PSI - Issue 33

Saki Hayashi et al. / Procedia Structural Integrity 33 (2021) 1162–1172 Hayashi et al / Structural Integrity Procedia 00 (2019) 000 – 000

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3.2 Combined model for segregation and fracture Although the ultimate goal is to determine the maximum allowable amount of Sn, it is difficult to conduct a number of experiments by various amounts of Sn at many tempering temperatures and holding times which may occur in welding. Therefore, a model was needed to estimate the transition temperature change Δ T by the tempering temperature, tempering holding time, and mass % of Sn. We tried to establish a model by combining of several different elements. The flowchart of the model configuration is shown in Fig. 12. i) Modelling of positive effect of tempering The temper parameter (Eq. (6)) proposed by Hollomon (1947) was used, and a term reflecting the effect of temper embrittlement was added later. The coefficients were obtained by fitting the experimental results, where T is the tempering temperature and t is the tempering holding time. First, the coefficients A and B in Eq. (6) were determined using the experimental results for 0.01% Sn, which is considered to cause little temper embrittlement. All fitting was done using the least squares method. Δ = ∗ (ln + ) (6) ii) Modelling for temper embrittlement Next, a term reflecting the effect of temper embrittlement was added to Eq. (6). This term was created by multiplying Y i by a time-variable factor C( t ), based on Kameda and McMahon (1981) 's consideration that the interface coverage Y i due to Sn segregation is proportional to the effect of temper embrittlement. ∆ = ∗ (ln + ) + ( ) ∗ ( , , ) (7) ･ Thermodynamic equation for calculating Sn cover ratio at GB, Y i The first step was to find Y i , which was created using the following equation for coverage at each holding time t derived by Mclean (1957) and Guttman (2002). ( , , ) = {1 − exp( 2 ) ∙ erfc( )} { ( ∞ ) − (0)} + (0) (8) = 2√ ( ∞ ) (9) Where, (∞) is the coverage of the interface after infinite time, i.e., the equilibrium value, obtained by the following well-known equilibrium equation ( ∞ ) = ( ∆ ) 1 + ( ∆ / ) (10) where X i B refers to the bulk concentration of Sn, and the Sn concentrations (0.01%, 0.1%, and 0.2%) were substituted. ･ Approximation of Y i as a normal distribution function