# Indentation Hardness and Elastic Recovery of Some Hardwood Species
## 3 Results  
Figure 5 summarizes the calculated Brinell hardness values (HB) based on the diameter of the imprint (\(d\)). The wood species in Figure 5 are arranged according to their increased density. The HB of the test wood samples varied depending on the grain direction. The highest HB values were in the L cross-section, while the smaller values were in the R and T sections. Hardness also depends on the measuring force used. The HB measured at the force of 100 kG were greater than those measured at 30 kG. The computed hardness confidence intervals (shown as error bars in Figure 5) had varying widths. With a measuring force of 30 kG in the R cross-section, they ranged from 2% to 13% (average 7%) of hardness, in the T cross-section from 8% to 18% (average 13%), and in the L section from 1% to 9 (average 4%). However, with a measuring force of 100 kG,  
Figure 4: The imprint creation during hardness tests: (**a**)—stage 1, the ball without load, (**b**)—stage 2, the ball loaded with measuring force, (**c**)—stage 3, the permanent indentation after a force is removed (P—measuring force, \(D\)—diameter of the ball, \(d\)—the permanent imprint diameter, \(H\)—the total imprint depth, \(h\)—the permanent (plastic) imprint depth, \(x\)—the elastic (temporary) component of imprint depth). Figure 5: The Brinell hardness of the tested wood in the three main cross-sections of wood at two measuring forces (30 kG and 100 kG). the confidence intervals ranged: in the R cross-section from 3% to 13% (average 12%), in the T cross-section from 5% to 15% (average 8%) and in the L cross-section from 4% to 9% (6% on average). It can be observed that the average measurement uncertainty seems to be smaller in the L cross-section than in the R and T cross-sections. The highest measurement uncertainty was calculated for linden and ash in the R section; they were 18%. The width of the confidence interval is related to the confidence level, the sample size, and the variability in the sample. We used a 95% confidence level and we performed twelve measurements for each tested combination: two measuring forces, three cross-sections, and six types of wood. The confidence intervals varied from 1% to 18%; this confirms the well-known high variability of wood properties [9]. Increasing hardness with increasing wood density was noticeable in all three cross-sections and at both measuring forces (Figure 6). Figures 7-9 present the measured imprint depths. The tested wood species are arranged in ascending order according to their density, and the graphs show the two components of the total imprint depth. The permanent (plastic) imprint (_h_), which remains after the measuring force, is marked in blue, and the elastic component of the imprint's depth (_x_) is marked in green, that is, the distance by which the imprint's depth was decreased. Figure 6: The Brinell hardness—wood density: **(a)**—30 kG measuring force, **(b)**—100 kG measuring force. Figure 7: Imprint depth under measuring load (radial direction). Regarding the study's primary aim, the most important is the permanent imprint depth (h) shares of the total imprint depth (\(H\)). These shares are shown in Figures 10-12 (the symbols R, T, L, and \(h\), \(H\) are set out in Figures 1 and 4). The imprint depths caused by the force of 30 kG (Figures 7-9) were from 2.1 to 3.0-times smaller than the imprint depth caused by the 100 kG measuring force. This proportion between the imprint depths was similar in all three main wood cross-sections (R, T, L). The depths of imprints in the R and T cross-sections were similar, while they were three-times greater than in the L cross-section. The shares of permanent imprint depth \(h\) in the total imprint depth \(H\) (including the elastic component of deformation \(x\)) did not depend on the cross-section of wood (R, T, and L) and the measuring force value. In each studied case, they ranged from 70 to 80%. Figure 8: Imprint depth under measuring load (tangential direction). Figure 9: Imprint depth under measuring load (longitudinal direction).