Strain-based approach to characterize mode I crack propagation in Norway Spruce directly from optical data

Strain-based approach to characterize mode I crack propagation in Norway Spruce directly from optical data | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Strain-based approach to characterize mode I crack propagation in Norway Spruce directly from optical data Jiří Kunecký, Martin Hataj, Jan Jochman, Jan Pošta, Michal Kloiber, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3962450/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The paper focuses on assessment and utilization of strain-based criterion obtained using the digital image correlation in characterization of fracture behavior of Norway spruce wood. The study employed a single-edge notched beam loaded in three-point bending (SEN-TPB) to examine mode I at three anatomical directions of crack propagation (radial, tangential, tangential-radial - R, T and TR). The criterion is evaluated at the maximal load (F max ), where the compliance-based beam method (CBBM) provides critical strain energy (G c ), which ensures the proper criteria representing equivalent crack length growth is described. The novel approach also enables one to determine the fracture process zone (FPZ) length using an algorithm which finds the onset of the nonlinear region. Uniqueness of the approach lies in processing a big set of optical data and simultaneous tracking of crack length on both sides of medium-size specimens. Results indicate that crack length is dependent on the anatomical direction, for instance in T direction the criterion ε 1crit is 2.5e-3 producing crack length equal to a c =23.9 mm, whilst in R direction, the ε 1crit is least and equals 1.3e-3 producing crack length of 22.1 mm. The highest ε 1crit is attained in TR (on average ε 1crit = 3.4e-3) and distance from the place where the crack started is 19.4 mm. Size of the non-linear region here attributed to FPZ length reaches the value of 38.4 mm in T, 30.1 mm in R and 36.3 mm in TR directions, respectively. The study presents a novel approach in characterization of fracture properties by coupling optical and energetical data and may find its usage in evaluation of other fracture modes. fracture strain energy release rate spruce mode I digital image correlation crack Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 1. Introduction Even despite the fact that most of forest management in Central Europe aims on mixed forests and that there is substantial decrease of spruce stands due to bark beetle attack, spruce wood remains the main material for the glued laminated timber (GLT) and cross-laminated timber (CLT) construction sector. Both materials have to be prepared and prefabricated with notches, drilled holes etc. which represent locations of potential stress concentrations that may be source of crack onset (similarly in Eurocode 5 ). The least fracture energy for crack onset is required in mode I that represents the most dangerous mode of fracture in wood if the tension appears perpendicular to fiber. The mode I is usually investigated by double cantilever beam (DCB), single-edge-notched three-point bending test (SEN-TPB), tapered double cantilever beam test (TDCB) or compact tension (CT) tests (Smith et al. 2003 ). Wood is heterogeneous and cellular material and, therefore, many questions arise regarding the convenient size of the test specimens, crack surfaces and regarding the applicability of either linear fracture elastic mechanics (LEFM) or nonlinear fracture approaches (Bažant et al. 2022 ). The impact of specimen size (from 10 to 320 mm in height) on fracture characteristics in mode I for spruce wood loaded in the RL crack plane was already studied in Aicher et al. (1993). Authors utilized the SEN-TPB and showed significant impact of size on nominal strength till height of a beam of 160 mm where nonlinear effects took place, meanwhile for higher beam heights, standard LEFM behavior was observed and confirmed utilization of scaling based on a theory developed by Bažant ( 1984 ) . Petterson and Bodig (1993) found the correlation of fracture toughness in mode I and tensile strength for ten conifers as well as the prediction of fracture toughness based on density and moisture content. Stanzl-Tschegg et al. ( 1995 ) investigated size effect in the CT test with respect to total crack length and specimen width and found their strong influence below ligament length of 70 mm due to different sizes of FPZ. Daudeville ( 1999 ) studied spruce and found that as size of specimen increases (from 45 to 100 mm), the nominal strength decreases, but specific fracture energy keε on similar levels. The author found significant differences in fracture energy between RL and TL planes. Morel et al. ( 2000 ) analyzed size effect in wood employing the Family-Viscek scaling and showed its strong influence as well as proved valid usage of this scaling for materials with toughening mechanisms. Morel et al. ( 2002 ) showed that for both Maritime Pine and Norway spruce the size of the specimens influences critical strain energy release rate ( G ) which can be attributed to roughness of crack onset and surfaces, the specific surface energy also strongly correlated with density for both species. Morel et al. ( 2003 ) analyzed the role of a specimen geometry on G values and found a certain dependency despite a limited sample size. The reason was found in a fact that the fracture process zone (FPZ) increases as specimen compliance increases due to higher stress intensity factor. Morel and Dourado (2005) validated usage of the “equivalent LEFM” to analyze spruce fracture behavior in mode I along the grain (LT crack plane) employing the Nordtest for beams of 70 mm height. This approach was enhanced in the work of Dourado et al. ( 2008 ) who employed it to develop cohesive laws that included both microcracking and fiber-bridging phenomena. One of the difficulties in fracture analysis of wood is to monitor the propagation of crack. This difficulty may be solved using an equivalent crack length approach and compliance-based beam method (CBBM). This advantageous coupling of both was shown in de Moura et al. ( 2010 ) for SEN-TPB test using triangular stress relief region (SRR). Dourado et al. ( 2011 ) utilized that approach for SEN-TPB test with rectangular SRR to determine damage zone extent at crack initiation for various beam heights and concluded that for beams higher than 560 mm, the size effect might be neglected. Xavier et al. ( 2014b ) employed a direct method utilizing Irwin-Kies equation, CMMB, and digital image correlation (DIC) to retrieve cohesive laws in mode I for pine wood at RL plane. Authors found a certain agreement between real and equivalent crack length, as well as good agreement between direct and indirect computation of G values. Dourado et al. ( 2015 ) utilized SEN-TPB test to analyze three different beam heights made of spruce using CMMB and concluded that for heights of 140 mm and 210 mm, the clear plateau and comparable G at peak load can be reached. Dourado et al. ( 2019 ) utilized CMMB to characterize pine wood in mode I loaded by fatigue-fracture way. The authors implemented the Paris law which enabled to evaluate crack propagation due to static load as well as damage due to fatigue effect. The effect of elevated temperature on G values of pine wood was also studied and it was found that G decreases with temperature even despite the fact that stiffness and ultimate load keep on comparable level (Dourado and de Moura 2019 ). More recently, Ostapska and Malo ( 2020 ) presented an alternative approach to characterize spruce wood fracture in mode I. The approach utilized full-field deformation data history to obtain crack tip locations by analytical decomposition to various modal components of fracture that allowed adjustment of fracture characteristics. An extension of this approach towards creation of a calibrated numerical model reflecting nonlinear fracture phenomena was presented by the same authors later (Ostapska and Malo ( 2021 ) . When searching for agreement with full-field data, their optimization procedure allowed to vary not only elastic parameters, but also stress at initiation, crack propagation and softening functions. Critical approach to full-field data was presented by Romanowicz ( 2022 ) who numerically analyzed the position of the real crack tip using two methods of adjustments and full-field DIC data. He has found that employing DIC in crack monitoring may underestimate crack extension due to FPZ and overestimate the energy required to form microcracks. Analysis of fracture behavior in mode I for other species than spruce, as well as for wood-based composites, is also available in literature, but their more detailed resume is omitted here for the conciseness ( Ardalany et al. 2012 , de Moura and Dourado 2018 , Majano-Majano et al. 2018 , Forsman et al. 2020 , Hu et al. 2021 , Gomez-Royuela et al. 2022 , Phan et al. 2017 ). However, it seems that optical data and DIC algorithms still offer a potential in crack evaluation, especially usage of strain criteria is promising. Since displacement control of experiments does not lead to dangerous and fast crack propagations, it is difficult to say when the crack is already formed and critically loaded. In reality, the structures are loaded by forces, which makes a crack propagate very quickly when loaded beyond the critical limit. Therefore, the crack is to be considered as critical even before it is visually seen. A capturing of a non-visible crack may be solved using strain-based criteria computed from DIC data, which is a general goal of the study. To respond to the general goal, following objectives were set: 1) to perform fracture test at medium-size timber beams using modified SEN-TPB setup; 2) to develop and verify strain-based approach to characterize fracture properties of wood in mode I using DIC; 3) to couple CBBM and direct optical approaches in evaluation of crack propagation. 2. Materials and methods The work utilized several different, but hence complementary approaches that are convenient to outline for clarity. The work focused on detailed analysis of the region around the crack using DIC, especially on the relation between strain-based criteria derived from optical data to the crack propagation length based on such a criterion. Such an optical-based value is compared to the assessed value of G c obtained using CBBM. In the work we distinguish the G c as the value of strain energy release rate when maximum force is applied, and G f which is the maximal value that can be attained. The CBBM is a method based on assumption of energy dissipation during the crack propagation, it is based on eqLEFM concept and deals thus with equivalent crack length that cannot be seen directly. Nevertheless, comparison of which size of ε 1 criterion in optical measurement induces which G c from CBBM is valuable, since it compares the methods and allows to determine reasonably safe criterion which can be applied to other cases in the same specie, anatomical direction and mode I loading. Additionally, an analysis of length of nonlinear region - length of FPZ, based on the optical data is also performed. Last, correlation between the results is critically reviewed. 2.1. SEN-TPB experiments The experimental work followed the test procedure from NT BUILD 422 standard (NT BUILD 1993) that is used for testing fracture properties in mode I. The specimen geometry and boundary conditions are shown in Fig. 1 . First, the crack-free timber beams with growth ring orientated in tangential (T), radial (R), and mixed (TR) orientations were cut from Norway spruce beams of big size. The specimens were then conditioned in a climate chamber using standard conditions (20°C and 65% relative humidity (RH) to reach 12% equilibrium moisture content (EMC). Then, wooden blocks with dimensions of 12 × 12 cm (height × width) were cut from the beams to create a middle element and glued to specimen arms using PVA-based dispersions of one-component adhesive (see Fig. 1 ). The orientation of grain in the middle element is rotated 90° to the arms, the specimens were held under pressure for one hour and then the middle element was cut vertically up to the half of the specimen height to introduce an initial and narrow crack, the detail of tree ring orientation is shown in Fig. 2 . All specimens were made from four different trees. In each of the groups (T, R, TR) are specimens from at least two trees (mixed half way). In T, R and TR groups, we measured 10, 12, and 9 specimens, respectively. The central parts 12x12x6 cm intended to be glued in between two arms were cut from one plank, that means, close to each other and thus should not have big differences. At the middle element with initiated crack was then applied with a stochastic pattern using Airbrush Revell Master Class together with acrylic pigments to create randomly distributed speckles (Fig. 3 ) to ensure high-quality computation by DIC in further work. The areas of interest (AoI) on specimens around the crack tip were filmed from both sides of the specimen using same cameras Basler acA2440-20gm with frame rate 1 Hz and resolution 2448 × 2048 px. The optical data were used to analyze crack onset and propagation - monitoring crack length. The semi-telecentric lens Computar TEC-M55MPW with focal length 55 mm was used to minimize optical distortion. The images were further processed using DICe software ( Turner et al. 2015) and used parameters of DIC were as follows: step = 30 px (equals ~ 0.675 mm), subset = 27 px, Gauss kernel = 5 px, transformation full affine. For the mechanical testing, the universal testing machine Galdabini Quasar 100 was used, equipped with a load cell with a range of 10 kN and Labtest testing software. The outputs from the test machine and sensors were acquired by the unit DEWE2602. For all samples, the load, the corresponding deflection measured by two control LVDTs (see Fig. 2 ) and one control LVDT to identify the initiation and opening of the crack were monitored. For the purpose LVDT sensors DTA-5G-CA (Micro-epsilon, Germany) throughout the duration of the load test were used, located on both sides of the test specimen. The average value of these LVDT sensors was used to evaluate the data. The tests were displacement-driven with a speed of 0.3 mm/min. CBBM evaluation was made according to Dourado et al. ( 2011 ). Due to the experimental variability, the interval for initial compliance was selected individually, but always was in the region of 0.2 to 0.4 of F max . Other parameters, although often with minor influence to the result were: k = 0.86, β = 1.07, E L =10 GPa and E T = E L /17. Elastic properties of the arms have very low influence on the final results. It is not possible to obtain the true crack length because the initial scatter of the algorithm strongly influences the value. That is why the value of G c was used for later analysis in processing optical data instead of the absolute crack length. Typical processing of data is shown in Fig. 4 and is described below. 