Fatigue testing of wood up to one billion load cycles

2.1 Material and sample preparation

The investigated material was flawless birch wood (B. pendula) from Austria. The material was obtained from a conventional timber trading company (Frischeis, Austria). For perfect fibre orientation, the samples were split from the board with a wedge, planed on four sides and sent to a special company for turning (Holzdrehscheibe Drechslerei Prohaska, Austria). Prior to sample preparation, the wood was stored in a climate chamber (65% rel. humidity, 20 °C) until equilibrium moisture content of 12%. Uniaxial fatigue tests were carried out with loading parallel to the grain. Prior to testing, the specimens were ground with abrasive paper up to a grade of #2000 to obtain a smooth surface finish for strain gauge application. The specimen shapes used in conventional and ultrasonic fatigue testing are shown in Figure 1.

Figure 1:

Specimen shapes used in the present investigation: in ultrasonic fatigue tests (a) and in servo-hydraulic fatigue tests (b); all dimensions are in mm.

The mechanical properties of the investigated material are listed in Table 1. 63 and fifteen specimens were used to determine density and Young’s modulus, respectively, by standardised procedure.

Additionally, Young’s modulus and static strength were determined using the specimen shape shown in Figure 1b, in order to avoid the need for considering possible size effects. For this purpose, a servo-hydraulic load frame operating in force-control mode was employed. Three specimens were used to measure ultimate tensile and compressive strength, respectively at a force rate of 0.03 kN/s. Four specimens were used to determine the Young’s modulus simultaneously by contact extensometer and strain gauge at a force rate of 0.015 kN/s.

The environmental condition for all tests performed was laboratory air, featuring a relative humidity of 50% and 23 °C. The specimens were stored under this condition for a minimum of three days prior to testing in order to ensure a uniform moisture content. It has to be noted that adapting temperature and humidity to meet standard conditions for wood testing (i.e. 20 °C and 65% RH) was not possible due to diverse experiments running simultaneously in the laboratory.

2.2 Ultrasonic fatigue testing at 20 kHz

In ultrasonic fatigue tests, specimens, rather than being stressed by external forces, are excited to resonance vibrations. Specimens are mounted into a load train consisting of components of specific shapes and lengths that are constrained by resonance condition at ultrasonic frequency. Both ends of each component vibrate in opposite directions resulting in vibration nodes with maximum strain and stress in their centres. The basic version of such a load train features an ultrasonic transducer to generate high frequency vibrations, a titanium horn to magnify the vibration amplitude, and the test specimen whose lower end vibrates freely under fully reversed loading. However, for the purpose of superimposing static loads or for suppressing undesired excitation modes, the ultrasonic load train can be extended by additional mounting parts.

A piezo-electric transducer generates soundwaves in the range of ultrasonic frequencies that travel through the components of the load train. The velocity, v_S, in a cylindrical component is determined by the Young’s modulus, E, and the density, ρ, of its constituting material according to:

with λ being the wavelength and f being the frequency of the ultrasonic soundwave.

The ultrasonic fatigue testing equipment employed in the present investigation is shown in Figure 2. The ultrasonic load train was extended by two titanium rods mounted at the upper and lower end of the specimen. The specimen itself was attached on both ends to aluminium threads by using ARALDITE^® 2014-1 adhesive, in order to fit into the load train.

Figure 2:

Ultrasonic fatigue testing equipment: Overview of electronic components and ultrasonic load train (left); detail of the specimen mounted between two titanium rods, pressurised air-cooling and infrared thermometer (right).

