13th International Conference on Fracture June 16–21, 2013, Beijing, China -4- 2.1. Experimental data The material analysed is an RPV 22NiMoCr37 ferritic steel, known as Euro Material A, for which we have the mechanical and fracture toughness properties at a number of temperatures and irradiation states within the lower shelf and in DBT from the Euratom FP6 project PERFECT [21] and FP7 project PERFORM60. The temperature dependence of Young’s modulus E, proportionality stress σ0, and ultimate tensile strength σu under un-irradiated conditions are 90 206000 =− + E T , (6) ( ) 91 421.2 63.9exp 0 T− = + σ , ( ) 108 564.1 70.2exp T u − = + σ , (7) where T is in oC and E, σ 0, and σu are in MPa. Poisson's ratio is ν = 0.3 independent of temperature. For the irradiated state considered here, fluence of 4.3 x 1019 n cm-2, En > 1 MeV at 285oC, E is given by Eq. (6) while σ0 and σu are given by ( ) 95.2 490.4 62.1exp 0 T− = + σ , ( ) 188.2 524.2 155.1exp T u − = + σ . (8) The fracture toughness properties of Material A were determined according to the ASTM standard [23] using SEN(B) specimens in three-point bending [21]. This standard is based on the Master Curve formalism, which defines the temperature dependence of a reference toughness, K0, relative to a reference temperature, T0, at which K0 = 108 MPa√m, for high-constraint cracked geometries with reference crack front length B0 = 25.4 mm ( ) [ ] 0 0 31 77 exp 0.019T T K − = + . (9) The scatter in measured cleavage fracture toughness values is described as a function of the probability of failure, p, and the actual crack front length, B, with ( ) 1 4 1 4 0 min 0 min 1 1 ln ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ − ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = + − p B B K K K K p , (10) where Kmin is a temperature independent threshold toughness, Kmin = 20 MPa√m in [23]. Eqns. (9) and (10) define the cleavage fracture toughness behaviour of a material with known T0. The reference temperatures for deep-notch (a0/W = 0.5) specimens reported in [21] are T0 = -104ºC for un-irradiated and T0 = -78ºC for irradiated state. In the present work, we assume that Eqns. (9) and (10) provide a relevant representation of experimental data and assess our model against it. The density and size distribution of cleavage initiating particles in Material A have been reported in [22]. The nature of the initiators has been determined by fractography revealing that cleavage in this material initiated predominantly at metal carbides, specifically M3C and M23C6, and occasionally at carbide-sulphate composites. Comprehensive metallographic examination of carbides provided number density ρ = 7.6×1017 m-3 and a probability density of particle sizes which was fit by ( ) ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ − ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ = − − − β β 0 1 0 0 exp r r r r r β f r , (11) with shape β = 2.7 and scale r0 = 0.036 μm. 2.2. Micro-mechanically informed model The expression for the probability of particle failure is based on experimental observations that this probability depends not only on the mechanical fields but also on the particle size, similarly to the
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