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Examination of the off-axis tension test method for evaluating the shear properties of wood.

Abstract

To obtain the shear properties of wood, we conducted various off-axis tension tests and examined their validity by comparing them with the Iosipescu tests. Shioji (Japanese ash, Fraxinus spaethiana Lingeish.) was used for the studies. Several uniaxial tension tests of the specimens with the off-axis angles of+45[degrees]/-45[degrees], 45[degrees], 15[degrees], and 20[degrees] were conducted, and the shear properties such as shear modulus, shear stress at the proportional limit, and shear strength were obtained from the shear stress/shear strain relation. By comparing the shear properties with those obtained by the Iosipescu shear tests conducted independently, we examined the validity of the off-axis tension test method for determining the shear properties of wood, and obtained the following results: 1) it was difficult to obtain the shear properties properly by the +45[degrees]/-45[degrees] off-axis tension test although this method is specified in the major standard for characterizing the shear properties o f fiber reinforced plastics; 2) in this experiment, the shear properties obtained from the 15[degrees] off-axis tension test were close to those obtained by the Iosipescu shear test; 3) in evaluating the overall shear stress/shear strain relation, the off-axis tension test is not effective because of the existence of other stress components. Therefore, another method is required for determining the shear stress/shear strain relation.

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To develop effective applications of wood and wood products, measurements must be taken of shear properties such as shear modulus and shear strength, as well as of tensile and compressive properties. For example, if a beam designed without considering the shear properties is used for a structure, it is deformed by the shearing force, which often causes it to fail. Thus the structure might collapse because of the failure of the beam. Therefore, it is desirable to estimate the shear properties as easily and accurately as possible.

It is difficult to measure the shear properties of a material because of the difficulty in simulating a pure shear stress condition. In spite of this difficulty, there are several methods for measuring the shear properties. For wood, shear test methods have been standardized by the American Society for Testing and Materials (ASTM) and Japanese Industrial Standards (115). These methods, however, can derive only the shear strength as a comparative index for evaluating the quality of a material (ASTM 1994, JIS 1994). They cannot determine the shear stress/shear strain behavior including the shear modulus and shear stress at the proportional limit. To determine these properties, the Iosipescu shear test is promising because the test can be done under the nearly pure shear stress conditions (ASTM 1998, Liu 2000b, Yoshihara et al. 2001). However, it requires a special attachment that limits the specimen configuration. Therefore, the Iosipescu shear test is rather difficult to conduct.

For advanced composite materials such as carbon fiber reinforced plastics (CFRP), the 45[degrees] off-axis tension test, consisting of two strips vertically cross-plied with each other, has been standardized as the +45[degrees]/-45[degrees] off-axis tension test (JIS 1991). In addition to the +45[degrees]/-45[degrees] off-axis method, a tension test method using a specimen whose length direction is inclined 10[degrees] with respect to the fiber direction was proposed (Daniel and Lieber 1975, Chamis and Sinclair 1977, Odegard and Kumosa 2000). Although a pure shear stress condition cannot be expected, the off-axis tension test is simple and promising as a standardized method determining the shear properties of wood (Ebrahimi 1979, Zhang and Sliker 1991, Liu and Ross 1998, Liu 2000a, Liu 2002). Unfortunately, the previous studies focused on the shear modulus or the shear strength, and the overall shear stress/shear strain relation was not evaluated. Thus, there is concern that the testing conditions under which the off-axis tension test is conducted may skew the measurement of shear properties.

In this research, we performed several off-axis tension tests for evaluating the shear properties of wood and examined whether the off-axis tension test is applicable or not by comparing the shear properties and overall shear stress/shear strain relation with those obtained by the Iosipescu shear test.

Experimental procedure

Materials

Shioji (Japanese ash, Fraxinus spaethiana Lingelsh.) whose density was in the range of 0.59 [+ or -] 0.03 g/[cm.sup.3] was used for the specimens. All specimens were cut from the same lumber, and were conditioned at 20[degrees]C and 65 percent relative humidity before and during the tests. Seven specimens were used for one testing condition. In the experiment conducted here, the shearing force was always applied in the longitudinal-tangential plane, hence the thickness direction coincided with the radial direction.