Components of the ultrasonic load train have to meet resonance condition that is determined by density, Young’s modulus and shape of the respective component. Hence, components of different materials and shapes will feature different lengths when vibrating in resonance. In order to find the correct length of each component, the experimental test set-up consisting of specimen, aluminium threads and titanium rods has been simulated and analysed concerning its modal behaviour with the finite-elements analysis (FEA) software Autodesk^® Inventor Nastran 2022. The study was set up as the “Normal Modes” type assuming linear elastic behaviour. In order to simplify the simulation, linear elastic isotropic material behaviour representing the axial direction was used. The soundwave travelling through the specimen is a planar, one-dimensional wave travelling in the axial (i.e., x) direction. Consequently, all but the x-x component of the stress tensor resulting from modal vibration are zero i.e., only the Young’s modulus in axial direction is relevant and all other elastic constants (i.e. Young’s modulus in other directions and Poisson numbers) do not influence the mode in x-x direction. Density and Young’s modulus used for FEA, and lengths of the analysed components are listed in Table 2.

The solid bodies were meshed with triangular elements, where mesh resolution was determined via modal frequency convergence. Sufficiently high resolution was indicated with 0.3 mm mesh resolution over the gauge section (the rods experience much less deformation, consequently a much coarser resolution of 2 mm was sufficient). FEA post-processing allowed to extract stress, strain and displacement for every mesh element. The resulting distributions of displacement and strain across the ultrasonic load train for modal vibration at 19.1 kHz are shown in Figure 3.

Ultrasonic fatigue tests are displacement controlled. The vibration amplitude is measured with a vibration gauge that is positioned at the lower end of the magnifying horn, i.e. at the location where a vibration antinode occurs. The signal of the vibration gauge is used to control cyclic loading. Displacement at all antinodes along the load train is proportional to the strain in the centre of the specimen. In order to perform an ultrasonic fatigue test at a given stress amplitude, the linear correlation between displacement and resulting strain in the specimen’s centre is determined prior to testing (see 2.3.). The resulting stress amplitude, σ_a, applied on the material can then be calculated according to Hooke’s law:

with E being the Young’s modulus and ε_a being the strain amplitude.

The ultrasonic fatigue testing equipment employed in the present investigation has been developed at BOKU (Mayer 2016) guaranteeing a very high accuracy of process control. Closed-loop control circuits ensure an agreement of pre-selected and actual vibration amplitudes within ±1% and of excitation and resonance frequency within ±1 Hz, respectively. Furthermore, it allows for intermittent loading, i.e. cyclic loading is applied in pulses of 100 ms followed by pauses of appropriate lengths correspondent to the load level. Effective testing frequencies, i.e. numbers of cycles per second, of 380 s⁻¹ at stress amplitudes of 60 and 52 MPa, and 920 and 1760 s⁻¹ at stress amplitudes of 40 and 30 MPa, respectively, were used. Thus, and in addition to pressurised air-cooling, excessive self-heating of the specimens was prevented. By temperature monitoring using an infrared thermometer, it was ensured that the specimens’ temperature remains below 30 °C throughout the tests. Eleven specimens have been tested using the above-described test set-up.

2.3 Strain gauge measurements

Prior to the tests, the linear correlation between vibration amplitude and strain amplitude was determined by strain gauge measurements. Strain gauges of the type KFGS-1-120-C1-23 featuring a resistance of 120 Ω and a gauge size of 1 × 1 mm were attached at the upper and lower end of the gauge section of each specimen using the instantaneous adhesive CC-33A-5. Both strain gauges and instantaneous adhesive were by KYOWA^®. The strain gauges were used as quarter bridge with a bridge voltage of 5 V.

In order to investigate the accuracy of strain gauge measurements, static tension-compression tests using strain gauges and a contact extensometer, respectively, have been carried out on four specimens as shown in Figure 1b, i.e. featuring a gauge length of 10 mm. The applied contact extensometer of the type DD1 by HBM^® featured a gauge length of 8.5 mm. Three specimens have been loaded by tension and compression stresses up to limiting values of 80 and −50 MPa, respectively. One specimen was loaded solely by tension stresses up to 80 MPa. The hereby obtained data has been further used to determine the Young’s modulus for the given material and grain orientation.

2.4 Servo-hydraulic fatigue testing at 50 Hz

Conventional, force-controlled fatigue tests using a servo-hydraulic load frame have been carried out under fully reversed sinusoidal loading for comparison using eight specimens. The employed specimen shape featured the same gauge volume as used in ultrasonic fatigue testing in order to avoid the need for considering possible size effects and can be seen in Figure 1b. Four specimens have been tested at a load level of 40 and 52 MPa, respectively, at a loading frequency of 50 Hz. Limiting lifetimes were 5 × 10⁶ cycles.