2.2. Optical data post-processing It is worth noting that the experimental determination of the crack tip position in quasi-brittle materials is difficult, since the development of FPZ is complicated and makes the method really challenging. The key questions here are: where the crack starts and what length the crack has. From the theoretical point of view it is clear - nevertheless from the experimental perspective it is a real challenge to answer those questions for a quasi-brittle material. The concept of eqLEFM serves as a good etalon and that is why we compared the optical data to the CBBM ones. Strain-based criteria are of certain importance because in testing of structural-size members, the recognition of presence of a crack is crucial for assessment of bearing capacity of notched beams. In such a case, CBBM cannot be applied because a significant amount of energy is dissipated in closure of the drying cracks, material inhomogeneities (like knots), contacts, embedments etc. Even for assessment of bearing capacity of timber beams using CZM we have to address the presence of a critical length using crack shape parameters, CZM itself is not capable of predicting critical crack growth. Despite the limitations encountered with the use of DIC, it is the only reasonable and cheap experimental technique which is not dependent on assumption of many parameters. This work intends to add one stone to the mosaic of understanding wood fracture. The DICe algorithm provided us with raw data, namely displacement, rotation and strain fields for each image in the whole image sequence representing the time domain. Such data were further post-processed using a Python-powered set of libraries SciPy and NumPy ( Scipy - Jones et al. 2001 ). First, the equivalent crack length ( a e ) and G were computed using CBBM, so we obtained a e vs. time and G vs. a e and could identify G c and G f (Fig. 4 ). The SEN-TPB induces pure mode I and thus tensile stresses/strains are of our interest. Therefore, the whole procedure used was based on an evaluation of the first principal strain ( ε 1 ) field, resp. its maxima. The ε 1 was computed for each pixel using linear algebra. The strain field is very handy especially in optical measurement, where strains computed from pixel values mean the same strains as in the studied plane when undistorted images are assumed. Another reason why principal strains instead of displacements were used for the evaluation is their invariant nature and simply the fact that displacements need two points selected and size of DIC step can become another additional parameter. Last, strain analysis was employed because of the ability to find the beginning of nonlinearity in the strain field across the height of the bent glued-in specimen. This nonlinearity ahead of the crack tip can be considered the very end of FPZ. The whole method described here follows the CBBM principle meaning there is no change in compliance linearity without crack propagation. The crack starts with the first positive change in compliance (see Fig. 5 a), where the bullets show the end of the linear region). The procedure can be further split into two tasks: (i) how to assess a strain criterion and (ii) how to determine the crack length itself based on such a criterion. For clarity, we start with the second task: the algorithm first chooses the region of interest (ROI) which is the one that is a subset of the original field, where there is the biggest peak when summed along width of the glued-in part and its size is usually ~ 5 mm in width and ~ 45 mm in length. This is crucial in order to remove imperfection influences (knots, other microcracks) from the analysis. After ROI has been selected, it detects zones along the height (45 mm) where the ε 1 is higher than the given strain-based criterion (in our case ε 1max = 3e-3). Because the detection utilizes discrete values of matrix element values, it employs a linear interpolation to get more precise crack length. This algorithm is applied on the whole sequence and allows to apply a set of criteria that return a set of crack lengths (as curves). In Fig. 5 d we can see for each of the cameras two curves representing the crack length in time if minimal and maximal strain criterion is used. This research is unique because we track both sides of the sample and account for different crack lengths in time. This is attained by specifying the correct strain criterion on each side of the sample - the first task mentioned above. The problem is, that if the crack starts on one side, it still does not have to be apparent on the other. So in the first step we apply to both sides a relatively safe strain criterion such as ε 1max = 3e-3. Using the above described algorithm, we get curves for both sides of the sample. This is illustrated in Fig. 5 b, where cracks from camera 1 (blue) and camera 2 (red) are depicted. Then, we determine the delay in time between the two curves (green curve) which allows us to analyze each side separately using the strain criterion at different positions in the sequence based on the delay. The results of this are shown in Fig. 5 d, colors distinguish the cameras. The first principal strains (Y axis) along the height of the scanned area (X axis) are depicted as bright solid curves. Note that both curves (red and blue) are at different time steps and determine the probable onset of crack. Further, for each of the curves, a linear part is automatically detected and fitted by a line. The difference between the curve and the fitted line is shown in the same picture as lines with semi-transparency using the second Y axis. These curves allow reading the first value representing onset of any nonlinearity, e.g. the highest possible FPZ length. The maximum represents the mouth of the crack, it is the value when the derivative of the difference line is the highest (dashed lines). Bullets in Fig. 5 c represent the value of the criteria, and from the whole procedure we can obtain two extreme values of strain criterion for each side, and further interpolate between them on the strain curve to obtain additional three points. This step outputs two vectors of five values of strain criteria and for each one, the crack length at each side of the specimen is computed. The final crack length is computed as the average of crack lengths obtained for each criterion in the time sequence. Such an average is also presented in the results as one criterion - for example, first two criteria for each side are assessed and used to produce respective crack lengths, however, in the end are together averaged for clarity of the results. Such a joined curve ( a = a l + a r )/2 can be used to compute the value of G c next to the maximal force using known Irwin-Kies (Irwin et al. 1954) equation: $$G=\frac{{F}^{2}}{2b}\frac{\partial C}{\partial a}$$ , where F is the acting force, C is compliance, b width of the sample, and a is the crack length determined using optical method. The derivation is made using the gradient method in discrete domain. In fact, we use the same compliance as is used in the CBBM method and couple it with the crack length determined from optical data. Because all variables were noisy and the noise in this equation even amplified, we used a polynomial fit in the region of F max to get stable and reliable results. 3. Results and discussion 3.1. Summary The experimental work provided several groups of results, but the overall outcomes of the work are summarized in Table 1 . Descriptive statistics of intragroup characteristics are listed as geometric average, standard deviation and variation coefficient in Table 1 . The groups have comparable densities which comes from the fact that specimens in each group come from at least two different trees. The maximal force ( F max ), however, is lowest in case of T orientation (63% of TR), the group with R orientation has higher mean (91% TR) and TR achieved the highest value. One of the possible reasons why TR has so high values can be the need to cross many interfaces of early/late wood for the crack, while in R this does not happen at all, T on the other side often propagates quickly on stiffer side and most of the crack length is present there. Similar trends are visible for fracture energies G c and G f . The mean G c , which is a more relevant value with respect to the work, is lowest in the T group (53% of TR mean) and slightly higher for the R group (57% of TR mean). Both crack length and obtained length of the FPZ show very comparable results among the groups, which is interesting with respect to the found differences in F max and G c . The data of G c in pure orientations (T and R groups) are in an alignment with literature sources for spruce, for instance Morel et al. ( 2005 ) obtained mean G C = 149 N/m for density of 440 kg/m 3 and 12% MC using the same test as used in this work; Dourado et al. ( 2015 ) obtained G C = 152 N/m for density approx. 410 kg/m 3 and height of the beam 140 mm; and more recently, Ostapska and Malo ( 2020 ) found G C = 179 N/m for RL and G C = 257 N/m for TL orientations when measuring by wedge splitting on spruce glulam of class GL30c. If we group the values according to tree number (not shown here, but sorted for readability), we cannot see differences except the group TR, where different trees provide very different results. Table 1 Final results showing Tangential, Radial and Tangential-Radial anatomical directions density G c_CBBM G f_CBBM a c a FPZ ε 1crit F max [kg/m 3 ] [N/m] [N/m] [mm] [mm] [-] [N] T average 497.8 154.4 212.1 23.9 38.4 0.0025 297.1 stdev 19.5 31.1 27.0 6.0 7.1 0.0012 21.6 var. coef 0.04 0.20 0.13 0.25 0.19 0.47 0.07 R average 479.1 165.6 249.0 22.1 30.1 0.0013 427.6 stdev 19.6 29.9 25.4 1.5 4.4 0.0006 40.1 var. coef 0.04 0.18 0.10 0.07 0.14 0.47 0.09 TR average 463.1 293.1 341.4 19.4 36.3 0.0034 470.1 stdev 23.7 38.0 28.5 6.4 14.0 0.0014 32.6 var. coef 0.05 0.13 0.08 0.33 0.39 0.41 0.07 3.2. Strain-based criteria vs. crack length Although general outputs are summarized in Table 1 , their importance shows up when plotting them in a perspective of developed strain-based criteria (Fig. 6 ). On the left side of the figure there is always depicted the value of the criterion which was used for particular assessment of G c value based on such a criterion. For each specimen this procedure forms a curve, into which can be interpolated the point G c obtained using CBBM method. Such an interpolated value may also be interpreted as a certain critical crack length even despite the fact that during the assessment the rate of crack growth is important. In Fig. 6 , the critical crack length (X axis) is plotted always on the right half of the figure for each respective point of the criterion from the left side of the figure. In these plots, we can also interpolate the crack length value to have all information compact. For example, when we applied the criterion of crack 1.8e-3 for the specimen T007, then obtained crack length to this point on the crack opening curve is 36.5 mm. Overall, there is one general and important result coming from the plots in Fig. 6 . It is that the higher strain-based criterion, the shorter the crack length and, at the same time, the slower the crack propagates. As seen, this relation is not linear, especially in the case of crack length, but it can be stated that higher criterion leads to higher G c . From the plots in Fig. 6 can also be read that T and R directions tend to behave in a similar way and bigger scatter is for criterion value rather than in the resulting crack length. The TR (combined) orientation shows much higher values than the ones from R and T orientation. The specific values can be read from Table 1 , but let us underline the most important: in the TR group, the F max value is reached when we apply approx. ε 1crit = 3.4e-3, which determines the distance from the place where the crack started as 19.4 mm. In T direction it is a bit lower ε 1crit = 2.5e-3, but higher crack length (23.9 mm), whilst in R it is the least ε 1crit = 1.3e-3 and crack length of 22.1 mm. The criterion further enables us to obtain the value of assessed F max . Important result is that the crack length does not change much within groups and that most of the G c - ε 1crit curves on the left sides are not purely but mostly linear. That is why the F max can also be considered as an approximate average value. Another question comes out of using the criteria in a quantile way. It should be clear that if we apply the value of criterion in all cases equal to quantile 0.05,0.95 = average ± 1.96*stdev, then we obtain unrealistic extreme values in all groups, sometimes even lower than zero. Such values would disable the use