Takuya Uehara

Phase field simulations of faceted growth for strong anisotropy of kinetic coefficient

Facet formation during crystal growth is simulated by using the phase field model in two dimensions. Instead of moderate anisotropy of the often-used form 1 þ d cos 4y; several functions having strong anisotropy are explored. For simplicity, the interfacial energy is assumed to be isotropic, so only the anisotropy in the kinetic coefficient is considered. This results in the formation of a nearly flat face when the anisotropy function has a narrow minimum at a certain direction, for example 45 � for four-fold symmetry. Two types of functions are studied in this paper; Type 1: q1ðy Þ¼ 1 þ d � 2dð1 � cos4yÞ n =2 n ; and Type 2: q2ðy Þ¼ 1 � d þ 2dtanhðk=jtan2yjÞ: A ‘‘facet’’ is formed at the 45 � direction for each case. This ‘‘facet’’ is not completely flat for q1; but a real facet is obtained for q2: The crystal shapes depend on the parameters d; n and k in the anisotropy functions. A wider facet is formed for larger d for both q1 and q2; whereas, larger values of n in q1 and k in q2 lead to more pronounced facets. Results obtained by using the phase field model are in good agreement with Wulff shapes for the kinetic coefficient. Finally, corner formation is simulated by using similar anisotropy functions with maxima at 45 � :

An Atomistic Study on Shape-Memory Effect by Shear Deformation and Phase Transformation

An atomistic study on the shape-memory effect is carried out by molecular dynamics simulations with the EAM potential for Ni-Al alloy. As preliminary simulations, the stable structures for several Ni contents at various temperatures are investigated, and reveal that the martensite structure is obtained at low temperature for models with 62% or higher Ni content, while bcc is stable at high temperatures. A 68% Ni model with martensite structure, which consists of several variants in two opposite orientations without macroscopic deformation, is applied for MD simulation under a series of thermo-mechanical conditions of shear loading, unloading, heating and cooling. When shear load is applied, some of the variants with unstable orientation against the load change orientation, and a permanent macroscopic deformation is obtained. When this deformed martensite is heated up, a phase transformation to bcc occurs and the deformation is diminished. The original martensite is regained by cooling. Since the orientation of the variants are random, the macroscopic deformation is not observed, which means that the deformation imposed by the external load recovers the original shape by the heat treatment.

Molecular dynamics simulation of shape memory behaviour using a multi-grain model

Shape-memory behaviour in multi-grain material is simulated using a molecular dynamics method. An embedded-atom-method potential for NiAl alloy is applied, and a sequence of conditions including loading, unloading, heating and cooling is imposed. Two types of grain arrangement are used, and the deformation and shape recovery due to phase transformation are observed for both models. The stress–strain relation is revealed to draw a hysteresis loop, and the individual curves are smoother than those previously obtained from a single-crystal model. The deformation mechanism during loading is discussed using local structure analysis. Local deformation is initiated at the grain boundaries, and the deformed region propagates along the twin plane in the grain. The propagation is then obstructed by the grain boundaries, and a band pattern of the deformed area is formed. The influence of the grain shape and distribution, as well as the crystal orientation of each grain, on the deformation behaviour is also investigated. Qualitatively common features in the deformation mechanism and stress–strain relation are observed despite different grain distributions, while the critical values in stress vary, owing to the crystal orientations of the grains.

Numerical Simulation of Homogeneous Polycrystalline Grain Formation Using Multi-Phase-Field Model

A modified multi-phase-field model for regenerating a homogeneous polycrystalline microstructure was presented. An extra term was introduced to the original formula by Steinbach et al. by assuming that the stability of every grain constituting the microstructure depends on the grain size distribution. The effect of the term on the obtained microstructure was then verified by numerical simulations, and it was found that a homogeneous microstructure having nearly the same shape and size was generated. The influence of the parameter was also investigated, and it revealed that the parameter was dominative on the grain size at the steady state.

Numerical study on the evolution of stress distribution in cellular microstructures

Abstract Stress generation and evolution in a cellular microstructure observed in the directional solidification process of a binary alloy system were simulated using a phase field model. The Ni–Cu system was chosen as a typical alloy, and two-dimensional simulations were carried out. The elastic stress induced by the volumetric contraction due to solidification was considered, and stress distribution in the solidified region was calculated. Results showed that a complex stress state is generated in the interfacial region, while it is homogeneous in the bulk solid. Under a condition causing the growing cells to coalesce, remarkably large stress was observed at the tip of the decayed cell, leading to a stress concentration around the liquid droplets and grooves subsequently generated. In order to show the effect of binary composition on the stress distribution, the dependence of Cu concentration on the elastic coefficient was considered, and simulations were carried out. Consequently, stress distribution in the bulk solid was observed along the cell boundaries, while no stress distribution was generated when this dependence was not taken into consideration.