3.1 Accuracy of strain gauge measurements

When comparing fatigue data obtained by servo-hydraulic and ultrasonic fatigue testing, the control mode of the respective testing system needs to be considered, i.e. force and displacement control, respectively. Given that ultrasonic fatigue tests are strictly performed in the linear elastic regime, the linear correlation between vibration amplitude and strain amplitude is determined prior to the test, and the resulting stress amplitudes are calculated by Hooke’s law. Hence, the validity of given values for applied stress amplitudes depends on the accuracy of the strain gauge measurement.

In particular, the quality of adhering of the strain gauge on the specimen’s surface may be an issue for a porous and fibrous material like wood since the required smoothness of surface is hardly achieved. Consequently, paste-like adhesives are usually applied in order to compensate for superficial unevenness, however, also leading to thicker adhesive layers that might generate measurement errors. Furthermore, the size of the strain gauge must be considered since inhomogeneous materials usually require larger and longer strain gauges. Therefore, the accuracy of the strain gauge measurements performed in the present study was investigated by comparing it to the signal obtained by a contact extensometer in stress-strain tests. The data generated in both the tensile and compressive regime up to 80 MPa and −50 MPa, respectively, are shown in Figure 4. The values for the Young’s modulus that were derived on basis of these data coincide within ±2% suggesting a high accuracy of the applied set-up.

Figure 3:

Results of finite element analysis: distribution of displacement (top) and strain (bottom) across the ultrasonic load train consisting of the specimen and two titanium rods and aluminium threads, respectively.

Figure 4:

Stress-strain data obtained by strain gauge and contact extensometer.

3.2 Presenting stress amplitudes against numbers of cycles to failures

Fatigue lifetime tests have been carried out under fully reversed loading conditions using eleven and eight specimens at testing frequencies of 20 kHz and 50 Hz, respectively. The results are shown in Figure 5. Stress amplitudes, σ_a, are plotted against numbers of cycles in a double-logarithmic diagram. Only two specimens tested at 20 kHz survived limiting lifetimes, i.e. 10⁹ load cycles, without failure. These are labelled run-outs and are marked with an arrow. Mean lifetimes as well as standard deviations are displayed by solid and dashed lines, respectively. Standard deviations were calculated assuming a Gauss-distribution of the fatigue lifetimes’ logarithms (Maenning 1997). Investigated lifetimes ranged from 10³ to 10⁹ load cycles. 50% fracture probability at 10⁴ and 10⁹ cycles were found at a stress amplitude of 55 and 29 MPa, respectively. Failures still occurred up to 10⁸ numbers of cycles, i.e. no fatigue limit has been found.

Figure 5:

Fatigue data of birch obtained by ultrasonic (red dots) and servo-hydraulic (blue dots) fatigue testing, stress amplitudes are plotted double-logarithmically against numbers of cycles to failure, specimens surviving limiting lifetimes of 10⁹ load cycles are marked with an arrow.

3.3 Influence of cycling frequency

As can be seen in Figure 5, there is good agreement between high and low frequency fatigue data. Considering the overlap of standard deviation of both data sets, S-N curves obtained at 20 kHz and 50 Hz are well comparable. This suggests a negligible effect of testing frequency for the investigated fully reversed cyclic tension-compression loading in the applied range of cycling frequencies. The ultrasonic fatigue testing technique is therefore appropriate for accelerated collection of fatigue data of birch. Furthermore, the present finding is well in accordance with a previous investigation of Sycamore maple, where no frequency effect on fatigue lifetimes could be observed (Schönbauer et al. 2022).

