Since the primary focus of this paper is on the identification of the yield point on the stress-strain curve influenced by a significant change in microstructural behavior, only the linear-elastic and plateau region on the stress-strain curve for wood under compression are of interest here.
The typical enlarged stress-strain curves with up to 20% compressive strain, including the full linear-elastic region and beginning of inelastic-plateau region for the jack pine and balsam poplar specimens at a certain condition are shown in Figs. 2 and 3.
As indicated with points A and B in Figs. 2 and 3 respectively, there is an initial low stiffness region at the beginning of each stress-strain curve. This low stiffness region can be attributed to the initial seating of the specimen in the test apparatus due to the unavoidable micro-surface irregularity on the specimen surface that is in contact with the loading platens (Erickson, 1955). When a specimen was placed in the compression module, there were only a few contact spots between the surface of a specimen and the loading platens initially. Therefore, the deformation of the specimen increased rapidly with even a small increase in applied load. As compression load increased further, a larger area of the specimen surface came to contact with the loading platens leading to a stiffer response, until the total surface of a specimen came to contact with the loading platens. At this point, the stress-strain response started to follow a linear trend, until the yield point. Since the initial low stiffness region is related to the surface roughness of the specimen, rather than a true mechanical response of the material, this region is generally ignored in the determination of the values of MOE for wood specimens under compression.
Typical stress-strain curves for jack pine and balsam poplar wood specimens compressed at a certain condition are shown in Figs. 5 and 6, respectively. To better explain the phenomena observed, Figs. 7, 8, 9 and 10 present photographs indicating the cellular-structural changes at different compressive stages for the two species tested. In these figures, the letter on the right lower corner of the photograph (O, P, Q, R, S, T, U, or V) refers to the deformation or failure of cell walls that corresponds to its compressive stage represented by the same letter on the stress-strain curve in Figs. 5 and 6.
Figure 5. Typical stress-strain curve for a jack pine wood in radial compression at moisture content = 12% and T = 90 ℃.
Figure 6. Typical stress-strain curve for a balsam poplar wood in radial compression at moisture content = 12% and T = 90 ℃.
Figure 7. Wood cells before (O) and after (P) cell wall collapse for a jack pine (Loading direction is left-right; Magnification: 80×).
Figure 8. Deformation and failure process of wood cells in earlywood for a jack pine wood (Loading direction is left-right; Magnification: 80×).
Figure 9. Structural changes in the first vessel elements before (S) and after (T) collapse for a balsam poplar wood (Loading direction is left-right; Magnification: 80×).
First failure of wood cells. Fig. 7-O shows the image indicating the shape and position of a row of seven wood cells (A, B, C, D, E, F, and G) in the earlywood near the boundary with the latewood of the previous year before failure, while Fig. 7-P presents anther one showing the onset of the failure of the same row of seven wood cells (a, b, c, d, e, f, and g) due to cell wall collapse. After reviewing the recorded images, the major deformation of wood cells in the linear-elastic region was found to occur in the thin-walled earlywood cells. With an increase in applied load, the radial cell walls were bent into their cell lumens. The magnitude of deformation on these radial cell walls was not uniform in the earlywood section. The most deformed cells were found to occur in the first cell row at earlywood layer, which is located in the new annual ring. However, this earlywood cell row is connected directly to the last row of the latewood layer in another old annual ring. It was observed that the first earlywood layer generally has the larger cell lumens and the thinnest cell wall thickness, which can be considered as the weakest location in the earlywood section during compression test, as shown in Fig. 7-O. In contrast, the thick-walled latewood cells did not appear to deform during the elastic compression stage. With an increase in compressive load, the most deformed wood cells in this earlywood layer started to fail first, as shown in Fig. 7-P. Most importantly, the occurrence on the first failure of these wood cells was observed to coincide with the turning point (yield point) in the transition zone between linear-elastic and non-elastic region, as indicated as the point P on the stress-strain curve in Fig. 5.
