Mechanics, Materials Science & Engineering, July 2017 – ISSN 2412-5954
Numerical Simulation of the Shear Resistence Test Proposed by NBR 7190 (1997) for a Wood of Corymbia Citriodora 1
Luciano Rossi Bilesky1, a, Cláudio De Conti2,b, Priscila Roel de Deus1,c 1 – Fatec, Capão Bonito, Brazil 2 – Unesp, Rosana, Brazil a – luciano.bilesky@fatec.sp.gov.br b – conti@rosana.unesp.br c – priscila.roel@fatec.sp.gov.br DOI 10.2412/mmse.73.10.710 provided by Seo4U.link
Keywords: MEF, specimens, eucalyptus, shear block test.
ABSTRACT. The mechanical tests are fundamental for the study of the mechanical behaviour of the materials. In Brazil, the tests for the verification of the mechanical behaviour of the wood are normalized by the norm NBR 7190 (1997). These tests seek to provide the necessary conditions to obtain these properties, which is not always achieved with wood, because it is an anisotropic material and with great variability in its radial and longitudinal constitution. The objective of this work was to study the tensile and deformation fields present in the specimen of the test of shear strength for wood proposed by the Brazilian standard NBR 7190 (1997) through numerical simulation using the finite element method with the aid of commercial software ANSYS 11®. In carrying out the test it is assumed that the stress fields in the shear region are homogeneous, as well as the strain fields are uniform, different from that verified by this present study, in which the stress fields were heterogeneous and the strain fields were not uniform, which shows that the values predicted by this test can be underestimated, since the rupture of the test body will occur in a region where the stress concentration is of greater intensity.
Introduction. Wood is one of the most present materials in the life of man, his biological origin and abundance in the beginnings of civilization, contributed to that it was one of the first materials to be manipulated by the man in the making of diverse utensils. In modern life one can find it with the most varied applications, such as in civil construction, furniture and objects essential to modern life, due to their natural characteristics such as density, strength and appearance. Wood is an anisotropic material, however, it may have its simplified behaviour for an orthotropic model [1]. In this model, three symmetry planes are defined orthogonal to each other, taking into account their anatomy, that is, the longitudinal direction to the fibres, the direction of the ray cells, which is radial the direction of the fibres and the direction that tangents the Growth rings as shown in Fig. 1. Other simplifications must be considered in order to apply the orthotropic model to the wood, such as admitting that the trunk has a homogeneous cylindrical geometry, absent from us and other defects and linear growth rings.
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© 2017 The Authors. Published by Magnolithe GmbH. This is an open access article under the CC BY-NC-ND license http://creativecommons.org/licenses/by-nc-nd/4.0/
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Mechanics, Materials Science & Engineering, July 2017 – ISSN 2412-5954
Fig. 1. Relative reference directions for wood material [2]. For the proper use of the wood it is necessary to know its physical and mechanical behavior, for that, they are realized through tests that try to provide the conditions necessary to obtain the properties. However many of these conditions are not obtained through the experimental investigation due to the heterogeneity, variability and anisotropy of the wood material. For the characterization of the shear behavior of the wood, some tests are proposed by technical standards, such as COPANT 30: 1-007, ASTM D143-94 (1994), EN 408 (2002) and NBR 7190 (1997). Although they are widely used and indicated by the technical norms, these tests present limitations in the characterization of the behavior of the wood to the shear, since they are tests initially developed for composite materials with isotropic or orthotropic behavior, which were adapted for wood material without considering Its real behavior due to the heterogeneity of its constitution. Among the difficulties encountered in the use of the tests in the literature, it is possible to consider the absence of a global test to characterize all the mechanical properties of the wood, simultaneously in all planes of symmetry (LR, RL and RT) of the wood. Another difficulty found is that not all tests are applicable to all planes of symmetry of the wood material, that is, certain tests are specific to certain planes of orthotropic. In Brazil, the standard test proposed for the determination of shear strength is NBR 7190 (1997), which consists of a prismatic test specimen