Determination of shear stresses in the measurement area of a modified wood sample

1 Introduction

There are many reports on the results of shear strength tests of polymer composites and natural wood available in the literature whereas only few studies have covered the shear strength of modified wood.

El-Hajjar and Haj-Ali [1] applied a modified Arcan fixture with butterfly specimen geometry to measure the in-plane shear response of thick-section pultruded fiber-reinforced polymer (FRP) composites.

The objective of the proposed testing method is to determine both material shear stiffness and its nonlinear stress–strain response up to ultimate stress. Finite element models (FEMs) for the butterfly specimen are generated to examine the effects of the notch radius and material orthotropy on the uniformity and distribution of stresses in the gage area. Butterfly geometry with a blunted notch and roving orientation parallel to the applied load is found to have a uniform shear stress in the gage section. The axial shear response is measured under different biaxial stress states by varying the angle of the applied load. The tested nonlinear shear stress–strain responses compare favorably to results previously obtained from off-axis compression tests used to calibrate a multiaxial constitutive model for this material.

Bank [2] noted the nonlinear shear response in pultruded composites using the Iosipescu fixture to test specimens cut from pultruded beams. Several methods have been proposed for the measurement of the in-plane shear properties in pultruded composites. These include off-axis test methods, such as the ±45° tension/compression test, the cylinder–torsion method, and variations to the Iosipescu specimen.

However, Haj-Ali and Kilic [3] proposed the use of the ±45° compression test for thick pultruded composites. Its application to laminated composite systems has been limited due to its inability to preclude buckling before a shear-induced failure. In the cylinder torsion method, a torque is applied to a thin cylindrical specimen at the ends to induce a state of shear. A major disadvantage is the likelihood of failure at the ends (grips).

Barbero et al. [4] used torsion tests on pultruded rods made of only roving layers to determine the shear stiffness and strength.

Davalos et al. [5] used torsion tests on rectangular bars to determine the shear moduli in E-glass/vinylester pultruded composites.

Zureick et al. [6] proposed the use of a modified Iosipescu specimen for shear property measurement in pultruded composites. A major advantage of this method compared with the off-axis test was the low levels of the longitudinal strain and the large gage section.

Arcan et al. [7] proposed a biaxial fixture, commonly known as the Arcan fixture, to produce biaxial states of stress. The compact nature of the Arcan fixture enables obtaining the shear properties in all in-plane directions in a relatively simple manner. The Arcan fixture can be used to apply both shear and axial forces to the test specimen.

Voloshin and Arcan [8] used this method to determine the longitudinal and through-thickness shear modulus in a unidirectional laminated FRP composite. Their results compared favorably with those obtained from cylinder torsion tests.

Hung and Liechti [9] used Moire’s interferometry to examine the strain fields and their uniformity in unidirectional laminated specimens of AS4/PEEK tested in an Arcan fixture. They found that aligning the fibers with the loading direction and using a 90° notch produced a uniform “pure shear” state in the gage section.

Xie et al. [10] have presented the composite sandwich matting comprising paulownia woods as core material and glass FRP as face skins and lattice webs. Compressive tests and shear tests were carried out to characterize the mechanical properties of the paulownia wood and poplar wood core according to ASTM C365 and ASTM C273, respectively. Core shear failure occurred when the shear stress exceeded the shear strength of paulownia wood core.

Taghiyari et al. [11] investigated the shear strength of heat-treated solid wood of three species (beech, poplar, and fir) bonded with polyvinyl acetate adhesive reinforced by nanowollastonite. After the heat treatments, the samples were prepared for the determination of their shear strength. Dimensions of the specimens and testing method used were according to the ASTM D143-14 (2014) standard. Determination of shear strength was carried out using an Instron 4486 universal testing machine. The results demonstrated that shear strength was significantly dependent upon the density of the specimens.

In turn, Janowiak and Pellerin [12] evaluated the shear strength properties of three wood composite materials. A modified Iosipescu test apparatus was used to determine shear strength. In-plane shear was also characterized using ASTM D1037-87 test standards.

This study specifically utilized the University of Wyoming version of the original shear test device. Transverse shear strength values were found to exceed the magnitude of previously published ASTM test results.

When Yoshihara et al. [13] examined the applicability of the Iosipescu shear test for measuring the shear properties of wood, sitka spruce and Japanese ash were used for the specimens. The test results showed that the Iosipescu shear test is effective in measuring the shear modulus and the yield shear stress. To measure the shear strength properly by the Iosipescu shear test, the configuration of the specimen and the supporting conditions should be examined in more in detail.

