CLUB utilisateurs Cast3M 28 novembre 2014 - Hôtel Mercure Porte d Orléans PHAN Ngoc Anh, MOREL Stéphane, CHAPLAIN Myriam Université de Bordeaux, I2M/Dépt. GCE Email : na.phan@i2m.u-bordeaux1.fr Projet VS2C : 1
2 Wood : * hygroscopic * quasi-brittle Objective Relative Humidity Influence Crack propagation Mechanical properties depend on temperature and moisture content. Varying moisture induces internal stresses may cause crack propagation. (FPZ) Fracture Process Zone
3 Linear Elastic Fracture Mechanics equivalent R-curve and Cohesive Zone Model (CZM) Integration of rapid variation of MC in CZM Our model and results Conclusions and perspectives
The crack length monitoring is very difficult to be accurately performed on wood. Due to the presence of FPZ at the crack tip, LEFM cannot be directly applied to estimate the fracture energy equivalent LEFM is usually applied on quasi-brittle fracture and provides useful approximations (Bazant and Planas (1998); Morel et al (2005)). 4
5 The crack length monitoring is very difficult to be accurately performed on wood. Due to the presence of FPZ at the crack tip, LEFM cannot be directly applied to estimate the fracture energy equivalent LEFM is usually applied on quasi-brittle fracture and provides useful approximations (Bazant and Planas (1998); Morel et al (2005)). Développement de FPZ Réel a 0 Da < Da c Equivalent crack length Taille critique de la FPZ P P max a 0 +Da a 0 Da c Réel Equivalent crack length Propagation de la FPZ a 0 +Da c a 0 +Da * a 0 Da * > Da c Load displacement curve d
6 Grc ac
7 Joint element 2D, 3D Illustration of the bilinear traction-seperation law (STL) in CZM A damage parameter d is used to describe the state of the interface (joints): The opening stress is related to the opening displacement w : is the maximum separation for the interface element over the entire loading history.
8 Parameter of CZM Numerical results Experimental data Optimization Conclusion
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10 Crack mouth opening Note that: (assumption : G fµ =G fb ) Bazant (2002) Crack tip opening G Rc Traction free crack l b l µ Crack bridging Microcrack Fracture process zone (FPZ) l coh = l b + l µ Remarks : Stress field in the mtdcb specimen using CZM (FEA with Cast3m 2013) Fracture properties (R-curve, parameters of CZM) depend on the moisture. G Rc, l coh increase with the increasing of MC.
11 The second Fick s law for diffusion: with α (L,R,T). See Dubois et al. (2006, 2009, 2011, 2014) In this study, MC surface (the equilibrium moisture) is changed to simulate the variation of relative humidity (RH).
12 The RH variation is rapid and has only a direct impact on fibers in the FPZ which is assumed to be linear. In the FE code, during the time increment Δt n, the crack opening w is considered f constant and fictive stress σ n+1 is written as : Δσ n is converted into the external mechanical nodal force increment along the cohesive zone during Δt n, translating incorporating the mechanical response history and the MC.
End t n+1 = t n + t Start 13 YES Remesh with a sf (t n ) Projection of hydrothermal field At time: t n a sf (t n ) > a sf (t n 1 ) NO Mechanical field: σ n, ε n Hydro thermal field: MC n, T n Variable internal (CZM): w n, d n, a sf (t n ), a sf (t n 1 ) Mesh without joint elements Mesh with joint elements Projection of hydrothermal field Hydro-thermal field : MC n, T n Use a sf (t n ) to calculate MC n(fpz) Hydro-thermal field : MC n, T n Hydro-thermal properties : D n+1 (L,T,R), K n+1 Condition limit (boundary) External hydro-thermal condition: MC surface (n + 1), T n+1 Run hydro-thermal routine Elastic properties : Young's Modulus (MC n ) External loading: f n+1 External hydro-thermal condition : MC surface (n + 1), T n+1 Influence of MC on cohesive interface Additional stress σ n Resolve NON-LINEAR problem (Cohesive Zone Model) Hydro-thermal field : MC n+1, T n+1 At time: t n+1 Mechanical field : σ n+1, ε n+1
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15 Cast3m 2013 version Développeur 30 files.eso Auteur : PHAN Ngoc Anh Université de Bordeaux, I2M/Dépt. GCE Email : na.phan@i2m.u-bordeaux1.fr
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18 Moisture content Time diffusion : 120 min
19 crack Middle section of the mtdcb specimen ELEM : CUB8 NBNO : 72850 NBEL : 64440 Memory : 24Gb Calculation time : 240 h Cluster Avakas MCIA crack crack
20 1 steps: 0.5 min In the wetting process while the imposed displacement is constant (phase 2), the stiffness decreases leading to reduced stress in the cohesive zone. The crack tends to be closed and the applied force tends to increase (crack does not further develop). All phenomena are converse in case of the drying phases. Phase 3 is continued with the increasing imposed displacement and constant moisture. We observe a continuity of the mechanical response which takes into account all previous changes.
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22 In this research, a new model, which integrates MC influence on the cohesive zone, is proposed and implanted in Cast3m. In further studies, this model will be analyzed with the moisture diffusion inside the whole specimen which results in viscoelasticity variation.
CLUB utilisateurs Cast3M 28 novembre 2014 - Hôtel Mercure Porte d Orléans 23