previously prepared, so that when subjected to a stress with the aid of a mechanism coupled to Universal testing machine, provides a shear stress in a specific region of the test body. A similar test to NBR 7190 (1997) is proposed by the ASTM D143-94 (1994) standard, known as a "shear block test", which differs only by the dimensions of the specimen and the loading rate of the overall load applied by the test machine universal. The test proposed by NBR 7190 (1997) admits that the critical plane of the test body has a homogeneous and uniform distribution of stresses, promoting a pure shear state in this region [3]. The shear block test ASTM D143-94 (1994) demonstrated a similarity to NBR 7190 (1997), and it can present values of shear strength, underestimated by up to 30% when compared to the results with other types of tests [4]. Values of the shear strength obtained by ASTM D143-94 (1994) are lower because the ratio of stress state in the critical plane of the specimen is not homogeneous as intended with said test [5]. This work aims to investigate by numerical simulation by the finite element method the verification of the behavior of the tensile fields and the deformation fields of said test specimen for Corymbia citriodora wood. MMSE Journal. Open Access www.mmse.xyz
Mechanics, Materials Science & Engineering, July 2017 – ISSN 2412-5954
Materials and Methods: In order to obtain the shear stress parallel to the wood fibers according to NBR 7190 (1997), a test piece with the geometry and dimensions shown in Fig. 2 is used, the precision of the dimensions being 0.1 mm. The region of the specimen, where the shear will actually occur, is called a critical section plane (Av), in which the arrangement of this plane is configured parallel to the radial direction of the wood. The tension is requested from the test body with the aid of the mechanism shown in Fig. 3. To provide a shearing tension, the coupling device is moved vertically downwards with a monotonic loading increasing at a rate of 2.5 MPa / min.
Fig. 2. Dimensions of the specimens for the shear strength test proposed by NBR 7190 (1997).
Fig. 3. Mechanism of aid for the solicitation of force in the specimens. For the numerical simulation by the finite element method the commercial software ANSYS 11 ®. The model was constructed using the geometry and dimensions shown in Fig. 2. In the construction of the model, the element selected for the analysis was the SOLID 64 of the ANSYS 11 ® software element library, because it shows good behavior for structural analysis, since it allows the entry of all engineering constants related to the study, as well as allowing accurate reading of the results of this simulation. The engineering constants used for numerical simulation are experimentally determined and are presented in Table 1 [6].
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Mechanics, Materials Science & Engineering, July 2017 – ISSN 2412-5954
Table 1. Engineering constants of Corymbia citriodora. Corymbia citriodora EL
16981 MPa
GLR
861 MPa
ER
1825 MPa
S11
0,058.10-12
νLR
0,23
S12
0,014.10-12
νLT
0,48
S22
0,548.10-12
νRT
0,70
S66
1,161.10-12
The engineering constants ET, GLT and GRT are not found in the literature, so they were determined analytically by the conversion factors of Equation 1 [1]. E L 20 ET 1,6
ET 1,6 ER 1
E L 20 ER 1
(1) G LR 10 G LT 9,4
G LT 9,4 G RT 1
G LR 10 G RT 1
For the construction of the mesh of the model under study, a convergence analysis was performed using as a criterion the stabilization of the data found in the center of line 4 indicated in Fig. 4, because it is a region present in the critical shear plane.
Fig. 4. Reference lines for analysis of strain and strain fields. To obtain the mesh, the number of elements at each interaction was increased, the data were obtained with the relation xicenter/ximaximum, where xicenter is the value of the greatness x (deformation or tension)
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Mechanics, Materials Science & Engineering, July 2017 – ISSN 2412-5954
in study in the center of line 4 in the reference x, y or z of the model and ximaxmum is the largest value of the magnitude in line 4. The criterion used for the choice of the mesh was the comparison with the stabilization of the variation of the normalized values of the quantities x, y, z, xy, xz, yz, εx, εy, εz, εxy, εxz and εyz, and thus the option for the mesh that presents the convergence of these data with less number of nodes used. The boundary conditions imposed on the model were the fixation of the areas A1 and A2 indicated in Fig. 5 in the x, y and z directions; and the application of a stress in the downward direction y, with an intensity of 16.3 MPa in area A3, referring to the shear modulus of Corymbia citriodora wood [7].