of timber due to its low performance in tension perpendicular to grain. Instead, it is rather advantageous to use the average value and make the quantile value of the F max which can be obtained from the time point where the strain criterion around the crack is reached. Because the result of the work can serve as a procedure and benchmark to simplify the assessment of bearing capacity of structural scale timber beam with cracks tested by means of DIC and loaded predominantly in mode I, we ought to conclude that in such a case one should be aware when the criterion is applied to different parts of the beam. For instance in the case of notched timber beams where the effective height ( h eff ) of the notched beam reaches the value of h eff = 0.5 h , we should be aware that a rather lower criterion such as the one in T direction should be used instead. On the other hand, in the case of h eff = 0.8 h , the TR criterion may be valid. This recommendation does not look appealing from a practical perspective, but is proven also from the simple fact. It is that very different results of F max shown in the Table 1 for each anatomical plane conclude that timber in the TR group is able to withstand much higher deformation energy in mode I than in other two groups. Even though the presented approach in utilizing strain criterion from optical data brings novelty, it also has certain limitations one should be aware of. First, development of FPZ and crack length can be influenced by the testing procedure itself and, therefore, many authors rather use the tapered double cantilever beam (TDCB) technique to avoid problems related to SEN-TPB where bending is more present in the remaining height of the sample (de Moura and Dourado 2018 ). The authors took this limitation into account already and have prepared TDCB specimens from the same timber and plan to make comparative study of both and present results in near future. Such a comparison will bring insight into an influence of testing protocol on application of optical-based strain criterion. Second, validity of present results is likely limited only to pure mode I loading which represents the most dangerous scenario in wood when forces open crack perpendicular to fiber. In reality, there is always mixed mode occurring in a material, so the strain energies needed to onset a crack are greater than for the opening itself. Authors of the study have already carried out mixed-mode testing where these questions will be analyzed in future. Despite mentioned limitations, we are convinced that data presented in this study bring important insights into the evaluation of fracture behavior of wood. 3.3. Length of FPZ in Norway spruce mode I The optical data also provides scientific evidence of length of non-linear zone which can be well correlated with and attributed to the length of FPZ. In some cases, the FPZ length grew outside the ROI of the camera, thus the value was interpolated and based on relatively stable crack growth. ROI length was 45 mm ahead of the crack tip and the overall length of the remaining part was 60 mm, so the value of FPZ length is safely asessed, see in Table 1 . Values of FPZ length range from 38.4 mm in T, over 30.1 mm in R, up to 36.3 mm in the TR direction. This represents the maximum value that can be measured, and to our best knowledge it does not seem to be higher, actually it is based on very low values of the ε 1crit , probably not a realistic one (e.g. 6e-4). More realistically, the values would be rather lower than the values from Table 1 . We define the FPZ length as the distance from the notch to the end of the nonlinear region, however, during development of FPZ, the crack length also increases, so the area ahead of the crack tip can be computed as a FPZ - a c . 3.4. Correlation of the measured quantities Obtained qualities were further correlated among each other using Pearson’s correlation coefficient, it is shown in Table 2 , where correlations greater in absolute value than 0.5 are bold. As clear from Table 2 , it is hard to find common patterns in correlations for particular qualities among the groups. One of the reasons might be that those are very different qualities - some coming from the optical data (crack length, FPZ length, strain criterion), some related to energy ( G c , G f , and F max ) or material density. For instance, correlation between length of crack and the strain-criterion is high for T and TR groups, but weak for R group. Other qualities usually show different correlation patterns in all three groups. Fracture energy G c correlates positively with density (with T group the lowest) even though with a high scatter, which is likely due to density variation around the crack. For instance Konukcu et al. ( 2021 ) showed the fracture energy differs depending on whether the crack allocates in early or late wood. Further, G f does not correlate with F max strongly at all ( R lies between − 0.07 and 0.21). Another reason for the T group is a presence of micro-cracks that appeared due to drying and were visible by the naked eye. It was visible during the test they somehow open, but not propagate, which can nonetheless influence the results. Although the drying process was carried out properly, the nature of medium-size timber brings certain difficulties. In the other two directions the result looks more consistent. Length of FPZ strongly correlates with ε 1crit for the R direction, which can be attributed to a fact the crack does not go through complicated early/late wood interfaces and propagates only in one of them, usually in weaker early wood. This can be the reason why the crack behaves more as expected, i.e. greater opening of crack means longer FPZ. In general, it is suggested that in searching for strong correlations regarding fracture behavior in such a complex material as wood of medium size, one ought to have a bigger sample set. However, extreme amount of work to process all the data can be a limitation to increase the set significantly. Table 2 Cross correlation table - Pearson’s coefficients with notable values shown in bold, all experiments in the order T, R, TR, respectively T density G c_CBBM G f_CBBM a c a FPZ ε 1crit F max density - - - - - - - G c_CBBM 0.60 - - - - - - G f_CBBM 0.50 0.83 - - - - - a c -0.25 -0.56 -0.38 - - - - a FPZ -0.10 -0.46 -0.10 0.52 - - - ε 1crit 0.11 0.31 0.43 -0.62 0.07 - - F max 0.47 0.16 0.08 0.43 0.10 -0.46 - R density G c_CBBM G f_CBBM a c a FPZ ε 1crit F max density - - - - - - - G c_CBBM 0.40 - - - - - - G f_CBBM 0.21 0.36 - - - - - a c 0.23 0.42 0.00 - - - - a FPZ -0.16 0.52 0.05 0.18 - - - ε 1crit -0.20 0.43 0.21 -0.21 0.84 - - F max 0.45 0.55 0.21 -0.26 0.11 0.21 - TR density G c_CBBM G f_CBBM a c a FPZ ε 1crit F max density - - - - - - - G c_CBBM 0.33 - - - - - - G f_CBBM 0.59 0.45 - - - - - a c 0.37 -0.26 0.49 - - - - a FPZ 0.13 0.19 0.50 0.49 - - - ε 1crit -0.83 -0.02 -0.59 -0.73 -0.08 - - F max 0.25 0.60 -0.07 -0.64 -0.57 0.06 - 4. Conclusions The paper focuses on detailed description of processes occuring in the FPZ region during crack propagation in Norway spruce wood in mode I. The FPZ was examined using the DIC method which showed to be a valuable means providing strains in contour plots around a crack. Uniqueness of the proposed solution lies in the simultaneous tracking and considering of cracks on both faces of a relatively wide specimen, which has not been published to date. We found relatively stable criterion for all studied anatomical directions (R, T and TR). For practical purposes for testing of big timber members (often in T and TR directions visible, R is hidden), one can consider the crack to be critically loaded when the strain criterion reaches the value 2.5e-3 (minimum of T and TR groups) and the distance of such a strain from the singularity/notch is 19.4 mm (similarly minimum of T and TR groups). Our results suggest that proposed criteria cannot be used in a quantile way since these quantile values are too low to be practically grasped. FPZ length showed to be even larger than expected and reaches the value of 38.4 mm in T, 30.1 in R and 36.3 mm in TR directions. Stress distribution is not so easy to assess, especially ahead of the crack tip, so it is not an easy task to evaluate the energy dissipated in this region. Declarations Author Contribution J.K. did conceptualisation, idea, financial support, writing, data processing, data evaluation, programming. V.S.: writing and reviewing, J.J + M.H. + J.P. performed the experiments, M.K. prepared samples and chose the material Acknowledgments This paper was created with financial support from a grant project of the Czech Science Foundation GACR No. 21-29389S “Experimental and numerical assessment of the bearing capacity of notches in timber beams at arbitrary locations using LEFM”. The authors gratefully acknowledge the provider. 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Critical energy rate analysis of fracture strength. Weld J Res Suppl, 33:193s. Jones E., Oliphant T., Peterson P. and others, 2001. SciPy: Open Source Scientific Tools for Python, http://www.scipy.org/ Konukcu, A.C., Franklin, Q., Jilei Z. 2021. Effect of Growth Rings on Fracture Toughness of Wood. European Journal of Wood and Wood Products 79:1495–1506. Majano-Majano, A., Lara-Bocanegra, A., Xavier, J., Morais, J., 2018. Measuring the Cohesive Law in Mode I Loading of Eucalyptus globulus. Materials 12, 23. https://doi.org/10.3390/ma12010023 Morel, S., Bouchaud, E., Schmittbuhl, J., Valentin, G., 2002. [No title found]. International Journal of Fracture 114, 307–325. https://doi.org/10.1023/A:1015727911242 Morel, S., Dourado, N., Valentin, G., 2005. Wood: a quasibrittle material R-curve behavior and peak load evaluation. Int J Fract 131, 385–400. https://doi.org/10.1007/s10704-004-7513-0 Morel, S., Mourot, G., Schmittbuhl, J., 2003. Influence of the specimen geometry on R-curve behavior and roughening of fracture surfaces. International Journal of Fracture 121, 23–42. https://doi.org/10.1023/A:1026221405998 Morel, S., Schmittbuhl, J., Bouchaud, E., Valentin, G., 2000. Scaling of Crack Surfaces and Implications for Fracture Mechanics. Phys. Rev. Lett. 85, 1678–1681. https://doi.org/10.1103/PhysRevLett.85.1678 NT BUILD 422 (1993) Wood: Fracture energy in tension perpendicular to the grain. Nordtest Method, 11. Tekniikantie, Finland. Ostapska, K., Malo, K.A., 2020. Wedge splitting test of wood for fracture parameters estimation of Norway Spruce. Engineering Fracture Mechanics 232, 107024. https://doi.org/10.1016/j.engfracmech.2020.107024 Ostapska, K., Malo, K.A., 2021. Calibration of a combined XFEM and mode I cohesive zone model based on DIC measurements of cracks in structural scale wood composites. Composites Science and Technology 201, 108503. https://doi.org/10.1016/j.compscitech.2020.108503 Petterson, R.W., Bodig, J., 1983.. Prediction of fracture toughness of conifers Journal of Wood and Fiber Science 15(4):302-316. Phan, N.A., Chaplain, M., Morel, S. et al. Influence of moisture content on mode I fracture process of Pinus pinaster : evolution of micro-cracking and crack-bridging energies highlighted by bilinear softening in cohesive zone model. Wood Sci Technol 51, 1051–1066 (2017). https://doi.org/10.1007/s00226-017-0907-8 Reiterer, A., Stanzl-Tschegg, S.E., Tschegg, E.K., 2000. Mode I fracture and acoustic emission of softwood and hardwood. Wood Science and Technology 34, 417–430. https://doi.org/10.1007/s002260000056 Romanowicz M., Numerical assessment of the apparent fracture process zone length in wood under mode I condition using cohesive elements, Theoretical and Applied Fracture Mechanics, Volume 118, 2022, 103229, ISSN 0167-8442, https://doi.org/10.1016/j.tafmec.2021.103229. Stanzl-Tschegg, Stefanie E., Tan, D.-M., Tschegg, E., 1995. New splitting method for wood fracture characterization. Wood Sci.Technol. 