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In-plane mechanical properties of birch plywood are experimentally determined.•
An exhaustive dataset on strength and elastic properties of birch plywood in tension, compression, and shear has been established.•
High load-to-face-grain angle dependency is observed for each property.•
Analytical models that show sufficient closeness to the test data are suggested.
Abstract
There is an increasing demand for engineered wood products in modern structures. Birch plywood is promising in structural applications, due to the combined advantages of its superior mechanical properties and the cross lamination configuration. However, the off-axis mechanical properties of birch plywood have not been thoroughly investigated. The aim of this paper is to establish a comprehensive experimental dataset that could serve as the input in the analytical or numerical models to design birch plywood under various load conditions. Specifically, tensile, compressive and shear tests were conducted under five different angles to the face grain, i.e., from 0° (parallel) to 90° (perpendicular) to the face grain, with an interval of 22.5°. The stress–strain relationships, failure modes, strength and elastic properties of birch plywood are highly dependent on the load-to-face-grain angle. The strength and the elastic properties are also predicted by various analytical and empirical models. Parametric analyses are performed to study the influence of the interaction coefficient F12 in Tsai-Wu failure criterion and the Poisson’s ratio νxy in the transformation model on the predicted strength and modulus respectively. Lastly, the possibilities of predicting the on-axis shear modulus based on the off-axis uniaxial tests are discussed in this paper.
Keywords
Birch plywoodMechanical propertiesLoad-to-face-grain angleFailure criteriaAnalytical models
1. Introduction
The history of using timber for load-bearing structural purposes can be traced back to the Neolithic age [1]. However, only recently, during the 20th century, have engineered wood products (EWPs) been introduced in the marketplace [2]. The fundamental merits of the EWPs compared to the sawn timber from the structural perspective comprise the decreased variability (e.g., more homogeneous mechanical properties and higher dimensional stability), the possibility to break through the dimensional limitation caused by the normal size of the trees, the redistributed natural defects and the utilization of residuals [3], [4]. As a result, the continuous invention of various types of EWPs and the development of advanced technology bring significant potential to the design and construction of modern timber structures.
Plywood, as one of the earliest produced EWPs, is composed of an uneven number of thin veneers (also called plies), normally with the thickness from less than one millimeter to several millimeters, bonded together with an adhesive and with the grain direction of adjacent veneers perpendicular to one another [5].
The first construction plywood was made of 3-ply Douglas Fir (Pseudotsuga menziesii), displayed at the Lewis and Clark Exposition of the World’s Fair in 1905. In the next three decades, the application of structural plywood spread widely to the fields of building construction and transportation industry (see Fig. 1a [6]). Until the 1920 s, the adhesives in use to bond each layer of veneer were basically from animal, casein, starch and soybean. They were not waterproof (the glue made from soybean meal and protein was water-resistant to some extent but not waterproof) and therefore only had good reputations in interior application [7], [8], [9]. The emergence of synthetic waterproof adhesive in 1934 was the other breakthrough with great influence after the rotary lathe, leading to the further expansion of the applications of plywood and the rapid development of the relevant industries [10]. One of the most famous plywood products during World War II was the British de Havilland Mosquito (DH-98) as shown in Fig. 1b [11]. After World War II, the production of plywood increased remarkably due to the continuous advancement of technology and the growing demand from the industries. For instance, plywood has been commonly applied in building construction systems, e.g., sub-flooring, decking, sheathing, bracing, etc., and beam system [12], e.g., webs in I-beam or box beam, etc.
In the field of timber connections, although one of the typically adopted techniques is to fit slotted-in steel plates in pre-cut timber members and then connect both timber and steel by mechanical fasteners, plywood plate is suitable to be applied in the connection system as well. Plywood, as a gusset plate in timber-to-timber connection, could resist multiple types of stresses acting in different directions due to its cross lamination configuration [13]. Moreover, compared to the steel plate, plywood is considered to be more environmental-friendly, cost-efficient and less prefabrication demanding. During the 1980 s, plywood made of Douglas Fir was studied as the gusset plate in the roof truss system (Fig. 1c) [14], [15], [16]. More recently, birch (Betula pendula) plywood was experimentally investigated for the potential application in connections (e.g., roof and beam-to-column connections in Fig. 1d and 1e) [17], [18], [19].
Birch has wide natural distribution on the Eurasian continent, especially in northern Europe. It makes up 11% to 28% of the total volume of the standing crop in the Nordic and Baltic countries [20]. This type of hardwood is not significantly different from other hardwood species such as beech (Fagus sylvatica) and oak (Quercus robur), but is superior to most softwood in terms of physical and mechanical properties [21]. Tensile properties of the birch ply have been characterized by several researchers [22], [23], [24]. It is indicated that, for the individual birch ply, the tensile strength parallel to the grain is more than 100 MPa. In spite of that, birch plywood is rarely used in structural engineering applications and only the mechanical properties parallel and perpendicular to the face grain of birch plywood are partially available in the literature [25], [26].
The in-plane off-axis mechanical properties of plywood made of some other species were studied in the past few decades. Norris [27] carried out the experimental tests to study the load-to-grain angle dependency on the strength and stiffness of yellow-poplar (Liriodendron tulipifera) plywood. He also proposed a quadratic failure criterion to predict the strength properties at varying angles to the face grain. This failure criterion was further employed by Bier [28] to make comparison with the experimental tensile and bending strength data of pinus radiata (Pinus insignis) plywood. Popovska et al. [29] conducted tension tests on beech plywood with different cross-sectional patterns. The test results are highly related to both the face grain angle and the composition of plywood. In addition, Yang et al. [30] performed the failure analysis of laminated bamboo with bidirectional fibers by off-axis tension tests.
This paper aims to establish a comprehensive experimental dataset of the in-plane mechanical properties of birch plywood, which could serve to implement analytical or numerical models for design purposes. More specifically, tension, compression and shear tests were conducted in this study under five different angles to the face grain, i.e., from 0° (parallel) to 90° (perpendicular) to the face grain, with an interval of 22.5°. Failure modes, stress–strain relationships, the mean and characteristic strength, elastic modulus and shear modulus were analyzed. Moreover, analytical and empirical models were employed to predict the strength and the elastic properties. The applicability of each model was also assessed by comparing the predicted values with the experimental data.
