Mechanical modelling of SiC/SiC composites and design criteria F. Bernachy CEA, DEN/DMN/SRMA/LC2M, Gif-sur-Yvette, France L. Gélébart CEA, DEN/DMN/SRMA/LC2M, Gif-sur-Yvette, France J. Crépin Centre des Matériaux, Mines ParisTech, Evry, France M. Bornert Laboratoire Navier, Ecole des Ponts ParisTech, Marne-la-Vallée, France AIEA FR13 Paris 06/03/2013 13 MARS 2013 CEA 06/03/2013 PAGE 1
CONTEXT AND MOTIVATIONS OF THE STUDY CEA 06/03/2013 PAGE 2 13 MARS 2013
SiC/SiC COMPOSITES FOR FUEL CLADDING New operating conditions for GFRs (Gas-cooled Fast Reactors) Higher temperatures (nominal 400-1000 C, accidental 1600-2000 C) High flux of fast neutrons SiC/SiC composites possess a deterministic mechanical behavior, high strains at failure (compared to monolithic SiC) and good properties under irradiation SiC/SiC GFR nuclear fuel cladding Due to open porosity : ϕ 9.6mm SiC/SiC tube elaborated at CEA (C. Sauder), similar to the tubular fuel cladding concept Leak-tightness is ensured by a thin metallic liner with no mechanical function (CEA patent) : Fuel pellet SiC/SiC layers Liner (refractory alloy) 13 MARS 2013 CEA 06/03/2013 PAGE 3
MOTIVATIONS OF THE STUDY Few studies exist about the mechanical behavior of 3rd gen. SiC/SiC composites with a complex architecture, and under complex loadings There is a need for several mechanical characterizations : Damage criteria Elastic properties (anisotropic) Failure criteria Non-linear constitutive laws Elastic-linear simulations for normal operating conditions Non-linear simulations for accidental conditions The anisotropy of the material requires multiaxial tests Measurement techniques, mechanical tests, models are developped on a reference material 13 MARS 2013 CEA 06/03/2013 PAGE 4
REFERENCE MATERIAL Microstructure 1 internal filament winding layer at 45 2 2D-braided layers at 45 (32 tows per layer, 500 fibers per tow) Porosity ~ 10% No metallic liner 2 porosity scales: intertow, intratow Elaboration process Fiber preform of 3 rd gen. SiC fibers Hi-Nicalon S (ϕ 13µm) Chemical Vapor Infiltration (CVI) of pyrocarbon interphase (100 nm) Consolidation : deposition of the SiC matrix (CVI) After Murakami etching 13 MARS 2013 CEA 06/03/2013 PAGE 5
BIAXIAL TESTS CEA 06/03/2013 PAGE 6 13 MARS 2013
EXPERIMENTAL SETUP Hydraulic testing machine Piezoelectric sensor Resin Lights Low noise camera Axial-shear extensometer Sample Telecentric lens To AE amplification & acquisition SiC/SiC tube 13 MARS 2013 CEA 06/03/2013 PAGE 7
UNIAXIAL TESTS : TENSION Anisotropic elastic properties Highly non-linear behavior due to damage : Creation and opening of matrix cracks, arrested by the fibers After saturation of matrix cracking, ultimate failure due to fibre failures Cyclic tension Effects : Decrease of the elastic properties Tension/compression asymmetrical behavior (cracks close under compressive stresses) Hysteresis loops due to friction of crack surfaces 13 MARS 2013 CEA 06/03/2013 PAGE 8
UNIAXIAL TESTS : TORSION Torsion damage on tubes causes a loss of orthotropy in the tube axes Orientation of cracks dependent on the principal stress orientation from SEM observations of surface matrix cracks Cyclic torsion Orientation of crack normals/tube axis 13 MARS 2013 CEA 06/03/2013 PAGE 9
BIAXIAL TESTS 13 monotonic tests at constant biaxiality ratio : β = σ zz /σ θz (β = 0, β = 0,5, β = 1, β = 2, β = ) Shear strain Axial strain Circ. strain 13 MARS 2013 CEA 06/03/2013 PAGE 10
DESIGN CRITERIA CEA 06/03/2013 PAGE 11 13 MARS 2013
Normalized cumulated energy DAMAGE AND FAILURE THRESHOLDS (1/2) From experimental data, we define 2 experimental damage thresholds Acoustic damage threshold - Criterion on the normalized cumulated acoustic energy For example, for 10% total energy Simple tension : σ zz d = 115 MPa Axial stress (MPa) Mechanical damage threshold - Criterion on the non-linear strains Initial computed compliance tensor We use here the usual tensor norm and we assume no out-of-plane damage 13 MARS 2013 CEA 06/03/2013 PAGE 12
