# Indentation Hardness and Elastic Recovery of Some Hardwood Species
## 2 Materials and Methods  
The research was carried out on six hardwoods. The test samples, 30 mm \(\times\) 30 mm \(\times\) 20 mm in size, were made of: alder, linden, birch, ash, iroko, and beech. All logs used to prepare the test samples had a regular structure (not eccentric). The test samples were clear and made from logs without any structural defects of the wood. The logs were primarily cut into lumber according to three principal anatomical planes of reference in the stem: radial (R), tangential (T), and axial/longitudinal (L) cross-sections (Figure 1). Twelve samples were made for each of the wood species tested. Figure 1: The clear test specimen oriented according to the main cross-sections in the stem. After the primary cut, the planks were dried at a temperature lower than 60 \({}^{\circ}\)C. The test samples were cut and then conditioned at a temperature of 20 \(\pm\) 2 \({}^{\circ}\)C and relative humidity of 65 \(\pm\) 3% for three months. The moisture content of the test samples immediately before the hardness measurements was 10 \(\pm\) 0.5%, and their average densities are given in Table 1.  
Brinell hardness tester, model HBRV-187.5E (Huatec, Beijing, China), was used. We performed the uniaxial hardness measurements in the all three main cross-sections (R, T, and L) and used two measuring force values (30 and 100 kG). Symbolic specifications of the hardness measurement conditions HB 10/294.2/60 and HB 10/980.7/60 were assigned to both sets of test conditions, respectively:  
* Measuring ball diameter \(D=10\) mm
* Total force 1 \(P_{30}=30\) kG \(\left(F=294.2\) N, \(\left(F/D_{\text{max}}^{2}=3.2\right)\right)\)
* Total force 2 \(P_{100}=100\) kG \(\left(F=980.7\) N, \(\left(F/D_{\text{max}}^{2}=10.6\right)\right)\)
* Partial force \(P_{1}=10.0\) kG (98.07 N)
* Total load time \(t=125\) s
* Number of measurements for each material \(n=12\)  
Figure 2 shows the Brinell tester used and the measuring force application mode. The Brinell hardness (HB) is calculated based on the diameter of the imprint. The boundary of the imprint on the wood is unclear [8, 11, 12]. An additional factor that makes \begin{table}
\begin{tabular}{l l} \hline \hline
**Species** & **Average Density** \\  & **(g/cm\({}^{3}\))** \\ \hline Alder (_Alnus glutinosa_ ([PERSON]) & 0.500 \\ Linden (_Tilia europaea_ L) & 0.505 \\ Birch (_Betula alb_ L.) & 0.595 \\ Ash (_Frazinus excelsior_ L.) & 0.660 \\ Iroko (_Milicia excelsa_ ([PERSON]) & 0.690 \\ Beech (_Fagus sylvatica_ L.) & 0.740 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Wood species names and average densities of test samples used. Figure 2: Hardness tester and measuring force: (**a**)–HBRV-187.5E (Brinell hardness tester (Huatec, Beijing, China), (**b**)—force exertion modes. hardness measurement difficult is the \"sinking-in effect\" [12], especially in the T and R main cross-sections of wood [7]. Therefore, we used the Dino-Lite AM4815 ZT EDGE digital microscope (IDCP B.V., Almere, The Netherlands) with extended dynamic range (EDR), extended depth of field (EDOF), and the possibility of measuring under polarized light. Figure 3 shows example images taken during tests. The HB values were calculated according to the following formula:  
\[\mathrm{HB_{d}}=\frac{2\cdot P}{\pi\cdot D\cdot\left(D-\sqrt{D^{2}-d^{2}}\right)}\]  
where:  
\(P=\) applied force (kG);  
\(D=\) diameter of the indenter (mm);  
\(d=\) diameter of the imprint (mm). Figure 4 shows three stages of imprint creation during the hardness test: before the loading, a ball indenter under full load, and an indenter after removing the load. The total imprint depth (\(H\)) is the sum of the depth of the permanent imprint \(h\) (the one that remains after the measuring force \(P\) is removed) and the depth of an elastic imprint \(x\) (only under load with the measuring force \(P\)). The hardness tester used allows measuring the depth of the elastic component \(x\) of the total imprint depth, which is readable after  
Figure 3: Examples of imprints (iroko wood, 37\(\times\) magnification).