Abstract
The cohesive laws (CLs) have been investigated by means of direct and inverse methods concerning wood bonded joints under pure mode I. The experimental results were obtained by tests with double cantilever beam. The direct method is based on the differentiation of the relation between strain energy release rate and crack opening displacement at the crack tip. An equivalent crack method was used to evaluate the strain energy release rate in the course of the test without monitoring the crack length, which is difficult to observe exactly. The crack opening displacement was determined by postprocessing local displacements measured by digital image correlation. The inverse method requires a previous assumption of the CL shape, and as such, a trilinear law with bilinear softening relationship was selected. The cohesive parameters were identified by an optimization procedure involving a developed genetic algorithm. The idea is to minimize an objective function that quantifies the difference between the experimental and the numerical load-displacement curves resulting from the application of a given law. A validation procedure was performed based on a numerical analysis with finite elements. Both methods in focus provided good agreement with the experimental data. It was observed that CLs adopted by the inverse method are consistent with the ones obtained with the direct method.
This work was supported by European Union Funds (FEDER/COMPETE – Operational Competitiveness Programme) and by national funds (FCT – Portuguese Foundation for Science and Technology) under the project FCOMP-01-0124-287 FEDER-022692. The authors thank FTC for supporting the work presented in this publication through the research project PTDC/EME/PME/114443/2009 and Ciência 2008 program.
References
Andena, L., Rink, M., Williams, J.G. (2006) Cohesive zone modelling of fracture in polybutene. Eng. Fract. Mech. 73:2476–2485.Search in Google Scholar
Andersson, T., Biel, A. (2006) On the effective constitutive properties of a thin adhesive layer loaded in peel. Int. J. Fracture 141:227–246.10.1007/s10704-006-0075-6Search in Google Scholar
ARAMIS commercial software. GOM. http://www.gom.com/.Search in Google Scholar
Bianchi, S., Corigliano, A., Frassine, R., Rink, M. (2006) Modelling of interlaminar fracture processes in composites using interface elements. Compos. Sci. Technol. 66:255–263.Search in Google Scholar
Conceição António, C.A., Dourado, N.M. (2002) Metal forming process optimisation by inverse evolutionary search. J. Mater. Process. Technol. 121:403–413.Search in Google Scholar
de Moura, M.F.S.F., Campilho, R.D.S.G., Gonçalves, J.P.M. (2008a) Crack equivalent concept applied to the fracture characterization of bonded joints under pure mode I loading. Compos. Sci. Technol. 68:2224–2230.10.1016/j.compscitech.2008.04.003Search in Google Scholar
de Moura, M.F.S.F., Morais, J.J.L., Dourado, N. (2008b) A new data reduction scheme for mode I wood fracture characterization using the double cantilever beam test. Eng. Fract. Mech. 75:3852–3865.10.1016/j.engfracmech.2008.02.006Search in Google Scholar
de Moura, M.F.S.F., Gonçalves, J.P.M., Magalhães, A.G. (2012) A straightforward method to obtain the cohesive laws of bonded joints under mode I loading. Int. J. Adhes. Adhes. 39:54–59.10.1016/j.ijadhadh.2012.07.008Search in Google Scholar
Dourado, N., Morel, S., de Moura, M.F.S.F., Valentin, G., Morais, J. (2008) Comparison of fracture properties of two wood species through cohesive crack simulations. Compos. Part A Appl. S. 39:415–427.Search in Google Scholar
Dourado, N., de Moura, M.F.S.F., Morais, J.J.L., Silva, M.A.L. (2010) Estimate of resistance-curve in wood through the double cantilever beam test. Holzforschung 64:119–126.10.1515/hf.2010.010Search in Google Scholar
Gonçalves, J.P.M., de Moura, M.F.S.F., Magalhães, A.G., de Castro, P.M.S.T. (2003) Application of interface finite elements to three-dimensional progressive failure analysis of adhesive joints. Fatigue Fract. Eng. M. 26:479–486.Search in Google Scholar
Jeong, G.Y., Zink-Sharp, A., Hindman, D.P. (2010) Applying digital image correlation to wood strands: influence of loading rate and specimen thickness. Holzforschung 64:729–734.10.1515/hf.2010.110Search in Google Scholar