DAMAGE AND FAILURE THRESHOLDS (2/2) 5.10-4 non-linear strain damage surface Scattered failure stresses correspond to identical damage thresholds Good agreement between AE and Mechanical thresholds 13 MARS 2013 CEA 06/03/2013 PAGE 13
MECHANICAL MODELLING CEA 06/03/2013 PAGE 14 13 MARS 2013
ELASTIC PROPERTIES Optimization of in-plane compliance tensor coefficients on biaxial stress-strain curves Comparison with numerical homogeneization of the composite : Experimental approach : Elastic properties from experimental data (assuming material orthotropy) Multiscale numerical approach : Homogeneization of the tow (Chateau, 2011) Homogeneization of the composite (Lestringant, 2012) Full initial stiffness tensor of the composite 13 MARS 2013 CEA 06/03/2013 PAGE 15
GOALS OF DAMAGE MODELLING Correct simulation of the tension-torsion tests in the identification set Taking into account unilateral effects (restauration of the initial elastic properties in compression) Simple model, based on few micromechanical assumptions Few model parameters to identify Chosen representation of damage : 4 crack systems at 0, 90, 45, -45 Independant crack systems, no interaction 13 MARS 2013 CEA 06/03/2013 PAGE 16
MACROSCOPIC DAMAGE MODELLING (1/2) Strain from cracks of system i is given by the homogeneisation of a microcracked elastic material with no interaction between cracks : Crack density Crack opening displacement Crack normal vector We use a deactivation index η, evolving between 0 (compression) and 1 (tension) to reproduce unilateral damage : Thus, our constitutive law is : Crack density Deactivation index Crack opening displacement Crack normal vector Stored strain Elastic deformation Deformation due to damage Crack opening displacement law : linear function of the stress vector Damage growth law : saturating (Weibull type) law 13 MARS 2013 CEA 06/03/2013 PAGE 17
MACROSCOPIC DAMAGE MODELLING (2/2) Identified model gives good results at all tested biaxiality ratios Accurate prediction of compression torsion test Possible improvements : 2 nd mechanism : fibre failure Better representations of damage (more crack systems, coupling between systems...) Crack opening laws in accordance with micromechanics Complex loading paths have still to be tested 13 MARS 2013 CEA 06/03/2013 PAGE 18
MODEL IMPLEMENTATION IN CAST3M Implementation of the model in CEA's FE code CAST3M Stress formulation implies inversion of the stress-strain relation using Newton-Raphson iterations Simulation of a SiC/SiC tube under 3-point bending Crack density (ρ 0 +ρ 90 +ρ 45 +ρ -45 )/4 Deflection (mm) 13 MARS 2013 CEA 06/03/2013 PAGE 19
Outcomes and perspectives Definition of damage criteria, easy to measure and reproducible Useful for design purposes Results about the biaxial mechanical behavior of the tubes Construction and identification of a damage model Measurement of elastic properties in good agreement with multiscale simulations Non-linear behavior has still to be adressed using a multiscale approach. Possible strategies : Building of a 3D homogeneous damage model of the tow Simulation of the initiation and propagation of cracks through the composite More experimental results coming to adress several issues Non proportional tests (complex loading paths) Investigation of crack opening/closure mechanism Tension-internal pressure tests Mechanical properties along the orthoradial direction Tests on other microstructures (braiding and winding angles) Bending tests Test of the mechanical model and close to industrial issues 13 MARS 2013 CEA 06/03/2013 PAGE 20
Thank you for your attention! PAGE 21 CEA 06/03/2013 Commissariat à l énergie atomique et aux énergies alternatives Centre de Saclay 91191 Gif-sur-Yvette Cedex T. +33 (0)1 69 08 56 13 F. +33 (0)1 69 08 71 67 DANS DMN SRMA 13 MARS 2013 Etablissement public à caractère industriel et commercial RCS Paris B 775 685 019