13th International Conference on Fracture June 16–21, 2013, Beijing, China -6- as-received condition (t = 0) and during aging at 450°C. Full details can be found elsewhere [10]. The results are compared to experimental measurements in Fig. 4 where it is observed that in the as-received condition (t = 0), phosphorus and carbon atoms are already segregated. Carbon atoms desegregate during aging while phosphorus concentration is increasing. This results from the repulsive interaction between C and P atoms (Eq. 9). The calculated values are in good agreement with the experimental values. Figure 4. Phosphorus (P) and carbon (C) concentration at grain boundaries (expressed in atomic %) a function of aging time at 450°C. Experimental results and calculated curves. 5. Prediction of fracture toughness – Influence of impurity segregation It has been shown that the fracture mode of our material in the DBTT regime was bimodal: transgranular cleavage and intergranular. A recent model has been proposed for this situation [2]. However this model includes a number of parameters (Weibull shape factors, critical cleavage and intergranular fracture stress, σu) which have to be discussed first. This is related to the fact that aging produces a variation in the concentration of impurities (C and P) segregated along the grain boundaries. It is well to remember that C atoms produce a strengthening effect of the grain boundaries while P atoms have an opposite effect [17]. It has been shown previously that the intergranular fracture stress decreases linearly with gb pC [18, 19] as soon as the grain boundary concentration in P is larger than about 10 at %. These results can be used to predict the variation of the fracture toughness with aging using the kinetics models developed in the preceding section. The cleavage fracture stress is also dependent on the grain boundary composition as explained below. This effect is related to the crossing of grain boundaries by cleavage cracks, which has already been studied in some detail by Qiao [20, 21]. This crossing depends on the misorientation between two adjacent grains, as depictured in Fig. 5 where the tilt, φ, and the twist, ψ, components
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