Off-axis tension tests of +45[degrees]/-45[degrees] and 45[degrees] specimens

From the material just described, strips with the grain direction at 45[degrees] were cut into the dimensions of 300 mm in length, 20 mm in width, and 3 mm or 6 mm in thickness. A pair of strips was laminated by acetic-vinyl adhesive with the grain directions perpendicular to each other, and making the thickness 6 mm or 12 mm. The specimen fabricated by cross-plying was defined as +45[degrees]/-45[degrees] specimen. Specimen configurations are shown in Figure 1. The tapered specimen had the thicknesses of 6 mm and 12 mm, whereas the straight specimen had the thickness of 6 mm. To prevent stress concentration due to the grips, rubber tabs with the thickness of 5 mm were bonded at both ends by cyano-acrylate adhesive. For determming the strain components, triaxial strain gauges (gauge length = 2 mm) (FRA-2-11, Tokyo Sokki Co., Ltd.) were bonded on both longitudinal-radial planes. Figure 2 shows the triaxial gauge arrangement. The loading direction, transverse direction, and 45[degrees] inclined direction were defined a s I, II, and III, respectively. Tensile displacement was applied at the crosshead speed of 5 mm/mm. and the load and three strains were simultaneously recorded by a data logger (TDS-303, Tokyo Sokki Co., Ltd.) at intervals of 5 seconds. From the tensile stress in the loading direction ([[sigma].sub.I]) and the strains in the loading and transverse directions ([[epsilon].sub.I] and [[epsilon].sub.II], respectively), the shear stress ([[tau].sub.xy]) and shear strain ([[gamma].sub.xy]) were derived as follows:

[[tau].sub.xy] = [[sigma].sub.1]/2 [1]

[[gamma].sub.xy] = [[epsilon].sub.I] - [[epsilon].sub.II] [2]

The shear modulus ([G.sub.xy]) and shear stress at the proportional limit ([Y.sub.xy]) were determined by formulating shear stress/shear strain relation (Yoshihara et al.). By the method of least squares, the [[tau].sub.xy]-[[gamma].sub.xy] relation was regressed into Ramberg-Osgood's function (Ramberg and Osgood 1943) represented as follows:

[[gamma].sub.xy] = [[tau].sub.xy]/[G.sub.xy] + K[([[tau].sub.xy]/[G.sub.xy]).sup.n] + c [3]

where:

[G.sub.xy] = shear modulus

K and n = material parameters

C = offset strain

The shear modulus was determined from Eq. [3], whereas the shear stress at the proportional limit was determined by the stress at the intersecting point of Eq. [31 and a straight line segment reducing the initial inclination by 3 percent, which is represented as follows (Kitahara 1956):

[[gamma].sub.xy] = [[tau].sub.xy]/[0.97G.sub.xy] + c [4]

From Eqs. [3] and [4], [Y.sub.xy] is derived as:

[Y.sub.xy] = [G.sub.xy] [(3/97K).sup.1/n=1] [5]

The shear strength [F.sub.xy] was derived from the maximum stress.

To examine the effect of cross-plying in the +45[degrees]/-45[degrees] specimen, off-axis tension tests of the specimens without cross-plying were also conducted. The specimen without cross-plying was defined as the 45[degrees] specimen. Tapers were cut on both sides of the specimen with the thickness of 6 mm and rubber tabs were bonded on both sides. Off-axis tension tests were performed by the same procedure as that for the +45[degrees]/-45[degrees] specimen and the shear stress and shear strain were obtained by Eqs. [1] and [2], respectively. The shear modulus, shear stress at the proportional limit, and shear strength were determined by a similar procedure to that in the +45[degrees]/-45[degrees] off-axis tension test.

Off-axis tension tests of 15[degrees] and 20[degrees] specimens

As just mentioned, uniaxial tension tests of 10[degrees] off-axis specimens have often been conducted (Daniel and Lieber 1975, Chamis and Sinclair 1977, Odegard and Kumosa 2000) for determining the shear properties of CFRP. In a previous paper, however, it was shown that the off-axis angle should be larger than 10[degrees] for wood (Yoshihara and Ohta 2000). In the 10[degrees] off-axis tension test, the stress in the longitudinal direction has a serious influence on the measurement because the shear strength/longitudinal tensile strength ratio of wood is often smaller than that of CFRP, and it was suggested that the proper off-axis angle ranged from 15[degrees] to 30[degrees]. In this study, we conducted uniaxial tension tests of the specimens with the grain angles of 15[degrees] and 20[degrees], which were defined as 15[degrees] and 20[degrees] specimens, respectively. A tapered specimen with the thickness of 6 mm was used, and rubber tabs were bonded on both sides similarly to the +45[degrees]/-45[degrees] and 45[degrees] specimens. Triaxial strain gauges were bonded on the specimen as shown in Figure 2. The tensile tests were performed with the same loading conditions as those in the +45[degrees]/45[degrees] tensile test. When the grain direction was inclined [theta] with respect to the loading direction, shear stress ([[tau].sub.xy]) and shear strain ([[gamma].sub.xy]) were obtained from the following equations:

