1 Introduction
Multiaxial and complex stress states can arise in timber structures depending on the position and direction of the applied force with regards to the wood grain direction. This requires special attention due to the material’s anisotropy as a consequence of its heterogeneous and porous microstructure (Kollmann et al.
2012). In particular on the material scale, where the local material orientations are commonly different from the global specimen geometry and loading, multiaxial stress states occur. The annual ring structure in a radial (R)-tangential (T) cross-section of wood that is loaded by uniform compression perpendicular to the grain leads to a non-uniform stress state and combination of normal stresses in the R and T direction with rolling shear. Compression perpendicular to the grain, such as a macroscopic phenomenon in timber engineering, and the influence of boundary conditions have been studied extensively by Hall (
1980), Hoffmeyer et al. (
2000), Blass and Görlacher (
2004), Bleron et al. (
2011), Leijten et al. (
2012) and Gehri (
1997). Phenomenological models for the engineering design have been developed by Madsen et al. (
1982), Van der Put (
2008), EN 1995-1-1 (
2004) and Lathuilliere et al. (
2015). However, on the local material scale, the interaction of stresses in the principal material directions should be considered, though reliable test data and validated design formulas are missing. The interaction of stresses perpendicular to the grain with rolling shear also has a significant role in the failure of cross-laminated, engineered wood-based products (Ehrhart and Brandner
2018). The very low value of the rolling shear modulus, which is as low as one-tenth to one-twentieth of the perpendicular to the grain modulus of elasticity, is a consequence of the anatomical and inhomogeneous, fibrous structure of wood.
The design of structural elements made from engineering wood-based products, connections, beam elements with holes and notches, etc. demands special attention in terms of material behavior under stress interaction. A failure envelope that can predict the strength of wood for such combinations of stresses is essential for reliable design. It should even consider the compression-tension asymmetry in combination with shear stresses (Steiger and Gehri
2011). Three-dimensional anisotropic phenomenological failure criteria have been proposed for this purpose. However, these merely describe the phenomenon of failure, but neither the material behavior nor the failure mechanism (Cabrero et al.
2012; Kasal and Leichti
2005). Most of these phenomenological failure criteria were developed for composite materials based on isotropic failure criteria. The validation of these anisotropic failure criteria for stress interaction in natural orthotropic materials such as wood has attracted less attention, especially for the combinations with rolling shear stresses.
The aim of this paper is to investigate the mechanical behavior of clear wood under stresses perpendicular to the grain in interaction with rolling shear stresses. More specifically, the objective of this study is to validate failure envelopes for this stress combination in Norway spruce (
Picea abies), based on experimental investigations. For this purpose, it was necessary to develop a test setup that allows controlling the stress interaction and loading of clear wood along pre-defined displacement paths. The experimentally defined failure states could then be compared to failure surfaces predicted by the phenomenological failure criteria. Previous experimental, analytical, and theoretical research related to stress interaction with shear stresses is reviewed in Sect.
2, before the experimental setup, and the materials used in this study are described in Sect.
3. Section
4 presents and discusses the results and Sect.
5 concludes the paper.
2 Experimental testing and analytical equations for stress interactions in wood
Most data from the material properties determined through experiments and reported in the literature are related to the uniaxial material behavior of wood, though very limited research has been carried out to study the mechanical behavior of wood under biaxial or more complex stress states. The failure criteria for materials are mainly defined based on uniaxial strength properties, though to validate the stress interaction prediction of the failure criteria, biaxial testing of wood is required. Biaxial testing requires more advanced testing equipment to control and quantify the stress and strain state of the specimen. The literature reviewed here relates to both biaxial test setups and uniaxial shear testing devices, which are discussed and have been used to develop the test series in the R-T plane performed in this work.
Several uniaxial test setups for rolling shear testing of clear wood are available and have been developed to establish a uniform shear stress state in the most critical part of a test specimen. These test setups include the Iosipescu shear test (Iosipescu
1967; Dumail et al.
2000), the Arcan shear test (Arcan et al.
1978), the two-rail shear fixture (Melin
2008), the single cube apparatus (Hassel et al.
2009), and the off-axis shear fixture according to EN 408 (
2010), which is a 14° inclined compressive test where the force is applied at an inclination of 14° to the shear plane or longitudinal axis of the specimen.
