13th International Conference on Fracture June 16–21, 2013, Beijing, China -8- three contributions: (i) the cleavage surface energy on the facets of the second grain, (ii) the intergranular energy of the “triangles”, and (iii) the energy spent in breaking the remaining ligaments. This model predicts that the number of segmentations along a given grain boundary is an increasing function of ψ, as observed experimentally [10] and that the = global? cleavage stress is also increasing with ψ. Figure 7. The four steps for a cleavage crack to cross a twisted grain boundary. This model of grain boundary crossing has been used to identify the parameters introduced in the Beremin-type model for predicting the fracture toughness of inhomogeneous materials [2] in which two modes of failure (intergranular and cleavage) are competing. The results shown in Fig. 8 were obtained using Vo = (50 µm) 3, mB = mSZ = 30 (Weibull shape factors for base metal (B) and segregated zones (SZ)) in the as-received and aged conditions), f = 10 % (volume fraction of segregated zones). The critical stresses were taken as: ( ) ( ) ( ) ( ) 3300 , 3230 , 3250 , 2750 B B u u SZ SZ u u MPa as received MPa aged MPa as received MPa aged σ = − σ = σ = − σ = It is thus observed that aging produces a small decrease of the cleavage stress (by about 2%), due to the mechanism for cleavage described in Figs. 6 & 7, and a larger decrease of the intergranular fracture stress in the segregated zones (by about 15%)due to phosphorus intergranular segregation after aging. This value is in good agreement with the measurements carried out on homogeneous material representing the composition of the segregated zones [18]. Fig. 8 shows that the bimodal model for fracture is able to reproduce the observed variations in fracture toughness with temperature in both conditions (as-received and aged). This model accounts also reasonably well for the shift in DBTT with aging (~ 30°C at 100 K MPa m = and Pr = 63 %). It accounts also for the increased scatter observed in test results on aged material. This model can also be used for predicting the variation of fracture toughness with longer aging times and lower
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