PSI - Issue 13

Michihiro Kunigita et al. / Procedia Structural Integrity 13 (2018) 198–203 Kunigita / Structural Integrity Procedia 00 (2018) 000 – 000

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Fig.2 Probability distributions of MA particle thickness and maximum size of nucleated cracks. Stage-II: Figure 3 shows bainitic microstructure containing MA particles and grain-boundary (GB) ferrite, schematically. The microstructure is subjected to applied stress and dislocations are piled up at MA particles, its pipe-up distance is √2 , where is inter-MA particle distance (assumed equal to bainite plate thickness) or GB ferrite thickness. Petch formulated the local fracture stress for a crack to propagate into ferrite matrix from a cementite particle, based on energy instability criterion (Petch, 1986). But, his formulation cannot apply to the present study because he assumed the Hall Petch relationship for yield strength. Therefore, his formulation was modified as (Kawata, 2018),

Fig.3 Bainitic microstructure containing MA particles and grain-boundary ferrite, schematic. = { 4 (1+1⁄√2)(1− 2 )( − 0 ) , ( < ) √ 4 (1− 2 ) − 2 ( − 0 ) 2 8 2 2 − ( − 0 ) 2√2 , ( ≥ ) where is Young’s modulus, is Poisson ’s ratio, is effective surface energy, is yield strength, 0 is friction stress. The critical crack length is expressed as, = (1+1⁄√2)(1− 2 ) 2 ( − 0 ) 2 8 (7) Probability distribution of can be determined experimentally, considering the GB ferrite, if any. The effective surface energy, , in Eq.(6) was assumed to depend on temperature as (Kawata et al, 2018), [J 2 ⁄ ] = 20 + exp (− 7 [ 0 0 ] ) (9) (6)