Magistris and Salmén (
2004,
2005) investigated the scope of using the Wyoming version of the Iosipesco and Arcan shear fixtures by adding some extra features to obtain an interaction of stresses through a uniaxially applied force. Two rotating plates were added to the lower and upper parts of the Wyoming version of the Iosipesco shear fixture to change the ratio between shear stress and normal stress. They conducted a feasibility study of their in-house modified Iosipescu device, for pure shear and combined shear with compression interaction on orthotropic, medium density fiberboard, and Norway spruce solid wood. The experiments were carried out on 90° notched specimens with a depth of 3.50 mm, for small displacements, within the elastic limit.
A U-shaped fixture was added to the Arcan shear device to prevent movement as well as rotation of the specimen in the third direction (Stenberg
2002). Magistris and Salmén (
2005) investigated the scope of using this in-house modified Arcan device for a comparatively thick wood specimen in the case of combined loading. After finding the device suitable for combined loading in wood, they used the setup to study the deformation pattern of wet wood fibers (Norway spruce) in the longitudinal (L)-tangential (T) plane at an elevated temperature of 50 °C and 90 °C, under compression, shear, and combined compression with shear loading. The device was even used for repeated loading to study the energy consumption required to collapse the wood cells under different loading combinations and repeated loading. The specimen size was 2 × 40 × 15 mm
3 (R, T, and L directions).
Even though, the setups developed by Magistris and Salmén (
2004) were found suitable for biaxial testing in proof-of-concept tests, they did not allow for the direct control and quantification of the displacements and forces in two orthogonal directions, which makes the derivation of a failure envelope difficult.
Spengler (
1982) performed a study on Norway spruce glued-laminated timber (glulam) specimens that were subjected to the combination of stress perpendicular to the grain with shear in L-R plane. He used L-shaped steel plates to apply loading on a rectangular shaped specimen in two perpendicular directions. The specimens had a length of 220 mm, a width of 80 mm to 140 mm and a thickness of 22 to 33 mm, and were adhesive-bonded with the steel plates. The setup was comparably simple, but required gluing of the specimens. Without a continuous force transmission through the adhesive bond, however, it would lead to stress concentrations in the corner points, which could be problematic particularly when studying the R-T plane with lower stiffness properties and different Young’s modulus to shear modulus ratios.
Phenomenological failure criteria generally describe a surface in the six-dimensional stress space represented by mathematical expressions. Most of the anisotropic strength criteria are based on isotropic yield criteria (Cabrero et al.
2012), of which only a few are developed for wood. This work focuses on the in-plane interaction of stresses perpendicular to the grain with rolling shear stress, and the corresponding failure criteria can be illustrated in a 2D representation.
In the case of uniaxial stress, a material fails when the maximum normal stress or shear stress reaches the corresponding strength value. When considering stresses parallel to the anatomical directions of wood, the maximum stress criterion in the R-T plane can be expressed as
$$\begin{aligned}&\frac{\sigma _{RR}}{f_R}=1, \end{aligned}$$
(1)
$$\begin{aligned}&\frac{\sigma _{TT}}{f_T}=1, \end{aligned}$$
(2)
$$\begin{aligned}&\frac{\tau _{RT}}{f_{v,RT}}=1, \end{aligned}$$
(3)
where
\(\sigma _{RR}\) and
\(\sigma _{TT}\) are the normal stress components of the stress tensor
\(\sigma _{ij}\), in the corresponding material directions,
\(f_{R}\) is the strength in the radial direction,
\(f_{T}\) is the strength in the tangential direction,
\(\tau _{RT}\) is the rolling shear stress, and
\(f_{v,RT}\) is the rolling shear strength of wood.
For in-plane stress states in orthotropic materials, this uniaxial strength criterion can simply be extended to one, which considers orthotropic material properties and linear interaction (Aicher and Klöck
2001). For stresses in the R-T plane of wood this reads as
$$\begin{aligned} \frac{\sigma _{RR}}{f_R}+\frac{\sigma _{TT}}{f_T}+\frac{\tau _{RT}}{f_{v,RT}}=1. \end{aligned}$$
(4)
The widely used Hankinson (
1921) formula to determine the strength,
\(f_{\theta }\), of wood loaded under an angle
\(\theta\) to the grain was derived from a linear strength criterion. The Hankinson’s formula can be expressed as
$$\begin{aligned} f_{\theta }={\frac{f_L\cdot {f_{\overline{RT}}}}{f_L\cdot {sin^{n}}\theta +f_{\overline{RT}}\cdot {cos^{n}}\theta }} , \end{aligned}$$
(5)
where
\(f_L\) is the strength parallel to the grain and
\(f_{\overline{RT}}\) is the strength perpendicular to the grain.