Few investigations about the effect of testing frequency on the fatigue life of wood are available in the literature and these are limited to the lower frequency range up to 10 Hz. The strongest influence of cycling frequency on stress-strain hysteresis and fatigue lifetimes was found in cyclic compression tests when loading was perpendicular to the grain direction (Clorius et al. 2000). In cyclic bending tests, where the principal stresses are parallel to the grain, influences of cycling frequency were found to be absent or small (Watanabe et al. 2014).

In the present study, no effects of frequency on fatigue lifetimes were observed. However, the investigated testing frequencies were of at least one order of magnitude higher than those studied in the literature. Whether wood shows an effect of frequency for lower frequencies than 50 Hz and for other loading modes (e.g. cyclic tension, cyclic compression), would therefore be a matter of further studies.

3.4 Presenting relative stress amplitudes against numbers of cycles to failure

In a previous study, the fatigue properties of Sycamore maple were studied at 50 Hz and ultrasonic frequency (Schönbauer et al. 2022). Sycamore maple, however, showed a lower cyclic strength than the presently investigated birch. In order to compare fatigue data of both materials, cyclic stresses can be normalised by the compressive strength of the respective material, when loaded at R = − 1. In this case, the stress amplitudes during the tensile and compressive part of a stress cycle are equal, however, the static compressive strength of wood is about half of its tensile strength, and therefore, the compressive part may be considered to be more damaging. This is in line with the cyclic strength being lower under cyclic compression than under cyclic tension (Schönbauer et al. 2022).

In Figure 6, fatigue lifetimes of birch are presented versus stress amplitudes, σ_a, normalised by the compressive strength, σ_c, obtained by using the same specimen shape as in fatigue tests in a double-logarithmic plot. Relative stress amplitudes, σ_a/σ_c, range from 68% to 36% of the compressive strength, σ_c, correspondent to fatigue lifetimes between 10⁴ and 10⁹ load cycles.

Figure 6:

Fatigue data of birch obtained by ultrasonic (red dots) and servo-hydraulic (blue dots) fatigue testing, relative stress amplitudes are plotted double-logarithmically against numbers of cycles to failure, specimens surviving limiting lifetimes of 10⁹ load cycles are marked with an arrow.

In Figure 7, the results of low and ultrasonic frequency fatigue tests with Sycamore maple are shown using relative stress amplitudes, σ_a/σ_c (Schönbauer et al. 2022). Figures 6 and 7 are presented for the same range of lifetimes, i.e. from 10³ to 10⁹ load cycles. Mean lifetimes of 10⁷ cycles were measured for relative stress amplitudes, σ_a/σ_c, of 0.46 ± 0.05 for birch (Figure 6) and 0.43 ± 0.07 for Sycamore maple (Figure 7) indicating that the correlation between relative stress amplitudes and cycles to failure is comparable for both materials.

Figure 7:

Fatigue data of sycamore maple (Schönbauer et al. 2022) obtained by ultrasonic (red dots) and servo-hydraulic (blue dots) fatigue testing, relative stress amplitudes are plotted double-logarithmically against numbers of cycles to failure, specimens surviving limiting lifetimes of 5 × 10⁶ and 10⁹ load cycles, respectively, are marked with an arrow.

This observation is in good agreement with the literature (Bond and Ansell 1998). In this study, a master S-N curve was derived from fatigue data obtained by three scarf-jointed species, Khaya, poplar and beech that have been tested under fully reversed axial fatigue loading up to limiting lifetimes of 10⁷. Taken into account the compressive ultimate strength of the respective wood composite, σ_c, the following correlation between cycles to failures, N and stress amplitude, σ _a , was obtained (Bond and Ansell 1998):

If this equation is used to predict the cyclic strength at numbers of cycles, N, of 10⁹, the formula predicts a fatigue strength, σ _w , of approximately 4% of the ultimate compressive strength, σ _c . This would suggest that wood could hardly be used for applications where such high numbers of load cycles occur. In the present study, experimentally observed fatigue strengths at 10⁹, however, were approximately 36% of the static strength for birch and 31% for Sycamore maple, respectively. Thus, the difference to the predicted value is significant and implies the necessity of actually performing very high cycle fatigue tests in order to accurately determine the fatigue strength.