Keunecke, D., Stanzl-Tschegg, S., Niemz, P. (2007) Fracture characterisation of yew (Taxus baccata L.) and spruce (Picea abies [L.] Karst.) in the radial-tangential and tangential-radial crack propagation system by a micro wedge splitting test. Holzforschung 61:582–588.10.1515/HF.2007.089Search in Google Scholar
Landis, E.N., Navi, P. (2009) Modeling crack propagation in wood and wood composites. A review COST Action E35 2004–2008: wood machining – micromechanics and fracture. Holzforschung 63:150–156.10.1515/HF.2009.010Search in Google Scholar
Michalewicz, Z. Genetic algorithms+Data Structures=Evolution Programs. Springer, 1999. ISBN 3-540-60676-9.Search in Google Scholar
Peng, M., Ho, Y.-C., Wang, W.-C., Chui, Y.H., Gong, M. (2012) Measurement of wood shrinkage in jack pine using three dimensional digital image correlation (DIC). Holzforschung 66:639–643.10.1515/hf-2011-0124Search in Google Scholar
Que, N.S., Tin-Loi, F. (2002) An optimization approach for indirect identification of cohesive crack properties. Comput. Struct. 80:1383–1392.10.1016/S0045-7949(02)00096-2Search in Google Scholar
Sebera, V., Muszyński, L. (2011) Determination of local material properties of OSB sample by coupling advanced imaging techniques and morphology-based FEM simulation. Holzforschung 65:811–818.10.1515/HF.2011.110Search in Google Scholar
Slowik, V., Villmann, B., Bretschneider, N., Villmann, T. (2006) Computational aspects of inverse analyses for determining softening curves of concrete. Comput. Method Appl. M. 195:7223–7236.Search in Google Scholar
Smith, I., Snow, M., Asiz, A., Vasic, S. (2007) Failure mechanisms in wood-based materials: a review of discrete, continuum, and hybrid finite-element representations. Holzforschung 61:352–359.10.1515/HF.2007.055Search in Google Scholar
Sørensen, B.F. (2002) Cohesive law and notch sensitivity of adhesive joints. Acta Mater. 50:1053–1061.10.1016/S1359-6454(01)00404-9Search in Google Scholar
Sousa, A.M.R., Xavier, J., Morais, J.J.L., Filipe, V.M.J., Vaz, M. (2011) Processing discontinuous displacement fields by a spatio-temporal derivative technique. Opt. Laser Eng. 49:1402–1412.10.1016/j.optlaseng.2011.07.007Search in Google Scholar
Stanzl-Tschegg, S.E., Navi, P. (2009) Fracture behaviour of wood and its composites. A review COST Action E35 2004–2008: wood machining – micromechanics and fracture. Holzforschung 63:139–149.10.1515/HF.2009.012Search in Google Scholar
Taguchi, A., Murata, K., Nakamura, M., Nakano, T. (2011) Scale effect in the anisotropic deformation change of tracheid cells during water adsorption. Holzforschung 65:253–256.10.1515/hf.2011.017Search in Google Scholar
Tin-Loi, F., Que, N.S. (2002) Identification of cohesive crack fracture parameters by evolutionary search. Comput. Method Appl. M 191:5741–5760.Search in Google Scholar
Xavier, J.C., Garrido, N.M., Oliveira, M., Morais, J.L., Camanho, P.P., Pierron, F. (2004) A comparison between the Iosipescu and off-axis shear test methods for the shear characterization of Pinus pinaster Ait. Compos. Part A Appl. S. 35:827–840.Search in Google Scholar
Xavier, J., Avril, S., Pierron, F., Morais, J. (2007) Novel experimental approach for longitudinal-radial stiffness characterisation of clear wood by a single test. Holzforschung 61:573–581.10.1515/HF.2007.083Search in Google Scholar
Xavier, J., Avril, S., Pierron, F., Morais, J. (2009) Variation of transverse and shear stiffness properties of wood in a tree. Compos. Part A Appl. S 40:1953–1960.Search in Google Scholar
Xavier, J., Morais, J., Dourado, N., de Moura, M.F.S.F. (2011) Measurement of mode I and mode II fracture properties of wood-bonded joints. J. Adhes. Sci. Technol. 25:2881–2895.Search in Google Scholar
Xavier, J., Sousa, A.M.R., Morais, J.J.L., Filipe, V.M.J., Vaz, M. (2012a) Measuring displacement fields by cross-correlation and a differential technique: experimental validation. Opt. Eng. 51, 043602, 2012.Search in Google Scholar
Xavier, J., de Jesus, A.M.P., Morais, J.J.L., Pinto, J.M.T. (2012b) Stereovision measurements on evaluating the modulus of elasticity of wood by compression tests parallel to the grain. Constr. Build. Mater. 26:207–215.10.1016/j.conbuildmat.2011.06.012Search in Google Scholar
Yang, Q.D., Thouless, M.D., Ward, S.M. (1999) Numerical simulations of adhesively-bonded beams failing with extensive plastic deformation. J. Mech. Phys. Solids 47:1337–1353.10.1016/S0022-5096(98)00101-XSearch in Google Scholar
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