\(f_{\overline{RT}}\) is used in engineering applications as an effective strength perpendicular to the grain, which could be replaced by the strengths in the radial or tangential direction. In general,
n = 2 is used for compressive strength and
n = 1.5 is used for tensile strength (Mascia and Simoni
2013).
The simplest quadratic criterion resulting in an ellipsoidal failure surface for in-plane stress states in R-T plane can be written as
$$\begin{aligned} \left( \frac{\sigma _{RR}}{f_R}\right) ^2+\left( \frac{\sigma _{TT}}{f_R}\right) ^2+\left( \frac{\tau _{RT}}{f_{v,RT}}\right) ^2=1, \end{aligned}$$
(6)
and would allow for exploitation of a larger stress space compared to the linear interaction criterion given in Eq. (
4).
The von Mises strength criterion is based on the maximum distortional energy theory. It assumes that the hydrostatic part of the stress tensor does not contribute to the yielding of the material. The von Mises criterion is given as
$$\begin{aligned} \left( \frac{\sigma _{RR}}{f_R}\right) ^2-\frac{\sigma _{RR}\sigma _{TT}}{{f_R}{f_T}} +\left( \frac{\sigma _{TT}}{f_T}\right) ^2+3\left( \frac{\tau _{RT}}{f_{v,RT}}\right) ^2=1. \end{aligned}$$
(7)
This criterion includes an interaction term between the normal stresses that is not included in the quadratic failure criterion in Eq. (
6). This interaction term affects the shape of the failure envelope. The von Mises criterion is applicable to materials that exhibit metal-like plasticity, but not to wood.
Hill (
1950) extended the von Mises strength theory by considering that a material behaves anisotropic when plasticity occurs. For plane stress states, the criterion reads as
$$\begin{aligned}&\left( \frac{\sigma _{RR}}{f_R}\right) ^2-{\sigma _{RR}\sigma _{TT}}\left( \frac{1}{f_R^2}+\frac{1}{f_T^2}-\frac{1}{f_L^2}\right) \nonumber \\&\quad +\left( \frac{\sigma _{TT}}{f_T}\right) ^2+ \left( \frac{\tau _{RT}}{f_{v,RT}}\right) ^2=1. \end{aligned}$$
(8)
Later on, Azzi and Tsai (
1965) adopted this criterion to the case of transversely isotropic composite materials. This criterion is known as Tsai-Hill criterion and for plane stress states, it can be expressed as
$$\begin{aligned} \left( \frac{\sigma _{RR}}{f_R}\right) ^2-\left( \frac{\sigma _{RR}\sigma _{TT}}{f_R^2}\right) +\left( \frac{\sigma _{TT}}{f_T}\right) ^2+\left( \frac{\tau _{RT}}{f_{v,RT}}\right) ^2=1. \end{aligned}$$
(9)
This criterion has been applied to a number of applications in timber engineering problems (Cabrero et al.
2012; Mascia and Simoni
2013).
One of the first strength criteria for wood was formulated by Norris (
1962), who postulated that failure of the material would happen if any one of the following three equations are satisfied,
$$\begin{aligned}&\left( \frac{\sigma _{RR}}{f_R}\right) ^2-\frac{\sigma _{RR}\sigma _{TT}}{{f_R}{f_T}}+\left( \frac{\sigma _{TT}}{f_T}\right) ^2+\left( \frac{\tau _{RT}}{f_{v,RT}}\right) ^2=1, \end{aligned}$$
(10)
$$\begin{aligned}&\left( \frac{\sigma _{RR}}{f_R}\right) ^2=1, \end{aligned}$$
(11)
$$\begin{aligned}&\left( \frac{\sigma _{TT}}{T}\right) ^2=1. \end{aligned}$$
(12)
The only difference between the von Mises criterion in Eq. (
7) and the Norris criterion in Eq. (
10) is the factor, which multiplies with the shear term. Hence, it gives the same surface as von Mises in a normal stress plane, but a different surface when considering the interaction between normal and shear stress.
All of the above-mentioned anisotropic failure criteria consider the tensile and compressive strength of a material to be the same, which is not the case for wood. Note, for plane stress states for the herein considered combination of normal and shear stress, Quadratic, Tsai-Hill, Hill, and Norris failure criteria reduce to the same limit curve.