2. Materials and methods
2.1. Materials
The studied birch plywood is the commercial product produced by Koskisen (Järvelä, Finland). It is composed of 15 veneers with the nominal thickness of 21 mm. The inner 13 veneers have the identical thickness while the face veneers are slightly thinner due to the fact that the surfaces of the plywood were sanded during the panel processing in the production line for the control of the total thickness. Phenol formaldehyde resin was used as adhesive between each veneer. Five different loading angles to the face grain were tested in tension, compression and shear, with the interval of 22.5°, i.e., 0°, 22.5°, 45°, 67.5° and 90°, and with 12 replicates for each test group. In total, 180 specimens were cut from six plywood panels from different batches. Each plywood panel is 1500 mm by 3000 mm. The cutting plan of the specimens from one birch plywood panel is shown in Fig. 2. All the tests were performed in the universal testing machine (MTS 810) with the load cell capacity of 100 kN. Before the tests, the specimens were conditioned in the climate chamber (Binder MKFT 240) under the temperature of 20 °C and the relative humidity (RH) of 65% until the mass equilibrium was reached. Moisture content (MC) was measured on 12 birch plywood samples with similar mass to the tested specimens, by using the oven-dry method, described in EN 322 [31], after the conditioning. The mean MC was determined to be 11.9% (the coefficient of variation (COV), which is defined as the ratio of the standard deviation to the mean value, equals 2.2%).
2.2. Experimental procedure
2.2.1. Tension
Several standards give guidance on how to conduct tensile tests, i.e., ASTM D3500, EN 789 and AS/NZS 2269 [32], [33], [34]. These standards have slightly different requirements in terms of the specimen shape and size. Some scholars conducted plywood tensile tests based on these standards or other wood-related standards but with the dimension of their specimens modified depending on their specific aims of study [27], [29], [30], [35]. In this paper, the dumbbell-shaped specimens were prepared based on the standard ASTM D3500 [32], with adapted dimensions, i.e., the length 400 mm, the width 48 mm and the reduced width in the middle section 25 mm. The principal idea is to avoid failure in the zone of the specimens between the grips. The shape and dimension are constant for all the tensile specimens.
After the conditioning, the specimens were installed to the universal testing machine by a pair of grips (100kN-capacity wedge grip THS527-100) and a set of pyramid surface jaws (THS527-100-BP28). The loading head motion was constant with the rate of 0.9 mm/min throughout the tests so that the specimens broke within 3–10 min after the initiation of loading. The load was measured by the load cell while the strain in the area with reduced width was measured by two 38-mm long strain gauges attached on the side surfaces of the specimen. Both strain gauges were positioned along the loading direction and symmetrical with respect to the in-plane biaxial central lines. The data from the load cell and the strain gauges were transmitted to the electronic equipment simultaneously and post-processed for further analysis. See Fig. 3a for the tensile test setup and the detailed information regarding the tensile specimens.
The tensile strength of the test piece is defined as the maximum force during the loading over the area of the reduced cross section. The tensile elastic modulus is calculated as the slope of the linear portion of the stress–strain curve belonged to the elastic part, as illustrated in Eq. (1).(1)Et=σtεt=ΔF/AtΔu/l1
where Et is the tensile elastic modulus;σt is the tensile stress; εt is the tensile strain; ΔF is the increment of the load between 15% and 35% of the maximum force; Δu is the increment of strain measured from the strain gauges corresponding to ΔF; l1 is the original length of strain gauge; and At is the cross-sectional area with reduced width.
2.2.2. Compression
The conduction of the compressive tests followed the instruction of the standard ASTM D3501 [36] method A for small specimens. Here, the width and the length of the plywood specimen loaded in compression were chosen to be 50 mm and 100 mm respectively. The end surfaces were sanded to be smooth, thereby reducing the friction on the contact surface. Meanwhile, it is of importance to make sure that the end surfaces are parallel with each other and they are at right angles to the length direction.
Prior to the test when the conditioning was completed, density was measured for each compressive specimen, with the mean value of 693.0 kg/m3 (COV = 2.0%). These values are assumed to be representative for all the birch plywood specimens including tensile and shear specimens, considering the difficulties in evaluating the volume with irregular shapes. Moreover, compressive tests were carried out at a constant loading rate of 0.3 mm/min. One spherical seat platen was connected to the loading head and two strain gauges were centered on the side surfaces (see Fig. 3b). The compressive strength and elastic modulus of the test piece are defined similar to the tensile strength and elastic modulus.
2.2.3. Shear
The shear property investigated in this study indicates the panel shear (or edgewise shear), with its normal direction perpendicular to the plywood panel. Panel shear tests have been conducted on solid wood or EWPs by using a wide range of test methods, e.g., two-rail test, bending test and V-notched beam test (also known as the Iosipescu and Arcan methods), etc [33], [37], [38], [39], [40], [41], [43], [44]. Among them, the two-rail test seems to be the most standardized test method, described in the standards EN 789, ASTM D1037, ASTM D2719 with different specifications of the sizes [33], [37], [38]. By conducting the two-rail test, the specimen is clamped by two pairs of rails made of either lumber or steel, either by a suitable adhesive or mechanical connectors, through the long edges. Then the specimen is loaded via the rails. The center shear area is subjected to almost constant shear stresses. Bending tests, e.g., asymmetric four-point bending test, are commonly employed for the determination of panel shear properties as well [39], [40], [41]. However, even though the bending stress could be minimized by adjusting both the shape and the loading of the specimen, the bending stress can be barely perfectly excluded. Another challenge is that the height-to-span ratio should be sufficiently large in order to ensure the shear failure takes place prior to the bending failure, especially for birch plywood with its relatively high ratio between the shear and bending stresses. In addition, the V-notched beam method is mentioned in the standard for composite materials [42] and has been utilized in the field of timber engineering. This method was compared with other shear test methods by some researchers [41], [43], [44].
Here in this study, the two-rail test method was chosen because it is the standardized test method for wood-based panels [33], [37], [38]. The shear specimen was mechanically connected to two pairs of L-shaped steel rails along the long edges by four bolts with a diameter of 8 mm on each side. The short edges were neither loaded nor restrained. The grips were connected to the steel plates and then pulled by the universal testing machine at the constant rate of 0.6 mm/min. The length and the width of the shear specimen are 250 mm and 110 mm respectively. The loading angle to the face grain of the shear specimen was always organized in the way that the face veneer would be subjected to tensile stress, which is illustrated in Fig. 4c. It is worth noting that the geometry of the shear test specimen was designed with a reduced length in the middle (30 mm) to lower the capacity and induce shear failure in the central area. The reduced length was produced by cutting two slits along the center line in the length direction. To prevent the premature crack initiated due to the stress concentration on edges, round holes with a diameter of 6 mm were drilled at the end of the slits.