Shear strength has been determined based on uniaxial tension tests of off-axis specimens and the examination of the proper off-axis angles. Three tree species were used for the studies by Yoshimura and Oto [14]. Uniaxial tension tests of the specimens with various off-axis angles were conducted, and the shear stress at failure was obtained. The authors thought that the shear strength predicted by uniaxial tension tests should be treated as an approximate value despite the simplicity of the tension test. Other test methods should be adopted to obtain the precise shear strength of wood.

In their paper, Warguła et al. [15] have presented the results concerning tensile, compression, and shear of pine wood samples in all significant directions. The static shear test was performed using instrumentation. Its geometry allowed the stress conditions as close to technical shearing as possible.

The Iosipescu sample has gained more recognition in composite testing due to its shape [16,17,18]. The geometry of the Iosipescu sample according to ASTM D5379M:93 is shown in Figure 1.

Figure 1

Geometry of the Iosipescu sample.

Destruction of the Iosipescu sample can be achieved in a uniform stress condition although the presence of unwanted transverse stress complicates the interpretation of shear strength [16,19]. The definition of shear strength is not unambiguous [19,20]. For instance, for the same material, Broughton refers to “destructive stress” of 58 MPa [19], Morton et al. [21] specify “shear strength” of 68 MPa, but Adams abd Lewis [8] refers to “shear strength” of 115 MPa [22].

When testing a flat sample, it should be noted that obtaining the criterion of destruction necessitates the production of shear forces. The homogeneity of stress in the sample area under examination is an important feature of the sample. According to the authors, the correct determination of the modulus of elasticity (MOE) of wood, has not been fully resolved yet [17,23] whereas the determination of tangential stress is far from being resolved [20,24].

2 Materials and methods

2.2 Methods

In this work, the measurement of the shear resistance of the composite Iosipescu specimens in the test are according to the V method (ASTM D5379M:93).

A new method for testing material properties has been applied to determine the shear strengths of specimens of P. sylvestris. The method permits the realization of pure shear in the critical section of the specimen. The large strength ranges of wood fibers and the vast differences in strength between earlywood and latewood fibers can still cause significant scatter in the test data, but the effect of combined stresses can be effectively controlled. Owing to the special properties of wood, failure always follows the slope of the grain. The new method can only yield shear strength parallel to grain, which is required for engineering design purposes. The determination of shear strength of solid wood has been hampered by the difficulty in devising specimens and loading devices to produce a state of uniform shear stress. Many investigators have studied this problem and developed different methods for shear testing, but the presence of complex stress conditions at the site of failure remains unresolved [23].

The following assumptions were made for measuring the shear strength of wood composite samples. The essence of the tests is to maintain a uniform stress state, in the examined sample area, so a number of tests have been carried out and the literature has been analyzed in detail, ultimately taking the appropriate shape and dimensions [26,27,31,32,33]. The shear strength and load distribution were studied in complex load conditions (shear/tensile and shear/compression) in the measurement section of the sample.

In the literature, the following letters are used to denote the anatomical directions of the wood: R – radial direction, T – tangent, and L – longitudinal with respect to the surface of individual layers of fibers. On the other hand, in the theory of elasticity, the index notation 1, 2, 3 is used, in particular: x ₁ – radial direction, x ₂ – tangent, and x ₃ – longitudinal as shown in Figure 2.

Figure 2

Indicators and letter notation of the anatomical directions of wood.

Finally, the shape and dimensions of the wooden test sample are shown in Figure 3. The angle of the notch, β, is 45° and the depth of the notch is p = 7.5 mm. Samples of different layers of early- and latewood have been tested. On average, the sample contained nine layers of earlywood and eight layers of latewood or vice versa. The thickness ratio of late-to-earlywood layers was 0.5. The depth of the notch was considered in relation to the thickness of the layers so that the beginning of notch does not occur halfway through the thickness of the layer, but at its edge. It has been assumed that the layers are arranged in parallel and have a constant thickness over their entire length. In the measurement section, the outer layer may be a layer of early- or latewood (Figure 3).

Figure 3

Shape and dimensions of the sample for determining shear strength: clear layers – earlywood and – dashed layers – latewood.

The determination of strength on the wall of the tested materials required the use of appropriate instrumentation. The device used in the tests was designed according to a proprietary concept [26,27,31,33,34].