Apart from the thinner tracheid cell wall in the earlywood cell row, the first failure location in jack pine can also be explained by the "boundary effect" caused during compression. The transition between earlywood and latewood is abrupt meaning that there is a sudden change in material mechanical properties going from earlywood (lower-density section) to latewood (higher- density section). From the viewpoint of the material science, when two types of materials with distinctly different mechanical properties are bonded together, high stress concentration occurs at the boundary where the composite is under stress, resulting in the first failure occurring to the material with lower density.
The appearance of the first failure of wood cells on the weakest row of earlywood tracheids was also observed by others (Bodig, 1965; Ando and Onda, 1999; Tabarsa and Chui, 2000), despite in different location (cell row) from the beginning of the growth ring due to a variety of softwood resources selected from different studies. In addition, Kunesh (1961) reported that the main cause of failure of the compressed specimens from softwoods was due to buckling of the rays, by investigating the mechanical behavior of Douglas fir (Pseudotsuga menziesii) and western hemlock (Tsuga heterophylla) in radial compression. However, it was observed from this study that the uniseriate rays in test jack pine specimens began to deform and then fail simultaneously with the weakest tracheid cell walls in the earlywood cell row. These very fine rays did not act as spaced columns in support of compressive load. This finding is different from the observation results reported by Kunesh (1961). It should be noted that Kunesh's conclusion was not based on real-time observation of micro-structural deformation during compression test. Rather it was based on microscopic examination of failed specimens after the test. Because of this, it was not possible for him to identify the first failure of the cellular structure that preceded the buckling of ray cells.
Progressive failure of wood cells. After failure of the first earlywood layer, the earlywood cell-layer next to the first failed layer started to fail one after another gradually along the direction to latewood section, as shown in Fig. 8-Q.
This progressive failure of earlywood cell rows continued until all the earlywood cells collapsed, as indicated in Fig. 8-R. The region between points Q and R on the stress-strain curve corresponds to the plateau region (Fig. 5). It follows that the length of the plateau region is directly proportional to the ratio of the earlywood width to growth ring width. However, Ando and Onda (1999), who studied the microscopic deformation behavior for three softwoods: hinoki, sugi and kuromatsu, under radial compression, reported that failures could started to occur in cell-layers to both sides of the first failed cell-layer, and subsequent failures continued to earlywood cell-layers along two opposite directions to earlywood and latewood section until all the earlywood cells failed. The softwoods with different cellular structure used by Ando and Onda (1999), which caused the first failed cell-layer occurring in different location on earlywood layer, was thought to be the reason for different phenomena on progressive failure of wood cells in earlywood section. Because the collapse of the cell wall is related to an instability problem in material mechanics, which explains the flat plateau region whereby there was only a slight increase in stress over a large deformation region. After all the radial walls of earlywood tracheid are buckled and collapsed, resulting in the removal of the cell lumens and likely wall cavities, the cell wall substance was densified. This signifies the start of the densification region on the stress-strain curve, in which the stress increases rapidly with increasing strain.
First failure of wood cells. Fig. 9-S presents an image indicating the cellular structure and position of six vessels (A, B, C, D, E, and F) before failure, while Fig. 9-T shows another one that corresponds to the onset of failure of the same six vessels (a, b, c, d, e, and f). The examination of the recorded images during compression test, the deformation during the elastic region was found to occur primarily in the vessels (Fig. 9-S). With increasing compression, deformation in these vessels increased eventually leading to collapse of the vessels. However, deformation was hardly observed in the fibres which have small lumen and thick walls. For the balsam poplar specimens, first failure occurred generally at vessels with large diameter, and could be located anywhere within a growth ring. Similar to the jack pine specimens, the occurrence of the first failure of vessels in Fig. 9-T was found to correspond to a transition point T between elastic and plateau regions on the stress-strain curve in Fig. 6. The first failure occurred in a balsam poplar specimen could be attributed to its inherent anatomical features and structure. As a diffuse-porous hardwood species, balsam poplar wood contains vessels evenly distributed over the structure of balsam poplar. The diameter of a vessel is approximately 7-8 times larger than that of a fiber. This explains the location of first failure at large diameter vessels in balsam poplar. In addition, it was found that uniseriate rays in the earlywood layer deformed and failed together with the vessels during radial compression.
