Inductive Determination of Rate-Reaction Equation Parameters for Dislocation Structure Formation Using Artificial Neural Network.

The reaction-diffusion equation approach, which solves differential equations of the development of density distributions of mobile and immobile dislocations under mutual interactions, is a method widely used to model the dislocation structure formation. A challenge in the approach is the difficulty in the determination of appropriate parameters in the governing equations because deductive (bottom-up) determination for such a phenomenological model is problematic. To circumvent this problem, we propose an inductive approach utilizing the machine-learning method to search a parameter set that produces simulation results consistent with experiments. Using a thin film model, we performed numerical simulations based on the reaction-diffusion equations for various sets of input parameters to obtain dislocation patterns. The resulting patterns are represented by the following two parameters; the number of dislocation walls (p2), and the average width of the walls (p3). Then, we constructed an artificial neural network (ANN) model to map between the input parameters and the output dislocation patterns. The constructed ANN model was found to be able to predict dislocation patterns; i.e., average errors in p2 and p3 for test data having 10% deviation from the training data were within 7% of the average magnitude of p2 and p3. The proposed scheme enables us to find appropriate constitutive laws that lead to reasonable simulation results, once realistic observations of the phenomenon in question are provided. This approach provides a new scheme to bridge models for different length scales in the hierarchical multiscale simulation framework.

Diameter-Change-Induced Transition in Buckling Modes of Defective Zigzag Carbon Nanotubes.

In general, the insertion of Stone-Wales (SW) defects into single-walled carbon nanotubes (SWNTs) reduces the buckling resistance of SWNTs under axial compression. The magnitude of reduction is more noticeable in zigzag-type SWNTs than armchair- or chiral-type SWNTs; however, the relation between the magnitude of reduction and aspect ratio of the zigzag SWNTs remains unclear. This study conducted molecular dynamics (MD) simulation to unveil the buckling performance of zigzag SWNTs exhibiting SW defects with various tube diameter. The dependencies of energetically favorable buckling modes and the SW-defect induced reduction in the critical buckling point on the tube diameter were investigated in a systematic manner. In particular, an approximate expression for the critical buckling force as a function of the tube diameter was formulated based on the MD simulation data.

Nonsingular Stress Distribution of Edge Dislocations near Zero-Traction Boundary.

Among many types of defects present in crystalline materials, dislocations are the most influential in determining the deformation process and various physical properties of the materials. However, the mathematical description of the elastic field generated around dislocations is challenging because of various theoretical difficulties, such as physically irrelevant singularities near the dislocation-core and nontrivial modulation in the spatial distribution near the material interface. As a theoretical solution to this problem, in the present study, we develop an explicit formulation for the nonsingular stress field generated by an edge dislocation near the zero-traction surface of an elastic medium. The obtained stress field is free from nonphysical divergence near the dislocation-core, as compared to classical solutions. Because of the nonsingular property, our results allow the accurate estimation of the effect of the zero-traction surface on the near-surface stress distribution, as well as its dependence on the orientation of the Burgers vector. Finally, the degree of surface-induced modulation in the stress field is evaluated using the concept of the L2-norm for function spaces and the comparison with the stress field in an infinitely large system without any surface.

Analytic formulation of elastic field around edge dislocation adjacent to slanted free surface.

Explicit and tractable formulation of the internal stress field around edge dislocations is indispensable for considering the mechanics of fine crystalline solids, because the motion of edge dislocations in a slanted direction with respect to the free surface often plays a vital role in the plastic deformation of the solids under loading. In this study, we formulated an analytical solution for the stress distribution that occurs around edge dislocations embedded in a semi-infinite elastic medium. This formulation is based on the image force method and the Airy stress function method; it describes the variation in the stress distribution with changes in the slanted angle between the traction-free flat surface of the medium and the Burgers vector of the edge dislocation. Furthermore, our analytical solution shows that the attractive force acting on the edge dislocation due to the presence of the free surface is always perpendicular to the surface, regardless of the relative angle of the Burgers vector with the surface.

Coarse-Grained Molecular Dynamics Simulation of Polycarbonate Deformation: Dependence of Mechanical Performance by the Effect of Spatial Distribution and Topological Constraints.

Polycarbonate is an engineering plastic used in a wide range of applications due to its excellent mechanical properties, which are closely related to its molecular structure. We performed coarse-grained molecular dynamics (CGMD) calculations to investigate the effects of topological constraints and spatial distribution on the mechanical performance of a certain range of molecular weights. The topological constraints and spatial distribution are quantified as the number of entanglements per molecule (Ne) and the radius of gyration (Rg), respectively. We successfully modeled molecular structures with a systematic variation of Ne and Rg by controlling two simulation parameters: the temperature profile and Kuhn segment length, respectively. We investigated the effect of Ne and Rg on stress-strain curves in uniaxial tension with fixed transverse strain. The result shows that the structure with a higher radius of gyration or number of entanglements has a higher maximum stress (σm), which is mainly due to a firmly formed entanglement network. Such a configuration minimizes the critical strain (εc). The constitutive relationships between the mechanical properties (σm and εc) and the initial molecular structure parameters (Ne and Rg) are suggested.

Machine-Learning-Based Atomistic Model Analysis on High-Temperature Compressive Creep Properties of Amorphous Silicon Carbide.