Fig. 5. Contour conditions imposed on the specimen model. Regions A1, A2 and A3 that will be considered in this study. Results. The graphs of Figs. 6 and 7 show the values obtained by the grid convergence analysis using the ratio xijcenter / xijmaximum as a function of the number of nodes generated.
Fig. 6. Analysis of the convergence of the meshes of the test specimens by the stabilization of the stresses σij. MMSE Journal. Open Access www.mmse.xyz
Mechanics, Materials Science & Engineering, July 2017 – ISSN 2412-5954
Fig. 7. Analysis of the convergence of the meshes of the test specimens by the stabilization of the deformation εij. The mesh determined by the convergence analysis for the numerical simulation consists of 14813 nodes and 9759 elements and can be seen in Fig. 8.
Fig. 8. Specimen mesh. For the verification of the stress fields σx generated in the test specimen, Fig. 9 is presented, composed of the model generated by the FEM, accompanied by the graphs of the normalized stress along the lines representing the shear area.
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Mechanics, Materials Science & Engineering, July 2017 – ISSN 2412-5954
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Fig. 9. (a) Stress fields σx with unit of measurement in Pa. (b) Graph of stress σx normalized along reference lines 1 and 3; (c) Graph of stress σx normalized along reference lines 2 and 4. It can be seen from Fig. 9 that a homogeneous stress state does not occur for the stress σx, because along the reference line 1 and 3 the stress do not show homogeneity. In lines 2 and 4 the homogenization of the stresses occurs in a considerably large region, but in its extremities, an accentuation of tensions σx is undesirable, due to the strains εx in the test body are not uniform, as shown in Fig. 10.
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Mechanics, Materials Science & Engineering, July 2017 – ISSN 2412-5954
Fig. 10. Strain fields εx in the test body model proposed by NBR 7190 (1997) with unit of measure in m. Fig. 11 shows the strain fields εy in the specimen model. As can be seen, the strains εy occurring in the region of the shear area can be considered uniform in a large region. However when taken as reference lines 2 and 4, it is found that the strain fields near the lower support base are shown without uniformity.
Fig. 11. Strain fields εy in the model of the test body proposed by NBR 7190 (1997) with unit of measurement in m. Fig. 12 shows the stress fields σy obtained by the numerical simulation by MEF, together with the graphs of stress σy normalized along the reference lines of the shear area. The stress fields σy can not be considered homogeneous, it is possible to verify through Fig. 12 the absence of a region with σy homogeneous voltages along the reference lines 1, 2 3 and 4 due to the deformations found not to be uniform nature. In lines 2 and 4, the stress modulus σy is accentuated at the ends of the specimen.
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Mechanics, Materials Science & Engineering, July 2017 – ISSN 2412-5954
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Fig. 12. (a) Stress fields σy with unit of measurement in Pa. (b) Graph of stress σy normalized along reference lines 1 and 3. (c) Graph of stress σy normalized along reference lines 2 and 4. Fig. 13 shows the stress fields σz, obtained in the test body model, along with the graph of the stress σz normalized along the reference lines around the shear area. The stress fields σz, present in Fig. 13, can not be considered homogeneous. In reference lines 1 and 3 of the shear area the stresses are not homogeneous over the entire length of these lines, due to the non-uniform deformation of the specimen. In the reference lines 2 and 4, the tensions σz can be considered homogeneous in a great extension of these lines, however, the stresses at the extremities of the test body occur, due to the deformation due to the poisson effect found in the junctions of lines 1 and 2, 2 and 4, 3 and 4, and 3 and 2.
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Mechanics, Materials Science & Engineering, July 2017 – ISSN 2412-5954
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Fig. 13. (b) Stress fields σz. (b) Graph of stress σz normalized along reference lines 1 and 3. (c) Graph of the stress σz normalized along the reference lines 2 and 4. (Unit of measurement of σ in Pa). The deformations εz can be observed in Fig. 14.
