Chapter3 On Numerical Evaluation of Mixed Mode Crack Propagation Coupling Mechanical and Thermal Loads in Wood Material Hassen Riahi, Rostand Moutou Pitti, Frédéric Dubois, and Eric Fournely Abstract The mixed-mode crack growth coupling mechanical and thermal loads in wood material is investigated in this numerical work. The analytical formulation the crack driving force, namely the energy release rate, is introduced by T-integral that takes into account mixed mode fracture, thermal process in orthotropic material and pressure applied on the crack lips. This new formulation is based on Nother’s theorem and the definition of the strain energy density according to Lagrangian’s and Eulerian’s configurations. Moreover, this analytical formulation is implemented in finite element software Cast3m. First of all, several numerical examples, dealing with isotropic material, are provided to illustrate the accuracy of the FEM model. Then, the crack resistance of a timber CTS (Compact Tension Specimen) is investigated to show the efficiency of the proposed approach in the case of orthotropic material. Keywords Wood fracture • Mixed mode • Thermal fields • Path independent integral • Finite element method 3.1 Introduction Due to the advantages provided by its mechanical behaviour particularly under extreme loading conditions such as fire and seismic events, in addition to its aesthetic and environmental effects, timber is commonly employed in building and civil engineering structures. Hence, the accurate knowledge of its mechanical properties seems to be essential. Although the considerable efforts devoted in this field of scientific research, the physics related to the real behaviour of timber material is still misunderstood. Timber is considered as orthotropic material having three planes of symmetry, which usually results in complex forms of the governing equation (e.g. stress-strain relationship). Moreover, due to its natural origin, timber contains an array of defects such as knots which locally modify its mechanical properties, and hence, timber is rather a heterogeneous material. As well known, timber elements exhibit micro-cracks which can propagate due to fatigue, overload or creep loading and cause failure of the structure. In addition, timber is a hygroscopic material whose mechanical behaviour is very sensitive to climatic changes such as temperature and moisture variations which contribute to a redistribution of stresses in the material that can be followed by degradation. For example, drying process accelerate the crack growth, while wetting process induce the delay of the crack propagation. To predict the crack growth process many numerical methods were developed to characterize the mechanical fields in the neighbourhood of the crack. Among them, the background of energy methods come from invariant integrals which enables to evaluate the crack driving forces such as the crack growth rate and the stress intensity factors. The most popular is the J-integral proposed by Rice [1] based on the assessment of the strain energy density and Noether’s theorem [2]. This method is inefficient when dealing with mixed mode crack growth problems because it is necessary to separate the displacement field into a symmetric and antisymetric parts. To circumvent this difficulty, Chen and Shield [3] have developed the M-integral which enables us to get separated fracture modes based on a bilinear form of the strain energy density introducing virtual mechanical fields. Unfortunately, these tools are still H. Riahi • R. Moutou Pitti ( ) • E. Fournely Clermont Université, Université Blaise Pascal, Institut Pascal, BP 20206, F-63000 Clermont-Ferrand, France CNRS, UMR 6602, Institut Pascal, F-63171 Aubiere, France e-mail: hassen.riahi@etudiant.univ-bpclermont.fr; rostand.moutou_pitti@univ-bpclermont.fr F. Dubois Heterogeneous Material research Group, Université de Limoges, Egletons, France J. Carroll and S. Daly (eds.), Fracture, Fatigue, Failure, and Damage Evolution, Volume 5: Proceedings of the 2014 Annual Conference on Experimental and Applied Mechanics, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-06977-7__3, © The Society for Experimental Mechanics, Inc. 2015 21
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