## 3 Results and Discussion
During the plastic deformation at temperatures that are below glass transition, the chains of glassy polymers obtain a limited degree of mobility under the applied stress, and the strain hardening will depend on the degree of cross linking [26]. A molecular dynamic simulation study of indentation on PS [27] demonstrated that during the plastic indentation stage, the movement of polymer chains was restricted, providing a low atomic-level strain and very small volume affected region in terms of chain slipping. It was attributed to the presence of benzene rings that restrict chain movement that allow PS to withstand great loading forces. The most displaced and affected areas were close to the edge with the top polymer surface. They also demonstrated that the indenter bluntness and loading rates have a strengthening effect on PS. Considering all above, and taking into account that the material surface adjacent to the indenter hardens during the deformation [28], it explains the higher or unchanged hardness and modulus values at a separation of 1. At _d_/h = 1, the second indent takes place on one of the imprinted faces of the pyramid, and depending on the indent orientation might be close to the pyramid edge (Figure 6a). The load-displacement curves (Figure 7) corresponding to _d_/_h = 1 clearly show the displacement to be smaller for the indents 2 and 3 at the same recorded loading force, indicating the presence of a harder surface. The materials that tend to work harden during the indentation, such as glasses and ceramics, usually preferentially sink-in. The pile-up is largest for those that have little or no capacity to work harden [29; 30]. The experimentally measurable ratio of the final depth, _h_/, to the maximum depth, _h_max, was introduced to identify the threshold value at which the material will pile-up or sink-in. It was found that irrespective of work-hardening characteristics and penetration depth, pile-up occurs when _h_/_h_max > 0.7 [30]. In our case, the ratio of _h_/_h_max is 0.65 for a depth of 1 \(\upmu\)m and 0.70 for a depth 5 and 10 \(\upmu\)m, yet the pile-up of material is observed at all indentation depths on all three sides of the pyramid imprint. It seems that this ratio is not the best indicator to determine material behavior in the case of polymers, as was also shown in [31]. The pile-up, together with the formation of radial crazes or crack type defects, is mostly prominent on the right side where the next indent will take place (Figure 6). In the nanoindentation studies of polymeric scratched surfaces [32; 33], it was noted that the indenter encountered less resistance on the damaged surface than that of undeformed glassy polymers like PS and PMMA. This \"softening\" was attributed to the presence of subsurface voids in the form of crazes that were formed during the scratching. Our results indicate, that even though PS might experience strain hardening during the indentation, there is still some degree of upward material flow that can induce certain subsurface defects, with the not-so-closely packed chains that have softer regions. At _d_/_h_ = 2, the apex of the next indent will start on the edge (or close to it) of the imprint within the piled-up, cracked/crazed region (Figure 6a). Loading-displacement curves (Figure 7) at these depths show larger displacements due to the softer nature of the surface, with respect to the first indent obtained at the same load. At this separation, the lowest mechanical properties were recorded for almost all depths (Figure 4). Irrespective of material work-hardening, piling-up, or sinking-in, permanent deformation occurs, creating a plastic zone with certain shape and radius surrounding the indent. For piling-up and non-strain hardening materials, the plastic zone will extend outside the radius of contact, while for sinking-in materials, the zone will most likely be contained within the boundary of the indent [30].