In this paper, we compared the shear stress/shear strain relations of wood obtained by Iosipescu and torsion tests.Quartersawn boards of Sitka spruce (Picea sitchensis Carr.) and shioji (Japanese ash, Fraxinus spaethiana Lingelsh.) provided the specimens. Iosipescu tests were conducted with specimens loaded in the radial direction, and the shear stress/shear strain relations were obtained. Shear stress/shear strain relations were obtained independently of the Iosipescu tests by torsion tests of rectangular bars. The following results were obtained:(1) The shear moduli, shear yield stresses, and shear strengths obtained from both methods showed good agreement with each other, except for the shear strength of ash.(2) As for spruce, the difference between the shear stress/shear strain relations obtained by Iosipescu and torsion tests was significant in the 5% significance level, whereas that for the ash was not significant.(3) Although the Iosipescu test can derive the shear stress/shear strain relation directly, it has the drawback that failure occurs earlier than with the torsion test. In contrast, the torsion test has the drawback that the procedure for obtaining the stress/strain relation is quite complicated. In determining the shear stress/shear strain relation of wood properly, shear stress/shear strain data should be measured more frequently by these methods

Kubojima, Yoshitaka

Ohsaki, Hisashi

Ohta, Masamitsu

Yoshihara, Hiroshi

English

Wood and Fiber Science (E-Journal)