29. https://doi.org/10.1007/BF00196930 Tan, D.M., Stanzl-Tschegg, S.E., Tschegg, E.K., 1995. Models of wood fracture in Mode I and Mode II. Holz als Roh-und Werkstoff 53, 159–164. https://doi.org/10.1007/BF02716417 Turner, DZ, Digital Image Correlation Engine (DICe) Reference Manual, Sandia Report, SAND2015-10606 O, 2015. Xavier, J., Monteiro, P., Morais, J.J.L., Dourado, N., de Moura, M.F.S.F., 2014a. Moisture content effect on the fracture characterisation of Pinus pinaster under mode I. J Mater Sci 49, 7371–7381. https://doi.org/10.1007/s10853-014-8375-0 Xavier, J., Oliveira, M., Monteiro, P., Morais, J.J.L., de Moura, M.F.S.F., 2014b. Direct Evaluation of Cohesive Law in Mode I of Pinus pinaster by Digital Image Correlation. Exp Mech. https://doi.org/10.1007/s11340-013-9838-y Additional Declarations No competing interests reported. Supplementary Files Annex.docx Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-3962450","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":273321116,"identity":"b32e4e69-e0bf-4432-98ae-0367e419f67e","order_by":0,"name":"Jiří Kunecký","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA2ElEQVRIiWNgGAWjYBACCTB5gEGOjWQtxmxE64FpSWwgWovkjNyDD36cOZzeJ9/8dANDjZ09A/vxB3i1SEvkJRv23Dic28bGZnaD4VhyYgNPQgJeLXISOWbSDB9AWhjMbjA2MCcA3XqAkBbz30At6Wxs7N+AWurtGSQYGwg4LMeMmeHG4QQ2Nh6QLYcZGySY8epgkOx5YyzZcybdsI0tp+xGwrHjiW08afi1SBzPMfzw45i1vHzz8W03PtRU2/MTCjEoaIZQCUBMbPzUEaluFIyCUTAKRiQAAKVwQTK9PRbGAAAAAElFTkSuQmCC","orcid":"","institution":"Institute of Theoretical and Applied Mechanics","correspondingAuthor":true,"prefix":"","firstName":"Jiří","middleName":"","lastName":"Kunecký","suffix":""},{"id":273321117,"identity":"fb55fec6-9225-46a3-bb2e-972b5c7e3bb5","order_by":1,"name":"Martin Hataj","email":"","orcid":"","institution":"University Centre for Energy Efficient Buildings of CTU (UCEEB)","correspondingAuthor":false,"prefix":"","firstName":"Martin","middleName":"","lastName":"Hataj","suffix":""},{"id":273321118,"identity":"fd5463e1-8113-4612-b79d-6cf23328fe8c","order_by":2,"name":"Jan Jochman","email":"","orcid":"","institution":"University Centre for Energy Efficient Buildings of CTU (UCEEB)","correspondingAuthor":false,"prefix":"","firstName":"Jan","middleName":"","lastName":"Jochman","suffix":""},{"id":273321119,"identity":"0dd72011-348a-4e8e-a827-40f4ab589246","order_by":3,"name":"Jan Pošta","email":"","orcid":"","institution":"University Centre for Energy Efficient Buildings of CTU (UCEEB)","correspondingAuthor":false,"prefix":"","firstName":"Jan","middleName":"","lastName":"Pošta","suffix":""},{"id":273321122,"identity":"61504a06-22c8-4e62-bc3c-5129fa9b5e68","order_by":4,"name":"Michal Kloiber","email":"","orcid":"","institution":"Institute of Theoretical and Applied Mechanics","correspondingAuthor":false,"prefix":"","firstName":"Michal","middleName":"","lastName":"Kloiber","suffix":""},{"id":273321124,"identity":"9dde40f6-04ce-48e6-9a1b-c13ffee61bac","order_by":5,"name":"Václav Sebera","email":"","orcid":"","institution":"Mendel University in Brno","correspondingAuthor":false,"prefix":"","firstName":"Václav","middleName":"","lastName":"Sebera","suffix":""}],"badges":[],"createdAt":"2024-02-16 21:59:42","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3962450/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3962450/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":51394172,"identity":"3cddac34-a9fa-4cad-ae07-9e0720ee83f4","added_by":"auto","created_at":"2024-02-20 19:07:12","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":28315,"visible":true,"origin":"","legend":"\u003cp\u003eExperimental setup and sample dimensions (h = 0.12 m, b = 0.5h, a0 = 0.5h, w=~1.45 mm)\u003c/p\u003e","description":"","filename":"1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-3962450/v1/85a865a725286af10626e083.jpg"},{"id":51393723,"identity":"43bb947b-da46-41e4-8b08-ce79d7121cd5","added_by":"auto","created_at":"2024-02-20 18:59:13","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":105552,"visible":true,"origin":"","legend":"\u003cp\u003eThe test with the DIC setup (left) and orientation of anatomical direction (right); samples shown from the bottom side (R = Radial, TR = Tangential-Radial with an inclination about 40-50°, T = Tangential)\u003c/p\u003e","description":"","filename":"2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-3962450/v1/33524072311a0a803168a411.jpg"},{"id":51393726,"identity":"2a25d3c1-9e29-4059-98e1-ef838d9ea760","added_by":"auto","created_at":"2024-02-20 18:59:14","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":161622,"visible":true,"origin":"","legend":"\u003cp\u003eSpeckle patterns for DIC of both sides of the sample for tracking both crack lengths. Figure shows the same time step of loading, note different crack lengths at both sides.\u003c/p\u003e","description":"","filename":"3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-3962450/v1/4dd800055151eb89ca631df2.jpg"},{"id":51393720,"identity":"1e192130-e31a-48f2-a2b8-f7e4003e9ad6","added_by":"auto","created_at":"2024-02-20 18:59:12","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":56048,"visible":true,"origin":"","legend":"\u003cp\u003eTypical data processing using eqLEFM and CBBM approaches with an identification of crucial points (Gc, Gf), left - compliance in green and force in red.\u003c/p\u003e","description":"","filename":"4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-3962450/v1/d0e1c3e3a6b0548763ee6345.jpg"},{"id":51393725,"identity":"094249cc-0d9e-4e71-b713-548804a49d1c","added_by":"auto","created_at":"2024-02-20 18:59:14","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":134648,"visible":true,"origin":"","legend":"\u003cp\u003eProcessing the optical data: a) the algorithm identifies the end of the linear region (upper left) and searches for the criteria b) when the cracks are formed (upper right, blue is camera 1, red is camera 2). c) At both sides, criteria are found by producing a vector of strain from the end of the linear strain region to the biggest change in slope (bottom left). d) Length of FPZ and length of crack mouth is determined (bottom right). Note the red a\u003csub\u003emth\u003c/sub\u003e goes out of the ROI, but interpolation of this quality is nevertheless possible.\u003c/p\u003e","description":"","filename":"5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-3962450/v1/3da8403fbbf0b6f5c38d864e.jpg"},{"id":51393724,"identity":"ad6455fb-6d7c-4e64-a192-9d751aae13f1","added_by":"auto","created_at":"2024-02-20 18:59:14","extension":"jpg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":93357,"visible":true,"origin":"","legend":"\u003cp\u003eInfluence of strain criterion on assessed value of \u003cem\u003eG\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e (shown always in color bullets). Colors of the curves and bullets represent the same specimen on both the left and right side. Inlined histograms show distribution of results.\u003c/p\u003e","description":"","filename":"6.jpg","url":"https://assets-eu.researchsquare.com/files/rs-3962450/v1/d892830ed2d8cbd7ace1f4cf.jpg"},{"id":51394628,"identity":"21befc97-5e0c-48cc-802f-032f26d94a87","added_by":"auto","created_at":"2024-02-20 19:23:14","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":851262,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3962450/v1/fd9b650a-b741-43cf-94df-72a28c0b276a.pdf"},{"id":51394221,"identity":"a0b6c0ee-ed06-41ab-aedb-30793c61327a","added_by":"auto","created_at":"2024-02-20 19:15:12","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":22424,"visible":true,"origin":"","legend":"","description":"","filename":"Annex.docx","url":"https://assets-eu.researchsquare.com/files/rs-3962450/v1/af4e225779120d00cff37494.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Strain-based approach to characterize mode I crack propagation in Norway Spruce directly from optical data","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eEven despite the fact that most of forest management in Central Europe aims on mixed forests and that there is substantial decrease of spruce stands due to bark beetle attack, spruce wood remains the main material for the glued laminated timber (GLT) and cross-laminated timber (CLT) construction sector. Both materials have to be prepared and prefabricated with notches, drilled holes etc. which represent locations of potential stress concentrations that may be source of crack onset (similarly in \u003cb\u003eEurocode 5\u003c/b\u003e).\u003c/p\u003e \u003cp\u003eThe least fracture energy for crack onset is required in mode I that represents the most dangerous mode of fracture in wood if the tension appears perpendicular to fiber. The mode I is usually investigated by double cantilever beam (DCB), single-edge-notched three-point bending test (SEN-TPB), tapered double cantilever beam test (TDCB) or compact tension (CT) tests \u003cb\u003e(Smith et al. 2003\u003c/b\u003e). Wood is heterogeneous and cellular material and, therefore, many questions arise regarding the convenient size of the test specimens, crack surfaces and regarding the applicability of either linear fracture elastic mechanics (LEFM) or nonlinear fracture approaches (Bažant et al. \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2022\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe impact of specimen size (from 10 to 320 mm in height) on fracture characteristics in mode I for spruce wood loaded in the RL crack plane was already studied in \u003cb\u003eAicher et al. (1993).\u003c/b\u003e Authors utilized the SEN-TPB and showed significant impact of size on nominal strength till height of a beam of 160 mm where nonlinear effects took place, meanwhile for higher beam heights, standard LEFM behavior was observed and confirmed utilization of scaling based on a theory developed by Bažant (\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e1984\u003c/span\u003e\u003cb\u003e)\u003c/b\u003e. \u003cb\u003ePetterson and Bodig\u003c/b\u003e (1993) found the correlation of fracture toughness in mode I and tensile strength for ten conifers as well as the prediction of fracture toughness based on density and moisture content. Stanzl-Tschegg et al. (\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e1995\u003c/span\u003e) investigated size effect in the CT test with respect to total crack length and specimen width and found their strong influence below ligament length of 70 mm due to different sizes of FPZ. Daudeville (\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e1999\u003c/span\u003e\u003cb\u003e)\u003c/b\u003e studied spruce and found that as size of specimen increases (from 45 to 100 mm), the nominal strength decreases, but specific fracture energy keε on similar levels. The author found significant differences in fracture energy between RL and TL planes. Morel et al. (\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2000\u003c/span\u003e) analyzed size effect in wood employing the Family-Viscek scaling and showed its strong influence as well as proved valid usage of this scaling for materials with toughening mechanisms. Morel et al. (\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2002\u003c/span\u003e) showed that for both Maritime Pine and Norway spruce the size of the specimens influences critical strain energy release rate (\u003cem\u003eG\u003c/em\u003e) which can be attributed to roughness of crack onset and surfaces, the specific surface energy also strongly correlated with density for both species. Morel et al. (\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2003\u003c/span\u003e) analyzed the role of a specimen geometry on \u003cem\u003eG\u003c/em\u003e values and found a certain dependency despite a limited sample size. The reason was found in a fact that the fracture process zone (FPZ) increases as specimen compliance increases due to higher stress intensity factor. \u003cb\u003eMorel and Dourado (2005)\u003c/b\u003e validated usage of the \u0026ldquo;equivalent LEFM\u0026rdquo; to analyze spruce fracture behavior in mode I along the grain (LT crack plane) employing the Nordtest for beams of 70 mm height. This approach was enhanced in the work of Dourado et al. (\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2008\u003c/span\u003e) who employed it to develop cohesive laws that included both microcracking and fiber-bridging phenomena.\u003c/p\u003e \u003cp\u003eOne of the difficulties in fracture analysis of wood is to monitor the propagation of crack. This difficulty may be solved using an equivalent crack length approach and compliance-based beam method (CBBM). This advantageous coupling of both was shown in de Moura et al. (\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2010\u003c/span\u003e) for SEN-TPB test using triangular stress relief region (SRR). Dourado et al. (\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2011\u003c/span\u003e) utilized that approach for SEN-TPB test with rectangular SRR to determine damage zone extent at crack initiation for various beam heights and concluded that for beams higher than 560 mm, the size effect might be neglected. Xavier et al. (\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2014b\u003c/span\u003e) employed a direct method utilizing Irwin-Kies equation, CMMB, and digital image correlation (DIC) to retrieve cohesive laws in mode I for pine wood at RL plane. Authors found a certain agreement between real and equivalent crack length, as well as good agreement between direct and indirect computation of \u003cem\u003eG\u003c/em\u003e values. Dourado et al. (\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2015\u003c/span\u003e) utilized SEN-TPB test to analyze three different beam heights made of spruce using CMMB and concluded that for heights of 140 mm and 210 mm, the clear plateau and comparable \u003cem\u003eG\u003c/em\u003e at peak load can be reached. Dourado et al. (\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2019\u003c/span\u003e) utilized CMMB to characterize pine wood in mode I loaded by fatigue-fracture way. The authors implemented the Paris law which enabled to evaluate crack propagation due to static load as well as damage due to fatigue effect. The effect of elevated temperature on \u003cem\u003eG\u003c/em\u003e values of pine wood was also studied and it was found that \u003cem\u003eG\u003c/em\u003e decreases with temperature even despite the fact that stiffness and ultimate load keep on comparable level (Dourado and de Moura \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2019\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eMore recently, Ostapska and Malo (\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2020\u003c/span\u003e\u003cb\u003e)\u003c/b\u003e presented an alternative approach to characterize spruce wood fracture in mode I. The approach utilized full-field deformation data history to obtain crack tip locations by analytical decomposition to various modal components of fracture that allowed adjustment of fracture characteristics. An extension of this approach towards creation of a calibrated numerical model reflecting nonlinear fracture phenomena was presented by the same authors later (Ostapska and Malo (\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2021\u003c/span\u003e\u003cb\u003e)\u003c/b\u003e. When searching for agreement with full-field data, their optimization procedure allowed to vary not only elastic parameters, but also stress at initiation, crack propagation and softening functions. Critical approach to full-field data was presented by Romanowicz (\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2022\u003c/span\u003e\u003cb\u003e)\u003c/b\u003e who numerically analyzed the position of the real crack tip using two methods of adjustments and full-field DIC data. He has found that employing DIC in crack monitoring may underestimate crack extension due to FPZ and overestimate the energy required to form microcracks. Analysis of fracture behavior in mode I for other species than spruce, as well as for wood-based composites, is also available in literature, but their more detailed resume is omitted here for the conciseness \u003cb\u003e(\u003c/b\u003eArdalany et al. \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2012\u003c/span\u003e, de Moura and Dourado \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2018\u003c/span\u003e, Majano-Majano et al. \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2018\u003c/span\u003e, Forsman et al. \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2020\u003c/span\u003e, Hu et al. \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2021\u003c/span\u003e, \u003cb\u003eGomez-Royuela et al. 2022\u003c/b\u003e, Phan et al. \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2017\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eHowever, it seems that optical data and DIC algorithms still offer a potential in crack evaluation, especially usage of strain criteria is promising. Since displacement control of experiments does not lead to dangerous and fast crack propagations, it is difficult to say when the crack is already formed and critically loaded. In reality, the structures are loaded by forces, which makes a crack propagate very quickly when loaded beyond the critical limit. Therefore, the crack is to be considered as critical even before it is visually seen. A capturing of a non-visible crack may be solved using strain-based criteria computed from DIC data, which is a general goal of the study.