38 mm-long strain gauges were attached to the shear specimen at 45°to the loading axis. However, the shear deformation may not be uniformly distributed within the area of the attached strain gauges but be concentrated in the vicinity of the central line. Thus, the combination of the 38 mm-long strain gauge and the designed geometry would underrate the shear strain, thereby overestimating the shear modulus. Consequently, to compensate for the aforementioned effects, non-destructive tests were performed on homogenous birch plywood samples without slits, at 0°, 45° and 90°, with 5 replicates for each angle, so as to derive the correction factor for the shear modulus. See Fig. 3c for the shear test setup and the detailed information regarding the shear specimens.
The shear strength is defined as the maximum applied force divided by the contact area between the vertical slots. The shear modulus derived from the destructive tests is shown in Eq. (2).(2)Gdestructive=τγ=ΔF/lr∙t2Δu∙/l1
where Gdestructive is the shear modulus derived from the destructive tests; τ is the shear stress; γ is the shear strain; ΔF is the increment of the load between 15% and 35% of the maximum force; lr is the reduced length; t is the thickness of the specimen; Δu is the increment of deformation measured from the strain gauges corresponding to ΔF; and l1 is the length of the strain gauge; The shear modulus derived from the non-destructive tests is shown in Eq. (3).(3)Gnon-destructive=ΔF/l∙t2Δu/l1
where Gnon-destructive is the shear modulus derived from the non-destructive tests; ΔF is the increment of the load in the linear portion; l is the length of the specimen; and Δu is the increment of deformation measured from the strain gauges corresponding to ΔF. Correction factor is defined as the mean ratio between the shear modulus measured from the non-destructive tests and the destructive tests at 0°, 45° and 90°, as expressed in Eq. (4).(4)γcorrection=13∑θ=0°,45°,90°Gnon-destructive,θGdestructive,θ
where γcorrection is the correction factor; Gnon-destructive,θ and Gdestructive,θ are the mean shear modulus at an angle θ to the face grain, derived from the non-destructive tests and the destructive tests respectively. The modified shear modulus Gmodified is shown in Eq. (5).(5)Gmodified=γcorrection∙Gdestructive
2.2.4. Derivation of the characteristic values
The mechanical properties mentioned in Section 2.2 involve the tensile and compressive strength and elastic modulus, and the panel shear strength and modulus. The 5th percentile characteristic values of these properties were derived from the mean values. Student’s t-distribution was assumed based on the consideration of small sample size, i.e., 12 replicates for each test group.
2.3. Numerical analysis on the configuration of shear specimens
In this paper, the distribution of the shear strain in the vicinity of the central line is also numerically investigated. Finite element analyses were performed via commercial FEM package Abaqus (Simulia, USA). Both the specimens with slits in the destructive tests and without slits in the non-destructive tests were studied at 0°, 45° and 90° to the face grain. The shear specimen and the steel rails were modeled as 3D deformable shell and solid elements, respectively.
The isotropic elastic material properties were assigned to the steel rail. Birch plywood is characterized as an orthotropic material. The properties assigned to birch plywood contain the density (ρ), the elastic modulus (Eij), the Poisson’s ratio (νij) and the shear modulus (Gij) (see Table 1).
Table 1. Material properties of birch plywood for numerical analysis.
| ρ(kg/m3) | Exx(MPa) | Eyy(MPa) | Ezz(MPa) | νxy |
|---|---|---|---|---|
| 693 | 9400 | 6700 | 1110 | 0.034 |
| νxz | νyz | Gxy(MPa) | Gxz(MPa) | Gyz(MPa) |
| 0.431 | 0.439 | 610 | 206 | 186 |
Note: subscripts i, j = x, y, z used in Table 1, stand for the principal material directions. Axis × and y are parallel and perpendicular to the face grain, while axis z is through the thickness. The density ρ and the shear modulus Gxy were from the experimental data. The elastic modulus Exx and Eyy were obtained from the tensile tests (see Table 5). Additionally, the Poisson’s ratios νij were derived based on the mechanical properties of birch and the cross-sectional pattern of plywood according to the Ref. [45]. The elastic modulus Ezz and the rolling shear modulus Gxz and Gyz were available in [25], [46].
Regarding the modeling details, the birch plywood was tied to the steel rails around the holes where bolts ought to be inserted as the simplification of the bolt connection. Load was applied on the holes on one side of the rail corresponding to 35% of the ultimate capacity assessed from the test results and the lateral deformation is limited. On the other side, both the translational and rotational constraints were assigned to the holes. The mesh element size was 4 mm and 2 mm for the steel rail and the birch plywood separately and it is refined around the holes and alone the slit edges with the element size of 1 mm.
2.4. Prediction of off-axis strength
For the off-axis loaded specimens, there is an angle θ between the loading axis and the face grain direction. The uniaxial stress in the 1–2 (parallel – perpendicular to the loading axis) coordinate system is transformed to the x-y (parallel – perpendicular to the face grain of the birch plywood) coordinate system, as shown in Fig. 4. The transformation equation between the off-axis stresses and the on-axis stresses is shown in Eq. (6).(6)σxσyτxy=m2&n2&2mnn2&m2&-2mn-mn&mn&m2-n2σ1σ2τ12
where m=cos(θ); n=sin(θ);θ is the angle between the load direction and the face grain; σ1, σ2 and τ12 are the off-axis stresses in the 1–2 system; and σx, σy and τxy are the on-axis stresses in the x-y system. σ1, σ2,σx and σy are defined as positive in tension and negative in compression while τ12 and τxy are positive with the direction shown in Fig. 4b and 4c. For the uniaxial tensile and compressive tests, when σ2=τ12=0, Eq. (6) is rewritten as Eq. (7).(7)σxσyτxy=m2n2-mnσ1
For the shear test, when σ1=σ2=0, Eq. (6) is rewritten as Eq. (8).(8)σxσyτxy=2mn-2mnm2-n2τ12
The stress transformation of the tensile, compressive and the shear specimens is illustrated in Fig. 4.
Having the principal stresses in the material coordinate system at hand, it is possible to employ the failure criteria to predict the off-axis strength based on the on-axis strength obtained from the experimental tests. Two linear and five quadratic failure criteria that are widely utilized for the composite materials are listed in Table 2.