Ceramic matrix composites (CMCs) based on silicon carbide (SiC) are used for high-temperature applications such as the hot section in turbines. For such applications, the mechanical properties at a high temperature are essential for lifetime prediction and reliability design of SiC-based CMC components. We developed an interatomic potential function based on the artificial neural network (ANN) model for silicon-carbon systems aiming at investigation of high-temperature mechanical properties of SiC materials. We confirmed that the developed ANN potential function reproduces typical material properties of the single crystals of SiC, Si, and C consistent with first-principles calculations. We also validated applicability of the developed ANN potential to a simulation of an amorphous SiC through the analysis of the radial distribution function. The developed ANN potential was applied to a series of creep test for an amorphous SiC model, focusing on the amorphous phase, which is expected to be formed in the SiC-based composites. As a result, we observed two types of creep behavior due to different atomistic mechanisms depending on the strain rate. The evaluated activation energies are lower than the experimental values in literature. This result indicates that an amorphous region can play an important role in the creep process in SiC composites.

Velocity mode transition of dynamic crack propagation in hyperviscoelastic materials: A continuum model study.

Experiments of crack propagation in rubbers have shown that a discontinuous jump of crack propagation velocity can occur as energy release rate increases, which is known as the "mode transition" phenomenon. Although it is believed that the mode transition is strongly related to the mechanical properties, the nature of the mode transition had not been revealed. In this study, dynamic crack propagation on an elastomer was investigated using the finite element method (FEM) with a hyperviscoelastic material model. A series of pure shear test was carried out numerically with FEM simulations and crack velocities were measured under various values of tensile strain. As a result, our FEM simulations successfully reproduced the mode transition. The success of realising the mode transition phenomenon by a simple FEM model, which was achieved for the first time ever, helped to explain that the phenomenon occurs owing to a characteristic non-monotonic temporal development of principal stress near the crack tip.

Effect of cation dopants in zirconia on interfacial properties in nickel/zirconia systems: an atomistic modeling study.

Cation doping is often used to stabilize the cubic or tetragonal phase of zirconia for enhanced thermomechanical and electrochemical properties. In the present paper we report a combined density functional theory (DFT) and molecular dynamics study of the effect of Sc, Y, and Ce dopants on properties of Ni/[Formula: see text] interfaces and nickel sintering. First, we develop an MD model that is based on DFT data for various nickel/zirconia interfaces. Then, we employ the model to simulate Ni nanoparticles coalescing on a zirconia surface. The results show the possibility of particle migration by means of fast sliding over the surface when the work of separation is small (<[Formula: see text]). The sliding observed for the O-terminated Ni(1 1 1)/[Formula: see text](1 1 1) interface is not affected by dopants in zirconia because the work of separation of the doped interface stays small. The most pronounced effect of the dopants is observed for the Zr-terminated Ni(1 1 1)/[Formula: see text](1 1 1) interface, which possesses a large work of separation ([Formula: see text]) and thus restricts the sliding mechanism of Ni nanoparticle migration. DFT calculations for the interface revealed that dopants with a smaller covalent radius result in a larger energy barriers for Ni diffusion. We analyze this effect and discuss how it can be used to suppress nickel sintering by using the dopant selection.

Synchronization in flickering of three-coupled candle flames.

When two or more candle flames are fused by approaching them together, the resulting large flame often exhibits flickering, i.e., prolonged high-frequency oscillation in its size and luminance. In the present work, we investigate the collective behaviour of three-coupled candle flame oscillators in a triangular arrangement. The system showed four distinct types of syncronised modes as a consequence of spontaneous symmetry breaking. The modes obtained include the in-phase mode, the partial in-phase mode, the rotation mode, and an anomalous one called the "death" mode that causes a sudden stop of the flame oscillation followed by self-sustained stable combustion. We also clarified the correlation between the inter-flame distance and the frequency with which the modes occur.

Development of a new dipole model: interatomic potential for yttria-stabilized zirconia for bulk and surface.

We developed a new interatomic potential for yttria-stabilized zirconia (YSZ) based on the dipole model initially proposed by Tangney and Scandolo. It is demonstrated that the potential can successfully reproduce not only basic bulk properties, including interaction between point defects, but also energies and structures of clean (1 1 0) and (1 1 1) surfaces. We confirmed that the highly perturbed structure of (1 1 0) surface doped by yttria is in a good agreement with results of DFT calculations. Yttrium segregation at (1 1 1) surface was predicted and discussed by comparison with results of DFT simulations.

Stability and strength of covalent crystals under uniaxial and triaxial loading from first principles.

The response of three covalent crystals with a diamond lattice (C, Si and Ge) to uniaxial and a special triaxial (generally nonhydrostatic) loading is calculated from first principles. The lattice deformations are described in terms of variations of bond lengths and angles. The triaxial stress state is simulated as a superposition of axial tension or compression and transverse (both tensile and compressive) biaxial stresses. The biaxial stresses are considered to be adjustable parameters and the theoretical strengths in tension and compression along <100>, <110>, <111> crystallographic directions are calculated as their functions. The obtained results revealed that the compressive strengths are, consistently to fcc metals, almost linear functions of the transverse stresses. Tensile transverse stresses lower the compressive strength and vice versa. The tensile strengths, however, are not monotonic functions of the transverse biaxial stresses since they mostly exhibit maxima for certain values of the transverse stresses (e.g., tensile for <100> and <110> loading of Si and Ge or compressive for <100> loading of C).