At the first stage of work, the NI method was used to measure the radial distributions of the effective values of the microhardness Heff and Young’s modulus Eeff in annual rings of pine, oak, and linden wood (Fig. 3). They are effective, because at the selected maximum load on the indenter Pmax = 500 mN, the indentation of the Berkovich diamond trihedral indenter had transverse dimensions of more than 100 μm and exceeded the average transverse size of a wood cell by several times. As a result, the data obtained under such deformation conditions refer to the properties of the highly porous cellular cell structure of wood, and not to individual cell walls, which have several times higher mechanical properties and density. The properties of cell walls vary little from layer to layer and from one annual ring to another, which makes them unsuitable for use in dendrochronology and dendroclimatology.

Radial distributions of effective values of the microhardness Heff and Young’s modulus Eeff in the annual rings of scotch pine (a), pedunculate oak (b), and small-leaved linden (c) for ten successive annual rings, measured by NI at the maximum load applied to the Berkovich indenter, Pmax = 500 mN. x is the distance across the annual rings. The boundaries of the annual rings are shown by dotted lines. Numbers from 2004 to 2013 indicate the years of wood growth (dry year 2010 highlighted in red).

Each point on the graphs in Fig. 3 was obtained by averaging the results of 5–10 independent tests conducted with the same experimental parameters. As can be seen from these figures, in contrast to the mechanical properties of the cell walls, in the effective values Heff and Eeff there is a pronounced periodicity of effective mechanical properties. It was in good agreement with the position of the boundaries of the annual rings, which are detected optically by a change in the color of the wood. At the boundary of the rings, in all the studied wood samples, the mechanical properties underwent an abrupt change. When moving from EW to LW inside annual rings Heff and Eeff changed in a jumplike manner only in oak, while in pine and linden, it was smooth.

The values Heff and Eeff inside each EW layer in different annual rings remained constant from year to year with a deviation of no more than 10%, despite the fact that the weather conditions of growth could differ significantly. For example, 2010 was very dry, which affected the width of the annual ring W (in particular, in pine, the value W decreased by more than half compared to previous years), but this had almost no effect on the value of Heff and Eeff in the EW.

The maximum value variations of Heff and Eeff from year to year in LW were slightly higher but did not exceed several tens of percent. Thus, variations in the width of the annual rings occur mainly due to the different number of cells in the layer, the transverse size of capillaries, and the porosity of the wood in the layer.

The presence of a sharp jump in Heff and Eeff at the boundaries of annual rings (Fig. 3) made it possible to determine their width WNI according to scanning NI. Then they were compared to the value Wo, which was determined by the optical method (by the contrast of the photographic image). This was similar to that used in the LINTAB equipment line. Comparison data for these two methods for determining the width of annual rings is shown in Fig. 4, from which it follows that the discrepancies between them do not exceed 2–3% in pine and 4–5% in oak and linden. The average deviation for 10 annual rings was half as much. In fact, this means that the scanning NI method can be used as an alternative to the optical method or supplement it with information about local mechanical properties.

Results of measurements of the width of annual rings by the method of nanoindentation WNI and the optical method Wo (a) and discrepancies between these methods (b).

Next, profiling of the mechanical properties of pine, oak, and linden wood was performed using the scratch method (digital sclerometry). Both components Fn and Fl of the force on the probe as a function of distance traveled x along the sample surface were simultaneously recorded (Fig. 2). These force components are determined by the mechanical properties of the wood, the geometry of the tool tip, and the specified scratch depth d. In this series of experiments d varied in the range from 10 to 100 µm. Depending on d and the mechanical properties of a particular wood, the maximum normal force Fnmax also changed in the range from 5 to 110 N. Figure 5 shows examples of dependences of the components of the force acting on the probe for each type of wood studied in the work.

Profile of the normal Fn (1) and lateral Fl (2) component of the force acting on the probe during the scratching of pine wood (a, b) at d = 50 µm, oak (c, d) at d = 33 µm, linden (e, f) at d = 40 µm at different scales along the horizontal axis.

When scratching in the specified range of d at a lateral velocity of V = 0.3 mm/s, the relative strain rate was \(\dot \) = V/d = 3–30 s–1 (depending on the set value d), which completely eliminates the effect of creep on the results. On the other hand, if it is necessary to study time-dependent properties (viscoelasticity, creep, stress relaxation), the value \(\dot \) can be reduced by several orders of magnitude.

The spatial resolution and information content of the method can be improved by optimizing the geometry of the probe tip and the value d. From the obtained data it follows that with an increase in d and load on the probe, although the signal-to-noise ratio grows, the ratio that carries the main information Fmax/Fmin decreases. This is due to an increase in the contact area of the probe with the surface and, as a consequence, greater averaging of the mechanical properties over the bulk of the material, including at the GR boundaries. In addition, at large Fmax plastic deformation of the material can be replaced by fracture. In pine, when using a Rockwell indenter as a probe with a tip radius of R = 200 µm, this happens at d > 65 µm, which corresponded to Fnmax > 40 N. A decrease in d up to a few micrometers increases the requirements for surface smoothness, and leads to an increase in interference and a decrease in the signal-to-noise ratio. Considering these circumstances, the scratching data at d from 10 to 50 μm were used for analysis and calculations, which corresponded to Fn max = 6–25 N. At such a depth of scratching, it was carried out by a small part of the spherical tip of the Rockwell indenter. These conditions made it possible to resolve well not only annual rings, but also intra-annular features of the mechanical properties of the wood (Figs. 5b, 5d, and 5f). The study of the intraring structure makes it possible to assess, in addition to average annual climate changes, intraseasonal ones, which is of great interest for dendrochronology and dendroclimatology.