Table 2. Failure criteria for the prediction of off-axis strength properties.
| Failure criteria | Formula | Eq |
|---|---|---|
| Hankinson | σxfx+σyfy=1 | (9) |
| Linear criterion with shear effect | σxfx+σyfy+τxyfxy=1 | (10) |
| Empirical Norris | σxfx2+σyfy2+τxyfxy2=1 | (11) |
| Theoretical Norris | σxfx2-σxσyfxfy+σyfy2+τxyfxy2=1orσxfx2=1orσyfy2=1 | (12) |
| Tsai-Hill | σxfx2-σxσyfx2+σyfy2+τxyfxy2=1 | (13) |
| Hoffman | σx2-σxσyfxcfxt+σy2fycfyt+fxc-fxtfxcfxtσx+fyc-fytfycfytσy+τxyfxy2=1 | (14) |
| Tsai-Wu | σx2fxcfxt+σy2fycfyt+2F12σxσy+fxc-fxtfxcfxtσx+fyc-fytfycfytσy+τxyfxy2=1 | (15) |
It is noted that, in Table 2, σx and σy are the stresses parallel and perpendicular to the face grain. fx and fy are the mean strengths parallel and perpendicular to the face grain. For the prediction of the off-axis tensile strength, fx (fxt) and fy (fyt) are the mean tensile strengths tested from the specimens loaded 0° and 90° to the face grain. The prediction of the off-axis compressive strength is based on the mean on-axis compressive strengths fx (fxc) and fy (fyc) instead.τxy is the on-axis shear stress of the specimen while fxy is the mean panel shear strength when the specimens are loaded at 0° and 90° to the face grain. In Eq. (15), F12 is the interaction coefficient.
Hankinson’s failure criterion (Eq. (9)) [47] is used in EN 1995–1-1 (Eurocode 5) [48] but applied to solid timber, glulam or other engineered wood products whose grain runs essentially in one direction. The applicability of this equation on cross-laminated products, e.g., plywood, was examined in this paper.
Compared to the Hankinson’s failure criterion, linear criterion with shear effect is in the linear format as well, but takes the shear effect into consideration. Nevertheless, both linear models could only predict the off-axis tensile and compressive strength but not the shear strength. This is due to the fact that the Hankinson’s criterion does not consider the shear contribution while the term including the shear effect is only in the first order for the latter linear criterion.
Empirical Norris failure criterion is simplest quadratic failure criterion taking normal and shear stresses into account, provided by Norris [27]. This criterion was suggested for the design of aircraft structures made of plywood [49].
The theoretical Norris failure criterion is composed of two parts. The first part is a quadratic equation with the interaction of two normal stresses and the rest are the boundary conditions. Norris [27] applied the Von Mises theory to orthotropic materials under the plane stress condition. This adaptation results in the quadratic equation in Eq. (12) if the plane x-y is chosen.
Azzi and Tsai [51] adapted Hill’s theory [50] for plane stress and transversal isotropic material, which is expressed in Eq. (13), called Tsai-Hill failure criterion. Compared to the theoretical Norris failure criterion, Tsai-Hill failure criterion does not distinguish the normal strengths parallel and perpendicular to the grain in the coupling term.
Hoffman [52] added the linear terms as the odd functions in Hill’s equation to differ tension and compression, as shown in Eq. (14). He also verified this criterion by conducting unidirectional tests on fiber-reinforced composite materials.
In Tsai-Wu failure criterion (Eq. (15)) [53], the interaction coefficient F12 is unknown due to the complexity in experimentally determining this value for different types of materials. However, certain stability conditions are associated with the strength tensors and the magnitude of F12 is constrained by the inequality Eq. (16).(16)-1fxcfxtfycfyt≤F12≤1fxcfxtfycfyt
0 was firstly assigned to F12 to compare with the experimental data and other failure criteria. Sensitivity analyses were performed in Section 3.5 to investigate the influence of this parameter on the predicted strength.
It is noticed in Fig. 4c that the uniaxial shear force was applied in the direction that the specimen was subjected to the tensile force parallel to the face grain and the compressive force perpendicular to the face grain. Therefore, fx (fxt) and fy (fyc) ought to be substituted into the empirical Norris, theoretical Norris and Tsai-Hill failure criteria. Moreover, due to the existence of the linear terms in the Hoffman and Tsai-Wu failure criteria, two solutions would be obtained. Given the aforementioned definition of the shear stress, the positive solution should be taken as the off-axis panel shear strength.
In order to quantify the closeness of the predicted strength to the experimental data, the least squares analysis was carried out and the root mean square error (RMSE) was compared between each failure criterion. RMSE is described in Eq. (17).(17)RMSE=15∙∑θfθ,exp-fθ,pre2(θ=0°,22.5°,⋯,90°)
where fθ,exp is the strength obtained from the experimental tests at an angle θ to the face grain and fθ,pre is the strength predicted by utilizing the failure criteria. The failure criterion with the minimum RMSE is considered as the one fits the best to the test data.
2.5. Prediction of off-axis elastic modulus and shear modulus
2.5.1. Prediction of off-axis elastic modulus
Three models employed for the prediction of off-axis elastic modulus are displayed in Table 3.
Table 3. Off-axis elastic modulus prediction models.
| Off-axis elastic modulus prediction models | Formula | Eq |
|---|---|---|
| Hankinson | Eθ=Ex∙EyEy∙cos2θ+Ex∙sin2θ | (18) |
| Transformation model (elastic modulus) | 1Eθ=1Excos4θ+-2νxyEx+1Gxycos2θsin2θ+1Eysin4θ | (19) |
| Saliklis and Falk | 1Eθ=1Excos4θ+1A2AGxycos2θsin2θ+1Eysin4θ | (20) |
It is noted that, in Table 3, Eθ is the off-axis elastic modulus at an angle θ to the face grain; Ex and Ey are the elastic modulus parallel and perpendicular to the face grain.Gxy is the on-axis shear modulus; and νxy is the Poisson’s ratio in x-y plane, which is defined as the proportion of the strain in y-axis to the strain in x-axis in the same linear elastic range when the material is loaded in x-axis. The parameter A in the model proposed by Saliklis and Falk (Eq. (21)) is defined as the ratio between Ey and Ex.
An empirical method based on the Hankinson’s equation (Eq. (18)) was studied for the effectiveness on the prediction of off-axis elastic modulus of birch plywood.
The off-axis elastic modulus could also be theoretically derived based on the coordinate transformation of orthotropic elasticity relations (Eq. (19)) [54], [55].The Poisson’s ratio νxy in Eq. (19) was not tested in the paper and barely available in the literature. However, it could be possibly derived based on the mechanical properties of solid birch and the cross-sectional configuration of the plywood panels, as shown in Eq. (21) [45].(21)νxy=νLTETTETTa+ELTb
where νLT is the Poisson’s ratio of birch in the longitudinal-tangential plane; ET and EL are the elastic modulus of birch in the tangential and longitudinal direction, respectively; T, Ta and Tb are the thickness of birch plywood, the thickness of the veneers with the direction parallel and perpendicular to the face grain, respectively. νLT, ET and EL were found in the literature [46], which are 0.43, 0.62 GPa and 16.3 GPa, separately.