\u003c/p\u003e \u003cp\u003eTo respond to the general goal, following objectives were set: 1) to perform fracture test at medium-size timber beams using modified SEN-TPB setup; 2) to develop and verify strain-based approach to characterize fracture properties of wood in mode I using DIC; 3) to couple CBBM and direct optical approaches in evaluation of crack propagation.\u003c/p\u003e"},{"header":"2. Materials and methods","content":"\u003cp\u003eThe work utilized several different, but hence complementary approaches that are convenient to outline for clarity. The work focused on detailed analysis of the region around the crack using DIC, especially on the relation between strain-based criteria derived from optical data to the crack propagation length based on such a criterion. Such an optical-based value is compared to the assessed value of \u003cem\u003eG\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e obtained using CBBM. In the work we distinguish the \u003cem\u003eG\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e as the value of strain energy release rate when maximum force is applied, and \u003cem\u003eG\u003c/em\u003e\u003csub\u003e\u003cem\u003ef\u003c/em\u003e\u003c/sub\u003e which is the maximal value that can be attained. The CBBM is a method based on assumption of energy dissipation during the crack propagation, it is based on eqLEFM concept and deals thus with equivalent crack length that cannot be seen directly. Nevertheless, comparison of which size of \u003cem\u003eε\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e criterion in optical measurement induces which \u003cem\u003eG\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e from CBBM is valuable, since it compares the methods and allows to determine reasonably safe criterion which can be applied to other cases in the same specie, anatomical direction and mode I loading. Additionally, an analysis of length of nonlinear region - length of FPZ, based on the optical data is also performed. Last, correlation between the results is critically reviewed.\u003c/p\u003e \u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1. SEN-TPB experiments\u003c/h2\u003e \u003cp\u003eThe experimental work followed the test procedure from NT BUILD 422 standard \u003cb\u003e(NT BUILD 1993)\u003c/b\u003e that is used for testing fracture properties in mode I. The specimen geometry and boundary conditions are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. First, the crack-free timber beams with growth ring orientated in tangential (T), radial (R), and mixed (TR) orientations were cut from Norway spruce beams of big size. The specimens were then conditioned in a climate chamber using standard conditions (20\u0026deg;C and 65% relative humidity (RH) to reach 12% equilibrium moisture content (EMC). Then, wooden blocks with dimensions of 12 \u0026times; 12 cm (height \u0026times; width) were cut from the beams to create a middle element and glued to specimen arms using PVA-based dispersions of one-component adhesive (see Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe orientation of grain in the middle element is rotated 90\u0026deg; to the arms, the specimens were held under pressure for one hour and then the middle element was cut vertically up to the half of the specimen height to introduce an initial and narrow crack, the detail of tree ring orientation is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. All specimens were made from four different trees. In each of the groups (T, R, TR) are specimens from at least two trees (mixed half way). In T, R and TR groups, we measured 10, 12, and 9 specimens, respectively. The central parts 12x12x6 cm intended to be glued in between two arms were cut from one plank, that means, close to each other and thus should not have big differences.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAt the middle element with initiated crack was then applied with a stochastic pattern using Airbrush Revell Master Class together with acrylic pigments to create randomly distributed speckles (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e) to ensure high-quality computation by DIC in further work. The areas of interest (AoI) on specimens around the crack tip were filmed from both sides of the specimen using same cameras Basler acA2440-20gm with frame rate 1 Hz and resolution 2448 \u0026times; 2048 px. The optical data were used to analyze crack onset and propagation - monitoring crack length. The semi-telecentric lens Computar TEC-M55MPW with focal length 55 mm was used to minimize optical distortion. The images were further processed using DICe software (\u003cb\u003eTurner et al. 2015)\u003c/b\u003e and used parameters of DIC were as follows: step\u0026thinsp;=\u0026thinsp;30 px (equals\u0026thinsp;~\u0026thinsp;0.675 mm), subset\u0026thinsp;=\u0026thinsp;27 px, Gauss kernel\u0026thinsp;=\u0026thinsp;5 px, transformation full affine. For the mechanical testing, the universal testing machine Galdabini Quasar 100 was used, equipped with a load cell with a range of 10 kN and Labtest testing software. The outputs from the test machine and sensors were acquired by the unit DEWE2602. For all samples, the load, the corresponding deflection measured by two control LVDTs (see Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e) and one control LVDT to identify the initiation and opening of the crack were monitored. For the purpose LVDT sensors DTA-5G-CA (Micro-epsilon, Germany) throughout the duration of the load test were used, located on both sides of the test specimen. The average value of these LVDT sensors was used to evaluate the data. The tests were displacement-driven with a speed of 0.3 mm/min.\u003c/p\u003e \u003cp\u003eCBBM evaluation was made according to Dourado et al. (\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2011\u003c/span\u003e). Due to the experimental variability, the interval for initial compliance was selected individually, but always was in the region of 0.2 to 0.4 of \u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003emax\u003c/em\u003e\u003c/sub\u003e. Other parameters, although often with minor influence to the result were: \u003cem\u003ek\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.86, \u003cem\u003eβ\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1.07, \u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003eL\u003c/em\u003e\u003c/sub\u003e=10 GPa and \u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003eT\u003c/em\u003e\u003c/sub\u003e=\u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003eL\u003c/em\u003e\u003c/sub\u003e/17. Elastic properties of the arms have very low influence on the final results. It is not possible to obtain the true crack length because the initial scatter of the algorithm strongly influences the value. That is why the value of \u003cem\u003eG\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e was used for later analysis in processing optical data instead of the absolute crack length. Typical processing of data is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e and is described below.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2. Optical data post-processing\u003c/h2\u003e \u003cp\u003eIt is worth noting that the experimental determination of the crack tip position in quasi-brittle materials is difficult, since the development of FPZ is complicated and makes the method really challenging. The key questions here are: where the crack starts and what length the crack has. From the theoretical point of view it is clear - nevertheless from the experimental perspective it is a real challenge to answer those questions for a quasi-brittle material. The concept of eqLEFM serves as a good etalon and that is why we compared the optical data to the CBBM ones. Strain-based criteria are of certain importance because in testing of structural-size members, the recognition of presence of a crack is crucial for assessment of bearing capacity of notched beams. In such a case, CBBM cannot be applied because a significant amount of energy is dissipated in closure of the drying cracks, material inhomogeneities (like knots), contacts, embedments etc. Even for assessment of bearing capacity of timber beams using CZM we have to address the presence of a critical length using crack shape parameters, CZM itself is not capable of predicting critical crack growth. Despite the limitations encountered with the use of DIC, it is the only reasonable and cheap experimental technique which is not dependent on assumption of many parameters. This work intends to add one stone to the mosaic of understanding wood fracture.\u003c/p\u003e \u003cp\u003eThe DICe algorithm provided us with raw data, namely displacement, rotation and strain fields for each image in the whole image sequence representing the time domain. Such data were further post-processed using a Python-powered set of libraries SciPy and NumPy (\u003cb\u003eScipy -\u003c/b\u003e Jones et al. \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2001\u003c/span\u003e). First, the equivalent crack length (\u003cem\u003ea\u003c/em\u003e\u003csub\u003e\u003cem\u003ee\u003c/em\u003e\u003c/sub\u003e) and \u003cem\u003eG\u003c/em\u003e were computed using CBBM, so we obtained \u003cem\u003ea\u003c/em\u003e\u003csub\u003e\u003cem\u003ee\u003c/em\u003e\u003c/sub\u003e vs. time and \u003cem\u003eG\u003c/em\u003e vs. \u003cem\u003ea\u003c/em\u003e\u003csub\u003e\u003cem\u003ee\u003c/em\u003e\u003c/sub\u003e and could identify \u003cem\u003eG\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eG\u003c/em\u003e\u003csub\u003e\u003cem\u003ef\u003c/em\u003e\u003c/sub\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe SEN-TPB induces pure mode I and thus tensile stresses/strains are of our interest. Therefore, the whole procedure used was based on an evaluation of the first principal strain (\u003cem\u003eε\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e) field, resp. its maxima. The \u003cem\u003eε\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e was computed for each pixel using linear algebra. The strain field is very handy especially in optical measurement, where strains computed from pixel values mean the same strains as in the studied plane when undistorted images are assumed. Another reason why principal strains instead of displacements were used for the evaluation is their invariant nature and simply the fact that displacements need two points selected and size of DIC step can become another additional parameter. Last, strain analysis was employed because of the ability to find the beginning of nonlinearity in the strain field across the height of the bent glued-in specimen. This nonlinearity ahead of the crack tip can be considered the very end of FPZ.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe whole method described here follows the CBBM principle meaning there is no change in compliance linearity without crack propagation. The crack starts with the first positive change in compliance (see Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ea), where the bullets show the end of the linear region). The procedure can be further split into two tasks: (i) how to assess a strain criterion and (ii) how to determine the crack length itself based on such a criterion. For clarity, we start with the \u003cb\u003esecond\u003c/b\u003e task: the algorithm first chooses the region of interest (ROI) which is the one that is a subset of the original field, where there is the biggest peak when summed along width of the glued-in part and its size is usually\u0026thinsp;~\u0026thinsp;5 mm in width and ~\u0026thinsp;45 mm in length. This is crucial in order to remove imperfection influences (knots, other microcracks) from the analysis. After ROI has been selected, it detects zones along the height (45 mm) where the \u003cem\u003eε\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e is higher than the given strain-based criterion (in our case \u003cem\u003eε\u003c/em\u003e\u003csub\u003e\u003cem\u003e1max\u003c/em\u003e\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;3e-3). Because the detection utilizes discrete values of matrix element values, it employs a linear interpolation to get more precise crack length. This algorithm is applied on the whole sequence and allows to apply a set of criteria that return a set of crack lengths (as curves). In Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ed we can see for each of the cameras two curves representing the crack length in time if minimal and maximal strain criterion is used.