T Nozawa et aL / Joumal of Nuclear Materials 384(2009)195-211 Maximum applied load: 600 mN ato:0.05s-1 Indent Progressive debonding contact regime 400 Complete debonding initiation sliding 00 ⅸx|Fi 100 Indenter men holder 0 2000 3000 4000 Displacement curve of the fiber push-out test. Two experimental parameters: (1)a debond initiation load (ad)and (2)a complete debonding and liding load (omax)are defined. clamping stresses have a close relationship with a measured sliding undergoes shrinkage first and swells with increasing neutron flu- stress(σmax)as ence in the direction perpendicular to the deposition plane, while Er(+Ve(oth+rough +girad lexp 2ktcvyrt it shrinks monotonically in the direction parallel to the deposition plane [26]. An empirical fit of the swelling was provided in [27- here e and v are Youngs modulus and Poisson 's ratio Subscripts f List of material properties applied in the analytical model the modified Shetty's model assumes a fiber surrounded by a com- High-density isotropic carbon /2 irradiated and c denote the fiber and the composites, respectively. Note that valuables Irradiated verage,Le→ em, since there is Dens =d1+ lo clear solution for multi-phase system so far. When specimen Elastic modulus(GPa) Ea(1+023小) are sufficiently thin, tr consequently becomes proportional to Poisson's rat Assuming no change Omax/t regardless of material properties of the constituents, (10-°c) Linear swelling Fig. 3 in Ref. [261 (4) Low-density isotropic carbon (glassy carbon)/35] Density (g/cm) =d1+3e) Elastic modulus(GPa) Eo Fig. 4 in Ref. [35] 2.5. Materials properties for calculation o=0.2(assumed) suming no change Linear swelling Fig. 1 in Ref [ 35] The input values used in calculation are empirically obtained CVD-SiC (4) [2, 4, 26-38] and are summarized in Table 2. According to the study Density (g/cm2) by Yan et al. [39. Pyc as an F/M interphase is more graphitic Elastic modulus(GPa) =Eo(1-9e)when the fibers(6-10 nm), while the structure becomes more turbot atic along the radial direction, i.e., near-isotropic. It is noteworthy that the structure of Py c depends significantly on processing con- Poisson's ratio vo=0.2 Assuming no change ditions. Because of this structural uncertainty for PyC, this study CTE(10-/C) Assuming no change considers two types of turbostratic carbon: a high-density carbon Linear swelling 26 and a low-density carbon 35]. A major difference between Hi-Nicalon Type-S/38) the high-density PyC and low-density Py C is in thermal expansivity Density (g/cm") =d(1+3e) as well as density and this issue is discussed later. The actual struc- Elastic modulus(GPa) ure of PyC applied in this study should be classified between these Poissons ratio suming no change two materials suming no change a high-density(2 g/cm)turbostratic carbon with Bacon Linear swelling suming same with anisotropy factor of 1 med for Pyc CVD-SiC cient of thermal expansion(CTE)is assumed to be 5.5 x 10-6/ C. Linear swelling (c) From many irradiation studies, the high-density isotropic carbon Neutron fluence(o)in units of 10-n/mclamping stresses have a close relationship with a measured sliding stress (rmax) as rmax ¼  Efð1 þ mcÞ Ecmf rth r þ rrough r þ rirrad r exp 2lEcmft rfEfð1 þ mcÞ    1  ; ð3Þ where E and m are Young’s modulus and Poisson’s ratio. Subscripts f and c denote the fiber and the composites, respectively. Note that the modified Shetty’s model assumes a fiber surrounded by a com￾posite average, i.e., the two-phase cylindrical system, since there is no clear solution for multi-phase system so far. When specimens are sufficiently thin, sf consequently becomes proportional to rmax/t regardless of material properties of the constituents, sf ffi  rf 2  rmax t : ð4Þ 2.5. Materials properties for calculation The input values used in calculation are empirically obtained [2,4,26–38] and are summarized in Table 2. According to the study by Yan et al. [39], PyC as an F/M interphase is more graphitic near the fibers (6–10 nm), while the structure becomes more turbost￾ratic along the radial direction, i.e., near-isotropic. It is noteworthy that the structure of PyC depends significantly on processing con￾ditions. Because of this structural uncertainty for PyC, this study considers two types of turbostratic carbon: a high-density carbon [26] and a low-density carbon [35]. A major difference between the high-density PyC and low-density PyC is in thermal expansivity as well as density and this issue is discussed later. The actual struc￾ture of PyC applied in this study should be classified between these two materials. A high-density (2 g/cm3 ) turbostratic carbon with Bacon anisotropy factor of 1 is assumed for PyC interphase. The coeffi- cient of thermal expansion (CTE) is assumed to be 5.5 106 /C. From many irradiation studies, the high-density isotropic carbon undergoes shrinkage first and swells with increasing neutron flu￾ence in the direction perpendicular to the deposition plane, while it shrinks monotonically in the direction parallel to the deposition plane [26]. An empirical fit of the swelling was provided in [27]. 0 100 200 300 400 500 600 700 0 1000 2000 3000 4000 Displacement [nm] Applied Load [mN] Debond initiation Indenter penetration Progressive debonding regime Complete debonding & sliding Indenter contact Matrix Fiber Matrix Fiber Matrix Fiber Maximum applied load: 600 mN Load rate/load ratio: 0.05 s-1 Matrix Fiber Berkovich indenter Specimen holder with a groove Fig. 2. Schematic of the load-displacement curve of the fiber push-out test. Two experimental parameters: (1) a debond initiation load (rd) and (2) a complete debonding and sliding load (rmax) are defined. Table 2 List of material properties applied in the analytical model. Valuables Non-irradiated Irradiated High-density isotropic carbon [26] Density (g/cm3 ) d0 = 1.9 =d0(1 + 3e) Elastic modulus (GPa) E0 = 25 =E0(1 + 0.23/) Poisson’s ratio m0 = 0.2 Assuming no change CTE (106 /C) a0 = 5.5 Assuming no change Linear swelling – Fig. 3 in Ref. [26] Low-density isotropic carbon (glassy carbon) [35] Density (g/cm3 ) d0 = 1.5 =d0(1 + 3e) Elastic modulus (GPa) E0 = 25 Fig. 4 in Ref. [35] Poisson’s ratio m0 = 0.2 (assumed) Assuming no change CTE(106 /C) a0 = 2.8 Assuming no change Linear swelling – Fig. 1 in Ref. [35] CVD-SiC [4] Density (g/cm3 ) d0 = 3.2 =d0(1 + 3e) Elastic modulus (GPa) E0 = 460 =E0(1  .9e) when Tirr < 1000 C Assuming no change when Tirr > 1000 C Poisson’s ratio m0 = 0.2 Assuming no change CTE(106 /C) a0 = 4.4 Assuming no change Linear swelling – Fig. 22 in Ref. [4] Hi-NicalonType-S [38] Density (g/cm3 ) d0 = 3.1 =d0(1 + 3e) Elastic modulus (GPa) E0 = 420 =E0(1  20.9e) when Tirr < 1000 C Poisson’s ratio m0 = 0.2 Assuming no change CTE(106 /C) a0 = 5.1 Assuming no change Linear swelling – Assuming same with CVD-SiC Linear swelling (e). Neutron fluence (/) in units of 1025 n/m2 . 198 T. Nozawa et al. / Journal of Nuclear Materials 384 (2009) 195–211