Figure 4 shows a prototype device producing a flat stress state in the test sample. In this instrument, the position of the axis of the sample relative to the direction of load, F, may be variable. Therefore, depending on the angle of alignment of the sample in relation to the load direction, in addition to shear, compressive and torsional forces are also applied. The purpose of the study was therefore to determine the shear strength and load distribution in complex load conditions (shear/tensile and shear/compression) in the measurement section of natural and modified wood samples.

Figure 4

Device for producing a plain stress state in the samples: (a) load pattern, (b) equipment diagram, 1, housing; 2, bracket; 3, base; 4, guide; 5, guide bushing; 6, right-hand holder; 7, left-hand holder; 8, jaw insert of the left-hand holder; 9, jaw insert of the right-hand holder; 10, left-hand retaining block; 11, right-hand retaining block; 12, guide bushing; 13, spheres and sphere mount ϕ12; and 14, M6 bolt [26,27,31].

Resultant reactions, to which pressures at four points of the sample are reduced, shall be determined using the following equations:

(2) F A = F C = F 1 + a b , F B = F D = F a b ,

where F A > F B , F C > F D , a > b , F is theforce applied by the strength testing machine and a and b are distances describing the location of the resultant reactions.

The geometry and kinematic load pattern of the sample are shown in Figure 5. The device (Figure 4) consists of mobile blocks which move along an inclination of α relative to the axis of the sample. The measured value shall be the force dependent on the movement of the sample.

Figure 5

Sample kinematic load diagram.

Depending on the angle α between the direction of the effective load and the longitudinal axis of the sample, it is possible to determine the load distribution in the test sample for shear, shear/tensile, shear/compressive, and compressive and tensile forces. For the load sample, the stress distribution was primarily analyzed in the 7.5 mm length measurement section with a notch. If the angle α = 0°, the stress state is closest to the pure shear. The apparatus allows for an angle change from −45 to +45°. Tensile and compressive forces were applied in the direction of axis x ₃, with the sample mounted directly in the jaws of the strength testing machine. The values of tensile strength (α = +90°) and compressive strength (α = −90°) were determined by stretching and compressing the samples on the MTS 810.12 machine at temperature 23°C and air humidity of 42%, with the use of a 50 kN load cell. Moving and stationary blocks are preclamped so that the F force component of F _x3 is less than the friction force between the blocks and the sample. However, this clamping introduces a preliminary stress condition. Therefore, the clamp value was determined experimentally to be sufficient while not significantly affecting the strength of the sample.

Figure 5 shows some displacement of the upper blocks relative to the lower ones. This offset has been experimentally established. It is sufficiently large to produce common displacements on the interfaces of the blocks with the sample. This is particularly relevant in view of the calculation model used for FEM stress analysis.

The tests have been carried out on the apparatus shown in Figure 3. For angle α = 0°, the sample is sheared under the influence of a vertical displacement applied along the axis x ₁ (Figures 4 and 5). The sample weighing apparatus records the force to which the movement Δl corresponds. During the shear of the sample, the displacement along the axis x ₁ (right part of the instrument) corresponding to the force F = F _t is directed along the x ₁ axis. For negative angles of rotation of the sample in the instrument (counterclockwise) (Figure 4), force F induces shear (F _t) and compression (F _c) in the sample whereas for positive angles of rotation (clockwise), force F induces shear (F _t) and stretch (F _m) in the sample.

3 Results

Table 1 shows the strength values of the wood samples K0 and K35 depending on the angle α until the first crack.

Figure 6 shows the relation between the load of the natural wood sample K0 and the modified K35 and the displacement of the holder for α = 0°. The digits 1 to 4 mark subsequent cracks in the natural wood sample.

Figure 6

Displacement curve–load, with characteristic points of the beginning of the crack (1, 2, 3, 4 – subsequent stages of the cracking of the wood sample), course of force F versus displacement Δl with marked points 1–4 illustrating the successive stages of wood sample cracking.

The characteristics in Figure 6 illustrate the change in the sample load with time for woods K0 and K35. Differences can be observed in the transfer of wood load at K0 and K35. In a sample made of natural wood K0, when loaded, the layers of early- and latewood are destroyed alternately, hence the large number of distinctive “peaks,” both ascending and descending. The K35 material, in which the mechanical properties of the early- and latewood layers are similar, displays an entirely different behavior.