\u003c/p\u003e \u003cp\u003eThis research is unique because we track both sides of the sample and account for different crack lengths in time. This is attained by specifying the correct strain criterion on each side of the sample - the \u003cb\u003efirst task\u003c/b\u003e mentioned above. The problem is, that if the crack starts on one side, it still does not have to be apparent on the other. So in the first step we apply to both sides a relatively safe strain criterion such as \u003cem\u003eε\u003c/em\u003e\u003csub\u003e\u003cem\u003e1max\u003c/em\u003e\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;3e-3. Using the above described algorithm, we get curves for both sides of the sample. This is illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eb, where cracks from camera 1 (blue) and camera 2 (red) are depicted. Then, we determine the delay in time between the two curves (green curve) which allows us to analyze each side separately using the strain criterion at different positions in the sequence based on the delay. The results of this are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ed, colors distinguish the cameras. The first principal strains (Y axis) along the height of the scanned area (X axis) are depicted as bright solid curves. Note that both curves (red and blue) are at different time steps and determine the probable onset of crack. Further, for each of the curves, a linear part is automatically detected and fitted by a line. The difference between the curve and the fitted line is shown in the same picture as lines with semi-transparency using the second Y axis. These curves allow reading the first value representing onset of any nonlinearity, e.g. the highest possible FPZ length. The maximum represents the mouth of the crack, it is the value when the derivative of the difference line is the highest (dashed lines). Bullets in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ec represent the value of the criteria, and from the whole procedure we can obtain two extreme values of strain criterion for each side, and further interpolate between them on the strain curve to obtain additional three points. This step outputs two vectors of five values of strain criteria and for each one, the crack length at each side of the specimen is computed.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe final crack length is computed as the average of crack lengths obtained for each criterion in the time sequence. Such an average is also presented in the results as one criterion - for example, first two criteria for each side are assessed and used to produce respective crack lengths, however, in the end are together averaged for clarity of the results. Such a joined curve (\u003cem\u003ea\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003ea\u003c/em\u003e\u003csub\u003e\u003cem\u003el\u003c/em\u003e\u003c/sub\u003e+\u003cem\u003ea\u003c/em\u003e\u003csub\u003e\u003cem\u003er\u003c/em\u003e\u003c/sub\u003e)/2 can be used to compute the value of \u003cem\u003eG\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e next to the maximal force using known Irwin-Kies \u003cb\u003e(Irwin et al. 1954)\u003c/b\u003e equation:\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$G=\\frac{{F}^{2}}{2b}\\frac{\\partial C}{\\partial a}$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003e, where \u003cem\u003eF\u003c/em\u003e is the acting force, \u003cem\u003eC\u003c/em\u003e is compliance, \u003cem\u003eb\u003c/em\u003e width of the sample, and \u003cem\u003ea\u003c/em\u003e is the crack length determined using optical method. The derivation is made using the gradient method in discrete domain. In fact, we use the same compliance as is used in the CBBM method and couple it with the crack length determined from optical data. Because all variables were noisy and the noise in this equation even amplified, we used a polynomial fit in the region of \u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003emax\u003c/em\u003e\u003c/sub\u003e to get stable and reliable results.\u003c/p\u003e \u003c/div\u003e"},{"header":"3. Results and discussion","content":"\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e\n \u003ch2\u003e3.1. Summary\u003c/h2\u003e\n \u003cp\u003eThe experimental work provided several groups of results, but the overall outcomes of the work are summarized in Table \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e. Descriptive statistics of intragroup characteristics are listed as geometric average, standard deviation and variation coefficient in Table \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e. The groups have comparable densities which comes from the fact that specimens in each group come from at least two different trees. The maximal force (\u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003emax\u003c/em\u003e\u003c/sub\u003e), however, is lowest in case of T orientation (63% of TR), the group with R orientation has higher mean (91% TR) and TR achieved the highest value. One of the possible reasons why TR has so high values can be the need to cross many interfaces of early/late wood for the crack, while in R this does not happen at all, T on the other side often propagates quickly on stiffer side and most of the crack length is present there. Similar trends are visible for fracture energies \u003cem\u003eG\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eG\u003c/em\u003e\u003csub\u003e\u003cem\u003ef\u003c/em\u003e\u003c/sub\u003e. The mean \u003cem\u003eG\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e, which is a more relevant value with respect to the work, is lowest in the T group (53% of TR mean) and slightly higher for the R group (57% of TR mean). Both crack length and obtained length of the FPZ show very comparable results among the groups, which is interesting with respect to the found differences in \u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003emax\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eG\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e. The data of \u003cem\u003eG\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e in pure orientations (T and R groups) are in an alignment with literature sources for spruce, for instance Morel et al. (\u003cspan class=\"CitationRef\"\u003e2005\u003c/span\u003e) obtained mean \u003cem\u003eG\u003c/em\u003e\u003csub\u003e\u003cem\u003eC\u003c/em\u003e\u003c/sub\u003e = 149 N/m for density of 440 kg/m\u003csup\u003e3\u003c/sup\u003e and 12% MC using the same test as used in this work; Dourado et al. (\u003cspan class=\"CitationRef\"\u003e2015\u003c/span\u003e) obtained \u003cem\u003eG\u003c/em\u003e\u003csub\u003e\u003cem\u003eC\u003c/em\u003e\u003c/sub\u003e = 152 N/m for density approx. 410 kg/m\u003csup\u003e3\u003c/sup\u003e and height of the beam 140 mm; and more recently, Ostapska and Malo (\u003cspan class=\"CitationRef\"\u003e2020\u003c/span\u003e) found \u003cem\u003eG\u003c/em\u003e\u003csub\u003e\u003cem\u003eC\u003c/em\u003e\u003c/sub\u003e = 179 N/m for RL and \u003cem\u003eG\u003c/em\u003e\u003csub\u003e\u003cem\u003eC\u003c/em\u003e\u003c/sub\u003e = 257 N/m for TL orientations when measuring by wedge splitting on spruce glulam of class GL30c. If we group the values according to tree number (not shown here, but sorted for readability), we cannot see differences except the group TR, where different trees provide very different results.\u003c/p\u003e\n \u003cp\u003e\u003c/p\u003e\u0026nbsp;\u003ctable id=\"Tab1\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eFinal results showing Tangential, Radial and Tangential-Radial anatomical directions\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\u0026nbsp;\u003c/th\u003e\n \u003cth align=\"left\"\u003e\u0026nbsp;\u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003edensity\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eG\u003csub\u003ec_CBBM\u003c/sub\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eG\u003csub\u003ef_CBBM\u003c/sub\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003ea\u003csub\u003ec\u003c/sub\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003ea\u003csub\u003eFPZ\u003c/sub\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003e\u0026epsilon;\u003c/em\u003e\u003csub\u003e\u003cem\u003e1crit\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eF\u003csub\u003emax\u003c/sub\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e[kg/m\u003csup\u003e3\u003c/sup\u003e]\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e[N/m]\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e[N/m]\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e[mm]\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e[mm]\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e[-]\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e[N]\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eT\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eaverage\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e497.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e154.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e212.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e23.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e38.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.0025\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e297.1\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003estdev\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e19.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e31.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e27.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.0012\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e21.6\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003evar. coef\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.04\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.13\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.19\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.47\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.07\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eaverage\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e479.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e165.6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e249.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e22.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e30.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.0013\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e427.6\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003estdev\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e19.6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e29.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e25.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.0006\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e40.1\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003evar. coef\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.04\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.18\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.07\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.47\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.09\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eTR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eaverage\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e463.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e293.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e341.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e19.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e36.3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.0034\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e470.1\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003estdev\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e23.7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e38.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e28.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e14.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.0014\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e32.6\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003evar. coef\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.05\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.13\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.08\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.33\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.39\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.41\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.07\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003cp\u003e\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e\n \u003ch2\u003e3.2. Strain-based criteria vs. crack length\u003c/h2\u003e\n \u003cp\u003eAlthough general outputs are summarized in Table \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e, their importance shows up when plotting them in a perspective of developed strain-based criteria (Fig. \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e). On the left side of the figure there is always depicted the value of the criterion which was used for particular assessment of \u003cem\u003eG\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e value based on such a criterion. For each specimen this procedure forms a curve, into which can be interpolated the point \u003cem\u003eG\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e obtained using CBBM method. Such an interpolated value may also be interpreted as a certain critical crack length even despite the fact that during the assessment the rate of crack growth is important. In Fig. \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e, the critical crack length (X axis) is plotted always on the right half of the figure for each respective point of the criterion from the left side of the figure. In these plots, we can also interpolate the crack length value to have all information compact. For example, when we applied the criterion of crack 1.8e-3 for the specimen T007, then obtained crack length to this point on the crack opening curve is 36.5 mm.