obtained through the input of experimentally-observable failure loads and mechanical property, represents a characteristic tensile strength of the top layer in the structure itself. This tensile strength is an important mechanical property when designing coated systems.