PSI - Issue 35

E. Emelianova et al. / Procedia Structural Integrity 35 (2022) 203–209 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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given at length by Romanova et al. (2019b). The EBSD analysis revealed the microstructure consisting of equiaxed grains with an average size of 70  m (Fig. 2a). Following these observations, the 1050×1050×350 µm model consisting of 1000 grains was generated on a regular mesh with 1 250 000 finite elements (Romanova et al., 2021). The model of this size was shown to correctly reproduce the mesoscale deformation phenomena up to 15% of tensile strain which is reasonable for examining the texture severity effect. The constitutive behavior of grains was described in terms of crystal plasticity . The generalized Hooke’s law for the case of small strains was formulated in the rate form as ( ) p ij ijkl ij ij C    = − , (1) where the ijkl C matrix included five non-zero modules: 1111 C =162 GPa, 1122 C =92 GPa, 1133 C =69 GPa, 3333 C =181 GPa, and 2323 C =47 GPa. The strain rate tensor components ij  were kinematically related to the displacement field, while the plastic strain tensor components p ij  were calculated in terms of crystal plasticity through a summary of plastic shear strains over active slip systems (Diard et al., 2005). The contributions from prismatic, basal and pyramidal slip systems were taken into account as reported by Emelianova et al. (2021). Shear resistance i  on the i th slip system was calculated individually for each finite element as an empirical function of accumulated equivalent plastic strain p  ( ) ( ) 0 1 exp / p i i a b    = + − − (2) The first term of the right-hand sum is the critical resolved shear stress necessary to initiate slip on a certain slip system. In the simulations at hand the 0 i  values for the prismatic, basal and pyramidal slip systems were 50, 110, and 170 MPa. The constants a =14 MPa and b =0.06 were chosen to approximate the experimental stress-strain curve. The model validation was provided by Romanova et al. (2019a) and Emelianova et al. (2021) for a polycrystal with the grain orientations assigned to fit a basal texture observed experimentally (cf. Fig. 2b and c). A close agreement between the numerical and experimental stress-strain curves proved the model validation at the macroscale. Additionally, the numerical model was validated by a comparison of numerical and experimental roughness patterns at the mesoscale. As an illustration, the numerical roughness curve is plotted in Fig. 2d in comparison with the experimental data. The dependences in Fig. 2d represent a dimensionless roughness parameter R d proposed by Romanova et al. (2019a) to quantify the experimental and numerical surface profiles in the range of tensile strains. The R d value is calculated as a ratio of the rough profile length L r to the profile evaluation length L e : = − 1 . (3) The more the surface shape deviates from an ideal plane, the larger the R d value.

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Fig. 2. Experimental microstructure (a) and IPFs (b) for commercially pure titanium, IPFs for a model polycrystal (c), and the strain-dependent roughness curves obtained experimentally and numerically (Romanova et al., 2019a).