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Surface tension plays a significant role in micro- and nanoindentation tests. Based on the solution of a concentrated force acting on an elastic half-plane with surface tension, the two-dimensional indentations of an elastic half-plane by a cylindrical indenter, a wedge indenter and a flat-ended indenter are formulated, and by employing the Gauss–Chebyshev quadrature formula, the corresponding singular integral equations are numerically solved. For each indentation, the analytic solutions of two limit cases considering only bulk elasticity or surface tension are derived. Then through simple combinations of the results of two limit cases, the analytic relations between load and contact half-width or indent depth are formulated for the general case, and compared with the numerical results. The analytic relations established in this paper facilitate better characterization of mechanical properties of materials by micro/nanoindentation tests.

Physical aging widely exists in amorphous polymers, which refers to the nonequilibrium structure of amorphous polymers evolving towards the equilibrium state. Aging can significantly influence the thermomechanical properties and subsequently the macroscopic response of polymers. In our recent work, we performed a series of uniaxial compression tests on amorphous thermoplastic poly(ethyleneterephthalate)-glycol (PETG) subject to different annealing temperature and time. The results showed that both annealing time and temperature have a significant influence on the yield strength. Here we apply a two-temperature continuum model to simulate the stress response of PETG with different thermal treatments. The model employs the effective temperature as a variable to characterize the nonequilibrium state. The physical aging is characterized by the evolution of the effective temperature. The effective temperature is also coupled with the viscoplastic deformation to describe strain softening induced by mechanical rejuvenation. The simulation results can reasonably reproduce the main experimental observations with some discrepancies. The possible reasons for the discrepancies between experiments and simulations are also critically analyzed. The theory is also used to simulate the response of amorphous glassy polymers in the creep and strain-rate-switching tests. The model successfully captures the important features of experimental observations in the literature.