Analysis of the properties of strain gage measuring points on wood
Introduction
Strain measurements on wood materials using directly applied electrical strain gages (SG) have been successfully carried out at various research facilities in the past. Basic observations and application examples can be found in [1].
Article [2] also concerns itself with questions about reliability and measurement
accuracy. In [3], SG measurements are compared with results obtained from Moiré measurements.
In comparison to the standard applications of SGs on metallic components, the following additional problems arise:
- Natural wood and wood-based materials such as chipboard do not have a homogenous structure. They are cellularly irregular in structure or composed of individual components. This results in large local strain differences. If an average strain value display is required, an SG must be selected with an active measuring area where the length and width are significantly larger than the cell structure and the dimensions of the individual components
- The installation of the SG, which creates a solid joint between the SG carrier and the component, must not influence the material properties of the component. This can only be approximately fulfilled when preparing
wood materials, as all standard adhesives penetrate into the porous surface and solidify it. - Ideally, an SG will follow the deformation of the component surface without interaction with it. This cannot be met in full. Although the metallic conductor, which influences the stiffness of the SG, is extremely
thin at just 5 μm, its modulus of elasticity is approx. 20 times greater than that of wood. - To determine the resistance change of the SG, it is operated in a Wheatstone bridge circuit with a constant bridge excitation voltage of UB = 0.5 …5 V as standard. The small amount of heat generated in the SG
passes into the base or the environment and plays practically no role in measurements on metallic components. Wood is a very poor heat conductor which hinders the compensation and leads to significant
heating of the measuring point and to thermal-based measurement errors. - In general, automatic temperature compensation on wood measurements are possible, but inadequate. This is because the thermal
expansion coefficient depends on the direction and the moisture in natural wood. Also, during warming, the process of positive thermal expansion is counteracted by the negative strain due to shrinkage.
Experimental investigations
Test setup
Test equipment was set up to investigate the properties of SG measuring points on wood, where a defined 4-point bending stress could be applied to the bending beams made of various types of wood (Fig. 1). An area was created
in the middle part of the beam where the lateral force disappears and only the bending moment occurs (Fig. 2). The bending line in this middle area corresponds to an arc. The reference strain can therefore be determined
from the difference in the deflection of the three measurement points. The loading is applied by a threaded spindle which is moved by means of an upper bridge. The total force P is divided here into the two partial forces P/2 acting on the beam.
Fig. 1: Test layout for the 4-point bending test
Fig. 2: Lateral force and bending moment curves
Fig. 3: User interface for data capture and limit value monitoring (catman®Easy)
The test layout comprised the following transducers for recording the total force, the deflection and the temperature, using HBM transducers for the mechanical parameters
- one force transducer (U2B - 10 kN)
- three displacement transducers (WA-T, measuring range 0 … 20 mm)
- one temperature sensor (Pt100).
All the transducers and the electrical strain gages under investigation were connected to a HBM Spider 8 amplifier system. The measurement settings and the measurements were implemented using HBM’s catman®Easy data capture software.
The user interface developed specially for these investigations is shown in Figure 3. All measured and calculated parameters (force, deflection, temperature, strain) were observed and easily recorded with this interface.
In addition, three measurement parameters – deflection in the center of the beam, force and strain values – were monitored to avoid any overload of the test specimen or damage to the SG due to excessive strain.
Test specimen and SG preparation
The test specimens were cut from three different wood types – Oak (Quercus robur), copper beech (Fagus sylvatica) and fir (Abies etis) – to a precise length of 300 mm and a square crosssection of 20 x 20 mm.
The fiber direction was orientated along the test specimen. At the start of the test, all samples had the same moisture content and same temperature.
Strain gages with measuring grid lengths of 6, 10, 20 and 50 mm were applied with superglue X60 precisely in the middle of each test specimen. The SGs were connected with the amplifier in a half-bridge configuration, with one SG acting as a dummy for temperature compensation.
This SG was applied to an identical test specimen positioned in front of the test equipment that is not mechanically loaded. Figure 4 shows prepared SGs.
Determination of the reference strain
The reference strain was determined on the basis of the deflection measured at three points. To minimize the influence from the impression of the bearings, the measuring points must lie in the middle area and be a certain distance from the force application points. The strain of the edge fibers results through geometric observations of the curvature. If one observes the curvature of the neutral fibers, this gives rise to the conditional equation (1).
Fig. 4: Wood samples with SGs of different lengths
Here, d is the distance between the measurement points (displacement transducers), s the difference of the deflections between the middle and side transducers, and H the height of the beam cross-section.
A similar relationship arises when the curvature of the outer fibers is observed, whereby this case is closer to the experimental layout.
There is practically no difference between the two equations at small deformations. The determined strains deviate less than 0.2 % from each other. This presupposes that the neutral fibers are positioned at half the cross-section height.
Test program and results
In the preliminary tests, the accuracy of the equations (1) and (2), which are based on the evaluation of the curvature, are compared with another evaluation equation which results from the bending line and which only requires the deflection f in the middle of the beam as the measurement value.
These results are shown in Figure 5 and show that the strain values determined from the pure bending measurement as in equation (3) are significantly too high. This deviation can be explained by the unavoidable impressions at the force application points, which simulate a strain that is too high. Therefore all following measurements are evaluated using equation
(2).
