**2. Contributions**

The exceptional properties of various metallic polycrystalline systems, such as high strength, excessive hardness, grea<sup>t</sup> ductility at room temperature, superior energy absorption capacity, and good corrosion resistance, make them outstanding candidates for a wide variety of applications where one or another of the mentioned qualities, or the combination of several, is of crucial importance. The presented contributions [1–9] evidently demonstrate that the properties of metallic materials are microstructure-dependent and, therefore, the thermomechanical processing (TMP) of the polycrystalline aggregates should be strictly controlled to guarantee the attainment of the desired suite of qualities. Given this, the assessment of microstructure evolution in metallic systems is of extraordinary importance. Since the trial–error approach is a time-consuming and rather expensive methodology, the materials research community tends to employ a wide spectrum of computational approaches to simulate each chain of TMP and tune the processing variables to ensure the necessary microstructural state for achieving the desired performance in the final product.

In the most general case, the TMP of metals involves a sequence of deformation and annealing processes (or the combination of both into one technological step) that lead to morphological changes in the polycrystalline aggregate, the evolution of crystallographic texture, or phase transformation. All these aspects of microstructure development are partially discussed in the presented contributions [1–9]. In the first manuscript [1], the deformation flow in a single-phase alloy with a face-centered crystal structure is analyzed

**Citation:** Sidor, J.J. Modelling the Deformation, Recrystallization, and Microstructure-Related Properties in Metals. *Metals* **2021**, *11*, 1759. https://doi.org/10.3390/met11111759

Received: 20 October 2021 Accepted: 29 October 2021 Published: 2 November 2021

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**Copyright:** © 2021 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

by means of a finite element (FEM) approach and computationally efficient flow-line model (FLM), which enabled the effective simulation of cold rolling in terms of the evolution of crystallographic texture. It was shown that by using the flow-line model, coupled with a Taylor-type homogenization crystal plasticity model, it is possible to carry out a texture simulation that is close to the one performed with the deformation history obtained by means of computationally expensive FEM. In addition, the correlation between the FLM model parameters and the rolling process quantitative indicators was defined, implying that the employed analytical approach was efficient in performing simulations of cold rolling without fitting constraints.

The second contribution [2] likewise addresses the crystallographic aspect of deformation by employing a well-established viscoplastic, self-consistent (VPSC) crystal plasticity approach. The numerical investigation is related to the deformation mechanisms in a magnesium alloy with a hexagonal crystal structure, where the polycrystalline system was subjected to uniaxial tension and compression. The influence of slip systems on the plastic deformation, mechanical response, and texture evolution was analyzed by the VPSC via engaging various slip and twinning activities.

The annealing phenomena are addressed in the third paper [3], where the authors investigated the phenomenon of dynamic recrystallization in a FeMnSiCrNi shape memory alloy subjected to hot compression. The analysis is based on a simulation of recrystallization using a cellular automaton approach, and apart from the microstructural features, both flow stress and dislocation density were predicted.

The latest advances in the modeling of mechanical performance based on microstructural features of polycrystalline systems are described in five contributions [4–8], which reveal the behavior of different materials under diverse processing operations. The springback phenomenon was simulated for the hot-stamping process in [4]. The calculations rely on the analysis of microstructures that evolved in the investigated boron steel. The relationship developed in the frame of the contribution [4] enables the estimation of the springback angle based on the area fraction of microstructures that evolved during the quenching. The following paper [5] deals with the analysis of the hot workability of 300 M steel, where the relation between the flow stress and microstructure evolution was examined. The investigation was conducted via in situ and ex situ compression tests. In another manuscript [6] equally concerned with hot deformation, the double-open multidirectional forging process is analyzed. In this investigation, the authors present a constitutive equation for GH4169 superalloy and simulate the microstructure evolution during dynamic recrystallization using the finite element approach. Anisotropy of plastic yielding is described in [7], where the authors investigate the mechanical response of the cross-rolled aluminum sheets. The simulation of cup earing is based on the evolved crystallographic texture. The model employed for the simulation of anisotropic behavior takes texture intensities into account, which appear in the {h00} pole figures. The performance of monocrystalline Cu-13.7% Al-4.2% Ni alloy is characterized in [8]. In that contribution, the authors investigate the so-called reversible martensitic transformation and describe both physical and structural changes in the complex metallic system induced by the thermocyclic treatments under applied loads.

Phase transformation is studied in [9]. In this study, high-strength steel was subjected to a hot-stamping process, and phase transformation was investigated via simulation of the transformation during the pressure-holding quenching process. The kinetics of phase alteration, which leads to the formation of ferrite, pearlite, and bainite, was analyzed according to the Kirkaldy–Venugopalan model.

#### **3. Conclusions and Outlook**

In this Special Issue, we present a wide spectrum of articles dealing with the modeling of microstructural aspects involved in deformation and recrystallization as well as simulation of microstructure-based and texture-based properties in various metals. The latest advances in the theoretical interpretation of mesoscopic transformations based on

experimental observations are also partially discussed. The studies dealing with the modeling of structure–property relationships are likewise analyzed in the present collection of manuscripts.

Although, in the submitted works, many hidden facets of various technological processes and related microstructural changes were revealed by employing advanced computational approaches, the contributions collected in this issue nevertheless clearly show that further efforts are required in the field of modeling to understand the complexity of the material's world. The ultimate goal of modeling efforts is, arguably, the development of a comprehensive model that is capable of describing many aspects of microstructure evolution during thermomechanical processing.

**Funding:** This research was funded by the EFOP-3.6.1-16-2016-00018 project: "Improving the role of research + development + innovation in higher education through institutional developments assisting intelligent specialization in Sopron and Szombathely". The work was performed in the frame of the Széchenyi 2020 program: "Innovative processing technologies, applications of energy engineering, and implementation of wide-ranging techniques for microstructure investigation".

**Conflicts of Interest:** The author declares no conflict of interest.
