This is an author-deposited version published in: Eprints ID: 8849

Transcription

1 Open Archive Toulouse Archive Ouverte (OATAO) OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. This is an author-deposited version published in: Eprints ID: 8849 To cite this version: Welemane Hélène and Goidescu Cristina and Pantalé Olivier and Barelli Florent and Dalverny Olivier Micromechanical modeling of brittle damage in composite materials: primary anisotropy, induced anisotropy and opening-closure effects. (2012) In: ESMC 12, 09 July July 2012 (Graz, Austria). Any correspondence concerning this service should be sent to the repository administrator:

2 8 th EuropeanSolidMechanicsConference Graz, Austria-July, 9 th 2012 Micromechanicalmodelingof brittledamage in composite materials: primary anisotropy, induced anisotropy and opening-closure effects H. Welemane, C. Goidescu, O. Pantalé, F. Barelli, O. Dalverny University of Toulouse INP/ National School of Engineers of Tarbes (France) Engineering Production Laboratory

3 Damage phenomena Macroscopic consequences DAMAGE IN LAMINATED COMPOSITES Various degradation mechanisms Fiber-matrix debonding in carbon-epoxy [Aussedat-Yahia 97] Matrix cracking in SiC-SiC [Guillaumat 94] Fiber breakage in glass-epoxy [François 04] 2/20

4 Damage phenomena Macroscopic consequences DAMAGE IN LAMINATED COMPOSITES Influence on the macroscopic behavior : non linearity degradation of elastic properties induced anisotropy unilateral effect Carbon-epoxy [Goidescu 11] /20

5 Damage phenomena Macroscopic consequences DAMAGE IN LAMINATED COMPOSITES Influence on the macroscopic behavior : non linearity degradation of elastic properties induced anisotropy unilateral effect open state Carbon-epoxy [Moffat 94] 0 45 SiC-SiC[Gasser 94] closed state 4/20

6 General framework Thermodynamic potential State laws Damage evolution law CDM MODELING APPROACH Thermodynamic of irreversible processes 1 2 Thermodynamic potential 3 Damage evolution law 5/20

7 General framework Thermodynamic potential State laws Damage evolution law CDM MODELING APPROACH Thermodynamic of irreversible processes Micromechanics-based formulation 1 2 Thermodynamic potential 3 Damage evolution law P (P) (,) rigorous, physical meaning arbitrarymicrocracksorientation interactions between: initial and induced anisotropies opening-closure effects 6/20

8 General framework Thermodynamic potential State laws Damage evolution law CDM MODELING APPROACH Assumptions Small transformations, rate-independent and isothermal conditions 2D framework (fracture mechanics solutions) Initial orthotropic media Dilute concentration, no interaction Flat microcracks(unit normal n), open or closed (no friction) virgin material microcracked material RVE = square cellarea e 2 e 1 n 7/20

9 General framework Thermodynamic potential State laws Damage evolution law CDM MODELING APPROACH 1 Discretedescription Internal variables = damage densities d i of N families of parallel microcracks Orientations n i regularly spaced 8/20

10 General framework Thermodynamic potential State laws Damage evolution law CDM MODELING APPROACH 2 Thermodynamic potential Micromechanicaldirect approach Goidescuet al. 12 Extension of works by : Andrieuxet al. 86 anisotropic context Gruescu04 closure effects based on jump displacements [u]= u + u - = [u n ]n+[u t ]t (opening) (sliding) formulation in strain (free energy) : W(E,, ) open state : 0 closedstate : = 0 9/20

11 General framework Thermodynamic potential State laws Damage evolution law CDM MODELING APPROACH 2 Thermodynamic potential Expression of the free energy «isotropic» coupling (preserves initial orthotropy) weak anisotropic coupling (similar to isotropic context) strong anisotropic coupling with Closed-form expression accounting for interaction between initial and induced anisotropies 10/20

12 General framework Thermodynamic potential State laws Damage evolution law CDM MODELING APPROACH 2 Thermodynamic potential Unilateral effects open state : closedstate : opening-closure criterion(=0) : with Mathematicalconsistence: W of class C 1 11/20

13 General framework Thermodynamic potential State laws Damage evolution law CDM MODELING APPROACH 3 Damage evolution law Standard framework Systematic satisfaction of the 2 nd principle of thermodynamics Dissipation potential (Marigo 85) : material strength damage rate How? When? 12/20

14 Predictive ability Elastic properties Dissipative behavior PREDICTIVE ABILITY ELASTIC PROPERTIES Elongation and volumetric moduli one family of microcracks along principal axis SiC-SiC[Aubard 92] n e 2 m e 1 virgin state (orthotropic) open state closedstate «isotropic-like» effect(open and closedstates) recovery mode identical to isotropic context(welemane 02) 13/20

15 Predictive ability Elastic properties Dissipative behavior PREDICTIVE ABILITY ELASTIC PROPERTIES Elongation and volumetric moduli one family of microcracks with arbitrary orientation e 2 m e 1 n virgin state (orthotropic) open state closedstate stronganisotropiccoupling(open and closedstates) complex recovery mode 14/20

16 Predictive ability Elastic properties Dissipative behavior PREDICTIVE ABILITY DISSIPATIVE BEHAVIOR Influence of initial orthotropy stress-strain response 15/20

17 Predictive ability Elastic properties Dissipative behavior PREDICTIVE ABILITY DISSIPATIVE BEHAVIOR Influence of initial orthotropy TENSION density distribution = 0 = 45 16/20

18 Predictive ability Elastic properties Dissipative behavior PREDICTIVE ABILITY DISSIPATIVE BEHAVIOR Influence of unilateral effects Dissymetry between tension and compression 17/20

19 Predictive ability Elastic properties Dissipative behavior PREDICTIVE ABILITY DISSIPATIVE BEHAVIOR Influence of unilateral effects opening-closure domains(=0 ) tension E 22 mixed open E 11 closed compression mixed 18/20

20 Predictive ability CONCLUSION AND PERSPECTIVES Micromechanics-based model of brittle damage in 2D-orthotropic materials Rigorous approach Verification of mathematical and thermodynamical principles Account of main features of microcracking interaction of initial and induced anisotropy opening-closure effects for arbitrarily oriented microcracks More complete validation on experimental results Account of other dissipative mechanisms : dissipative sliding (closed microcracks), viscosity, plasticity 19/20

21 8 th EuropeanSolidMechanicsConference Graz, Austria-July, 9 th 2012 Thanks for your attention! H. Welemane, C. Goidescu, O. Pantalé, F. Barelli, O. Dalverny 20/20