## 2 Materials and Methods
### Microindentation Stress-Strain (MSS) Protocols
The following relationships are utilized:  
\[P=\frac{4}{3}E_{eff}R_{eff}^{\frac{1}{2}}h_{e}^{\frac{3}{2}} \tag{1}\]  
\[a=\sqrt{R_{eff}h_{e}} \tag{2}\]  
where \(P\) and \(h_{e}\) are the indentation load and the elastic indentation displacement, respectively, and \(a\) is the contact radius (see Figure 2). \(E_{eff}\) and \(R_{eff}\) are the effective indentation modulus and the effective radius of the indenter-specimen system, and are defined as  
\[\frac{1}{E_{eff}}=\frac{1-\
u_{s}^{2}}{E_{s}}+\frac{1-\
u_{i}^{2}}{E_{i}} \tag{3}\]  
\[\frac{1}{R_{eff}}=\frac{1}{R_{i}}+\frac{1}{R_{s}} \tag{4}\]  
where \(E\), \(R\), and \(\
u\) are [PERSON]'s modulus, radius, and [PERSON]'s ratio, respectively, and the subscripts \(i\) and \(s\) denote indenter and specimen, respectively. In the MSS protocols, one employs [PERSON]'s theory described above to each unloading segment to estimate the contact radius needed to compute the indentation stress and the indentation strain corresponding to the start of the unloading segment (see Figure 3a). [PERSON] and [PERSON] [24] reformulated [PERSON]'s theory (Equations (1) and (2)) to derive the definitions of indentation stress and strain used in MSS protocols as  
\[\sigma_{ind}=\frac{P}{\pi a^{2}} \tag{5}\]  
Figure 3: (**a**) A typical measured load-displacement response in the indentation protocols used in this work. The initial elastic response shown is analyzed using [PERSON]’s theory. (**b**) The corresponding indentation stress-strain curve extracted from (**a**). \[\varepsilon_{ind}=\frac{4}{3\pi}\frac{h}{a} \tag{6}\]  
[PERSON] et al. [25] validated the above definitions for indentation stress and strain in their indentation simulations by observing indentation responses in the context of stress and strain fields. The indentation analysis described above produces a linear relationship in the initial elastic loading and exhibits a smooth transition to a nonlinear elastic-plastic response. MSS protocols start with the analyses of the initial elastic segment (see Figure 3a). One of the main challenges in this analysis is the zero-point correction to correct for various unavoidable factors such as imperfect initial contact, sample surface irregularities, imperfect indenter shape, etc. This task is accomplished by fitting the initial elastic segment to the following expression derived from [PERSON]'s theory expressed above:  
\[\left(\widetilde{h}-h^{*}\right)=k\left(\widetilde{P}-P^{*}\right)^{\frac{2} {3}} \tag{7}\]  
Figure 2:0  
where \(\widetilde{P}\) and \(\widetilde{h}\) denote the measured load and displacement, respectively, and \(P^{*}\) and \(h^{*}\) denote the zero-point corrections for the load and displacement, respectively. Note that for the initial elastic loading \(R_{eff}=R_{i}\) and all of the indentation displacement is elastic. Therefore, the regression analyses of the initial loading segment will also provide an estimate of \(E_{eff}\), which is assumed to remain the same even after the initiation of plastic deformation in the indentation experiment. [PERSON] and [PERSON] [26] observed that because the averaged plastic strain experienced under the spherical indenter is relatively low, there were no significant changes to the effective indentation modulus of the sample material in the primary indentation zone (see Figure 2). The \(P^{*}\) and \(h^{*}\) corrections identified in this analysis are applied to the entirety of the measured load-displacement curve. Next, each unloading segment after the initiation of plastic deformation in the indentation experiment is analyzed to produce a single data point on the indentation stress-strain curve (see Figure 3b). This is accomplished by fitting the unloading segment to the following expression derived from [PERSON]'s theory described above:  
Figure 2:1  
where \(h_{t}\) and \(h_{r}\) are the total indentation displacement and the residual displacement after the disengagement of the indenter (see Figure 2), respectively.