Saliklis and Falk [56] proposed a simplified model based on the transformation elastic modulus model (Eq. (19)) that they eliminated the need to experimentally determine the Poisson’s ratio, as shown in Eq. (20).
2.5.2. Prediction of off-axis shear modulus
Additionally, it is also possible to derive the off-axis shear modulus from the transformed constitutive equations [54], [55]. See Eq. (22) in Table 4.
Table 4. Off-axis shear modulus prediction models.
| Off-axis shear modulus prediction models | Formula | Eq |
|---|---|---|
| Transformation model (shear modulus) | 1Gθ=4(1Ex+1Ey-2-νxyEx)cos2θsin2θ+1Gxy(cos2θ-sin2θ)2 | (22) |
| Modified transformation model (shear modulus) | Gθ=Gxy∙G45Gxy∙sin22θ+G45∙cos22θ | (24) |
It is evident that the inputs of Eq. (22) contain the on-axis elastic modulus, shear modulus and the Poisson’s ratio. By assuming θ=45° in Eq. (22), Eq. (23) is derived.(23)1G45=1Ex+1Ey-2-νxyEx
Therefore, Eq. (22) can be rearranged by replacing the right part of Eq. (23) with its left part. The rearranged formula (Eq. (24)) is referred to the modified transformation model (shear modulus) in Table 4.
Here, the root mean square error (RMSE) was also calculated to evaluate each method mentioned in Section 2.5.
2.6. Prediction of on-axis shear modulus based on off-axis tensile or compressive tests
By rewriting Eq. (19), Eq. (25) provides one alternative method to predict the on-axis shear modulus based on the off-axis tensile or compressive elastic modulus, when there are difficulties performing shear tests directly.(25)1Gxy=1Eθ-1Excos4θ-1Eysin4θcos2θsin2θ+2νxyEx
In this study, the tensile or compressive elastic modulus at 22.5°, 45° and 67.5° would be substituted in Eq. (26) as Eθ, separately, to calculate the on-axis shear modulus and then compare with the test data.
3. Results and discussion
To analyze the load-to-grain angle dependency of the tensile, compressive and shear behavior of birch plywood, the specimens with five different angles from 0° to 90° with the interval of 22.5° to the face grain were tested. Each angle group has 12 replicates.
3.1. Failure mode analysis
Fig. 5a and 5b show the typical tensile failures at varying angles to the face grain on the plan view and side view respectively. The tensile specimens failed by the fracture of the veneers with the direction parallel to the loading axis and the separation of the veneers perpendicular to the loading direction simultaneously. For the specimens loaded 22.5°, 45° and 67.5° to the face grain, when the tensile strength was reached, the cracks occurred along the fiber in those veneers with the same direction as the face veneers. The cross veneers were, however, not torn out completely. Hence, the specimens loaded at 0° and 90° were completely torn apart during the test, while the ones loaded at other angles were not.
The compression failure with the fractured plane and side surfaces is shown in Fig. 5c and 5d. From the plan view in Fig. 5c, the horizontal ‘failure line’ for the birch plywood loaded parallel to the face grain and the shearing failure along the face grain for the birch plywood loaded at 22.5°, 45° and 67.5° are visible. For the specimen loaded perpendicular to the face grain, no clear sign of failure can be observed from the plane surface. From the side view in Fig. 5d, it is noticed that the specimens at 0° and 90° were slightly deformed through the thickness (out-of-plane) direction. For the specimen at 0°, the localized buckling of the veneers with the grain parallel to the loading axis resulted in the final failure on the plywood level. For the specimen at 90°, the local buckling took place in the inner veneers with the grain parallel to the loading axis. These inner veneers generated brace forces to the adjacent veneers in the out-of-plane direction. Hence, the specimens at 0° and 90° had severer local bending deformation but less visible crack on the plane. The deformation in the out-of-plane direction was less noticeable on the specimen at 22.5° and 67.5° while the specimen loaded at 45° was nearly straight during the whole loading history. The failure mode of the specimens at 22.5°, 45° and 67.5° is classified as shearing failure along the face grain [57].
In terms of the shear failure modes, it is clearly seen in Fig. 5e that the specimen at 0° failed with the crack along the face grain in the middle part with the reduced length. For the specimens at 22.5° and 45°, the combination of the crack along the face grain and the fiber fracture appeared when the shear stress reached the maximum. For the specimens at 67.5° and 90°, from the observation on the surfaces of the face veneers, fibers started to separate. With the increase of the load, the separation phenomenon became more visible. In the post-peak stage, the crack appeared firstly in the vicinity of the root of the slits, and then started to propagate along the face grain direction.
It can be concluded that the failure modes under all types of the load investigated in this paper, i.e., tension, compression and shear, differ significantly with the varying load-to-grain angles.
3.2. Experimental stress–strain relationships and test data
Fig. 6 depicts all the stress-stain curves for each type of test and each loading angle until the maximum stress has been reached, with the typical ones highlighted. It is worth noting that only 8 curves were chosen for the specimens loaded at 0° in tension. This is due to the fact that, among the 12 replicates, 4 of them failed in the gripping area during the loading, which was not considered as the typical tensile failure and thus was not involved in Fig. 6 and further analysis. In the stress–strain curves, the maximum stress implies the strength, and the slope of the curve ranging from 15% to 35% of the maximum stress indicates the elastic modulus, respectively. All the test data are shown in Fig. 7, with the red points indicating the mean value of each mechanical property. The mean values, COV and the characteristic values are summarized in Table 5. It can be readily seen in Fig. 6, Fig. 7 and Table 5 that all the studied properties are highly dependent on the loading angle to the face grain.