Figure 7 shows images of cracks in natural wood K0 versus modified wood K35. The nature of cracks in natural and modified wood samples varies significantly. The beginning of cracks 1 and 2 in sample K0 starts at low loads, close to the base of the notch (Figure 7a and b) during the test period (points 1 and 2, Figure 6). These cracks develop very quickly and only stop in the area of high compressive stresses, below the laden surface. The load values at which cracks 1 and 2 occur are very sensitive to the flexure applied by the instrument in the plane. Cracks 3 and 4 also develop from the notch, but closer to the incision slope, as can be seen in Figure 7. Their development is much slower and cannot always be linked to declining load. Further cracks indicate the end of the duration of the sample. They are related to a very abrupt load decline and appear very quickly, one after the other, developing immediately, similarly to cracks 1 and 2 (Figure 6). Some authors suggest that the final crack occurred in a state of homogeneous shear stress, but no attempt was made to clarify this issue [19,22,35]. Other authors even proposed to interpret the shear stress after the end cracks have appeared, as is done for shear strength.

Figure 7

Images of shear cracks in samples: (a) natural wood K0, (b) modified wood K35, (1, 2, 3, 4 – subsequent cracking stages).

The cracks in samples K35 resemble the nature of cracks in homogeneous materials. Cracks 1 and 2 start to form slowly with a significant loading force close to the base of the notch (Figure 7b) during the test period. These cracks are slowly developed with significant loads passing through cracks 3 and 4 leading to the destruction of the sample (Figure 7b). Differences in the nature of cracks in samples of modified wood K35 and natural wood K0 can be observed with the naked eye. It is difficult to capture the location and moment of initiation of cracks 3 and 4 which are formed below the notch in Figure 7b. Their development is rapid and only a computer record of the data allows the character of cracks to be restored. The cracking of the K35 material has not been thoroughly analyzed. For both natural wood and modified wood, we have assumed the limit strength for the samples – a load value corresponding to one crack (Figures 6 and 7). The analysis carried out with the FEM showed the presence of tensile and compressive stress in the measurement section of the sample for α = 0°, with prevalent shear stress at points 1 and 2. Harmful clockwise bending moment in the plane shall increase the transverse tensile stress at point 1 and apply transverse compressive stress at point 2. As a result, the total transverse tensile stress in this point 1 is reduced. This causes a crack 1 to form earlier than crack 2. This was observed during the tests. The above course of sample cracking concerned applied to compression. Similarly, depending on the selected angle α of axial alignment of the sample in relation to the direction of load, the values of force F were recorded, assuming that the strength of the sample corresponds to the first crack (point 1 in Figure 7).

By changing the angle of the sample, every 15° at −45 to +45°, a force F corresponding to the first rupture from angle α was obtained. Figure 8 shows the relation between the loading of natural wood samples K0 and modified wood samples K35 and the angle α.

Figure 8

Dependence of sample loading direction on the angle α (an initial instance of a first crack appearing in the sample), α – rotation angle of sample relative to its horizontal.

Based on the graph shown in Figure 8, it can be noted that both natural wood K0 and modified wood K35 exhibit a higher tensile and tensile/shear strength (right part of the graph) than compression and compression/shear (left part of the graph).

A numerical simulation has been carried out to obtain the distribution of stresses inside the sample. The calculation model assumes a flat stress state whereas it was decided that each of the layers of soft and hard wood be described relative to their transverse direction by nine-node biquadratic elements. The physical characteristics of individual layers are described by means of the generalized Hooke law for orthotropic materials.

In the modified Iosipescu sample (Figure 3), the load distribution was mainly analyzed in the section marked with a bold line in Figure 9. When calculating the stress distribution in the section, the F force per sample was distributed to normal F ¯ x 3 and shear F ¯ x 1 . Stress values have been determined using the following dependence

where A is the transverse section of the sample.

Figure 9

Sample section analyzed.

The relationship between stress and deformation for the flat stress state was

On the basis of the tests, the parameters of elasticity of the layers of soft and hard wood were determined, which are given in the studies under [25–27,33]. Tables 2 and 3 provide the parameters of elasticity of the natural and modified wood layers.

The determination of stress distribution values in the analyzed measurement section of the samples was possible through the use of numerical methods. The stress distribution in orthotropic material subjected to uniaxial load can therefore be observed. The analysis showed that there are tangential stresses in addition to pure stretching (compression). Studies have shown that anisotropic materials do not have a homogeneous stress state when exposed to pure tensile, compressive, or shear forces as is the case with isotropic materials. In any case, there is a heterogeneous stress state with one or the other stresses prevailing. The stress values obtained in the measurement section are certain, approximate values. The data adopted in the calculation model were not always consistent with reality. For calculations, it was adopted that the sample contained 17 layers of wood. The ratio between the thickness of late and early wood fibers, 0.5, was different from reality. Although the face of the sample was in line with the assumptions, it may have been completely different at the rear of the sample. This is due to the structure of the wood. However, the calculated figures only roughly deviate from reality.