Progressive failure of wood cells. Following the failure of the weakest vessels, it was found that subsequent failure occurred in other vessels that were not necessarily close to the first failed vessels, as indicated by the arrows in Fig. 10-U. Further application of compressive load led to more vessel failure as shown in Fig. 10-V. This observed phenomenon can be explained by the unique anatomical feature of balsam poplar, with all vessels having similar diameter and uniformly distributed within a growth ring. With the progressive compression, some of vessel cavities were found to be removed gradually. When all of the vessel cavities were removed, this point corresponded to the start of densification region at the stress-strain curve, as shown in Fig. 6. Because of the limitations of the observation techniques used in this study, the deformation and failure occurred to fibres around vessels could not be observed after compression level reached the densification region of the stress-strain curve. This behavior is different from jack pine which is a softwood species with abrupt earlywood/latewood transition, and as a result collapse of cellular structure is progressive from first cell row in the earlywood towards the latewood of the same ring, as shown in Fig. 8.
As stated above, the identification of yield point on the compression stress-strain curve cannot be achieved solely from the examination of the stress-strain data. The finding from this study clearly shows that the yield point is related to the onset of first collapse of wood cell under compression. Therefore, with the use of on-line monitoring of micro-structural deformation behavior of the cellular structure in conjunction with a mechanical test arrangement whereby the load and deformation are recorded, it is possible to accurately locate the yield point on the stress-strain curve. Once the yield point (including yield stress: σy and yield strain: εy) for a tested specimen is located on the compression stress-strain curve, its correspondent MOE value can be determined by computing the slope of the linear part of a line below the yield point on the stress-strain curve (MOE = tan α = σy/εy), which is illustrated and described in Fig. 1. By using the proposed technique, the yield point and MOE values of the five Jack pine and five balsam poplar specimens were tested and estimated. The determined results on the yield stress and MOE values for each of the jack pine and balsam poplar specimens are presented in Fig. 11, Fig. 12.
From Fig. 12, it can be noticed that a sudden-drop (load inflection drop) right after the yield point was found on each of the stress-strain curves for balsam poplar specimens. The "load inflection drop" occurrence on the stress-strain curve for balsam poplar specimens could be explained as follows. After examination of the video made by recorded images, it was found that the first failure occurred generally at vessels with large diameter, resulting in the appearance of the yield point at stress-strain curve. After almost all of the large-diameter vessels failed, other medium-diameter vessels began to fail, thereby causing the "load- inflection drop" appearance on the stress-strain curve. Once all of the large- and medium- diameter vessels failed completely, the load-inflection drop stopped and the load-increase appeared on the stress-strain curve.
Table 1 summarizes the mean values for the yield stress and MOE values for the two species tested. As shown in Table 1, it was found that jack pine wood had lower mean yield stress (3.45 MPa) and MOE (48.32 MPa) than balsam poplar wood (yield stress of 4.17 MPa and MOE of 58.25 MPa). This can be attributed to the structural differences in the first failed wood cell layer between jack pine and balsam poplar. For jack pine, the first failed wood layer was found to be on the earlywood cell layer made up of the rather thin cell walls, which can only withstand lower external load. In addition, the fine and uniseriate rays in jack pine specimens are not sufficiently strong to support the compressive load applied in radial direction.
Tested species σy (MPa) MOE (MPa) Mean SD Mean SD Jack pine 3.45 0.18 48.32 2.53 Balsam poplar 4.17 0.20 58.25 3.17 Notes: SD, standard deviation; MOE, modulus of elasticity.
Table 1. Means of yield stress (σy) and MOE for two tested species.