Ceramic matrix composites have good thermomechanical properties at high or very high temperatures. The modeling of the crack networks associated to the degradation of such composites using damage mechanics is not straightforward. The main reason is the presence of a crack network mainly oriented by the loading direction, which is a priori unknown. To model this, compliance tensorial damage variables are used in a thermodynamic potential able to account for crack closure effects (unilateral contact). The damage kinematic is initially completely free and imposed by the evolution laws. The key point of the present paper is to account for friction in such cracks that can result in an apparent activation/deactivation of the shear damage. The initial model is enriched with an inelastic strain and a friction law. The plasticity criterion is expressed only using tensorial variables. The model is identified and illustrated on multiaxial data obtained at ONERA on tubes loaded in tension and torsion.
AndrieuxSBambergerYMarigoJJ (1986) Un modèle de matériau microfissuré pour les bétons et les roches. Journal de Mécanique Théorique et Appliquée5(3): 471–513.
2.
Aubard X (1992) Modélisation et identification du comportement mécanique des matériaux composites 2D-C/SiC. PhD Thesis, Paris 6 University, France.
3.
BarangerE (2013) Building of a reduced constitutive law for ceramic matrix composites. International Journal of Damage Mechanics22(8): 1222–1238.
4.
BarangerE (2016) Extension of a fourth-order damage theory to anisotropic history: Application to ceramic matrix composites under a multi-axial non-proportional loading. International Journal of Damage Mechanics27(2): 238–252.
5.
BarangerE (2018) Modeling mechanical behavior of ceramic matrix composites. In: ZwebenCHBeaumontPW (eds) Comprehensive Composite Materials IIVol. 5.. Ceramic and Carbon Matrix Composites. Elsevier, pp. 237–268. .
6.
BarangerECluzelCLadevèzeP, et al. (2011) Effects of the thermomechanical loading path on the lifetime prediction of self-healing ceramic matrix composites. Science and Engineering of Composite Materials18(4): 259–264.
7.
Bernachy-Barbé F (2014) Caractérisation des mécanismes d'endommagement et modélisation du comportement mécanique sous chargements multi-axiaux de tubes composites SiC/SiC. PhD Thesis, ENMP, France.
8.
Bernachy-BarbeFGélébartLBornertM, et al. (2015a) Anisotropic damage behavior of SiC/SiC composite tubes: Multiaxial testing and damage characterization. Composites Part A: Applied Science and Manufacturing76: 281–288.
9.
Bernachy-BarbeFGélébartLBornertM, et al. (2015b) Characterization of SiC/SiC composites damage mechanisms using digital image correlation at the tow scale. Composites Part A: Applied Science and Manufacturing68: 101–109.
10.
BettenJ (1983) Damage tensors in continuum mechanics. Journal de Mecanique theorique et appliquee2(1): 13–32.
11.
BuiHD (1978) Mécanique de la Rupture Fragile, Paris: Masson..
12.
CarolIWillamK (1996) Spurious energy dissipation/generation in stiffness recovery models for elastic degradation and damage. International Journal of Solids and Structures33(20): 2939–2957.
13.
Chaboche J (1977) Sur l'utilisation des variables détat interne pour la description du comportement viscoplastique et de la rupture par endommagement. In: Proc. problemes non-linéaires de mécanique, symposium Franco-Polonais, Cracow, Poland, pp.137–159.
14.
ChabocheJ (1982) Le concept de contrainte effective appliqué à l'élasticité et à la viscoplasticité en présence d'un endommagement anisotrope. In: Boehler JP (ed.) Mechanical Behavior of Anisotropic Solids/Comportment Méchanique des Solides Anisotropes, Villard-de-Lans, France: Springer, pp. 737–760. .
15.
ChabocheJMaireJ (2001) New progress in micromechanics-based CDM models and their application to CMCs. Composites Science and Technology61(15): 2239–2246.
16.
ChabocheJL (1992) Damage induced anisotropy: On the difficulties associated with the active/passive unilateral condition. International Journal of Damage Mechanics1(2): 148–171.
17.