\u003c/p\u003e\n \u003cp\u003eOverall, there is one general and important result coming from the plots in Fig. \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e. It is that the higher strain-based criterion, the shorter the crack length and, at the same time, the slower the crack propagates. As seen, this relation is not linear, especially in the case of crack length, but it can be stated that higher criterion leads to higher \u003cem\u003eG\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e. From the plots in Fig. \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e can also be read that T and R directions tend to behave in a similar way and bigger scatter is for criterion value rather than in the resulting crack length. The TR (combined) orientation shows much higher values than the ones from R and T orientation. The specific values can be read from Table \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e, but let us underline the most important: in the TR group, the \u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003emax\u003c/em\u003e\u003c/sub\u003e value is reached when we apply approx. \u003cem\u003e\u0026epsilon;\u003c/em\u003e\u003csub\u003e\u003cem\u003e1crit\u003c/em\u003e\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;3.4e-3, which determines the distance from the place where the crack started as 19.4 mm. In T direction it is a bit lower \u003cem\u003e\u0026epsilon;\u003c/em\u003e\u003csub\u003e\u003cem\u003e1crit\u003c/em\u003e\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;2.5e-3, but higher crack length (23.9 mm), whilst in R it is the least \u003cem\u003e\u0026epsilon;\u003c/em\u003e\u003csub\u003e\u003cem\u003e1crit\u003c/em\u003e\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;1.3e-3 and crack length of 22.1 mm. The criterion further enables us to obtain the value of assessed \u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003emax\u003c/em\u003e\u003c/sub\u003e. Important result is that the crack length does not change much within groups and that most of the \u003cem\u003eG\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e-\u003cem\u003e\u0026epsilon;\u003c/em\u003e\u003csub\u003e\u003cem\u003e1crit\u003c/em\u003e\u003c/sub\u003e curves on the left sides are not purely but mostly linear. That is why the \u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003emax\u003c/em\u003e\u003c/sub\u003e can also be considered as an approximate average value. Another question comes out of using the criteria in a quantile way. It should be clear that if we apply the value of criterion in all cases equal to quantile\u003csub\u003e0.05,0.95\u003c/sub\u003e = average\u0026thinsp;\u0026plusmn;\u0026thinsp;1.96*stdev, then we obtain unrealistic extreme values in all groups, sometimes even lower than zero. Such values would disable the use of timber due to its low performance in tension perpendicular to grain. Instead, it is rather advantageous to use the average value and make the quantile value of the \u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003emax\u003c/em\u003e\u003c/sub\u003e which can be obtained from the time point where the strain criterion around the crack is reached.\u003c/p\u003e\n \u003cp\u003eBecause the result of the work can serve as a procedure and benchmark to simplify the assessment of bearing capacity of structural scale timber beam with cracks tested by means of DIC and loaded predominantly in mode I, we ought to conclude that in such a case one should be aware when the criterion is applied to different parts of the beam. For instance in the case of notched timber beams where the effective height (\u003cem\u003eh\u003c/em\u003e\u003csub\u003e\u003cem\u003eeff\u003c/em\u003e\u003c/sub\u003e) of the notched beam reaches the value of \u003cem\u003eh\u003c/em\u003e\u003csub\u003e\u003cem\u003eeff\u003c/em\u003e\u003c/sub\u003e = 0.5\u003cem\u003eh\u003c/em\u003e, we should be aware that a rather lower criterion such as the one in T direction should be used instead. On the other hand, in the case of \u003cem\u003eh\u003c/em\u003e\u003csub\u003e\u003cem\u003eeff\u003c/em\u003e\u003c/sub\u003e = 0.8\u003cem\u003eh\u003c/em\u003e, the TR criterion may be valid. This recommendation does not look appealing from a practical perspective, but is proven also from the simple fact. It is that very different results of \u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003emax\u003c/em\u003e\u003c/sub\u003e shown in the Table \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e for each anatomical plane conclude that timber in the TR group is able to withstand much higher deformation energy in mode I than in other two groups.\u003c/p\u003e\n \u003cp\u003eEven though the presented approach in utilizing strain criterion from optical data brings novelty, it also has certain limitations one should be aware of. First, development of FPZ and crack length can be influenced by the testing procedure itself and, therefore, many authors rather use the tapered double cantilever beam (TDCB) technique to avoid problems related to SEN-TPB where bending is more present in the remaining height of the sample (de Moura and Dourado \u003cspan class=\"CitationRef\"\u003e2018\u003c/span\u003e). The authors took this limitation into account already and have prepared TDCB specimens from the same timber and plan to make comparative study of both and present results in near future. Such a comparison will bring insight into an influence of testing protocol on application of optical-based strain criterion. Second, validity of present results is likely limited only to pure mode I loading which represents the most dangerous scenario in wood when forces open crack perpendicular to fiber. In reality, there is always mixed mode occurring in a material, so the strain energies needed to onset a crack are greater than for the opening itself. Authors of the study have already carried out mixed-mode testing where these questions will be analyzed in future. Despite mentioned limitations, we are convinced that data presented in this study bring important insights into the evaluation of fracture behavior of wood.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\n \u003ch2\u003e3.3. Length of FPZ in Norway spruce mode I\u003c/h2\u003e\n \u003cp\u003eThe optical data also provides scientific evidence of length of non-linear zone which can be well correlated with and attributed to the length of FPZ. In some cases, the FPZ length grew outside the ROI of the camera, thus the value was interpolated and based on relatively stable crack growth. ROI length was 45 mm ahead of the crack tip and the overall length of the remaining part was 60 mm, so the value of FPZ length is safely asessed, see in Table \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e. Values of FPZ length range from 38.4 mm in T, over 30.1 mm in R, up to 36.3 mm in the TR direction. This represents the maximum value that can be measured, and to our best knowledge it does not seem to be higher, actually it is based on very low values of the \u003cem\u003e\u0026epsilon;\u003c/em\u003e\u003csub\u003e\u003cem\u003e1crit\u003c/em\u003e\u003c/sub\u003e, probably not a realistic one (e.g. 6e-4). More realistically, the values would be rather lower than the values from Table \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e. We define the FPZ length as the distance from the notch to the end of the nonlinear region, however, during development of FPZ, the crack length also increases, so the area ahead of the crack tip can be computed as \u003cem\u003ea\u003c/em\u003e\u003csub\u003e\u003cem\u003eFPZ\u003c/em\u003e\u003c/sub\u003e-\u003cem\u003ea\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e\n \u003ch2\u003e3.4. Correlation of the measured quantities\u003c/h2\u003e\n \u003cp\u003eObtained qualities were further correlated among each other using Pearson\u0026rsquo;s correlation coefficient, it is shown in Table \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e, where correlations greater in absolute value than 0.5 are bold. As clear from Table \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e, it is hard to find common patterns in correlations for particular qualities among the groups. One of the reasons might be that those are very different qualities - some coming from the optical data (crack length, FPZ length, strain criterion), some related to energy (\u003cem\u003eG\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eG\u003c/em\u003e\u003csub\u003e\u003cem\u003ef\u003c/em\u003e\u003c/sub\u003e, and \u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003emax\u003c/em\u003e\u003c/sub\u003e) or material density. For instance, correlation between length of crack and the strain-criterion is high for T and TR groups, but weak for R group. Other qualities usually show different correlation patterns in all three groups. Fracture energy \u003cem\u003eG\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e correlates positively with density (with T group the lowest) even though with a high scatter, which is likely due to density variation around the crack. For instance Konukcu et al. (\u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e) showed the fracture energy differs depending on whether the crack allocates in early or late wood. Further, \u003cem\u003eG\u003c/em\u003e\u003csub\u003e\u003cem\u003ef\u003c/em\u003e\u003c/sub\u003e does not correlate with \u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003emax\u003c/em\u003e\u003c/sub\u003e strongly at all (\u003cem\u003eR\u003c/em\u003e lies between \u0026minus;\u0026thinsp;0.07 and 0.21). Another reason for the T group is a presence of micro-cracks that appeared due to drying and were visible by the naked eye. It was visible during the test they somehow open, but not propagate, which can nonetheless influence the results. Although the drying process was carried out properly, the nature of medium-size timber brings certain difficulties. In the other two directions the result looks more consistent. Length of FPZ strongly correlates with \u003cem\u003e\u0026epsilon;\u003c/em\u003e\u003csub\u003e\u003cem\u003e1crit\u003c/em\u003e\u003c/sub\u003e for the R direction, which can be attributed to a fact the crack does not go through complicated early/late wood interfaces and propagates only in one of them, usually in weaker early wood. This can be the reason why the crack behaves more as expected, i.e. greater opening of crack means longer FPZ. In general, it is suggested that in searching for strong correlations regarding fracture behavior in such a complex material as wood of medium size, one ought to have a bigger sample set. However, extreme amount of work to process all the data can be a limitation to increase the set significantly.\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\u0026nbsp;\u0026nbsp;\u003ctable id=\"Tab2\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eCross correlation table - Pearson\u0026rsquo;s coefficients with notable values shown in bold, all experiments in the order T, R, TR, respectively\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eT\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003edensity\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eG\u003csub\u003ec_CBBM\u003c/sub\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eG\u003csub\u003ef_CBBM\u003c/sub\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003ea\u003csub\u003ec\u003c/sub\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003ea\u003csub\u003eFPZ\u003c/sub\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003e\u0026epsilon;\u003c/em\u003e\u003csub\u003e\u003cem\u003e1crit\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eF\u003csub\u003emax\u003c/sub\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003edensity\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eG\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003ec_CBBM\u003c/strong\u003e\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.60\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eG\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003ef_CBBM\u003c/strong\u003e\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.50\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.83\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003ea\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003ec\u003c/strong\u003e\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-0.25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e-0.56\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-0.38\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003ea\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003eFPZ\u003c/strong\u003e\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-0.10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-0.46\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-0.10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.52\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026epsilon;\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e1crit\u003c/strong\u003e\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.31\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.43\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e-0.62\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.07\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eF\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003emax\u003c/strong\u003e\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.47\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.16\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.08\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.43\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-0.46\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eR\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003edensity\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eG\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003ec_CBBM\u003c/strong\u003e\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eG\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003ef_CBBM\u003c/strong\u003e\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003ea\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003ec\u003c/strong\u003e\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003ea\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003eFPZ\u003c/strong\u003e\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026epsilon;\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e1crit\u003c/strong\u003e\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eF\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003emax\u003c/strong\u003e\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003edensity\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n 