[[tau].sub.xy] = [[sigma].sub.1]/2 sin 2[theta] [6]

and

[[gamma].sub.xy] = [[epsilon].sub.1] (sin 2[theta] - cos 2[theta])-

[[epsilon].sub.II](sin 2[theta] + cos 2[theta]) + 2[[epsilon].sup.III] cos 2[theta] [7]

The shear modulus, shear stress at the proportional limit, and shear strength were determined by a similar procedure to that used for the +45[degrees]/-45[degrees] and 450 off-axis tension test.

As shown in Figure 3, off-axis tension tests were conducted using +45[degrees]/-45[degrees], 450, 15[degrees], and 20[degrees] specimens.

Iosipescu shear tests

The Iosipescu shear test is often conducted for CFRP because the approximately pure shear stress condition can be realized. With the specimen shown in Figure 4, we conducted the Iosipescu shear tests to compare the shear properties with those obtained by the off-axis tension tests. Details of the tests including the fixture diagram can be found in the literature (ASTM 1998, Liu 2000b, Yoshihara et al. 2001). The specimen was cut such that the longitudinal direction was perpendicular to the loading direction, which was in the tangential direction. Triaxial strain gauges similar to those used in the off-axis tests were bonded on both longitudinal-tangential planes. The axes of gauges were defined as i, ii, and iii, which coincided with the longitudinal direction, tangential direction, and the direction inclined at 450 to the longitudinal direction, respectively, and the load was applied at a rate of 3 mm/min. In the Iosipescu shear test, the shear stress was assumed to be uniformly distributed between the notc hes, and the shear stress ([[tau].sub.xy]) was calculated by the following equation:

[[tau].sub.xy] = P/td [8]

where:

P = vertical load

t = thickness of the specimen

d = distance between the notches

The shear strain was obtained from the following equation:

[[gamma].sub.xy] = 2[[epsilon].sub.iii] - [[epsilon].sub.i] - [[epsilon].sub.ii] [9]

where:

[[epsilon].sub.i],[[epsilon].sub.ii], and [[epsilon].sub.iii] = strains in the directions of axes i, ii, and iii, respectively.

From the shear stress/shear strain relation, the shear modulus, shear stress at the proportional limit, and shear strength were obtained by the procedure mentioned previously. T-tests were used to compare the properties obtained from the different test methods and examine the validity of the off-axis tests.

Results and discussion

Shear modulus obtained by off-axis tension tests

The shear modulus ([G.sub.xy]) corresponding to each test method is shown in Table 1. The statistical analyses revealed that the differences between the shear moduli obtained by the different methods were not significant, and so the off-axis tension tests examined here were appropriate for determining the shear modulus.

Shear stress at the proportional limit and shear strength obtained by off-axis tension tests

The shear stress at the proportional limit ([Y.sub.xy]) and shear strength ([F.sub.xy]) corresponding to each test method are also shown in Table 1. In the straight +45[degrees]/-45[degrees] off-axis specimen, failure always initiated at the grip. As mentioned previously, the uniaxial tension test using the straight +45[degrees]/-45[degrees] off-axis specimen with tabs whose stiffness is smaller than that of the specimen is standardized for the in-plane shear test of CFRP (JIS 1991). Nevertheless, the results obtained here indicate that the standardized method is not applicable for measuring the shear stress at the proportional limit and shear strength of wood. By cutting the tapers, the failure at the grip was prevented and it initiated at the gauge region, and the values of and increased with a decrease of thickness because of the effect of the adhesive. Even when the specimen was thin, however, the values of [Y.sub.xy] and [F.sub.xy] were significantly smaller than those obtained by the Iosipescu shear te sts. Test results would be improved by using thinner strips than those used here, but it is difficult to cut them thinner. Therefore, the +45[degrees]/-45[degrees] off-axis tension test is not recommended for determining the shear properties, except for the shear modulus.

