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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Meshcheryakov et al. (2020), Panin et al. (2018, 2020), Papadopoulou et al. (2019)). Thus, there are urgent demands on the research of multiscale deformation and fracture mechanisms to reveal characteristics that would serve as an early precursor of macroscopic fracture. Our recent studies (Romanova et al. (2019a, 2020)) showed that valuable information could be derived from the analysis of deformation-induced surface roughening inevitably accompanying plastic deformation of polycrystalline metals and alloys. The material free surface becomes rough under plastic deformation with the out-of-plane surface displacements developing throughout all length scales from micro- to macro (Raabe et al. (2003), Panin et al. (2018)). Particularly, a specific surface pattern develops at the mesoscale where not individual grains but grain clusters are involved in collective motion to form surface undulations. Our recent studies on polycrystalline titanium (Romanova et al. (2019a, 2020)) suggested that the mesoscale roughening linking the microscale where plastic deformation occurred by dislocation glide and the macroscale where the neck was formed shortly before fracture could serve as an early precursor of plastic strain localization. Generally, the mesoscale roughness characteristics depend on many factors, including crystalline structure, grain size and shape, crystallographic texture, loading conditions, and mechanical properties. Thorough studies are necessary to link the mesoscale roughness characteristics in particular materials and the deformation mechanisms involved. A useful tool for this kind of investigations is proved to be crystal-plasticity finite-element (CPFEM) simulations with an explicit description of grain structure (Romanova et al. (2019a, 2020)). Among the key problems in microstructure-based simulations is the definition of a representative volume element (RVE) size. Many discussions were given to the definition of a number of grains providing the macroscopic material response with a sufficient accuracy (e.g., Diard et al. (2005), Tang et al. (2020), Trovalusci et al. (2016)), while the model representability at the mesoscale has not been addressed so far. Our recent findings on multiscale surface roughening (Romanova et al. (2019a, 2020)) showed an urgent need in the study along this line. In this paper, we examine numerically the range of applicability of polycrystalline models with different numbers of grains to reproduce mesoscale deformation phenomena. 2. CPFEM simulations A micromechanical model is described at length by Romanova et al. (2019a, 2019b, 2020). Let us dwell briefly on the key points of the simulation procedure. The polycrystalline model is constructed using experimental data for commercial purity titanium reported by Romanova et al. (2019a, 2020), Kardashev et al. (2020), Panin et al. (2018). The EBSD analysis showed the presence of equiaxed grains with an average size of 70 μ m (Fig. 1b, c). A basal texture typical for rolled α-titanium is seen on the rolled surface (Fig. 1b), and a random texture is observed in the direction perpendicular to the rolling plane (Fig. 1c). The prismatic axes of hexagonal grains deviated from the direction normal to the rolled surface within 40°. Based on these data, the 1050×1050×350 µm model consisting of 1000 equiaxed grains is generated on a regular mesh with 1 125 000 hexahedral elements by the method of step-by-step packing proposed by Romanova and Balokhonov (2019). The constructed grain structure (Fig. 1d, e) (hereinafter referred to as a reference polycrystal) is periodical in all three directions and thus can be translated to obtain a larger model (Fig. 2a). In the simulations aimed at studying the grain model representability at the mesoscale, the reference polycrystal is translated along the rolling direction (RD) and transverse direction (TD) several times in different combinations. The geometrical parameters and grain numbers of the reference and translated models are listed in Table 1. The reference polycrystal is shown in Fig. 1d-e in the inverse pole figure (IPF) colors for the ND and RD directions. Crystallographic orientations of the model grains are defined by a set of Euler angles to simulate a basal texture similar to that observed experimentally. The grain constitutive behavior is described in terms of crystal plasticity, where plastic strain tensor components are calculated through a summary of plastic shear strains over active slip systems (see, e.g., Diard et. al (2005)). Commercial purity titanium has a hexagonal close-packed (hcp) crystal lattice (Fig. 1a) with three slip families being potentially active under quasi-static loading at room temperature, including three prismatic, three basal, and twelve pyramidal slip systems. A slip system is thought to become active if the resolved shear stress reaches its critical value. In order to take into account the strain hardening, the critical resolved shear stress (CRSS) is calculated as a function of accumulated plastic strain. The CRSSs initiating slip on the prismatic, basal and pyramidal slip systems are related as 1:2:3. Accordingly, the primary slip mode in α-titanium is prismatic, and the secondary one is basal. The role of