Fig. 14. Strain fields εz in the model of the specims proposed by NBR 7190 (1997) with unit of measure in m. MMSE Journal. Open Access www.mmse.xyz
Mechanics, Materials Science & Engineering, July 2017 – ISSN 2412-5954
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Fig. 15. (a) Stress fields σxy; (b) Graph of stress σxy normalized along reference lines 1 and 3; (c) Graph of stress σxy normalized along reference lines 2 and 4. (Unit of measurement of σ in Pa).
When analyzed in Fig.s 15, 16 and 17, corresponding to the stress fields σxy, σxz and σyz, a behavior trend is observed close to the stress fields of σx and σy, these stress fields being non-uniform and with accentuation in its module at the ends of the reference lines. This intensification of the stresses can be attributed to the non-uniform deformations occurring in the specimen.
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Mechanics, Materials Science & Engineering, July 2017 – ISSN 2412-5954
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Fig. 16. (a) Stress fields σxz; (b) Graph of stress σxz normalized along reference lines 1 and 3; (c) Graph of stress σxz normalized along reference lines 2 and 4. (Unit of measurement of σ in Pa). With the observation of the data obtained by the MEF analysis of the test to determine the shear behavior proposed by NBR 7190 (1997), it can be verified that the fields of stresses σx, σy, σz, σxy, σxz and σyz are not homogeneous, as well as the strain fields εx, εy and εz, are not found uniform, thus concluding that a homogeneous stress state is not found in the shear region Av, data obtained by this assay assuming a state of stress that does not occur are not accurate because shearing accompanied by rupture of the test specimen occurs first in isolated regions.
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Mechanics, Materials Science & Engineering, July 2017 – ISSN 2412-5954
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Fig. 17. (a) Stress fields σyz; (b) Graph of stress σyz normalized along reference lines 1 and 3; (c) Graph of stress σyz normalized along reference lines 2 and 4. (Unit of measurement of σ in Pa). Summary. Through the numerical analysis performed using the finite element method, it was possible to observe the non-existence of a uniform tensile and strain field in the shear area of the test shear strength test proposed by NBR 7190 (1997) due to the shear strength homogeneity it is possible to conclude that the values determined by the respective assay can be underestimated. References [1] Bodig, J., Jayne, B. A. Mechanics of Wood and Wood Composites. 2. ed., Florida. Krieger Publishing Company, 1993, 712p. [2] Calil Junior, C., Lahr, F. A. R., Dias, A. A. Dimensionamento de Elementos Estruturais de madeira. Barueri: Manole, 2003. 152 p. [3] Moreschi, J. C. Propriedades Tecnológicas da Madeira. Curitiba: UFPR, 2007. 168p. [4] Rammer, D. R., Soltis L. A. Experimental Shear Strength of Glued-laminated Beams. Madison, U.S. Department of Agriculture, Forest product Laboratory, 1994. 527p. [5] Liu, J.Y., Ross R.J., Rammer D. R.. Improved Arcan Shear Test for Wood. New Orleans: Gopu, 1996. MMSE Journal. Open Access www.mmse.xyz
Mechanics, Materials Science & Engineering, July 2017 – ISSN 2412-5954
[6] Ballarin, A. W., Nogueira, M. Caracterização elástica da madeira de Eucalyptus Citriodora. Revista Cerne, 9(1): 66-80, 2003. [7] Instituto de Pesquisas Tecnológicas do Estado de São Paulo. IPT. Madeira: Uso Sustentável na Construção Civil. São Paulo, 2009. 103p. [6] I. Kolin, S. Koscak-Kolin, M. Golub, Geothermal Electricity Production by means of the Low Temperature Difference Stirling Engine, Proceedings World Geothermal Congress 2000, Kyushu Tohoku, Japan, May 28 - June 10, 2000, 3199-3203 [7] J. Selwin Rajadurai, Thermodynamics and Thermal Engineering, New Age International, 2003, Heat engineering, 1102 p. [8] P. Mazzoldi, M. Nigro, C. Voci. (1991), Meccanica, Napoli, S.E.S., 314 p
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