CluzelCBarangerELadevèzeP, et al. (2009) Mechanical behaviour and lifetime modelling of self-healing ceramic-matrix composites subjected to thermomechanical loading in air. Composites Part A: Applied Science and Manufacturing40(8): 976–984.
18.
CordeboisJSidoroffF (1979) Anisotropie élastique induite par endommagement. Comportement Mécanique des Solides Anisotropes295: 761–774.
19.
CormeryFWelemaneH (2002) A critical review of some damage models with unilateral effect. Mechanics Research Communications29(5): 391–395.
20.
CurnierAHeQCZyssetP (1994) Conewise linear elastic materials. Journal of Elasticity37(1): 1–38.
21.
FriderikosOBarangerE (2016) Automatic building of a numerical simplified constitutive law for ceramic matrix composites using singular value decomposition. International Journal of Damage Mechanics25(4): 506–537.
22.
GasserALadevezePPossM (1996) Damage mechanisms of a woven SiC/SiC composite: Modelling and identification. Composites Science and Technology56(7): 779–784.
23.
GenetMMarcinLBarangerE, et al. (2012) Computational prediction of the lifetime of self-healing CMC structures. Composites Part A: Applied Science and Manufacturing43: 294–303.
24.
GenetMMarcinLLadevezeP (2014) On structural computations until fracture based on an anisotropic and unilateral damage theory. International Journal of Damage Mechanics23(4): 483–506.
25.
GuillaumatLLamonJ (1993) Multi-fissuration de composites sic/sic. Revue des Composites et des Materiaux Avances3: 159–171.
26.
HalmDDragonA (1998) An anisotropic model of damage and frictional sliding for brittle materials. European Journal of Mechanics – A/Solids17(3): 439–460.
27.
JuJ (1990) Isotropic and anisotropic damage variables in continuum damage mechanics. Journal of Engineering Mechanics116(12): 2764–2770.
28.
KachanovL (1958) Time of the rupture process under creep conditions. Isv Akad Nauk SSR Otd Tekh Nauk8: 26–31. .
29.
KachanovM (1992) Effective elastic properties of cracked solids: Critical review of some basic concepts. Applied Mechanics Reviews45(8): 304–335.
30.
LadevèzeP (2002) An Anisotropic Damage Theory with Unilateral Effects: Applications to Laminates and to Three-and Four-Dimensional Composites, Amsterdam, Netherlands: Elsevier,.
31.
LadevèzePBarangerEGenetM, et al. (2014) Damage and lifetime modeling for structure computations. In: BansalNPLamonJ (eds) Ceramic Matrix Composites: Materials, Modeling and Technology, New Jersey, USA: John Wiley & Sons, Inc., pp. 465–519. .
32.
LemaitreJChabocheJL (1994) Mechanics of Solid Materials, Cambridge, UK: Cambridge University Press..
33.
LemaitreJDesmoratRSauzayM (2000) Anisotropic damage law of evolution. European Journal of Mechanics – A/Solids19(2): 187–208.
34.
MaireJPacouD (1996) Essais de traction-compression-torsion sur tubes composites céramique-céramique. In: Baptiste D and Vautrin A (eds.) JNC 10: Comptes-Rendus des Dixièmes Journées Nationales sur les Composites, Paris: AMAC, pp. 1225–1234. .
35.
MarcinLMaireJFCarrèreN, et al. (2011) Development of a macroscopic damage model for woven ceramic matrix composites. International Journal of Damage Mechanics20(6): 939–957.
36.
MurakamiS (1988) Mechanical modeling of material damage. Journal of Applied Mechanics55(2): 280–286.
37.
MurakamiSOhnoN (1981) A continuum theory of creep and creep damage. Creep in Structures, Berlin, Germany: Springer, pp. 422–444. .
38.
ParkTVoyiadjisG (1998) Kinematic description of damage. Journal of Applied Mechanics65(1): 93–98.
RagueneauFLa BorderieCMazarsJ (2000) Damage model for concrete-like materials coupling cracking and friction, contribution towards structural damping: First uniaxial application. Mechanics of Cohesive-Frictional Materials5: 607–625.
41.
VoyiadjisGParkT (1997) Anisotropic damage effect tensors for the symmetrization of the effective stress tensor. Journal of Applied Mechanics64(1): 106–110.