COMPARISONS OF SHEAR STRESSISHEAR STRAIN RELATIONS OF WOOD OBTAINED BY IOSIPESCU AND TORSION TESTS Hiroshi Yoshihara Associate Professor, Department of Natural Products Resource Engineering Shimane University Matsue, Shimane Japan Hisashi Ohsaki Researcher, Hokkaido Forest Products Research Institute Asahikawa, Hokkaido Japan Yoshitaka Kubojima Researcher, Forestry and Forest Products Research Institute Tsukuba, Ibaraki Japan and Masamitsu Ohta Professor Graduate School of Agricultural and Life Sciences The University of Tokyo Bunkyo-ku, Tokyo Japan (Received November 1999) ABSTRACT In this paper, we compared the shear stresslshear strain relations of wood obtained by Iosipescu and torsion tests. Quartersawn boards of Sitka spruce (Piceu sitchensis Carr.) and shioji (Japanese ash, Fruxinus spaethianu Lingelsh.) provided the specimens. Iosipescu tests were conducted with specimens loaded in the radial direction, and the shear stresslshear strain relations were obtained. Shear stresslshear strain relations were obtained independently of the Iosipescu tests by torsion tests of rectangular bars. The following results were obtained: (1) The shear moduli, shear yield stresses, and shear strengths obtained from both methods showed good agreement with each other, except for the shear strength of ash. (2) As for spruce, the difference between the shear stresslshear strain relations obtained by Iosipescu and torsion tests was significant in the 5% significance level, whereas that for the ash was not signif- icant. (3) Although the Iosipescu test can derive the shear stresslshear strain relation directly, it has the drawback that failure occurs earlier than with the torsion test. In contrast, the torsion test has the drawback that the procedure for obtaining the stresslstrain relation is quite complicated. In determining the shear stresslshear strain relation of wood properly, shear stresslshear strain data should be measured more frequently by these methods. Keywords: Shear stresslshear strain relation, Iosipescu test, torsion test Wood and Fiber Science, 33(2), 2001, pp 275-283 0 2001 by the Society of Wood Science and Technology 276 WOOD AND FIBER SCIENCE, APRIL 2001, V. 33(2) Biaxial strain gage / Thickness = 8 mrn Strain gage FIG. 2. Diagram of the rectangular specimen subjected to the torsional force. FIG. 1. Iosipescu test specimen and triaxial strain gage arrangement in the Iosipescu test. Notes: Unit: mm. L, R represent the longitudinal and ra- dial directions, respectively. INTRODUCTION In determining the shear stresslshear strain relation of isotropic or transversely isotropic materials such as metals, concrete, and fiber- reinforced plastics (FRP), a torsion test of the specimen with a cylindrical cross section is often conducted because a rigorous equation representing the shear stresslshear strain rela- tion exists (Hill 1950). In a torsion test of a rectangular bar, a pure shear stress condition is expected in the specimen. In the torsion of an orthotropic material like wood, however, the shear stress in the rectangular section of the specimen is a function of aspect ratio and shear modulus, which is derived by Prandtl's membrane analogy, and is not distributed uni- formly in the surface (Lekhnitskii 1963). This phenomenon causes a difficulty in determining the shear stresslshear strain relation of wood by torsion (Yoshihara and Ohta 1995, 1997). The Iosipescu test is another promising meth- od because of the simplicity in characterizing the shearing properties (Janowiak and Pellerin 1991 ; Yoshihara et al. 1999; Kubojima et al, 2000; Dumail, et al. 2000). In determining the shearlstresslshear strain relation by an Iosipes- Yoshihara et a/.-COMPARISONS OF SHEAR STRESS/SHEAR STRAIN RELATIONS Luad P 1 ri , , Wedge adjusting screw Adjustable wedge to tighten the specimen 1 i Statlonary pottlon of fixture FIG. 3. Iosipescu shear test fixture. Notes: u = 22 rnm. b = 12 mm. cu test, however, there is concern that the cracks that occur at the notch roots of the specimen could have a serious influence on the stress distribution. Although Iosipescu and torsion tests are ef- fective in determining shear stresslshear strain properties, they have been rarely applied to wood, and there are few examples comparing the shear stresslshear strain properties ob- tained by these methods. Here we compared the shear stresslshear strain relations obtained by these methods and examined the applica- bility of these methods for determining the shear stresshhear strain relations of wood. THEORIES Shear stresslshear strain relations obtained by Iosipescu test Figure l a  shows the schematic diagram of an Iosipescu test specimen. The z- and x- axes are defined as those parallel and perpendicular to the long axis of the specimen. When rig- idly-clamped halves are displaced relative to each other, a pure shear stress condition is thought to be obtained in the mid-length of the specimen. In this loading condition, the bend- FIG. 4. Torsion test specimen (unit: mm). ing