Molecular Dynamics Simulation of the Variation in the Microstructure of a Polycrystalline Material under Tensile Load

Molecular dynamics simulations were carried out to investigate the change in the crystal orientation of polycrystalline materials placed under an external load. Two models were prepared, both comprising four grains but with different grain arrangements. Each grain had a face-centered cubic structure with (001) face on the x-y plane, whereas each grain had a different rotation of orientation around the z-axis. A tensile load was applied by extending the edge length in the y direction while the other directions were kept stress-free. As a result, a significant change in the microstructure was observed, with changes in both crystal orientation and shape along with the formation of subgrains. The structure and direction of the grain boundary against the external load were also found to affect the change in the microstructure.

Molecular Dynamics Simulation on Transformation-Induced Plastic Deformation Using a Lennard-Jones Model

Molecular dynamics simulations were carried out to clarify the atomistic mechanism of transformation plasticity. As the first step for the purpose, a simple thin-film model consisting of 8640 atoms was prepared. Phase transformation was assumed to be expressed by switching the material parameters of Lennard-Jones potential function. As a preliminary calculation, phase transformation was forced to occur homogeneously in the whole region of the model, resulting in no extra strain except volumetric transformation dilatation. In that case, perfect single crystal structure was maintained in the new phase. Simulations were carried out under external load, but specific strain was not generated. On the contrary, when the transformation region was set partially in the model and the region was expanded with time, a large deformation was observed. In the middle process of the phase transformation, slip-like deformation behavior and the change in crystal orientation occurred, indicating that extra plastic strain was induced during phase transformation. The strain was observed even when external load is not applied, and hence it was concluded that not only external load but also local stress distribution may cause the transformation plasticity.

Molecular Dynamics Simulation of Stick-Slip Friction on a Metal Surface

Friction on the atomistic scale was simulated using a molecular dynamics model consisting of a slider and substrate. The slider is in contact with the substrate through interatomic forces, while being pulled by a spring connected to a tractor moving parallel to the substrate surface at a constant velocity. The frictional force, which is defined as the force working on the connecting spring, is registered as the slider moves over the substrate, and consequently stick-slip behavior is observed. The static frictional force is higher if the lattice mismatch between slider and substrate is smaller. The sliding velocity affects whether atoms can rapidly settle into a stable site, and hence affects the kinetic friction; at high velocities, the atoms are forcibly moved resulting in a smaller kinetic friction force and a steady force curve.

Molecular Dynamics Simulation of Tensile Properties of Nano-Layered Materials

Mechanical properties of nanolayered materials were simulated using molecular dynamics method. Elastic modulus was especially focused in this study, and the effect of layer width and the interval of the layers on the deformation behavior were discussed. Tension was imposed by adding a mono-axial strain in the x direction at a constant rate, while the other two normal components of stress were controlled to be zero. The influence of the dimension was preliminarily checked to avoid the model-size dependency, and the suitable size was determined as a cube with 12 unit cells in the x, y and z directions. First, a single nanolayer was set in the model, and the layer width was varied. The obtained elastic modulus showed almost linear dependency with the layer width. Then the interval of the layer was varied, and it revealed that the elastic moduli depend on the cross-sectional ratio of the layered material rather than the layer interval.

An Atomistic Study on the Slip Deformation Mechanism of Crystalline Materials Using a Weak-Plane Model

Molecular dynamics simulations were carried out to investigate the plastic deformation mechanism of fcc crystalline materials using the conventional Lennard-Jones potential. An fcc structure with square cross-section was prepared, and a tensile load was applied in the longitudinal direction. A weak potential was assigned to a specific (111) plane to induce a slip on the specified plane. Accordingly, a slip was initiated in the weak plane following an elastic deformation. The step-by-step motion of the atoms on the slip plane was studied, and a detailed trajectory is presented. The slip then expanded to other planes, and plastic deformation progressed in the whole model. The weak plane was also set as (110) or (100) plane, where different deformation modes were observed: not only slip but also gradual distortion or brittle fracture occurred.