Nikita Sergeevich Kondratev

This study proposes and applies a mathematical model to describe the process of recrystallization nucleation on large d-phase particles in the Inconel 718 nickel alloy during annealing (the particle stimulated nucleation (PSN) mechanism). The investigation employs a multilevel approach based on an extended statistical model, in which the subgrain structure is explicitly described by an aggregate of Laguerre polyhedra. The model for the formation of new recrystallized grain nuclei is based on the physical mechanisms of recovery: subgrain coalescence and low-angle boundary migration. Additionally, the model accounts for lattice rotations of subgrains near the non-deformable particle resulting from the incompatibility of prior plastic deformation, as well as the retarding effect of dispersed γ′ and γ″ particles during subgrain boundary migration. Numerical experiments were conducted on a representative volume of subgrains at annealing temperatures range 450–950 °C. It is shown that at 450 - 850°C subgrain growth near the d-phase particle is retarded due to increased misorientation, which hinders coalescence. At temperatures above 950 °C, the dissolution of the strengthening phases γ′ and γ″ leads to a decrease in the Zener pinning force and intense boundary migration near the d-phase particle results in the active formation of recrystallization nuclei. It is established that a needle-shaped d-particle promotes more intense nucleation compared to a spherical one due to its larger interfacial area. The simulation results are in qualitative agreement with known experimental data.

This paper presents a novel modification of the multilevel statistical model for describing the subgrain boundary migration that can explicitly account for the topology of subgrain structures in the form of Laguerre polyhedra. The evolution of a representative volume of subgrains during annealing in the temperature range after plastic deformation taking into account competing recovery processes like coalescence and subgrain boundary migration is modeled. The material used in this study is the nickel-based superalloy Inconel 718 with complex hierarchical structure and specific phase composition. The results of modeling the changes in a polyhedral subgrain structure under recovery are presented. The contribution of subgrain coalescence and migration processes to recovery is evaluated. The abnormal growth of subgrains is described by the model, the conditions of its occurrence and implementation are defined. The calculated data demonstrate good agreement with experimental results.

This study employs a multilevel modeling approach to describe the deformation of specimens made from austenitic Wire Arc Additive Manufactured (WAAM) steel 308LSi. Two WAAM processing modes were investigated: (1) the Cold Metal Transfer (CMT) method and (2) Cold Metal Transfer combined with interlayer deformation strengthening (hammer peening/forging). Test specimens were cut from the deposited walls at 0° and 90° relative to the deposition direction. The grain and dendritic structures of the specimens were analyzed using optical stereomicroscopy. A statistical multilevel model has been developed, accounting for the features of the grain-dendritic and defect structures under various technological deposition modes. Parameter identification and model verification were conducted based on experimental data from uniaxial tensile tests of 308LSi steel specimens. The maximum deviation of the numerical results from the experimental data during the identification stage under uniaxial tensile loading did not exceed 3%, and during the verification stage it did not exceed 10%; the overall mean deviation did not exceed 1% for the identification stage and 2% for the verification stage. The model effectively captured the anisotropic mechanical behavior of WAAM-processed samples. The maximum calculated yield strength 360 MPa was obtained for specimens cut at an angle of 45°, while the minimum value 331 MPa was observed for vertically oriented specimens. Specimens subjected to interlayer forging (hammer peening) exhibited isotropic material properties. Explicit multilevel modeling, incorporating the presence of MnO oxide inclusions located within the austenite matrix, was performed. The results showed good correlation with experimental data and confirmed the localization of fatigue cracks at the phase boundary-matrix-oxide interface.

A hybrid multilevel model for a representative volume has been developed to describe the thermomechanical treatment of materials throughout the manufacturing–operation cycle. The model serves as an efficient tool for the digital design of functional materials and products. It quantitatively evaluates defects and grain structure formed under various thermomechanical treatment modes using statistical distributions of internal variables. These data are subsequently employed to construct polyhedral grain structure and to transfer defect-related information, expressed by using critical shear stresses and crystallographic lattice orientations in operational simulations. The model was calibrated, tested for Inconel 718 alloy, and applied to design alloy blanks during rolling and annealing, as well as to the analysis of low-cycle fatigue during operation.