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\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003ea\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003eFPZ\u003c/strong\u003e\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-0.16\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.52\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.05\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.18\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026epsilon;\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e1crit\u003c/strong\u003e\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-0.20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.43\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.21\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-0.21\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.84\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eF\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003emax\u003c/strong\u003e\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.45\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.55\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.21\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-0.26\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.21\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n 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align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026epsilon;\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e1crit\u003c/strong\u003e\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eF\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003emax\u003c/strong\u003e\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003edensity\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n 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align=\"left\"\u003e\n \u003cp\u003e0.37\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-0.26\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.49\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003ea\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003eFPZ\u003c/strong\u003e\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.13\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.19\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.50\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.49\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026epsilon;\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e1crit\u003c/strong\u003e\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-0.83\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-0.02\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e-0.59\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e-0.73\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-0.08\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003eF\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003emax\u003c/strong\u003e\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.60\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-0.07\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e-0.64\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cstrong\u003e-0.57\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.06\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n\u003c/div\u003e"},{"header":"4. Conclusions","content":"\u003cp\u003eThe paper focuses on detailed description of processes occuring in the FPZ region during crack propagation in Norway spruce wood in mode I. The FPZ was examined using the DIC method which showed to be a valuable means providing strains in contour plots around a crack. Uniqueness of the proposed solution lies in the simultaneous tracking and considering of cracks on both faces of a relatively wide specimen, which has not been published to date. We found relatively stable criterion for all studied anatomical directions (R, T and TR). For practical purposes for testing of big timber members (often in T and TR directions visible, R is hidden), one can consider the crack to be critically loaded when the strain criterion reaches the value 2.5e-3 (minimum of T and TR groups) and the distance of such a strain from the singularity/notch is 19.4 mm (similarly minimum of T and TR groups). Our results suggest that proposed criteria cannot be used in a quantile way since these quantile values are too low to be practically grasped. FPZ length showed to be even larger than expected and reaches the value of 38.4 mm in T, 30.1 in R and 36.3 mm in TR directions. Stress distribution is not so easy to assess, especially ahead of the crack tip, so it is not an easy task to evaluate the energy dissipated in this region.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eJ.K. did conceptualisation, idea, financial support, writing, data processing, data evaluation, programming. V.S.: writing and reviewing, J.J + M.H. + J.P. performed the experiments, M.K. prepared samples and chose the material\u003c/p\u003e\u003ch2\u003eAcknowledgments\u003c/h2\u003e \u003cp\u003eThis paper was created with financial support from a grant project of the Czech Science Foundation GACR No. 21-29389S \u0026ldquo;Experimental and numerical assessment of the bearing capacity of notches in timber beams at arbitrary locations using LEFM\u0026rdquo;. The authors gratefully acknowledge the provider.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eAicher, S., Reinhard, H.W., Ki, W., n.d. Nichtlineares Bruchmechanik-Malistabsgesetz fiir Fichte bei Zugbeanspruchung senkrecht zur Faserrichtung 1,2.\u003c/li\u003e\n\u003cli\u003eArdalany, M., Deam, B., Fragiacomo, M., 2012. Experimental results of fracture energy and fracture toughness of Radiata Pine laminated veneer lumber (LVL) in mode I (opening). 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Materials 12, 23. https://doi.org/10.3390/ma12010023\u003c/li\u003e\n\u003cli\u003eMorel, S., Bouchaud, E., Schmittbuhl, J., Valentin, G., 2002. [No title found]. International Journal of Fracture 114, 307\u0026ndash;325. https://doi.org/10.1023/A:1015727911242\u003c/li\u003e\n\u003cli\u003eMorel, S., Dourado, N., Valentin, G., 2005. Wood: a quasibrittle material R-curve behavior and peak load evaluation. Int J Fract 131, 385\u0026ndash;400. https://doi.org/10.1007/s10704-004-7513-0\u003c/li\u003e\n\u003cli\u003eMorel, S., Mourot, G., Schmittbuhl, J., 2003. Influence of the specimen geometry on R-curve behavior and roughening of fracture surfaces. International Journal of Fracture 121, 23\u0026ndash;42. https://doi.org/10.1023/A:1026221405998\u003c/li\u003e\n\u003cli\u003eMorel, S., Schmittbuhl, J., Bouchaud, E., Valentin, G., 2000. Scaling of Crack Surfaces and Implications for Fracture Mechanics. Phys. Rev. Lett. 85, 1678\u0026ndash;1681. https://doi.org/10.1103/PhysRevLett.85.1678\u003c/li\u003e\n\u003cli\u003eNT BUILD 422 (1993) Wood: Fracture energy in tension perpendicular to the grain. Nordtest Method, 11. Tekniikantie, Finland.\u003c/li\u003e\n\u003cli\u003eOstapska, K., Malo, K.A., 2020. Wedge splitting test of wood for fracture parameters estimation of Norway Spruce. Engineering Fracture Mechanics 232, 107024. https://doi.org/10.1016/j.engfracmech.2020.107024\u003c/li\u003e\n\u003cli\u003eOstapska, K., Malo, K.A., 2021. Calibration of a combined XFEM and mode I cohesive zone model based on DIC measurements of cracks in structural scale wood composites. Composites Science and Technology 201, 108503. https://doi.org/10.1016/j.compscitech.2020.108503\u003c/li\u003e\n\u003cli\u003ePetterson, R.W., Bodig, J., 1983.. Prediction of fracture toughness of conifers Journal of Wood and Fiber Science 15(4):302-316.\u003c/li\u003e\n\u003cli\u003ePhan, N.A., Chaplain, M., Morel, S. \u003cem\u003eet al.\u003c/em\u003e Influence of moisture content on mode I fracture process of \u003cem\u003ePinus pinaster\u003c/em\u003e: evolution of micro-cracking and crack-bridging energies highlighted by bilinear softening in cohesive zone model. \u003cem\u003eWood Sci Technol\u003c/em\u003e 51, 1051\u0026ndash;1066 (2017). https://doi.org/10.1007/s00226-017-0907-8\u003c/li\u003e\n\u003cli\u003eReiterer, A., Stanzl-Tschegg, S.E., Tschegg, E.K., 2000. Mode I fracture and acoustic emission of softwood and hardwood. Wood Science and Technology 34, 417\u0026ndash;430. https://doi.org/10.1007/s002260000056\u003c/li\u003e\n\u003cli\u003eRomanowicz M., Numerical assessment of the apparent fracture process zone length in wood under mode I condition using cohesive elements, Theoretical and Applied Fracture Mechanics, Volume 118, 2022, 103229, ISSN 0167-8442, https://doi.org/10.1016/j.tafmec.2021.103229.\u003c/li\u003e\n\u003cli\u003eStanzl-Tschegg, Stefanie E., Tan, D.-M., Tschegg, E., 1995. New splitting method for wood fracture characterization. Wood Sci.Technol. 29. https://doi.org/10.1007/BF00196930\u003c/li\u003e\n\u003cli\u003eTan, D.M., Stanzl-Tschegg, S.E., Tschegg, E.K., 1995. Models of wood fracture in Mode I and Mode II. Holz als Roh-und Werkstoff 53, 159\u0026ndash;164. https://doi.org/10.1007/BF02716417\u003c/li\u003e\n\u003cli\u003eTurner, DZ, Digital Image Correlation Engine (DICe) Reference Manual, Sandia Report, SAND2015-10606 O, 2015.\u003c/li\u003e\n\u003cli\u003eXavier, J., Monteiro, P., Morais, J.J.L., Dourado, N., de Moura, M.F.S.F., 2014a. Moisture content effect on the fracture characterisation of Pinus pinaster under mode I. J Mater Sci 49, 7371\u0026ndash;7381. https://doi.org/10.1007/s10853-014-8375-0\u003c/li\u003e\n\u003cli\u003eXavier, J., Oliveira, M., Monteiro, P., Morais, J.J.L., de Moura, M.F.S.F., 2014b. Direct Evaluation of Cohesive Law in Mode I of Pinus pinaster by Digital Image Correlation. Exp Mech. https://doi.org/10.1007/s11340-013-9838-y\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"fracture, strain energy release rate, spruce, mode I, digital image correlation, crack","lastPublishedDoi":"10.21203/rs.3.rs-3962450/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3962450/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe paper focuses on assessment and utilization of strain-based criterion obtained using the digital image correlation in characterization of fracture behavior of Norway spruce wood. The study employed a single-edge notched beam loaded in three-point bending (SEN-TPB) to examine mode I at three anatomical directions of crack propagation (radial, tangential, tangential-radial - R, T and TR). The criterion is evaluated at the maximal load (F\u003csub\u003emax\u003c/sub\u003e), where the compliance-based beam method (CBBM) provides critical strain energy (G\u003csub\u003ec\u003c/sub\u003e), which ensures the proper criteria representing equivalent crack length growth is described. The novel approach also enables one to determine the fracture process zone (FPZ) length using an algorithm which finds the onset of the nonlinear region. Uniqueness of the approach lies in processing a big set of optical data and simultaneous tracking of crack length on both sides of medium-size specimens. Results indicate that crack length is dependent on the anatomical direction, for instance in T direction the criterion ε\u003csub\u003e1crit\u003c/sub\u003e is 2.5e-3 producing crack length equal to a\u003csub\u003ec\u003c/sub\u003e =23.9 mm, whilst in R direction, the ε\u003csub\u003e1crit\u003c/sub\u003e is least and equals 1.3e-3 producing crack length of 22.1 mm. The highest ε\u003csub\u003e1crit\u003c/sub\u003e is attained in TR (on average ε\u003csub\u003e1crit\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;3.4e-3) and distance from the place where the crack started is 19.4 mm. Size of the non-linear region here attributed to FPZ length reaches the value of 38.4 mm in T, 30.1 mm in R and 36.3 mm in TR directions, respectively. The study presents a novel approach in characterization of fracture properties by coupling optical and energetical data and may find its usage in evaluation of other fracture modes.\u003c/p\u003e","manuscriptTitle":"Strain-based approach to characterize mode I crack propagation in Norway Spruce directly from optical data","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-02-20 18:59:07","doi":"10.21203/rs.3.rs-3962450/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"100ec0c4-f177-4896-a630-611a2a74905f","owner":[],"postedDate":"February 20th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-02-23T02:48:59+00:00","versionOfRecord":[],"versionCreatedAt":"2024-02-20 18:59:07","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-3962450","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3962450","identity":"rs-3962450","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}