Table 5. Test results of birch plywood in tension, compression and shear.
| Test | Angle (degree) | Strength | Modulus | ||||
|---|---|---|---|---|---|---|---|
| Mean (MPa) | COV (%) | Char. (MPa) | Mean (GPa) | COV (%) | Char. (GPa) | ||
| Tension | 0 | 62.5 | 5.8 | 60.0 | 9.4 | 3.0 | 9.2 |
| 22.5 | 30.6 | 3.3 | 30.1 | 4.2 | 11.5 | 4.0 | |
| 45 | 21.5 | 7.9 | 20.6 | 2.1 | 6.9 | 2.0 | |
| 67.5 | 30.0 | 9.4 | 28.5 | 3.1 | 5.4 | 3.0 | |
| 90 | 56.7 | 14.2 | 52.5 | 6.7 | 11.4 | 6.3 | |
| Compression | 0 | 31.3 | 4.0 | 30.7 | 11.9 | 10.2 | 11.2 |
| 22.5 | 26.5 | 3.1 | 26.1 | 5.4 | 14.1 | 5.0 | |
| 45 | 19.4 | 6.5 | 18.7 | 3.1 | 7.4 | 3.0 | |
| 67.5 | 23.0 | 3.7 | 22.5 | 4.4 | 11.2 | 4.1 | |
| 90 | 23.9 | 5.0 | 23.3 | 9.4 | 10.2 | 8.9 | |
| Shear | 0 | 11.9 | 7.7 | 11.4 | 0.61 | 11.6 | 0.57 |
| 22.5 | 24.4 | 12.5 | 22.8 | 1.08 | 6.8 | 1.05 | |
| 45 | 32.0 | 6.2 | 31.1 | 2.45 | 17.6 | 2.22 | |
| 67.5 | 20.4 | 3.0 | 20.0 | 1.15 | 19.1 | 1.04 | |
| 90 | 13.2 | 6.8 | 12.8 | 0.66 | 10.1 | 0.63 |
It is noticed in Fig. 6a that, the tensile specimens exhibited an elastic behavior under all the five loading angles to the face grain without significant plastic deformation before failure. This phenomenon was expected and also noticed by Popovska et al. [29] on nine-layer beech plywood at all these five angles.
The compressive stress–strain curves are shown in Fig. 6b. It can be observed that the compressive specimens at 0° and 90° exhibited the elasto-plastic behavior with the distinct plastic plateau while for the specimens at 22.5°, 45° and 67.5°, compressive stresses grew linearly with the increase of the strain, followed by the hardening type plasticity after the yielding.
As displayed in Fig. 6c, the shear specimens went through the linear elastic stage in the beginning but showed nonlinearity before the shear stress reached the peak. The nonlinear shear stress–strain relationships was also observed on beech plywood by conducting two-rail tests [58] and maritime pine clear wood by conducting the Iosipescu test [43]. The shear specimens at 22.5° and 67.5° exhibit similar elastic behaviors before the proportional limit. However, for the specimens at 22.5°, the shear stress still increased after the linear stage while the specimens at 67.5° tended to reach a plateau after the proportional limit. In spite of that, it might not intrinsically represent that the shear properties of birch plywood at 22.5° and 67.5° are different. In addition to the material behavior, it might also be resulted from the geometric configuration of the shear specimen. This issue is not fully addressed in this paper. The influence of geometric configuration and different test methods on the shear behaviors of birch plywood should be studied in the future.
Fig. 7a and 7b show that birch plywood has both the highest tensile strength, over 60 MPa, and elastic modulus, nearly 10 GPa, when it is loaded parallel to the face grain. The strength and the elastic modulus drop with the increase of the loading angle until the angle reaches 45°. After that, they increase gradually from 45° to 90°. The tensile properties at 90° are close to those at 0° due to the cross lamination configuration of the plywood while at 45° the tensile strength is roughly one-third of the tensile strength at 0° and the modulus of elasticity is lower than one-fourth of that at 0°.
As can be seen in Fig. 7c and 7d, the effect of the loading angle to the face grain on the compressive properties is similar to the effect on the tensile ones. However, for the compressive strength, the descending rate from 0° to 45° and the ascending rate from 45° to 90° are much slower than those for the tensile strength. The lowest compressive strength also occurs when the loading angle is 45° to the face grain, which is almost two-thirds of that at 0°.
On the contrary, as noticed in Fig. 7e and 7f, the shear strength and modulus show the lowest values at 0°. The highest shear strength takes place at 45°, which is more than two times larger than the one at 0°, while the highest shear modulus (45°) is four times as large as the lowest one (0°). As expected, the properties at 90° are very close to the ones at 0°.
The reason for the lowest tensile and compressive strengths, and the highest shear strength at 45° could be explained by Eq. (7)-(8) and Fig. 4. For instance, when the specimen is subjected to the off-axis tensile or compressive stress at 45° to the face grain, the on-axis shear stress in the x-y (parallel – perpendicular to the face grain) coordinate system transformed by the applied stress is the highest. The influence of the shear stress is dominant since the on-axis shear strength is much lower than the on-axis tensile or compressive strength parallel or perpendicular to the face grain, as shown in Table 5. On the other hand, when the specimen is subjected to the off-axis shear stress at 45° to the face grain, the on-axis shear stress in the x-y coordinate system disappears and only the on-axis normal stresses exist. The ‘negative’ influence of the shear stress is minimized in this case. A similar explanation could also be applied to the influence of the load-to-grain angle on the elastic and shear modulus. In the following sections, several analytical models were analyzed quantitatively to check whether they could predict the mechanical properties with sufficient accuracy. Meanwhile, the variation of the off-axis properties is associated with the on-axis inputs, which are originally dependent on the raw material characterizations and the composition of the plywood panels.
It is noted that although the elastic modulus measured from the tensile test should be equal to the one measured from the compressive test theoretically, this might not be the case in practice. Both situations, i.e., the measured tensile elastic modulus being larger or smaller than the compressive one, were reported in previous studies for wood and plywood [59], [60], [61]. As shown in Table 5, the compressive elastic modulus is slightly higher than the tensile elastic modulus at varying angles to the face grain, which might be caused by the friction generated by the contact between the spherical seat platen and the top surface of the specimen. This partial constraint at the ends of the compressive specimen might be likely to overrate the elastic modulus. In contrast, there is no constraint in the middle constant cross-sectional area of the dumbbell-shaped tensile specimen. Therefore, the elastic modulus measured from the tensile test is considered to be more representative in this study.
The ratio of the highest strength to the lowest strength in tension, compression and shear is 2.9, 1.6 and 2.7 separately. Some other commonly used structural timber elements, e.g., structural lumber C24 or glulam GL 30c, or with lower grades, etc., are only ‘strong’ in one direction. The lowest tensile and compressive strengths of birch plywood are around 20 MPa at 45°, which are still similar to the tensile and compressive strengths of structural lumber or glulam in their longitudinal (the strongest) directions. The lowest shear strength of birch plywood (at 0°) is also remarkably higher than the shear strength of the timber elements made of softwood [2].
