NDT.net - November 1999, Vol. 4 No. 11 |
- International Symposium on NDT Contribution to the Infrastructure Safety Systems, 1999 NOV 22-26 Torres, published by UFSM, Santa Maria, RS, Brazil |
TABLE OF CONTENTS |
Keywords: Orthotropy, Wood, Triaxial Test, Uniaxial Test, Elastic Constants.
In order to check these results with the theoretical values, it is necessary to transform the angles measured on the surface of the specimen to Euler angles and apply the correct coordinate transformation tensor.In this way, the goal of this paper is to analyze the results of confined compression test (three-axial test)in redwood and then comparing them with unconfined compression test(uniaxial test).
Many researchers, in the theoretical and experimental point of view have long studied the effect of grain angle. One of the most important procedures was formulated by Hearmon (1940), who reported the effect of grain angles in all the components of Sijkl , showing that for wood it is possible to obtain negative values of Poisson's ratio, which emphasized the wood anisotropy.
One important study about the coordinate transformation was developed by Saliklis (1992) testing paperboard cubes under three-axial compression and another by Hermanson (1996) testing redwood blocks through confined tests. In these works it was supposed that shear strain did not interact with normal strain and did not occur in orthogonal directions. The strain-stress relations were given by:
Saliklis(1992) used a set of three tests with three different test orientations, each one under 90( rotation. It should be noted that there are a series of 6 equations and 12 unknowns. Saliklis (1992) and Hermanson (1996) used a singular value decomposition to find the unknown values .
Hermanson (1996), studying the transformation of elastic properties for lumber to align these axes x_{i} (x, y, z) with the material axes x'_{i} (L, R, T), used three rotations l, r and j (denoted Euler 's angles) about x, y and z axes and the surface angles(a,b,g), as can be seen in the figure 1.
Figure 1- Surface angles b and g |
In this way, it was possible to find the Euler's angles by knowing the surface angles and evaluating all wood elastic constants (S_{ ijkl })by using the complete coordinate transformation to elastic properties, given by:
Now, by means of the equation (3), we can determine, for example, S_{1111 } , S_{2222} , _{S3333 } or, simply, the board elastic moduli, E_{i }by:
The geometry of the specimen, expressed by the length(l) and width (d)ratio, constitutes an important parameter to take into consideration. Saliklis (1992) presented a theoretical diagram showing this ratio, where the percent error of E decreases as the length and width ratio increases. For example, to l/d=l the error reaches about 30% and to l/d=ll the error is 0%.
Figure 2- Saliklis's theoretical diagram about the percent error of Modulus of elasticity. |
Mascia (1995) showed, analyzing unconfined compression test, that to the ratio 3, the stress field in the central region of the specimen was a uniform field.
The moisture content varied between 12 and 45% according to the temperature conditions. The specific gravity were between 0.29 and 0.45. Three different temperature conditions were used: ambient temperature (18°C), cold temperature (28°C) and hot temperatura (65°C). The tests consisted of applying vertical load to redwood cube confined in an instrumental steel box as we can see in the Figure 3.
Figure 3- Confined compression tests. |
The vertical load was applied to two quasi-static displacement rates of 0.03556 cm per minute for the first 10 minutes and 0.668 cm per minute after.
In the confined triaxial test it is not possible to attach any sort of strain measurement device in the central part of the specimen. In this way, to compute nominal strains from the displacement measurement we have to include the effects of boundary conditions, on the friction effects. The unconfined test were performed in the same way but the lateral plates were taken off.
Axes | E_{unc} | E_{conf} | E_{theo} |
Longitudinal | 8660 | 5660 | 7250 |
Radial | 575 | 623 | 605 |
Tangential | 236 | 378 | 445 |
The E_{unc}'s values in Table 1 may be considered to agree with range of the theoretical values of E, except for the tangential directions. On the other hand the E_{conf}'s values exhibit the effects of the boundary condition, or better, the effects of the friction and the these values, in general, do not agree with the theoretical values of E.
-We can observe that the use of the test device and the specimen configuration are important to avoid perturbation in stress and strain fields. It is convenient to measure the strains as far as possible of the contact between specimen and test device surface. Then, the effect of the friction constitutes an important parameter to be considered.
Finally,it is important to notice that these conclusions are restricted to the current experimental data.
ACKNOWLEDGEMENTS
The authors would like to thank the Civil and Environment Department of University of Wisconsin-Madison/USA and Fapesp- Fundação de Âmparo à Pesquisa do Estado de São Paulo/Brazil for technical and financial support to carry out this research.
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