The stress σ ₃₁ (for α = 0°) calculated with the FEM method is illustrated in the form of a contour map in Figure 9 for K0 wood and in Figure 10 for K35 wood. The tangential stress distribution in the measurement section of the K0 sample (Figure 10) indicates a much higher loading of latewood layers, compared to earlywood. In addition, throughout the measurement section under analysis, the material loading is more than twice as high as in the identical measured section of K35 wood (Figure 11). This is due to the “homogenization” of the material in the direction of latewood layers.

Figure 10

Shear stress distribution σ ₃₁ in a selected area of the sample for K0 wood.

Figure 11

Shear stress distribution σ ₃₁ in a selected area of the sample for K35 wood.

The loading of the sample was carried out by displacement of its edges in contact with the mobile blocks when inclined at α relative to the axis of the sample. When the force in section x ₃ = 0, calculated on the basis of the stresses, was equal to the value of the measured force, it was assumed that the resulting stress condition corresponded to the destruction of the sample. A comparison of the numerical values used in the calculation of the sample boundary displacement values and the measured values of these displacements pointed to degree of correctness of the calculation model applied. Figure 12a and b show the stress distribution in the analyzed section of the K0 and K35 wood samples, respectively (for α = 0°). Stress distributions in the analyzed section of the sample for angle α = 0° corresponding to pure shear indicate that both natural and modified wood samples have a complex stress state. The highest values result in shear stresses σ ₃₁ at almost zero normal stresses, that is, σ ₃₃ and σ ₁₁.

Figure 12

Stress distribution in the measurement section of natural wood samples K0 and modified wood samples K35: (a and b) α = 0°; c and d) α = 45°.

The nature of the stress distribution along the analyzed measurement section of the sample for natural and modified wood is different. The “sawtooth” nature of the stress distribution in the K0 sample section indicates a diverse load patters of hardwood layers in relation to soft wood layers. In modified wood, the stress distribution is close to the state of equilibrium, as the values of the solid elasticity of the layers of soft and hard wood are similar. The modification of soft layers resulted in the “homogenization” of the material; therefore the curve indicates a more homogeneous distribution of stresses. On the other hand, Figure 12c and d for K0 and K35 shows the stress distribution in the analyzed section of the sample for an angle of α = 45° corresponding to the tensile/compressive instance. Different stress distribution occurs in the measurement section for both natural and modified wood. The highest stresses occur along the axis of the sample (σ ₃₃), the values of which significantly exceed the values of the shear stresses (σ ₃₁) and normal stress (σ ₁₁). In this case (tensile/compressive force), a very large variation of stresses is observed in the measuring section of the sample because tensile stresses predominate, and their strength along the fibers exceeds that observed for other directions. This is characteristic of anisotropic materials, for which the strength characteristics vary. The tangential stress distribution in the measurement section of a natural wood sample indicates a much higher loading of hardwood layers, compared with softwood. Numerical calculations have shown that, throughout the measurement section under analysis, the loading of natural wood is more than twice as high as in the identical measured section of modified wood. This result can be justified by the “homogeneity” of the material strain toward hard wood layers. In natural wood, the whole load is transmitted by hard layers whereas in modified wood both hard and soft layers have similar strength properties, resulting in an even distribution of stress in the tested section.

4 Conclusions

Studies have shown that natural wood exhibits very different layer strain compared to modified wood. Modified wood layers have similar strength properties. The adoption of the proposed geometry of the samples for shear testing on the tested materials showed that, throughout the measurement section under analysis, the strain of natural wood is significantly higher than in the identical analyzed measurement section of modified wood. The reinforcement of modified wood results from the “homogenization” of the material in the direction of latewood layers. The outer load shall be broken down into latewood layers and reinforced earlywood layers. The results of the study show that filling the wood structure with polymer causes homogenization of the material, resulting in similar average material values for early- and latewood.

A modified Iosipescu test apparatus was used to determine shear strength.

As a result, in its central part, apart from shear, tension/compression is also performed.

Transverse shear strength values were found to exceed the magnitude of previously published ASTM test results.

The authors think that the assumed geometry of the sample for testing on the wood wall allows obtaining shear strength values exceeding the values of previously published results.

The shear strength predicted by uniaxial tension tests should be treated as an approximate value despite the simplicity of the tension test.