## 3 Results and Discussion  
Experimental Analysis for Indents in a Row with Orientations 0\({}^{\circ}\) and 90\({}^{\circ}\)  
The experimental hardness and modulus values for all three indents done in a single row with varying spacing at different depth are given in Figure 4. The average percentage difference values for three indents obtained at the same distance, \(\overline{D}\%\), shown in Figure 5, were calculated using Equation (6):  
\[\overline{D}\%=\frac{1}{n}\sum_{i=1}^{n}\lvert x_{i}-\overline{D}\rvert, \tag{6}\]  
where \(n\) is the number of the data points and the average of the set \(\overline{D}=\frac{1}{n}\sum_{i=1}^{n}x_{i}\). When comparing absolute values of single indents at different spacing (Figure 4), graphs clearly show that once the spacing, \(d\)/\(h\), is around 10, the hardness and modulus values between three indents remain more or less constant independent on the maximum indentation depth. In addition, from \(d\)/\(h\sim 10\), the properties do not change with spacing for depth 1 and 5 \(\upmu\)m. For \(h=10\)\(\upmu\)m, with the account for deviation, mechanical properties do not differ with spacing from \(d\)/\(h\sim 15\). Furthermore, the  
Figure 3: 3D model and meshing arrangement for one indent. average percentage difference between indents of less than 2% was obtained from nominal spacing as small as 5 times the indentation depth (Figure 5). Figure 5a,b also illustrates property dependence as a function of indent orientation. The influence of orientation is strong only at separations up to 4-5 times, and becomes ineffective at larger spacing if indents were done in a single row or column. Figure 4: Hardness (\(H\)) and reduced modulus (\(Er\)) for each indent measured in a single row (orientation 0\({}^{\circ}\)) at different indentation depth and spacing. (**a,b**) \(h=1\) μm; (**c,d**) \(h=5\) μm; (**e,f**) \(h=10\) μm. The closer the indent spacing is, the more affected the next indent will be, thus reducing the validity of obtained data. The results for the first indent remain constant as it is done on a non-disturbed surface, unless the indentation occurs at some defect point. The second indent will be influenced by the first, and the third will be affected by both indents until \(d/h\sim 3\)-4, depending on the maximum depth. Optical images demonstrating indent overlapping and corresponding typical load-displacement curves for small separations for \(h=5\)\(\upmu\)m are given in Figures 6a and 7, respectively. In general, hardness and modulus values are lower for indents 2 and 3 at the spacing \(d/h<5\)-6 when compared with the first indent, but they increase with increased separation. The exception is spacing \(d/h=1\), where values for indent 2 and 3 are higher or close to indent 1. PS is a glassy, brittle polymer that during indentation deforms elastic-plastically inducing chain displacement, possible strain hardening, creating some degree of pile-up and crazes. The variation in values at small indentation separation will depend on the position of the next indent with respect to the first and the local surface changes created during the process. With increasing indentation depth, and thus volume, those defects are increasing, creating larger overlapping of the plastic zone. In addition, the degree of indent overlapping will depend on the measurements set-up, i.e., single line vs. matrix, as demonstrated in Figure 6.  
Figure 5: The average percentage difference values for three indents obtained at the same spacing (**a**) orientation \(0^{\circ}\), \(h=1\)\(\upmu\)m; (**b**) orientation \(90^{\circ}\), \(h=1\)\(\upmu\)m; (**c**) orientation \(0^{\circ}\), \(h=5\)\(\upmu\)m; (**d**) orientation \(0^{\circ}\), \(h=10\)\(\upmu\)m.  
Figure 6: Optical microscope images of Berkovich indentation with \(h=5\) μm and different spacing (**a**) indents in a single row; (**b**) indents in a \(3\times 3\) matrix. Scale bar is \(50\) μm.