Moreover, all the COV values shown in Table 5 are less than 20%, with most of them within 10%. By comparing the average COV for sawn timber [62], it is likely to conclude that birch plywood exhibits decreased variability in strength and elastic properties.
3.3. Discussion on the configuration of shear specimen
It is mentioned in Section 2.2.3 that attaching the 38 mm-long strain gauge on the shear specimen with the reduced length in the center would overestimate the shear modulus. Thus, auxiliary non-destructive tests were carried out on the samples without slits. The ratio of the shear modulus measured from the specimens without slits and with slits was analyzed, which is 0.33, 0.35 and 0.32, at 0°, 45° and 90° to the face grain, respectively, leading to the mean correction factor (γcorrection) of 0.33. The shear results reported in Fig. 6, Fig. 7 and Table 5 have been modified based on γcorrection.
Fig. 8 displays the shear strain contour in the 1–2 (parallel – perpendicular to the loading axis) coordinate system when the birch plywood was loaded at 35% of the ultimate capacity. The non-uniformity of the shear strain (γ12) was noticed on the models with slits (representing the specimens in the destructive tests) within the range where the strain gauge was located. For all the specimens loaded at 0°, 45° and 90° in the destructive tests, the shear strain was relatively concentrated in the central line along the slits. However, the strain gauge measured the average strain within the located area, which underrated the shear strain and thus overestimated the shear modulus. Compared to the models with slits, the models without slits (representing the specimens in the non-destructive tests) have nearly uniform shear strain in the 1–2 system. The shear strain distribution shown in Fig. 8 shows the necessity to conduct the non-destructive tests for the correction of shear modulus.
3.4. Failure criteria
Two linear and five quadratic failure criteria were introduced in Section 2.4. They were utilized to predict the strength properties at varying angles to the face grain (see Fig. 9). Their closeness to the test data was quantified with the root mean square error (RMSE) (see Table 6).
Table 6. Root mean square error (RMSE) values of each failure criterion for tension, compression and shear strength properties. (unit: MPa).
| Failure criterion | Tension | Compression | Shear |
|---|---|---|---|
| Hankinson | 25.11 | 3.89 | – |
| Linear with shear effect | 5.39 | 6.56 | – |
| Empirical Norris | 1.39 | 1.05 | 6.27 |
| Theoretical Norris | 1.79 | 1.50 | 7.49 |
| Tsai-Hill | 1.75 | 1.31 | 6.78 |
| Hoffman | 6.45 | 1.88 | 6.70 |
| Tsai-Wu (F12 = 0) | 5.47 | 2.18 | 5.47 |
| Bilinear | – | – | 1.34 |
The inputs of the Hankinson’s failure criterion include the on-axis tensile or compressive strength. It is evident in Fig. 9a and 9b that the strength predicted by Hankinson’s failure criterion only varies between the strength at 0° and 90°. On the other hand, the other linear criterion, which considers the shear effect, considerably underestimates the compressive strength. Hence, the applicability of these two linear failure criteria should be questioned.
Compared to the linear ones, the difference between the quadratic criteria is much smaller. Among all the quadratic criteria, the empirical, theoretical Norris and Tsai-Hill failure criteria are similar to each other, indicating the limited influence of the coupling term with the interaction of the normal stress on the prediction of the off-axis stresses. In terms of tensile and compressive strengths, empirical Norris predicts the closest values to the test data (RMSE = 1.39 MPa and 1.05 MPa for tension and compression), firmly followed by the Tsai-Hill (RMSE = 1.75 MPa and 1.31 MPa for tension and compression) and theoretical Norris (RMSE = 1.79 MPa and 1.50 MPa for tension and compression). Hoffman failure criterion and Tsai-Wu failure criterion when the coefficient F12 is 0 are less accurate.
As can be revealed from Fig. 9c and Table 6, all the aforementioned quadratic criteria underrate the shear strength. The lowest RMSE is 5.47 MPa when using Tsai-Wu (F12=0) failure criterion.
It is worth mentioning that the coefficient F12 is set to be 0 when comparing Tsai-Wu with other criteria. The effect of this parameter on the strength predictions should be studied. Thus, sensitivity analysis was conducted by varying F12 from its minimum (labeled as -LIMIT) to the maximum (labeled as + LIMIT), as shown in Eq. (16). Fig. 10 shows RMSE values obtained from the Tsai-Wu failure criterion with the varying F12. The horizontal axis ranges from −1 to 1, standing for the ratio of F12 to + LIMIT. It is found that RMSE is the lowest when F12 is + LIMIT for tension and –LIMIT for compression. Nevertheless, the empirical Norris and Tsai-Hill are better than Tsai-Wu criterion no matter the value of F12.
Interestingly, the shear strength predicted by Tsai-Wu is strongly influenced by F12. When F12/LIMIT is around 0.5, RMSE is slightly over 4 MPa, which is the lowest among the others.
Based on the experimental results, the authors of this paper propose a simple bilinear model for the shear strength prediction, as shown in Fig. 9c and Eq. (26).(26)fv,θ=θ45fv,45-fv,xy+fv,xy,0°≤θ≤45°(90-θ)45fv,45-fv,xy+fv,xy,45°<θ≤90°
The proposed bilinear model fits the shear test data with the RMSE value of 1.34 MPa, as listed in Table 6. However, it is noted that one additional input data, i.e., the shear strength at 45° to the face grain, has to be known in advance when this bilinear model is adopted.
3.5. Prediction of off-axis elastic and shear modulus
As discussed in Section 3.2, the elastic modulus measured from the compressive tests is considered to be less representative than the tensile elastic modulus. Therefore, only the off-axis tensile elastic modulus and the shear modulus were predicted and compared to the test results, as shown in Fig. 11, with the closeness listed in Table 7 and Table 8.
Table 7. Root mean square error (RMSE) values of each analytical model for the prediction of the tensile elastic modulus.
| Analytical model | RMSE(GPa) |
|---|---|
| Hankinson | 3.72 |
| Transformation model (elastic modulus) | 0.28 |
| Saliklis and Falk | 0.89 |
Table 8. Root mean square error (RMSE) values of each analytical model for the prediction of the shear modulus.
| Analytical model | RMSE(GPa) |
|---|---|
| Transformation model (shear modulus) | 0.60 |
| Modified transformation model (shear modulus) | 0.07 |
When the Hankinson’s equation is adapted for the prediction of off-axis tensile elastic modulus (Eq. (18)), similar to the strength evaluation, it lies above the test data due to the ignorance of shear effects. The simplified formula which excludes the Poisson’s ratio (Eq. (21)), proposed by Saliklis and Falk, underestimates the elastic modulus. The transformation model (Eq. (19)) shows the highest closeness to the tested elastic modulus. See the curves named ‘Hankinson’, ‘Saliklis and Falk’ and ‘Transformation model (elastic modulus)’ in Fig. 11a. However, the transformation model does not show sufficient accuracy to predict the shear modulus (Eq. (22)) (see the curve named ‘Transformation model (shear modulus)’ in Fig. 11b). By rewriting Eq. (22) and adding one more shear property, i.e., the shear modulus at 45° to the face grain, as input, Eq. (24), namely, the modified transformation model (shear modulus), predicts much closer results to the test mean values (see Fig. 11b).
