論文

In this study, the effect of ferrite grain size on the mechanical properties and dislocation behavior of dual-phase (DP) steel is investigated using dislocation-based crystal plasticity finite element analysis. DP steel, composed of a soft ferritic phase and a hard martensitic phase, shows mechanical properties that are significantly influenced by ferrite grain size. The mechanism underlying this grain size effect is clarified by analyzing the partitioning and distribution of stress, strain, and dislocations in each phase. Three models with the same volume fraction of martensitic phase but different ferrite grain sizes are subjected to tensile loading. Interestingly, even though only the ferrite grain size is changed, the stress in the martensitic phase exhibited a notable dependence on ferrite grain size. This can be explained as follows. Geometrically necessary (GN) dislocations accumulate on the ferrite side of the ferrite–martensite grain boundary, and the grain boundary occupancy per unit area increases as the ferrite grain size decreases. As a result, smaller ferrite grain sizes make the ferritic phase less deformable owing to the effect of GN dislocations, shifting more deformation to the martensitic phase. This behavior is confirmed by the more uniform strain distribution and partitioning observed with decreasing ferrite grain size. As the martensitic phase takes on greater deformation, the statistically stored dislocation density in the martensitic phase becomes ferrite grain size dependent, which in turn leads to the observed grain size dependence of stress in the martensitic phase.

In this study, we derive a more generalized form of the Mathisson–Papapetrou force equation and perform an in-depth analysis of the variation in the Mathisson–Papapetrou force between two wedge disclinations across different calculation models in a two-dimensional plane. The results demonstrate that the stress field magnitude along the x1 and x2 axes consistently remains zero, facilitating the wedge disclination dipole in achieving equilibrium state along these two directions within the plane. Furthermore, the stress field enables the Mathisson–Papapetrou force acting on one wedge disclination in semicircular motion to be approximated by the force in linear motion within the same two-dimensional plane. This study contributes a more comprehensive understanding of wedge disclination by deriving a generalized Mathisson–Papapetrou force equation applicable to disclinations.

In this study, the effect of ferrite grain size on the mechanical properties and dislocation behavior of dual-phase (DP) steel is investigated using dislocation-based crystal plasticity finite element analysis. DP steel, composed of a soft ferritic phase and a hard martensitic phase, shows mechanical properties that are significantly influenced by ferrite grain size. The mechanism underlying this grain size effect is clarified by analyzing the partitioning and distribution of stress, strain, and dislocations in each phase. Three models with the same volume fraction of martensitic phase but different ferrite grain sizes are subjected to tensile loading. Interestingly, even though only the ferrite grain size is changed, the stress in the martensitic phase exhibited a notable dependence on ferrite grain size. This can be explained as follows. Geometrically necessary (GN) dislocations accumulate on the ferrite side of the ferrite–martensite grain boundary, and the grain boundary occupancy per unit area increases as the ferrite grain size decreases. As a result, smaller ferrite grain sizes make the ferritic phase less deformable owing to the effect of GN dislocations, shifting more deformation to the martensitic phase. This behavior is confirmed by the more uniform strain distribution and partitioning observed with decreasing ferrite grain size. As the martensitic phase takes on greater deformation, the statistically stored dislocation density in the martensitic phase becomes ferrite grain size dependent, which in turn leads to the observed grain size dependence of stress in the martensitic phase.

In this study, we derive a more generalized form of the Mathisson–Papapetrou force equation and perform an in-depth analysis of the variation in the Mathisson–Papapetrou force between two wedge disclinations across different calculation models in a two-dimensional plane. The results demonstrate that the stress field magnitude along the x1 and x2 axes consistently remains zero, facilitating the wedge disclination dipole in achieving equilibrium state along these two directions within the plane. Furthermore, the stress field enables the Mathisson–Papapetrou force acting on one wedge disclination in semicircular motion to be approximated by the force in linear motion within the same two-dimensional plane. This study contributes a more comprehensive understanding of wedge disclination by deriving a generalized Mathisson–Papapetrou force equation applicable to disclinations.

Dual-phase Mg alloys consisting of α-Mg phase and LPSO phase are attracting attention as structural materials of next-generation because of its high specific strength and relatively high ductility. These alloys have excellent mechanical properties attributed to kink deformation and grain refinement based on dynamic recrystallization. However, the influence of kink formation and difference in grain size on material strength of the alloys has never been clarified computationally. In this paper, a crystal plasticity Cosserat model is newly developed considering disclination density to take account of information of rotational crystal defect important for kink formation. Using the preset model, a two-dimensional FE analysis is performed for a rectangular three-crystal plate and a polycrystalline plate of the dual-phase Mg alloys with LPSO phase. Through such computation, the effects of shape of kink band and recrystallized grain size of α-Mg phase on change in material strength are numerically predicted in the process of reverse loading after compression one.

