PSI - Issue 31

V. Romanova et al. / Procedia Structural Integrity 31 (2021) 64–69 V. Romanova et al. / Structural Integrity Procedia 00 (2019) 000–000

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the pyramidal slip is debatable. Won et al. (2015) reported that the pyramidal slip contribution to plastic deformation was negligible in ordinary conditions. Many researchers have not included the pyramidal slip mode in numerical simulations (e.g., Diard et al. (2005)). We have found, however, that the pyramidal slip can be an important deformation mode in the rolled α-titanium with a basal texture where many grains have prismatic axes parallel to the load direction. While developing only in a small number of grains, the pyramidal slip has to be taken into account; otherwise, local stresses in some regions at the grain scale might take overestimated values nontypical for plastically deformed metals.

Table 1. Polycrystalline model parameters. RD×TD translations No. of elements

Model size, µm 1050×1050×350 3150×2100×350 4200×2100×350 4200×3150×350

Grain number

Reference

1 125 000 6 750 000 9 000 000 13 500 000

1000 6000 8000

3×2 4×2 4×3

12000

Fig. 1 HCP lattice and local frame (a), experimental (b, c) and model grain structures (d, e) shown in ND (b, d) and RD IPF colors (c, e).

Fig. 2 Model obtained by translation of the reference polycrystal (a) and necking in the experimental specimen (b).

The polycrystalline constitutive models are implemented in ABAQUS/Explicit. In the numerical implementation, the constitutive equations in the rate form of the generalized Hooke’s law are written for each finite element with