As mentioned previously, the recommended off-axis angle was larger than 10[degrees], which is often adopted for the advanced composites, for determining the shear strength of wood (Yoshihara and Ohta 2000). Comparing the results obtained from the off-axis tension tests of 15[degrees] and 20[degrees] specimens, the values of [Y.sub.xy] and [F.sub.xy] of 20[degrees] off-axis specimens were smaller than those of 15[degrees] off-axis specimens, which were close to those obtained by the Iosipescu shear tests. The t-tests between the values of [Y.sub.xy] and [F.sub.xy] obtained by the off-axis tension and the Iosipescu shear tests revealed that the differences were not significant between the values of the 15[degrees] off-axis and the Iosipescu test. Except for these comparisons, the differences were significant in the values of [Y.sub.xy] and [F.sub.xy] at the significance levels of 0.05 and 0.01, respectively. When an appropriate off-axis angle (which was 15[degrees] in this experiment) is chosen, the shear stress at t he proportional limit and shear strength can be obtained by the off-axis tension test as well as the Iosipescu shear test.

Shear stress/shear strain relation

Figure 5 shows the shear stress/shear strain relations obtained by the 15[degrees] off-axis tension test and Iosipescu shear test. As mentioned previously, the shear modulus, shear stress at the proportional limit, and shear strength might be properly determined by the 15[degrees] off-axis tension tests. As shown in this figure, however, the shear stress/shear strain relations obtained by the 15[degrees] off-axis tension tests were extremely different from those by the Iosipescu shear tests. The Iosipescu shear test exhibited more non-linear behavior than the 15[degrees] off-axis tension test, and the stress-strain curve for the 15[degrees] off-axis specimen was almost linear up to failure. This disagreement was due to the tensile stress components in the grain direction and the direction perpendicular to the grain, which inevitably occur in the off-axis tension test, and the combined stress condition had a serious influence on the stress-strain behavior in the inelastic region. In contrast, a purer shear str ess condition can be realized in the Iosipescu shear test, and the shear stress/shear strain relation obtained by the Iosipescu shear test is closer to the real shear stress/shear strain relation. Thus, although the off-axis tension test is simple and effective for determining the shear properties such as shear modulus, shear stress at the proportional limit, and shear strength, another test method is required for evaluating the overall shear stress/shear strain relation.

Conclusions

We conducted several off-axis tension tests for evaluating the shear properties of wood and examined whether the off-axis tension test is applicable or not by comparing the shear properties with those obtained by the Iosipescu shear test. The following results were obtained:

1. It was difficult to obtain the shear properties properly by the +45[degrees]/-45[degrees] off-axis tension test, which is specified as the standardized method for CFRP.

2. In this experiment, the shear properties obtained from the 15[degrees] off-axis tension test were close to those obtained by the Iosipescu shear test.

3. In evaluating the overall shear stress/shear strain relation, the off-axis tension test is not effective because of the existence of other stress components, and another method is required for determining the shear stress/shear strain relation.

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]
Table 1

Shear modulus ([G.sub.xy]), shear stress at the proportional limit
([Y.sub.xy]), and shear strength ([F.sub.xy]) obtained by the off-axis
tension and losipescu shear tests. (a)

 Test type [G.sub.xy] [Y.sub.xy]

 (GPa) (MPa)


TAP + 45[degrees]/45[degrees], t = 1.16[+ or -]0.13 7.3[+ or -]1.5
 6 mm
TAP + 45[degrees]/-45[degrees], t = 1.17[+ or -]0.12 4.4[+ or -]2.8
 12 mm
STR + 45[degrees]/-45[degrees], t = 1.03[+ or -]0.19 6.8[+ or -]1.0
 6 mm
TAP + 45[degrees], t = 6 mm 1.13[+ or -]0.08 6.1[+ or -]2.4
TAP + 15[degrees], t = 6 mm 1.28[+ or -]0.27 10.9[+ or -]2.6
TAP + 20[degrees], t = 6 mm 1.04[+ or -]0.15 6.1[+ or -]2.5
Iosipescu 1.24[+ or -]0.14 9.4[+ or -]2.0

 Test type [F.sub.xy]

 (MPa)


TAP + 45[degrees]/45[degrees], t = 10.4[+ or -]1.6
 6 mm
TAP + 45[degrees]/-45[degrees], t = 8.1[+ or -]1.1
 12 mm
STR + 45[degrees]/-45[degrees], t = 8.7[+ or -]0.7
 6 mm
TAP + 45[degrees], t = 6 mm 8.8[+ or -]0.6
TAP + 15[degrees], t = 6 mm 16.1[+ or -]1.9
TAP + 20[degrees], t = 6 mm 11.5[+ or -]2.0
Iosipescu 18.0[+ or -]3.4

(a)TAP = tapered specimens; STR = straight specimens; t = thickness.
Results are average [+ or -] standard deviations.


