13th International Conference on Fracture June 16–21, 2013, Beijing, China -5- thermal shock initial temperature is higher than 600oC. For without temperature-dependent material properties, it is considered to be the same as the crack resistance at 20oC. Table1. Temperature-dependent material properties of the diborides of zirconium based UHTC Material parameters Values and expressions E(GPa) ( ) 0 1 2 2 m m T T T T m m E E BTe B T BT T BT e − − = − + − + − E0(GPa), B0, B1, B2 500, 2.54, 1.9, 0.363 α (°C-1) (2.01ln(T)-6.7652)×10-6 k (W⋅(m⋅°C)-1) -16.79×ln(T)+178.2 ν 0.16 Cp(T) (cal/mol) 15.34+2.25×10-3T-3.96×105T-2 ρ(g.cm-3 ) 6.1 0 100 200 300 400 500 600 4.0 4.5 5.0 5.5 6.0 6.5 20oC 600oC Crack resistance (MPa·m1/2) Crack length (μm) Figure 2. Crack resistance under different temperature 0 200 400 600 800 1000 1200 1400 1600 0 30 60 90 120 150 180 Residual Strength (MPa) ΔT (oC) c0/a=0.1 (temperature-dependent) c0/a=0.1 (temperature-independent) h=50 kW/(m2⋅K) (a) 0 200 400 600 800 1000 1200 1400 1600 0 30 60 90 120 150 180 h=80 kW/(m2⋅K) Residual Strength (MPa) ΔT (oC) c0/a=0.1 (temperature-dependent) c0/a=0.1 (temperature-independent) (b) Figure 3. The relationship between thermal residual strength and thermal shock temperature difference ∆T ( (a), h=50kW/(m2·K), (b), h=80kW/(m2·K) ) As can be seen in Fig. 3, the curves of thermal shock residual strength have the same trends with the experiments results’ trends which are common in literatures [5,9]. When the thermal shock temperature difference ∆T is less than the critical thermal shock temperature difference ∆Tc, crack propagation didn’t occur and the strength remains unchanged. At ∆T =∆Tc, the strength drops
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