Issue 31

C.L. dos Santos et alii, Frattura ed Integrità Strutturale, 31 (2015) 23-37; DOI: 10.3221/IGF-ESIS.31.03 31 mixed mode damage propagation is simulated considering a linear energetic criterion, which takes into account the two fracture modes, according to: I II IC IIC 1 G G G G               (3) where i G and iC G are, respectively, the energy release rate and the critical energy release rate ( I, II i  stands for fracture pure modes). The fracture properties required for the application of the cohesive damage model were extracted from experimental works performed on Pine wood from the same population, and summarized in Tab. 5 [31]. These fracture properties corresponded to the RL crack propagation system, which is one of the most important crack propagation systems for this wood species ( max,I  = R  =maximum tensile radial stresses; max,II  = RL  = maximum shear stresses in the RL plane).  R (MPa)  RL (MPa) G IC (N/mm) G IIC (N/mm) 7.93 16 0.264 0.9 Table 5 : Fracture properties for Pine wood: RL propagation system [31]. Tab. 6 presents an overview of simulations performed in this investigation. Besides the fully elastic analysis, two elasto- plastic analyses were performed using the sets of plastic constants given in Tab. 3 (Elastic-plastic (1)) and in Tab. 4 (Elastic-plastic (2)). These tables (Tab. 3 and 4) present suggested yield stresses for tension/compression and shear loadings. Using these yield stresses, the anisotropic ratios were defined taking into account an arbitrary reference curve. Besides the yield stresses adopted for the plasticity model, strength properties extracted from experimental works performed on the same wood species and available in the literature [29], are also presented in the referred tables. These strength properties were used to estimate the yield stresses. The experimental strength properties were presented for both tension and compression longitudinal loading. For radial and tangential directions, only compression strengths were given in the tables (one value for each direction). Concerning the shear strengths, a range of experimental values are given, which resulted from alternative shear testing [29]. Constitutive Modelling Approach Centre member Side members Fully elastic Orthotropic elastic model with constants from Tab. 1 Elastic–plastic (1) Orthotropic elastic model with constants from Tab. 1 Hill’s plasticity model with constants from Tab. 3 Elastic–plastic (2) Orthotropic elastic model with constants from Tab. 1 Hill’s plasticity model with constants from Tab. 4 Elastic with cohesive Orthotropic elastic model with constants from Tab. 1 - Cohesive damage model with constants from Tab. 5 Elastic –plastic with cohesive (1) Orthotropic elastic model with constants from Tab. 1 Hill’s plasticity model with constants from Tab. 3 Cohesive damage model with constants from Tab. 5 Elastic –plastic with cohesive (2) Orthotropic elastic model with constants from Tab. 1 Hill’s plasticity model with constants from Tab. 3 - Cohesive damage model with constants from Tab. 5 Table 6 : Different approaches for the constitutive modelling. A fully elastic model was also simulated with a cohesive interface on the side member (Elastic with cohesive). The parameters of the cohesive damage model were given in Tab. 5. The model was implemented by means of a contact pair