Literature cited

American Society for Testing and Materials (ASTM). 1994. Standard methods of testing small clear specimens of timber. ASTM D 143-94. ASTM, West Conshohocken, PA.

_____. 1998. Standard test method for shear properties of composite materials by the V-notched beam method. ASTM D 5379-98. ASTM, West Conshohocken, PA.

Chamis, C.C. and J.H. Sinclair. 1977. Ten-deg off-axis test for shear properties in fiber composites. Exp. Mech. 17:339-346.

Daniel, I.M. and T. Liber. 1975. Lamination residual stresses in fiber composites. Contractor Rept. No. 134826. National Aeronautics and Space Admin,, Washington, DC.

Ebrahimi, G. 1979. Measurement of shear modulus in wood by a tension test. Wood Sci. 13:171-176.

Japanese Industrial Standard (JIS). 1991. Testing methods for in-plane shear properties of carbon fiber reinforced plastics by [+ or -] 45[degrees] tension method and two pairs of rails method. JIS K7079-91. JIS, Tokyo, Japan.

_____. 1994. Methods of testing for woods. JIS Z2101-94. JIS, Tokyo, Japan.

Kitahara, K. 1956. Mokuzai Rigaku Qyobi Kakou Jikkensho (Experimental Characterization of Physical and Machining Properties of Wood). Sangyo Tosho, Tokyo, Japan.

Liu, J.Y. 2000a. Effect of shear coupling on shear properties of wood. Wood and Fiber Sci. 32(4):458-465.

_____. 2000b. Shear test fixture design for orthotropic materials. In: Proc. ICCE/77th Ann. Inter. Conf. Composites Eng., Denver, Colorado. pp. 553-554. www.fpl.fs.fed.us/documnts/pdf2000/liu00c.pdf.

_____. 2002. Analysis of off-axis tension test of wood specimens. Wood and Fiber Sci. 34(2):205-211.

_____ and R.J. Ross. 1998. Wood mechanical property variation with grain slope. In: Proc. 12th Eng. Mech. Confer., La Jolla, Calif. pp. 1351-1354. www/fpl.fs.fed.us/docmnts/pdf2000/liu98a.pdf.

Odegard, G. and M. Kumosa. 2000. Determination of shear strength of unidirectional composite materials with the Iosipescu and 10[degrees] off-axis shear tests. Composite Sci. Technol. 60:2917-2943.

Ramberg, W. and W.R. Osgood. 1943. Description of stress-strain curves by three parameters. Tech. Note No. 902. National Advisory Committee for Aeronautics, Washington, DC.

Yoshihara, H. and M. Ohta. 2000. Estimation of the shear strength of wood by uniaxial-tension tests of off-axis specimens. J. Wood Sci. 46:159-163.

_____, Y. Kubojima, and T. Ishimoto. 2003. Several examinations of the static bending test methods of wood by using todomatsu (Japanese fir). Forest Prod. J. 53(2):39-44.

_____, H. Ohsaki, Y. Kubojima, and M. Ohta. 2001. Comparisons of shear stress/shear strain relations of wood obtained by Iosipescu and torsion tests. Wood and Fiber Sci, 33(2):275-283.

Zhang, W.H. and A. Sliker. 1991. Measuring shear moduli in wood with small tension and compression samples. Wood and Fiber Sci. 23(1):58-68.

The authors are, respectively, Associate Professor and Former Student, Dept. of Natural Products Resource Engineering, Shimane Univ., Nishikawazu-cho 1060, Matsue, Shimane 690-8504, Japan. This paper was received for publication in February 2002. Article No. 9444.

[c] Forest Products Society 2003.

Forest Prod. J. 53(5):75-79.
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Author:Yashihara, Hiroshi; Satoh, Toshiyuki
Publication:Forest Products Journal
Geographic Code:9JAPA
Date:May 1, 2003
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