PSI - Issue 14

Ritam Chatterjee et al. / Procedia Structural Integrity 14 (2019) 251–258 Author name / Structural Integrity Procedia 00 (2018) 000 – 000

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to recovery. The drop in flow stress in (a) signifies annihilation of old grains due to nucleation. The stabilization in flow stress occurs due to increase in dislocation density of the newly formed grains due to difference in stored energy between nuclei and their neighbouring grains. The flow stress behaviour observed in case of simulated curves compares well with the trends of flow stress saturation post critical strain as observed in the work of Zhou et. al (2017) and Blaz et. al (1983). As the number of new grains with low dislocation density keep on increasing, the average dislocation density over all grains decreases as shown in Fig. 2(b). Drop in dislocation density occurs exactly at the onset of DRX as observed in Fig. 2 (a) and (c) which further corroborates the claim of occurrence of DRX. The number of new nuclei is less than the number of grains having dislocation density greater than critical value as shown in Fig. 2 (c). The reason is attributed to nucleation probability of grains being less than the threshold value required to form a new nucleus from a grain. Since nucleation occurs due to a variety of yet undetermined physical parameters, it is modelled stochastically in the present work due to which a critical probability 0.5 is assumed. In the present work, the grain size effect in simulation is realised via a parameter called grain weight ‘ w ’ . After new grains ar e ‘added’ to the system post critical strain, the weights of all grains are re-normalized according to the following formulae: = ( ℎ / ) ∗ ℎ (13) = ( ℎ / ) ∗ ℎ (14) Here , ℎ and ℎ are phase fractions of non-recrystallized and recrystallized grains. Since, grain growth is not incorporated in the present model, these phase fractions remain unchanged during deformation. These have been obtained via trial and error to be 0.95 and 0.05 respectively while calibrating the non-DRX portion of the flow stress curve against the experimental results for CP Ti obtained by Xu & Zhu (2010) and Foul et. al (2018) at temperature 1173K and strain rate strain rate 0.001s -1 as shown in Fig. 3.

Fig. 3. Calibrated flow stress of Ti vs. strain for non-DRX vs experimental at 1173 K and 0.001 s -1

In Fig. 2 (d), the average grain size across all grains is found to decrease for the old grains and increase for the new grains. This is intuitive since the number of new grains increases rapidly with deformation and hence, the new grains occupy increasing volume in three dimensional space at the expense of older grains. At ~0.3 strain, both recrystallized and non-recrystallized grains have almost equal grain weights which signifies that an equiaxed microstructure has been realised via dynamic recrystallization. Almost all grains (~95%) are observed to have recrystallized at 0.3 strain as shown in Fig. 2(d).