Materials development requires numerous numbers of trial and error experiments. To reduce the experimental cost, numerical simulations which predict material microstructures and mechanical properties have a great potential to estimate the microstructures that should be produced for obtaining materials with the desired properties. There is a need to develop dual-phase (DP) steel with higher strength and ductility because DP steel is widely used due to its significant mechanical properties. DP steel consists of a soft phase (ferrite) and a hard phase (martensite), and the mechanical properties depend on the ratio of the two phases. The mechanical properties of DP steels are affected by the spatial distribution of martensite and ferrite, which requires a comprehensive consideration of a variety of microstructures. The problem is how to estimate microstructures of DP steel with the desired mechanical property because a comprehensive investigation of microstructures makes computational cost significantly expensive. For the purpose of reduction of the computational costs, we aim to develop a framework with low computational cost. The developed framework finds the optimal microstructure of DP steel by repeated random searches for a model that combines a generative adversarial network (GAN), which generates microstructures, and a convolutional neural network (CNN), which predicts the maximum stress and working limit strain from microstructures. Due to a low-dimensional search space provided by a latent variable of GAN, the proposed framework enables an efficient search for microstructures possible. To explore the desired microstructures under complex deformation modes, the multiple deformation modes are considered in this study. This framework is applicable not only for the microstructure of DP steel but also any other material microstructures. We are exhaustively able to explore the microstructure with desired properties of metallic or other composite materials in low-dimensional space thanks to this framework and contributes to accelerating materials development.

© 2018 The Authors. Published by Elsevier B.V. An FE analysis has been performed for a single crystal of long-period stacking ordered phase on the basis of the dislocation-based crystal plasticity model considering higher-order stress. The mesh dependence on the kink band formation has been discussed from the viewpoint of the strain gradient and size effect. Then, it is shown that the mesh dependence of kink deformation in the FE analysis can be removed even when the scale ratio is relatively small. Moreover, it is indicated that the disclination quadrupole structure in the kink band can be expressed qualitatively by use of the incompatibility of crystal slip.

© 2019 Author(s). In this paper, the conventional conservation laws are formulated by modeling the lattice behavior during phase transformation as the rotation of a director. More precisely, a crystal lattice in a metal is modeled during the recrystallization process as an elastic bar element subject to stretching. Using this model, the discrete conservation laws for micropolar theory are finally derived. These conservation laws are the basis of the governing equations of Kobayashi-Warren-Carter (KWC)-type phase-field models. Hence, the derivation of this theory is significant in gaining a deeper comprehension of KWC-type phase-field models. First, balance laws for the mass, momentum, angular momentum, and energy of a lattice element are formulated. These laws are summed over a phase in a representative volume element (RVE) and averaged over the RVE. This enables the development of macroscopic balance laws for a continuum mixture consisting of several phases. When the RVE is reduced to a material point in the final formulation, the present model can be regarded as a director model whose direction vector expressing the crystal orientation is attached to a material point of a simple body. By performing an order estimation, the balance law of angular momentum can be separated into bulk and lattice parts. The bulk part results in the usual form and the latter corresponds to the evolution equation of the crystal orientation in a KWC-type phase-field model.

©2019 The Society of Materials Science, Japan The dislocation-based crystal plasticity model has been extended to a model considering higher-order stress by explicitly considering the mechanical work induced by the strain gradient. Furthermore, a finite element (FE) analysis is performed for a single crystal with a long-period stacking ordered (LPSO) phase on the basis of the obtained model. The mesh dependence of the kink band formation is discussed from the viewpoints of the strain gradient, size effect and higher-order boundary condition. Then, it is shown that the mesh dependence of kink deformation in the FE analysis can be removed even when the size effect parameter is relatively small. The width of the kink band is determined by the intrinsic length scale. When the kink band occurs in the entire specimen, work hardening can be reproduced by appropriately defining the boundary conditions for slip. The effect of length scale ratio on the kink deformation is small. Moreover, it is shown that the disclination quadrupole structure in the kink band can be expressed qualitatively by using incompatibility of crystal slip.

