Yuichi Tadano

A Polycrystalline Analysis of Hexagonal Metal Based on the Homogenized Method

In this study, a three-dimensional finite element formulation for polycrystalline plasticity model based on the homogenization method has been presented. The homogenization method is one of the useful procedures, which can evaluate the homogenized macroscopic material properties with a periodical microstructure, so-called a unit cell. The present study focuses on hexagonal metals such as titanium or magnesium. An assessment of flow stress by the presented method is conducted and it is clarified how the method can reproduce the behavior of hexagonal metal.

A Phase-Field Simulation of Nucleation from Subgrain and Grain Growth in Static Recrystallization

A new recrystallization phase-field method is proposed, in which the three stages of recrystallization phenomena, i.e., recovery, nucleation and nucleus growth are sequentially taken into account in a computation. From the information of subgrain patterns and crystal orientations in a polycrystal that are obtained by a dislocation-crystal plasticity FE analysis based on a reaction-diffusion model, subgrain groups surrounded by high angle boundary are found out. Next, subgrains in the group are coalesced into a nucleus by rotation of crystal orientation and migration of subgrain boundaries through a phase-field simulation. Then a computation of nucleus growth is performed also using the phase-field method on account of an autonomic incubation period of nucleation, in which stored dislocation energy assumes a role of driving force. It is shown that the present method can numerically reproduce the three stages of recrystallization as a sequence of computational procedure.

Investigation on Intragranular Stress of Mg Including Several Twin-Bands Using Dislocation-Based Crystal Plasticity and Phase-Field Models

A coupled model based on crystal plasticity and phase field theories that express both plastic anisotropy of HCP metals and expansion/shrinkage of twin-bands is proposed in the present study. In this model, the difference of the hardening rate in each slip system is expressed by changing their dislocation mobility as a numerical parameter defined in the crystal plasticity framework. The stress calculated via crystal plasticity analysis becomes to the driving force of multi-phase filed equations that express the evolution of twin bands of several variants, which include both the growth and shrinkage. Solving this equation set, the rate of twinning/detwinning and the mirror-transformed crystal basis in the twinned/detwinned phase are obtained and then, crystal plasticity analysis is carried out again. Using the present model, a uniaxial cyclic loading simulation along [0001] direction on the specimen including two variants of twin-bands is carried out by means of finite element method (FEM). The results show that the detwinning stress decreases with increase of the pre-tensioned strain. This is caused by a residual compression stress resulting from the twin shearing that occurs in the vicinity of two twin boundaries approaching each other.

Effect of Texture on Plastic Flow Localization of FCC Polycrystals Using Homogenization-Based Polycrystalline Plasticity

In this study, a framework to predict the onset of plastic flow localization is introduced. The Marciniak-Kuczyński type approach, which is a classical method to predict the strain localization, and a crystal plasticity model with a homogenization-based finite element method are combined, and forming limit strains that are defined as the onset of plastic flow localization for FCC polycrystals are computed. The forming limit strains with several kinds of textures are evaluated with the present approach, and the results are compared with those obtained by the Taylor model, which is a widely used conventional polycrystalline model. Within the present application, the present method and the classical Taylor model give similar forming limit strains for FCC polycrystal sheets. According to the present results, the use of the Taylor model in the sheet necking analysis might be justified, at least for FCC polycrystal sheets with various textures.

Crystal Plasticity Modeling of Pure Magnesium Considering Volume Fraction of Deformation Twinning

In this study, a novel crystal plasticity model for pure magnesium involving the deformation twinning is presented. The deformation twinning is an important deformation mechanism of magnesium and other HCP metals. The deformation twinning has two important issues: first, the large rotation of crystal lattice caused by twinning occurs. Second, in the crystalline scale, the twinned and untwinned regions may simultaneously exist in a grain. Therefore, a crystal plasticity analysis of magnesium should introduce both of them, and the present framework takes these two key features into account. To represent the second issue, the volume fraction of deformation twinning is considered. This paper provides a framework of crystal plasticity model involving the effect of tensile twinning, and a numerical example is conducted to evaluate the evolution of volume fraction of twinned region. It is shown that the present scheme can describe the mixed state of twinned and untwinned regions. The obtained results suggest that the twinned and untwinned regions simultaneously exist even under the large deformation and the volume fraction of twinned region should be considered.