moment is equal to zero in the middle sec- tion of the specimen, whereas the shearing force equals P in the middle section. Thus, the shear stress 7, can be obtained by the follow- ing equation (Seerat-Un-Nabi and Derby 1990): where I is the thickness of the specimen, d is the distance between the notches. The engi- neering shear strain at the midpoint of the notches, y,, can be measured by bonding the strain gages between the notches, and the shear stresslshear strain relation can be deter- mined. The shear stresslshear strain relation in the elastic condition is represented by Hooke's law, whereas it is approximated by the Lud- 278 WOOD AND FIBER SCIENCE, APRIL 2001, V. 33(2) wik's power function (Chakrabarty 1989) in the plastic strain range. Thus, the shear stress1 shear strain relation all over the strain range is represented as follows: where S,  is the yield shear stress, and K and n are the material parameters with no dimen- sions. Shear stresslshear strain relation predicted .from the torsion testing data Figure 2 shows the torsion test diagram. When the rectangular bar is twisted around the z-axis by the torsional moment of M, the shear stress at the center of =-plane 7, would be approximated as follows (Yoshihara and Ohta 1998): where a and b are the length of the x- and y- directions, respectively, M y  is the torsional moment at the occurrence of yielding, G, and Six are the shear modulus and the yield shear stress on the zx-plane, respectively, and y, and y,P are the total shear strain and the plastic shear strain at the center of zx-plane, respec- tively. In this equation, p, is written as: X tanh 2a where G,, is the shear modulus on the yz- plane, and X tanh 2a ( 5 )  The yield shear stress is represented by the yield torsional moment as follows: The torsional moment/plastic strain relation is represented in the range of 7, > S, by a power function as: where a and m are the material parameters with no dimensions. The second term in the braces of Eq. (3b) is derived by substituting Eq. (7) into Eq. (3b) as: From Eqs. (3b), (6) ,  (7), and (8), M and M y  are eliminated and the shear stress in the range of 7, > S,, is represented as follows: Hence the plastic strain in the shear stress1 shear strain relation can be obtained as fol- lows: Yoshihara et a[.--COMPARISONS OF SHEAR STRESSISHEAR STRAIN RELATIONS 25'9 where When the M - y,p relation in the plastic re- gion is measured and regressed into Eq. (7), the shear stresslshear strain relation can be represented by Eq. (lo), which has a similar formula derived for the Iosipescu test, Eq. (2). EXPERIMENT Materials Sitka spruce (Picea sitchensis Carr.) and shioji (Japanese ash, Fraxinus spaethiana Lin- gelsh.) were used for the specimens. The den- sity of spruce was 0.43 g/cm3, whereas that of ash was 0.59 g/cm3. For both species, all spec- imens were cut from the same lumber, and were conditioned at 20°C and 65% relative hu- midity before and during the tests. In this experiment, we defined the radial, tangential, and longitudinal directions as x-, y-, and z-axes, respectively. Iosipescu tests The dimensions of the Iosipescu test spec- imen are shown in Fig. la. The long axis of the specimen coincided with the longitudinal direction, whereas the notch direction coincid- ed with the radial direction. To measure the strain condition between the opposed notches, a triaxial-strain gauge (gauge length = 2 mm, YFRA-2- 1 1, Tokyo Sokki Co., Ltd.) was bonded at the midpoint between the notches. Figure l b  shows the triaxial-strain gauge ar- rangement. The shear strain y, was obtained from the following equation: where and eII are the strains in the longitu- dinal and the radial directions, respectively, and eIII is the direction inclined at 45 degrees with respect to the longitudinal direction. Figure 3 shows the diagram of the Idaho test fixture (Conant and Odom 1995). The loading surfaces begin at points of 22 and 12 mm away from the center of the test specimen, and the load with the velocity of 1 mrn/min was applied on the specimen. From the loatl- strain relations recorded by an XY-recorder, the shear stresslshear strain relation was ob- tained by Eqs. (1) and (2). Six specimens weire used for each species. Torsion tests Figure 4 illustrates the torsion test speci- men. To measure the strains at the centers of the side surfaces, same strain gages used im the Iosipescu tests were bonded on the LF1- and LT-planes. The specimen was twisted by a manual torsion-test device, and the torsional momentlshear strains relations on both planes were obtained. The shear moduli G, and G& were obtained from the following equation (Lekhnitskii 1963; Yoshihara and Ohta 1993); (2j - 1)nb G,  X tanh 2a kl where ky, and k,, are the initial inclinations of the torsional momendshear strains relations and the plastic strain y,p was calculated by subtracting the elastic strain as shown in Fig. 5a. Then, the torsional momentlplastic shear strain relation on the LR-plane was regressed into Eq. (7), and the yield torsional moment My was determined as in Fig. 5b. In a previous paper, however, we pointed out that the value 280 WOOD AND FIBER SCIENCE, APRIL 2001, V. 33(2) FIG. 5.  