© 2020, © 2020 Informa UK Limited, trading as Taylor & Francis Group. The mechanical properties of metals used as structural materials are significantly affected by hot (or warm) plastic working. Therefore, it is industrially important to predict the microscopic behaviour of materials in the deformation process during heat treatment. In this process, a number of nuclei are generated in the vicinity of grain boundaries owing to thermal fluctuation or the coalescence of subgrains, and dynamic recrystallisation (DRX) occurs along with the deformation. In this paper, we develop a DRX model by coupling a dislocation-based crystal plasticity model and a multi-phase-field (MPF) model through the dislocation density. Then, the temperature dependence of the hardening tendency in the recrystallisation process is introduced into the DRX model. A multiphysics simulation for pure Ni is conducted, and then the validity of the DRX model is investigated by comparing the numerical results of microstructure formation and the nominal stress–strain curve during DRX with experimental results. The obtained results indicate that in the process of DRX, nucleation and grain growth occur mainly around grain boundaries with high dislocation density. As deformation progresses, new dislocations pile up and subsequent nucleation occurs in the recrystallised grains. The influence of such microstructural evolution appears as oscillation in the stress–strain curve. From the stress–strain curves, the temperature dependence in DRX is observed mainly in terms of the yield stress, the hardening ratio, and the change in the hardening tendency after nucleation occurs.

In this work, a phase-field model for recrystallization is developed based on the conservation laws. There has been no attempt to develop a phase-field model of recrystallization based on the conservation laws, even though various phase-field simulation models to reproduce the recrystallization phenomenon have been proposed. However, it is unclear what conservation laws are required for such a model. In the previous paper, toward solving this problem, we developed conservation laws of mass, momentum, angular momentum, and energy and a law of entropy at the lattice scale for the process of recrystallization. In this paper, first, two continuous variables, i.e., the order parameter and crystal orientation, are introduced into the balance equation of mass for a single phase and that of angular momentum for the lattice, respectively. Next, the fluxes of the order parameter and crystal orientation are derived from the law of entropy by the use of rational thermodynamics. Moreover, the diffusion coefficient and mass source are modeled to derive the evolution equations, i.e., phase-field equations of the order parameter and crystal orientation. Finally, for the phase-field equation of the crystal orientation, neglecting the conservative part and integrating the equation with respect to time under the first-order approximation, a phase-field model that is used for stable calculations is developed. This work aims to develop a phase-field theory on the basis of the change in crystal lattice during recrystallization. This paper gives a physical background to the methodological phase-field approach in the case of recrystallization.

Crystal orientation effects on the shear fatigue limits of iron single-crystals were investigated by considering the influence of normal stress of the slip plane on the critical resolved shear stress (CRSS). The shear fatigue limit with the (123) plane in the shear loading position was experimentally confirmed to exceed that with shear loading on the (110) plane. On the contrary, the shear yield stress of the (123) plane, evaluated by monotonic shear tests, was lower than that of the (110) plane. To solve this seeming contradiction, it was postulated that body-centred cubic crystals possessed 24 slip systems and that the CRSS was sensitive to the resolved normal stress (RNS) on the slip plane. That is, it was assumed that the CRSS decreased under the tensile RNS according to its magnitude, but increased under the compressive RNS. The mathematical model of the CRSS dependence on the RNS was simply introduced to the work-hardening law proposed by Peirce et al. allowing formulation of the algebraic equations yielding the crystalline slip rates. This crystal plasticity model was applied to analyse monotonic shear and shear fatigue tests. By considering the effect of the RNS sensitivity, the shear yield stress with the (123) plane in the shear loading position was calculated to be lower than that with the (110) plane, showing agreement with the experimental results of the monotonic shear tests. Furthermore, in the application of cyclic shear loads corresponding to the fatigue limits, it was confirmed that the plastic strain range of the primary slip plane converged to similar values despite the differences in the crystal orientations of the shear plane and the normal stresses to it. These results imply that the present method allows the prediction of fatigue limits under different crystal orientations and loading conditions.

The dislocation-based crystal plasticity model considering higher-order stress has been constructed and a finite element (FE) analysis is conducted for both a single crystal and polycrystal with a long-period stacking ordered (LPSO) phase on the basis of the obtained model. The mesh dependence of the kink band formation is discussed from the viewpoints of the strain gradient, size effect and higher-order boundary condition. Then, it is shown that the mesh dependence of kink deformation in the FE analysis can be removed even when the scale ratio is relatively small. The width of the kink band is determined by the intrinsic length scale. When the kink band occurs in the entire specimen, work hardening can be reproduced by appropriately defining the boundary conditions for slip. The effect of the micro-scale ratio on the kink deformation is small. The disclination quadrupole structure in the kink band can be expressed qualitatively by using the incompatibility of crystal slip. Moreover, it is shown the back stress behaves as the resistance to the slip deformation in a polycrystal consisting of LPSO phases in shape of rectangular strip.