Hoffman (
1967) proposed a failure criterion based on Hill’s criterion, accounting for the difference between the tensile and compressive strength of the material,
\(f_{c,R}\) for
\(\sigma _{RR}<0\),
\(f_{t,R}\) for
\(\sigma _{RR}>0\) and
\(f_{c,T}\) for
\(\sigma _{TT}<0\),
\(f_{t,T}\) for
\(\sigma _{TT}>0\). It was originally formulated as a quadratic function (Schellekens and De Borst
1990) with nine independent variables. By substituting the material coefficients determined from experiments, Hoffman’s failure criterion for plane stress can be written as
$$\begin{aligned}&\left( \frac{\sigma ^2_{RR}}{f_{t,R}{f_{c,R}}}\right) +\left( \frac{\sigma ^2_{TT}}{f_{t,T}{f_{c,T}}}\right) -\left( \frac{\sigma _{RR}\sigma _{TT}}{f_{t,R}{f_{c,R}}}\right) +\left( \frac{\tau ^2_{RT}}{f^2_{v,RT}}\right) \nonumber \\&\quad + \sigma _{RR}\frac{f_{c,R}-f_{t,R}}{f_{t,R}f_{c,R}}+\sigma _{TT}\frac{f_{c,T}-f_{t,T}}{f_{t,T}f_{c,T}}=1, \end{aligned}$$
(13)
where the index
\(_t\) indicates the tensile strength properties and
\(_c\) indicates the compressive strength properties. This criterion has been widely used in the ductile failure in metals, as well as for brittle failure in fibrous materials like wood (Mascia and Simoni
2013).
Tsai and Wu (
1971) proposed a considerably more versatile tool to handle multi-axial stress states, and thus the combination of normal stresses with shear stresses, in terms of strength tensors in polynomial form. This criterion is an invariant to coordinate transformation. It can be represented in index notation as
$$\begin{aligned} F_{ij}\sigma _{ij}+F_{ijkl}\sigma _{ij}\sigma _{kl}=1, \end{aligned}$$
(14)
where
\(F_{ij}\) is the second order strength tensor and
\(F_{ijkl}\) is the fourth order strength tensor. The equation can be written in expanded form for plane stress conditions in the R-T plane as
$$\begin{aligned}&F_{RR}\sigma _{RR}+F_{TT}\sigma _{TT}+F_{RRRR}\sigma _{RR}^2+ F_{TTTT}\sigma _{TT}^2 \nonumber \\&\quad + 2F_{RRTT}\sigma _{RR}\sigma _{TT}+F_{RTRT}\tau _{RT}^2=1 \end{aligned}$$
(15)
where the coefficients are defined as
$$\begin{aligned}&F_{RR}= {\frac{1}{f_{t,R}}}-{\frac{1}{f_{c,R}}}, \end{aligned}$$
(16)
$$\begin{aligned}&F_{TT}={\frac{1}{f_{t,T}}}-{\frac{1}{f_{c,T}}}, \end{aligned}$$
(17)
$$\begin{aligned}&F_{RRRR}=\frac{1}{f_{t,R}f_{c,R}}, \end{aligned}$$
(18)
$$\begin{aligned}&F_{TTTT}=\frac{1}{f_{t,T}f_{c,T}}, \end{aligned}$$
(19)
$$\begin{aligned}&F_{RRTT}=F_{RRTT}^{*}\sqrt{\frac{1}{f_{t,R}{f_{c,R}}{f_{t,T}}{f_{c,T}}}}, \end{aligned}$$
(20)
$$\begin{aligned}&F_{RTRT}=\frac{1}{f^2_{v,RT}}. \end{aligned}$$
(21)
Compared to the other failure criteria discussed above, the Tsai-Wu criterion includes an interaction coefficient,
\(F_{RRTT}\), that is independent of uniaxial strength values. A prior biaxial experiment is required to determine the value of this interaction term. In other failure criteria like Hill, Tsai-Hill, Norris, and Hoffman, the stress interaction term was defined from uniaxial strength values only. For stability conditions and to get a closed failure surface the following condition has to be fulfilled
$$\begin{aligned} F_{RRRR}F_{TTTT}-{F_{RRTT}}^2\ge {0}, \end{aligned}$$
(22)
which consequently limits the interaction term to
\({-1}\le {F_{RRTT}^{*}}\le {1}\).