Transformation of torsional momentlshear strain relation into moment-plastic shear strain relation. Note: (a): Torsional momentlshear strain relation, (b): Torsional rnomentJplastic shear strain relation. Legend: Circles indicate the measurement point. Solid and dashed lines in (b) are obtained by the direct regression of the experimental data into Eq. (7) and by the regression using the reduced value of yield moment, respectively. of My tends to be measured as higher than the after the initiation of yielding. According to real value by the torsion test because the elas- the numerical calculations based on the strain tic region is widely distributed soon after the incremental theory, we found that the shear occurrence of yielding, which initiates locally stresslshear strain relation can be derived at the wider surface of specimen in the torsion properly by torsion when My is evaluated as of a rectangular bar, and the torsional mo- 80% of the measured one (Yoshihara and Ohta mentslshear strain relation tends to be linear 1995). Using the reduced value of My,  the tor- , , , Spruce I - , , , Ash I I FIG. 6. Typical shear stress/shear strain relations obtained from the Iosipescu and torsion tests. Legend: Solid and dashed lines are obtained from the Iosipescu and torsion tests, respectively. 0 0 0 0.01 0.02 0.03 0 0.01 0.02 0.03 0.04 0.05 Shear strain y, Shear strain y, Yoshihara et a1.-COMPARISONS OF SHEAR STRESSISHEAR STRAIN RELATIONS 28 1 TABLE 1. Shear moduli obtained by the Iosipescu shear test und the torsion tests. TABLE 3. Shear strengths obtained by the Iosipescu and torsion tests. losipescu Torsion G,, (GPa) G, (GPa) Species Ave. S D  Ave. S D  f Spruce 1.04 0.38 1.07 0.14 0.181 (NS) Ash 1.05 0.13 1.00 0.11 0.719(NS) Notes: Ave and S D  represent the average and ~tandard  deviation, respec- hvely. 'The t values were obta~ncd by I-tczts between the loa~peacu and the torslon tcst. NS = not signllicant. sional moment/plastic shear strain relation was regressed into Eq. (7) again as in Fig. Sb, and the material parameters a and m were deter- mined. The yield shear stress S,  was calculat- ed from Eq. (6) by substituting the reduced value of My, whereas the value of K' was cal- culated by substituting cr and m into Eq. (1 l). With the mechanical properties, G,, S,, K' ,  and m, the shear stresslshear strain relations were obtained from Eq. (lo), and were com- pared with those obtained from the Iosipescu tests. The shear strength, F,, was determined by substituting the strain y, at the occurrence of failure into Eq. (lob). Six specimens were used for each species. RESULTS AND DISCUSSION Tables 1, 2, and 3 show the shear moduli, yield shear stresses, and shear strengths ob- tained from the Iosipescu and torsion tests. Comparing these properties by using t-tests re- veals a difference between the shear strength of ash. The other properties are in good agree- ment with each other for both species. The values of a and m obtained by regress- ing the torsional momentlshear strain relation into the power function of Eq. (7) are shown TABLE 2. Yield shear stresses obtained from the losipes- cu shear tests and the torsion tests. Species Ave. S D  Ave S D  f Spruce 6.2 1.4 7.0 1.6 0.922 (NS) Ash 7.8 2.1 7.9 1.0 0.105 (NS) Note: Ave., SD, t and NS: same as in Table 1 .  Yield stresses obtained from the torcion tests are calculated by using the 8 0 1  reduced value of y ~ e l d  tor- slonal moment. Iosipescu Torsion F : ~  (MPa) F, (MPa) S p e c ~ e s  Ave S D  Ave. S D  I - Spruce 10.3 1.6 11.9 2.1 1.484 (NS) Ash 13.7 1.2 15.7 0.8 3.397 (1%) - Notec. A v e ,  SD, f and NS: Fame as in Table 1. I %  = significant at the 1 W ~ignificance level. in Table 4. With these values, the torsion,al momentlshear strain relation was transformed into the shear stresslshear strain relation. Table 5 shows the comparisons of the parameters de- termining the shear stresslshear strain relation. For both species, the values of K and n ob- tained from the Iosipescu tests were smaller than those of K' and m obtained from the tor- sion tests, respectively. This tendency indi- cates that the plastic strain region predicted by the torsion test is larger than that predicted by the Iosipescu test. By substituting the average values of the parameters, the shear stresslshear strain relations were calculated, and are shown in Fig. 5. For examining the coincidence, we conducted the t-tests between the stress-strain curves obtained from the Iosipescu test artd the torsion test in the stress range where both stresslstrain relations existed. In the t-tests, ten pairs of shear strains obtained by substituting the shear stresses into Eqs. (2) and (10) weire used. The substituted stress values were 1.03 to 10.3 GPa at the intervals of 1.03 GPa (11 10 of F, by the Iosipescu tests) for spruce artd 1.37 to 13.7 GPa at