- 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

ABSTRACT INTRODUCTION THE EFFECT OF GRAIN ANGLE THE EFFECT OF THE FRICTION EXPERIMENTAL METHODS RESULTS CONCLUSIONS REFERENCES

ABSTRACT

Among the construction materials, wood, because of its internal structure, has axes of elastic symmetry longitudinal, tangential and radial, revealing an orthotropic pattern. Thus, there are 9 constants to be determined.
Many procedures have been used to analyze the wood behavior under a uniaxial stress field and determined the elastic constants of wood using uniaxial compression tests. On the other hand, the wood behavior when it is subjected to a three-dimensional stress field is unknown. Using triaxial (confined) compression tests this stress field can simulate and, consequently, it is possible to evaluate the wood's constants and their relationship. The specimen consisted of four-inch (about 10 cm) solid redwood cubes with different fiber orientation and physical properties.
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's 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 in redwood and then comparing them with uniaxial compression test. The current data may be considered to agree with the published values, except for the tangential directions. Theses values exhibit the effects of the boundary condition, or better, the effects of the friction.

Keywords: Orthotropy, Wood, Triaxial Test, Uniaxial Test, Elastic Constants.

INTRODUCTION

An investigation of the literature showed that many procedures have been used to analyze the wood behavior under a uniaxial stress field and determined the elastic constants of wood using uniaxial compression tests. Conversely, the wood behavior when it is subjected to a three-dimensional stress field is unknown, as described by Cramer, Hermanson and McMurthy (1996). This stress field can be simulated by using confined compression tests and, consequently, it is possible to evaluate the wood's constants and their relationship. This system was developed at the University of Wisconsin, Madison and the specimen consisted of 10 cm- solid redwood cubes with different fiber orientation and physical properties.

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).

THE EFFECT OF GRAIN ANGLE

Basically, the variation of grain angle constitutes the fundamental cause of wood anisotropy. It is responsible for the greatest changes in the values of the constitutive tensor components, and, thus in the wood elastic constant value.

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:

(1)

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:

(2)
where: are the direction cosines.

Now, by means of the equation (3), we can determine, for example, S₁₁₁₁ , S₂₂₂₂ , _S3333 or, simply, the board elastic moduli, E_i by:

(3)
where: i= x, y, z, G_ij are the shear moduli, n_ij are the Poisson´s ratios.

THE EFFECT OF THE FRICTION

Since the relationship between stress and strain must be uniform in order to determine the elastic constants, by applying the Hooke's Law, we must consider using a test device and a specimen configuration as well, to avoid perturbation in stress and strain fields. Then, it is convenient to measure the strains as far as possible from the contact between the specimen and the test device surface.

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.

EXPERIMENTAL METHODS

The specimens which were used consisted of solid cubes of 10.16cm by 10.16 cm , fabriced from 15.24cm by 15.24 cm lumber, 5.40m to 6.60m in length of Redwood species, with fiber orientation with respect to the applied vertical load varied from 0 to 90° in predetermined increments.

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.

RESULTS

The average modulus of elasticity (E) of 60 specimens can be seen in the following table:

Axes	Eunc	Econf	Etheo
Longitudinal	8660	5660	7250
Radial	575	623	605
Tangential	236	378	445

Table 1 - Measured and Theoretical Moduli of Elasticity(Mpa)

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.

CONCLUSIONS

In general, the most important conclusions can be summarize as follows:
-The current data of unconfined elastic moduli may be considered to agree with range of the theoretical values of E, except for the tangential directions. The same conclusion is not valid to the confined elastic moduli.

-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.

REFERENCES

1. Bodig, J., and Jayne, B.A. (1982). Mechanics of Wood and Wood Composites. Van Nostrand, New York, N.Y.
2. Cramer, S. M., Hearmonson, J.C., Mcmurthy, W. M. (1996)Characterizing Large Strain Crush Response of Redwood. SANDIA REPORT. SAND96- 2966.UC-820, Sandia National Laboratories.
3. Goodman, J.R., and Bodig, J. (1970) "Orthotopic Elastic Properties of Wood. "J. of Struct. Div., 96(11), 2301-19.
4. Hearmon, R.F.S. (1948) "The Elasticity of Wood and Plywood." Forest Products Res. Special Rep. No. 7, Dep. of Scientific and Industrial Res., London, U.K.
5. Hearmonson, J.C. (1996) "The Triaxial Behavior Of Redwood Using A New Confined Compression Device." PhD thesis, Dept. of Civil Engrg.,Univ. of Wisconsin.
6. Hearmonson, J.C., Stahl, D.C., Cramer, S.M., Shaler, S.M. (1997) "Transformation of Elastic Properties for Lumber with Cross Grain." J. of Struct. Div. 123(1), 1402-08.
7. Mascia, N.T. (1995) "A Study Of The Homogeneity In The Mechanics Of Wood Deformation". Proc.,PACAM IV- Fourth Pan American Congress of Applied Mechanics.Buenos Aires, Argentina.
8. Saliklis, E. (1992)"A Nonlinear Constitutive Model of Paperboard." PhD thesis, Dept. of Civil Engrg.,Univ. of Wisconsin.

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.