The black dots in Fig. 12 stand for the RMSE values of the transformation model for the prediction of elastic and shear modulus based on the derived Poisson’s ratio νxy according to Eq. (21). This derived Poisson’s Ratio is dependent on the properties of solid birch and the geometrical configuration of plywood. However, this property νxy has not been experimentally characterized. In order to assess how νxy would affect prediction accuracy of the transformation model for both the elastic and shear modulus, sensitivity analysis was performed by varying νxy from 0 to 0.2 (Fig. 12).
It is readily seen in Fig. 12 that the transformation model for the off-axis elastic modulus is nearly constant with the change of νxy, with the RMSE values close to 0.3 GPa. On the other hand, a significant change of RMSE values is observed when νxy is varied in the transformation model for the prediction of the off-axis shear modulus. Nevertheless, the modified transformation (shear modulus) is still the better one with the lowest RMSE value of 0.07 GPa.
3.6. Prediction of on-axis shear modulus based on off-axis tensile tests
The possibilities of predicting the on-axis shear modulus based on the off-axis uniaxial tests were checked in Table 9. It shows that the elastic modulus obtained from the off-axis tensile tests at 45° to the face grain predicts the closest on-axis shear modulus to the test mean value.
Table 9. Comparison between the predicted on-axis shear modulus and the test data.
| Input | Gxy(predicted) | Gxy(test mean value) |
|---|---|---|
| E22.5 | 0.789 | 0.636 |
| E45 | 0.611 | |
| E67.5 | 0.580 |
4. Conclusions
In this paper, the in-plane mechanical performances of birch plywood were investigated. A comprehensive experimental dataset was established by conducting tensile, compressive and shear tests under five different angles to the face grain, i.e., from 0° (parallel) to 90° (perpendicular) to the face grain, with an interval of 22.5°. The failure modes and the stress–strain relationships of the specimens at each angle were discussed. The strength and the elastic properties were experimentally determined and then predicted by analytical and empirical models. The applicability of these models was studied quantitatively by comparing the predicted values with the experimental data. Parametric analyses were performed to study the influence of the interaction coefficient F12 in Tsai-Wu failure criterion and the Poisson’s ratio νxy in the transformation model on the predicted strength and modulus respectively. In addition, the possibilities of predicting the on-axis shear modulus based on the off-axis uniaxial tests were checked. The main conclusions are summarized as follows:•
The failure modes differ significantly with the varying load-to-face-grain angles under all types of load investigated in this paper. The tensile specimens loaded at 0° and 90° failed by the facture of the veneers with the direction parallel to the loading axis and the separation of the veneers perpendicular to the loading direction simultaneously, while the cross veneers of the ones loaded at other angles were not torn out completely. For the compression specimens at 22.5°, 45° and 67.5°, the shearing failure along the face grain are visible. The compressive specimens at 0° and 90° were slightly deformed through the thickness (out-of-plane) direction due to the localized buckling of the veneers with the grain parallel to the loading axis, but had less visible crack on the plane surface. The failure modes of the shear specimens were: for 0°, the crack along the face grain in the middle part; for 22.5° and 45°, the combination of the crack along the face grain and the fiber fracture; and for 67.5° and 90°, fiber separation before the peak load and the crack propagation around the slit ends in the post-peak stage.•
The tensile specimens exhibited brittle elastic behavior without significant plastic deformation while the compressive stress grew linearly with the increase of the strain, followed by the distinct plastic plateau (for the compressive specimens loaded at 0° and 90°) and the hardening-type plasticity (for the compressive specimens loaded at 22.5°, 45° and 67.5°). The shear specimens went through the linear elastic stage in the beginning but showed nonlinearity before the shear stress reached the peak.•
The studied strength and elastic properties are highly dependent on the loading angle to the face grain. Birch plywood yields the highest strength and the elastic modulus at 0° to the face grain and both the lowest at 45° in tension and compression. The opposite trend was observed in shear tests. Birch plywood is considered to be relatively homogeneous in terms of the strength properties that even the lowest strength properties are competitive to the strength of most of the structural timber made of softwood in the longitudinal (strongest) direction. Moreover, birch plywood also exhibits decreased variability compared to the sawn timber in the properties investigated herein.•
The numerical analysis clarified the non-uniformity of the shear strain in the global coordinate system within the area where the strain gauges were located for the shear specimen with slits and further clarified the necessity to conduct the non-destructive tests on the specimen without slits for the correction of shear modulus.•
Empirical Norris failure criterion predicts the closest result with the tested tensile and compressive strength data, followed by Tsai-Hill and theoretical Norris failure criteria. However, all the existing criteria discussed in this paper underestimate the shear strength. A bilinear model is proposed for the prediction of off-axis shear strength, which shows the highest closeness to the shear strength data. No matter the change of F12, Tsai-Wu failure criterion is neither competitive to the empirical Norris criterion when predicting tensile or compressive strength, nor to the bilinear model when predicting the shear strength.•
The transformation model shows the highest closeness to the tested elastic modulus with the negligible effect from the Poisson’ ratio νxy while the influence of νxy is more significant on the prediction of shear modulus. Nevertheless, the modified one still predicts the shear modulus better.•
The elastic modulus obtained from the off-axis tensile tests at 45° to the face grain predicts the closest on-axis shear modulus to the test mean value.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
The authors wish to gratefully acknowledge Vinnova project 2017-02712 “Bärande utomhusträ” within the BioInnovation program, China Scholarship Council and Svenskt Trä for the financial support. Riitta Ahokas at Koskisen is sincerely acknowledged for supplying the birch plywood materials. Hassan Abdulazim Fadil Mohammed, Gürsel Hakan Taylan and Viktor Brolund are thanked for their technical support during the laboratory tests.
References
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- Experimental investigation on mechanical properties of acetylated birch plywood and its angle-dependence2022, Construction and Building MaterialsShow abstract
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