From the analysis of scratch profiles, the hardness Hs of the EW and LW layers at the mesolevel was determined (Table 1). Here Hs = Fn/Scont, where Scont is the area of the indenter embedded in the material, determined taking into account its geometry and the depth of the scratch d. To determine the hardness in EW we used Fn min on scratch profiles, and in LW, we used Fn max respectively. The average ratio of Hs in EW and LW was 4.1 ± 0.6 for pine, 3.7 ± 1.3 for oak, and 1.5 ± 0.1 for linden. Similar relationships were typical for the mechanical characteristics measured by NI methods, both for Heff and Eeff in EW and LW. For pine, this ratio is 3.1 ± 0.4; for oak, 3.3 ± 0.7; and for linden, 1.6 ± 0.4.

Since the mechanical properties of wood in the EW and LW layers differ significantly, it is technically possible to determine the width of annual rings Ws by scratching methods in different ways: (i) by the distance between the maxima (ii) or the minima on the charts Fn(x) or Fl(x), or (iii) between the maxima of their derivatives with respect to x.

Table 2 illustrates the average spread of the value Ws relative to Wo determined by the optical method. Table 2 shows that determining Ws by the distance between adjacent minima or maxima has a much greater uncertainty compared to the third method. A large error in determining the position of extrema reduces the accuracy of determining Ws, and random fluctuations form artifact extrema that enhance the negative effects. Therefore, in the work, the position of the boundaries between the annual rings was determined by the third method, i.e., by the position of the maxima of the derivatives on the graphs Fn(x) or Fl(x). Changing the scribing depth within the limits specified above does not lead to a significant change in the determined position of the boundary.Table 3

Figure 6 shows the width of the annual rings W of pine, oak, and linden, determined by two methods: optical method and scratch testing. The relative discrepancy between the measured annual-ring widths obtained optically and by scratching is 1.5% for pine and 4% for oak and linden (Fig. 7). The absolute standard deviation of this discrepancy in all cases was several tens of micrometers, which is comparable to the size of a cell in wood.

Correlation of data on the width of annual rings W of pine (1), oak (2), and linden (3) obtained by the optical Wo (large circles) and scratch Ws method (green squares, orange triangles, yellow circles).

Relative discrepancy between the measured annual-ring widths W obtained optically and by scratching pine (squares), oak (triangles), and linden (circles).

The results obtained by digital sclerometry, in comparison with climatic data for the same period of time, make it possible to identify correlations between the mechanical characteristics of annual rings, their intra-annular variations in individual layers (in particular, in the EW and LW layers) with the most important weather characteristics for plant vegetation: temperature, precipitation, illumination, etc. Such an analysis makes it possible to propose for dendroclimatology (a retrospective description of climate) a fundamentally new approach in comparison with the traditional one based on the analysis of annual-ring-width variations found using OMs [33–36]. By varying the time intervals at which certain mechanical and climatic characteristics are averaged, and the time lag between them, one can obtain a lot of new information about the relationships between such characteristics and identify the most significant weather factors affecting the quality of wood.

As typical examples of such correlations, Figs. 8–11 show the results reflecting the degree of influence of temperature and precipitation during the entire growing season, its first and second half in the middle zone of European Russia on the width of annual rings Ws, and hardness Hs of the most durable LW layers of Scotch pine. It follows from these data that in LW the greatest influence on both Ws and Hs is the average daily temperature throughout the growing season and especially in the second half. The average daily precipitation in the first half of the growing season has a noticeably smaller effect, and in the second half it has almost no effect on the result. The combination of variations of various, not completely independent factors and their deviation from the norm can further enhance the effects. Thus, a unique combination of climatic characteristics in 2010 for several decades led to the loss of corresponding points (they are indicated by asterisks in Figs. 8–11) from the general long-term trend for all analyzed pairs of parameters. Correlation coefficients and linear-regression parameters corresponding to these pairs are summarized in Table 3. A more thorough analysis of such relationships requires more statistics on wood samples, as well as weather conditions during its growth. This can be achieved both by increasing the studied time intervals and by expanding the geography of growth of the studied plants. It is of interest to study such correlations for different plant species in order to identify the most representative and accurate species as indicators of climate change.

Correlation of the width of annual growth rings Ws in pine with the average temperature T for different time intervals: (a) May–June, (b) July–August, and (c) May–August. An asterisk indicates characteristics for the unique dry year 2010.

Correlation of the width of annual growth rings Ws in pine with the average daily rainfall p in different time intervals: (a) May–June, (b) July–August, and (c) May–August. An asterisk indicates characteristics for the unique dry year 2010.

Correlation of the maximum hardness Hs of late wood in pine with the average temperature T for different time intervals: (a) May–June, (b) July–August, and (c) May–August. An asterisk indicates characteristics for the unique dry year 2010.

Correlation of the maximum hardness Hs of late wood in pine with the average daily rainfall p for different time intervals: (a) May–June, (b) July–August, and (c) May–August. An asterisk indicates characteristics for the unique dry year 2010.