Kasal and Leichti (
2005) mentioned that this term can be defined in several ways depending on the testing procedure of generating the biaxial stress state. Hence, different researchers have used different methods to account for this interaction. According to Kasal and Leichti (
2005), another interaction term involving shear stress should also be considered in Eq. (
15). They state the difficulties of determining this interaction coefficient as a reason for omitting additional shear interaction terms.
Eberhardsteiner (
2013) carried out numerous biaxial experiments on clear wood of Norway spruce in the L-R plane, which were subjected to two orthogonal normal stresses for the different load to grain angles. Cruciform Norway spruce test specimens were displacement-loaded along different displacement paths, prescribing different ratios of the orthogonal displacements. Tests were performed with different grain angles in the test specimen, which led to numerous investigated stress states with shear in the L-R plane. The point corresponding to the initial maximum stress value (Mackenzie-Helnwein et al.
2003) of any of the global normal stresses was considered as material failure. The obtained failure envelope revealed an elliptical surface that agrees well with the elliptical failure criteria, though this kind of phenomenological failure criterion was unable to distinguish between different failure modes. The experiments included even pure shear stress in the L-R plane, which was obtained for a grain angle of 45° and a displacement ratio of 1:1. Based on these experiments, Mackenzie-Helnwein et al. (
2003) defined a multi-surface orthotropic failure criterion in plane-stress that considered four surfaces for four failure modes; namely for tensile or brittle failure mode in the fiber direction, brittle tensile failure mode in perpendicular to the grain direction, parallel to the grain compression failure mode, and ductile failure mode in compression perpendicular to the grain. The biaxial experimental data from Eberhardsteiner (
2013) was further used by Cabrero et al. (
2012) to validate some of the established phenomenological anisotropic failure criterion for wood in the L-R plane. The study showed that none of the failure criteria could predict a full failure envelope, but failure envelopes rather depend on biaxial stress-state, in terms of the combination of tensile stress, compressive stress or both. The best suited criteria in one stress-state could be the worst in another stress-state. For the first quadrant with tension parallel and perpendicular to the grain combination, the best-suited criteria were Cowin, Norris, and Tsai-Wu, whereas in the fourth quadrant, comprising of compression parallel to the grain and tension perpendicular to the grain, Norris and Cowin were the worst-fitting criteria. However, it remains unclear whether similar conclusions would be found in the R-T plane, which is the aim of this work.
Mascia and Simoni (
2013) conducted a study of failure criteria, such as Hill, Tsai-Hill, Tsai-Wu, Hoffman, and Norris by comparing them to uniaxial and biaxial experimental tests carried out by Todeshini, cited in Mascia and Simoni (
2013), on two Brazilian wood species,
Pinus elliotti and
Goupia glabra. The experiments were conducted to combine the compression parallel to the grain with the perpendicular to the grain stress, shear, and off-axis tensile test. The investigation showed that Tsai-Hill and Hoffman criteria fitted more adequately than other criteria for both species. They mentioned that the failure curves generated by Tsai-Wu, Tsai-Hill, and Hoffman differ significantly in the third (combined compression) and fourth (compression with tension) quadrant, but they were similar in the first (combined tension) and second quadrant (tension with compression). However, regarding failure surface for the combination of stress perpendicular to the grain with rolling shear, the investigation is limited to two quadrants, since with the combination of rolling shear with compression or with tension perpendicular to the grain, no distinction between positive and negative shear stresses is made.
Steiger and Gehri (
2011) used the experimental results from Spengler (
1982) and other sources, as well as their own shear tests on glulam beams to validate the SIA 265 design equation (SIA 265
2012), defining the strength for the combination of stress perpendicular to the grain with L-R shear stress. They state that the tension perpendicular to the grain and shear strength, as well as their interaction, are influenced by the size of the stressed-volume, as seen from the determination of the shear stiffness and strength of glulam beams. Good correlation was observed between the biaxial experiments by Spengler (
1982) and the SIA 265 design equation. The latter is based on the assumption that
i
the applicable shear stress is equal to the shear strength when the stress perpendicular to the grain is zero;
j
shear stress reduces with increasing tensile stresses perpendicular to the grain and becomes zero when the tensile strength perpendicular to the grain is reached;
k
shear stress can be increased above the pure shear strength, up to maximum applicable shear stress at the compressive strength perpendicular to the grain. A further increase in loading will induce crushing failure due to compression perpendicular to the grain.