Additive manufacturing is extensively used for the production of complex-shaped parts from metals and polymers. Because of the influence of various physical factors, the structure of materials processed under different processing conditions may vary considerably, altering their properties. Application of a multi-level crystal plasticity approach helps explicitly describe the structure of materials at different scale levels. It makes possible the evaluation of basic mechanical properties of the samples fabricated by layer-wise laser melting. In this work, a two-level statistical constitutive model is suggested for calculation the main mechanical characteristics (elastic modulus, offset yield stress) of the AISI 316L stainless steel samples produced by selective laser melting. The model explicitly considers the grain structure and texture of metal parts, twinning defects, and residual stresses in the as-build structure of materials. Under predefined loading conditions, the primary mechanism of inelastic deformation is through intra-granular slips of edge dislocations. Thus, the mechanism of material hardening has been described by a modified form of the Hall-Petch law, where the boundaries of grains and original twins are counted as effective barriers to dislocations. All model parameters are properly identified based on own experimental data and the data found in literature. The elastic moduli and yield stresses are calculated at different residual deformations and are found to be in fair agreement with experiments.

This paper presents a combined approach to the solution of boundary value problems. The approach implies the joint application of a macro-phenomenological model and multilevel physical constitutive models for describing the behavior of a polycrystalline material. Within the framework of the proposed approach, the boundary value problem is solved for a certain product (structure) using a macro-phenomenological model of the material and the response in the chosen area is clarified using multilevel modeling techniques. The capabilities of the approach were demonstrated in a series of numerical experiments covering metal forming processes. In order to test and verify the proposed technique, in the first numerical experiment, the process of an upsetting of the sample was considered using only a multilevel physical model of the material and using the formulated combined approach. The response in the chosen domain was compared to the results obtained by different modeling approaches. The comparison showed good agreement in terms of the variables of the stress–strain state at the macro level, as well as in terms of the variables characterizing the internal structure of the material. At the same time, using the combined approach, the required computation time was reduced by more than 12 times. In the second and third numerical experiments, the process of sheet rolling and sample pressing was successfully simulated using a combined approach. The formulated approach is computationally efficient and applicable for solving the relevant boundary value problems of design and the optimization of technological processes.

Multilevel models of inelastic deformation that take into account microstructure evolution are promising for technology development for creating functional material structures with optimal performance characteristics. The paper discusses the mathematical formulation of a direct multilevel model to describe the inelastic deformation of a polycrystal representative volume (analogous to a macrosample), taking into account the formation and the martensitic structure evolution during the transformation process. The model considers three structural-scale levels. At the macro level, the boundary value problem is solved, the fields of stresses, strains and other model variables are determined. At mesolevel-I, a homogeneous original austenite grain is considered, in which a martensitic transition occurs due to external influences. For a detailed description of the material response at the grain level, an auxiliary scale level is introduced into consideration, i.e. mesolevel-II. At this level, the geometric features of the martensite packet formation are explicitly studied. An original method has been developed to describe martensite polyhedral structure, the construction of which is carried out when the new phase volume fraction in the austenite grain reaches a critical value. A packet description as union of polyhedra consisting of thin plates allows one to introduce the geometric characteristics of the structural elements into the model, in particular, plates and packet boundaries, linear dimensions, volumes etc., and supplement them with crystallographic orientations. The resulting geometric characteristics of martensite package with subsequent processing is transferred to an individual grain level. This makes it possible to take into account the mechanisms of deformation and hardening that occur during the interaction of phases. The results are presented of polyhedral martensite packet structure formations in AISI 304 steel in numerical experiments on uniaxial deformation at room temperature and strain rate 10–5s–1.

The paper is devoted to mathematical description of the inelastic deformation process, taking into account dynamic recrystallization. For this purpose, a multil The paper is devoted to mathematical description of the inelastic deformation process, taking into account dynamic recrystallization. For this purpose, a multil