the intervals of 1.37 GI'a for ash. The statistical analyses showed that there was a difference in the 5% significance level for spruce, whereas the difference wins not significant for ash. As shown in Fig. 5, the failure occurred ear- TABLE 4. Parameters determining the torsional momerzt/ shear strain relation, a and m. - 0 (X  10 2 ,  m - Species Ave. S D  Ave. S D  - Spruce 1.39 0.48 2.36 0.1 1 Ash 0.98 0.1 1 2.53 0.64 282 WOOD AND FIBER SCIENCE, APRIL 2001, V. 33(2) TABLE 5. Parameters determining the shear stress/shear strain relation obtained from the Iosipescu shear test data, K and n, and those obtained from the torsion test data, K' and m. Iosipescu Torsion K ( X  10 2, n K' ( X  m Spec~es Ave. SD Ave. SD Ave. SD Ave. SD Spruce 1.60 0.40 1.42 0.13 2.60 0.91 2.36 0.11 Ash 1.63 0.5 1 1.91 0.62 2.10 0.69 2.53 0.64 lier in the Iosipescu test than in the torsion test for both species. In the Iosipescu test, there is a concern that the cracking initiated at the notch roots would have a serious influence on the stress uniformity, and that the distorted stress condition might accelerate a catastroph- ic failure. The experimental results proved the acceleration of failure in the Iosipescu test. Torsion is free from the concern because pure shear stress condition is assured until failure occurs in the specimen. Nevertheless, the pro- cedure determining the stresslstrain relation is complicated, and the several hypotheses intro- duced in the determination such as the reduc- tion of yield stress might have a serious influ- ence on the torsion testing results. In deter- mining the shear stresslshear strain relation of wood properly, shear stresdshear strain data should be measured more frequently by these methods and the disadvantages existing in these methods should be reduced effectively. CONCLUSIONS Using the specimens of spruce and ash, we tried to determine the shear stresslshear strain relation by Iosipescu and torsion tests, and ob- tained the following results: ( I )  The shear moduli, shear yield stresses, and shear strengths obtained from both meth- ods showed good agreement with each other, except for the shear strength of ash. (2) As for spruce, the difference between the shear stresslshear strain relations obtained by the Iosipescu and torsion tests was sig- nificant at the 5 %  significance level, whereas that for ash was not significant. (3) Although the Iosipescu test can derive the shear stresslshear strain relation directly, it has the drawback that the failure occurs earlier than with the torsion test. In con- trast, the torsion test has the drawback that the procedure in obtaining the stresdstrain relation is quite complicated. In determin- ing the shear stresslshear strain relation of wood properly, these tests should be con- ducted more frequently. ACKNOWLEDGMENTS This research was supported partly by a Grant-in-Aid for Scientific Research (No. 09460072) from the Ministry of Education, Science and Culture of Japan. REFERENCES CHAKRABARTY, J.  1987. Theory of plasticity. McGraw- Hill, New York, NY. 9 pp. CONANT, N. R., AND M. ODOM. 1995. An improved Iosi- pescu shear test fixture. J. Comp. Techno]. Res. 1750- 55. DUMAIL, J.  E, K. OLOFSSON, AND L. SALMEN. 2000. An analysis of rolling shear of spruce wood by the Iosipes- cu method. Holzforschung 54(4):420-426. HILL, R. 1950. The mathematical theory of plasticity. Ox- ford Clarendon Press, London, UK, 84 pp. JANOWIAK, J. J.,  AND R. E PELLERIN. 1991. Iosipescu shear test apparatus applied to wood composites. Wood Fiber Sci. 23:410-418. KUBOJIMA, Y., H. YOSHIHARA, H. OHSAKI, AND M. OHTA. 2000. Accuracy of shear properties of wood obtained by simplified Iosipescu shear test. J.  Wood Sci. 46(4): 279-283. LEKHNITSKII, S. G. 1963. Theory of an anisotropic elastic body. Holden-Day, San Francisco, CA. Pp. 197-205. SEERAT-UN-NABI, A , AND B. DERBY. 1990. Iosipescu in- plane shear tests of Sic-Pyrex composites. J.  Mater. Sci. Lett. 9:63-66. YOSHIHARA, H., AND M. OHTA. 1993. Measurement of the shear moduli of wood by the torsion of a rectangular bar. Mokuzai Gakkaishi 39(9):993-997. , AND - . 1995. Shear stress-shear strain re- Yoshihara el a1.-COMPARISONS OF SHEAR STRESSISHEAR STRAIN RELATIONS 28:3 lation of wood in the plastic region. Mokuzai GaMcaishi stresslshear strain relation of wood. Bull. Tokyo Univ. 41 (6):529-536. Forest 99:11-17. , AND  . 1997. Analysis of the shear stress/ - , H. OHSAKI, Y. KUBOJIMA, AND M. OHTA. 19951. shear strain relations in wood obtained by the torsion Applicability of the Iosipescu shear test on the mea- tests. Mokuzai Gakkaishi 43(6):457-463. surement of the shear properties of wood. J Wood Sci , AND - 1998. Formulation of the shear 45(1):24-29. 

Comparisons of Shear Stress/Shear Strain Relations of Wood Obtained By Iosipescu And Torsion Tests

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Comparisons of Shear Stress/Shear Strain Relations of Wood Obtained By Iosipescu And Torsion Tests

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