The design equation is based on an elliptical failure criteria and is given below in R-T plane, for the range of
\(-f_{c,\overline{RT}}\le \sigma _{\overline{RT}}\le {f_{t,\overline{RT}}}\), with
\(f_{c,\overline{RT}}\) as the strength perpendicular to the grain in compression and
\(f_{t,\overline{RT}}\) as the strength perpendicular to the grain in tension.
$$\begin{aligned} \left( \frac{f_{c,\overline{RT}}+\sigma _{\overline{RT}}}{f_{c,\overline{RT}}+f_{t,\overline{RT}}}\right) ^2+\left( \frac{\tau _{RT}}{f_{v,RT}}\right) ^2\left[ 1-\left( \frac{f_{c,\overline{RT}}}{f_{c,\overline{RT}}+f_{t,\overline{RT}}}\right) ^2\right] \le {1}, \end{aligned}$$
(23)
where
\(\sigma _{\overline{RT}}\) is the stress perpendicular to the grain (
\(\sigma _{\overline{RT}}\) =
\(\sigma _{t,\overline{RT}}\) in case of tensile stresses perpendicular to the grain and
\(\sigma _{\overline{RT}}\) = −
\(\sigma _{c,\overline{RT}}\) in case of compressive stresses perpendicular to the grain), which in engineering applications as a simplification is not distinguished in radial and tangential directions but in design standards is rather specified as a tensile stress perpendicular to the grain
\(\sigma _{t,90}\) or compressive stress perpendicular to the grain
\(\sigma _{c,90}\). Note that this design equation is intended for application in timber engineering and commonly used with design values, with regards to material uncertainties.
5 Conclusion
A test setup to study the mechanical behavior of clear wood, under a combination of normal stresses perpendicular to the grain with rolling shear stress was developed. This was challenging due to the requirements of generating pure rolling shear, compressive, and tensile stress states as well as combined stress states in one experimental setup. The determined strain fields from experiments with a DIC system confirmed rather uniform and homogeneous strain development, and suitable failure modes were observed with the biaxial test setup. An investigation of the force imposing setup and specimen shape effects demonstrated the need for a continuous force transfer and force distribution effects in the specimen, which were most pronounced for testing in the tangential direction. Dog-bone shaped specimens were chosen to assess the biaxial failure criteria since the volume of interest and the failure region are well-defined.
Differences in material behavior in the radial and tangential directions were observed in the experimental study. Modulus of elasticity was found higher in the radial direction than in the tangential direction. Minor differences were even observed for the two orientations in rolling shear testing. Uniaxial material properties and strength, in tension, compression, and shear were in good agreement with previous studies.
Testing along 12 displacement paths with different ratios of tensile/compressive and shear displacements, covered the stress space in the transverse plane of wood well. A small transition zone from brittle failure in tension and shear to ductile failure in shear-compression combinations was observed. Moreover, the combination of rolling shear stress with compressive stress led to an increase in the rolling shear strength, before the shear strength was reduced at higher compressive stress levels. This phenomenon is also observed in combination with longitudinal shear stresses in wood.
Finally, the experimental data was compared with Hill’s and Hoffman’s failure criteria and the SIA 265 design equation for longitudinal shear interaction with stresses perpendicular to the grain. Overall, Hoffman’s failure criterion yielded the highest prediction quality with experimentally evaluated failure stresses, in specimens with radial compression. For tangential compression, however, Hill’s failure criterion gave less error than Hoffman’s criterion, due to higher variation in experimental results. A positive effect on rolling shear with compression perpendicular to the grain was observed in experiments, though it was not well predicted by Hill’s or Hoffman’s failure criteria. The SIA 265 design equation is better suited for this phenomenon in the transition from shear to compression. Thus, a more complex mathematical function or a combination of criteria in a so-called multi-surface failure criterion would be better suited to include the positive influence of rolling shear in the failure of wood for such stress interaction.
The findings of the experimental campaign demonstrate the challenge in determining material properties, which obviously are often rather system properties than material characteristics. Therefore, the combination of the experimental data with numerical modeling for the development of a material model that suitably represents the elasto-plastic macroscopic material behavior would give further insight into the suitability of the test setup. Corresponding numerical models of specimens in the test setup have been developed and the results will be presented in another article. The potential of the test setup can be utilized to build a sound database for engineering design and future model validation by investigating the material behavior at other moisture contents relevant for engineering applications and testing of further wood species.