A Triple-Scale Crystal Plasticity Simulation on Yield Behavior of Annealed FCC Fine-Grained Metals

In this study, the conventional Bailey-Hirsch’s relationship is extended in order to express the increase of critical resolved shear stress due to the lack of dislocation lines in a grain. This model is introduced into a triple-scale crystal plasticity model based on geometrically necessary crystal defects and the homogenization method. A FE simulation is carried out based on the proposed model for FCC polycrystals with different grain sizes. It is numerically predicted that yield behavior of fine-grained metals depends on the initial dislocation density and the initial grain size. Furthermore, yield point drop that is observed in annealed FCC fine-grained metal can be reproduced.

Subsequent Yield Behavior of Hexagonal Metal with Rolling Texture

The subsequent yield surface of a rolling textured polycrystalline hexagonal metal sheet is computed using homogenization-based crystal plasticity. Hexagonal metals, such as magnesium and titanium, generally shows poorer formability compared to than cubic metals. The subsequent yielding behavior of a polycrystalline metal strongly affects the formability. The abrupt strain path change method is used to evaluate the direction of plastic flow, allowing the non-normality effect of the hexagonal metal to be quantitatively determined. The homogenization-based crystal plasticity model is used for representing the polycrystalline behavior of a HCP metal. The role of each slip system in the subsequent yield behavior is investigated. The mechanism of subsequent yielding of the HCP metal, which induces the non-normality effect, is discussed.

Effect of Lattice Rotation on Hardening Behavior of HCP Metals

Strain hardening behavior is known to strongly affect the formability of metallic sheets. The effect of lattice rotation on the hardening behavior of hexagonal close-packed (HCP) metals is numerically investigated using a homogenization-based crystal plasticity model to represent the polycrystalline behavior. The effect of lattice rotation on strain hardening behavior evaluated using different initial textures, and the geometrical hardening effect of HCP metals is investigated. In addition, the critical resolved shear stress of each slip system is varied and is shown to affects the strain hardening in HCP metals. In this study, we further discuss the possibility to improve the formability of HCP metals.

Quantitative Evaluation of Deformation Twinning Behavior in Polycrystalline Pure Magnesium

A crystal plasticity analysis of polycrystalline pure magnesium is conducted to investigate deformation twinning behavior at the crystal grain scale. A dominant factor in the onset of deformation twinning is the resolved shear stress on a twinning system. More than one twin system may simultaneously be activated in a crystal grain, resulting from inhomogeneous stress distribution caused by constraints imposed by neighboring grains. In this study, a pure magnesium polycrystal is modeled using a fine finite element mesh and analyzed using the crystal plasticity model involving deformation twinning. The evolution of deformation twinning at the crystalline scale is numerically investigated, and the present approach demonstrates that two or more twinning systems are be activated in a single crystal grain because of the strong inhomogeneity in the grain.

Three-dimensional generalized element with quadratic deformation mode for geometrically nonlinear analysis

In this paper, a formulation of a novel three-dimensional finite element is presented in the framework of the generalized finite element method based on the partition of unity method. The 8-node conventional linear element is enriched by the reduced quadratic polynomial terms, and it can reproduce the quadratic deformation mode with only corner nodes. The presented element is a compatible element, and it can avoid linear dependency, which is a well-known problem of generalized finite elements. Linear and nonlinear bending analyses of a cantilever beam are demonstrated. The proposed element provides superior solution convergence in comparison with that of the conventional second-order elements. It is also shown that a high-precision solution can be obtained when the mesh is strongly distorted.