The influence of the excitation voltage on the measured strain was also investigated. These results are given in Figure 6. The influence of the bridge excitation voltage was, however, so low that it is barely visible in the graphical representation.
Fig. 5: Strain gradient based on equations 2 and 3, and an SG measurement
Fig. 6: Strain gradient dependent on bridge excitation voltage UB
It was thought that the heating of the SG could play a significant role. To test this temperature sensors were applied to the SGs.
Figure 7 shows the temperature increase on the SG, starting from the room temperature. However, the resulting temperature increase was very low. Although the effects on the measured strain could be taken into account, the resulting errors were so small that they could be ignored even when using a quarter bridge. In these tests, it was assumed that the temperature increase occurs in both SGs on the half-bridge (active SG and dummy) resulting
in an error that was virtually zero.
Numerous measurements were carried out to investigate the influence of the SG length. Test specimens made of oak were investigated using SG lengths of 6 mm, 10 mm, 20 mm and 50 mm. Following the evaluation of these results, the other wood types were tested using only 10 mm long SGs.
Examples of the results are shown in Figures 8 to 12.
Fig. 7: Temperature increase at SG with different excitation voltages
Fig. 8: Loading-strain curves for oak. SG length 6 mm
Fig. 9: Loading-strain curves for oak. SG length 10 mm
Fig. 10: Loading-strain curves for oak. SG length 50 mm
Fig. 11: Loading-strain curves for copper beech. SG length 10 mm
Fig. 12: Loading-strain curves for fir. SG length 10 mm
Numerical simulations
The experimental results show that the strains measured with the strain gages are generally smaller than the reference strain. One cause can be found in the stiffening effect of the SG system adhesive. For this reason, supplementary FEM simulations were implemented. The models used include the wood test specimens, the adhesive layer of X60 and the strain gages. The elastic properties of the individual components were depicted by the real geometry
and the determined E-moduli.
- Layer of X60 adhesive: d = 0.1 mm, E = 3500 N/mm2
- Strain gage: d = 0.075 mm, E = 6800 N/mm2
Fig. 13: FE simulation, Strain in longitudinal direction
Fig. 14: FE simulation, strain in longitudinal direction (section from Figure 13)
The longitudinal strain distributions along the beams and in the SGs are shown in Figures 13 and 14. Figures 15 and 16 show the trend of the longitudinal
strain in a track, longitudinally across the strain gages for SGs with different grid lengths. This makes it clear that the strain values in the SG are approximately 2 % below the strain at the side fibers of the bending beam.
Evaluation and conclusions
The aim of this investigation was the analysis of SG measuring point properties on wood. Different influences such as temperature increase, bridge
excitation voltage and SG length were investigated separately. An FE simulation, in which the wood beams, adhesive and SGs were modeled, completed the analysis. This attempted to determine the effects
of local reinforcement on the results and to explain the experimental findings.
Due to the different behavior of the wood with regards to tensile and compressive forces (E-modulus), the measured strain values of the top and
bottom fibers of the bent beam were not identical.
The neutral fibers apparently shift in the direction of the pressure side. The strain differences between the outer fibers increase with decreasing
SG length.
Fig. 15: FE simulation, longitudinal strain across SG (grid length 6 mm)
Fig. 16: FE simulation, longitudinal strain across SG (grid length 10 mm)
All measurements gave values smaller than the actual strain values. This is due to the local reinforcement effect caused by an SG fitted on a material with a low E-modulus. Recalibration of the SG is needed for correct measurements. The actual gage (k) factor* of the SG, which deviates from the gage (k) factor specified by the SG manufacturers for metallic component materials, was determined for this purpose. These k* factors are given for various investigated
SGs and wood types in Table 1.
Tab. 1: Experimentally determined gage (k) factors of SGs when installed on wood
These values represent the mean value of the values that apply for SGs on the pressure and tension sides. It can be seen that k* is dependent on the SG length and also on the E-modulus of the wood.
E-moduli were calculated for the investigated wood types during the evaluation of the investigation. These values are shown in Table 2 in comparison with data from various references ([4] – [8]).
Tab. 2: Measured E-moduli compared with values from literature
References
[1] F.-W. Bröker: Dehnungsmessungen an Holz mit direkt applizierten DMS, Messtechnische Briefe 21 (1985) Issue 1, Pages 18-23
[2] R. J. Beer; M. Vanek; H. D. Walden: Zuverlässigkeit einer DMS-Messstelle auf Holz, Kurzzeitstabilität-Langzeitverhalten, Holzforschung und Holzverwertung (Austria) 1990, 42(3) Pages 48-51
[3] P. Niemz, J. Schreiber, J. Naumann, M. Stockmann. Experimentelle Ermittlung der Dehnungen im Probenquerschnitt bei Biegebelastung von Holzpartikelwerkstoffen, Holz Roh Werkst, 65, pp. 459–468, 2007.
[4] DIN ; DIN 4076 Part 1, October 1985 / DIN 68364, November 1979; Beuth-Verlag
[5] Vorreiter, L.; Holztechnologisches Handbuch; Volume 1; Verlag Georg Fromme & Co.; Vienna 1949
[6] Sell, J.; Eigenschaften und Kenngrößen von Holzarten; 3. Edition; (collection of older sources); Baufachverlag AG; Zurich 1989
[7] Wagenführ, R., Scheiber, C. ; Holzatlas ; 3. Edition; VEB Fachbuchverlag Leipzig, Leipzig, 1989
