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.

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.

Ultrasmall-Scale Brittle Fracture Initiated from a Dislocation in SrTiO3.

Crystal defects often lead to an intriguing variety of catastrophic failures of materials and determine the mechanical properties. Here we discover that a dislocation, which was believed to be a source of plasticity, leads to brittle fracture in SrTiO3. The fracture mechanism, i.e., bond breaking at the dislocation core triggers crack initiation and subsequent fracture, is elucidated from an atomic view by hybrid quantum and molecular simulations and in situ nanomechanical experiments. The fracture strength of the dislocation-included SrTiO3 was theoretically evaluated to be 8.8-10.7 GPa, which was eminently lower than that of the pristine one (21.7 GPa). The experimental results agree well with the simulated ones. Moreover, the fracture toughness of the ultrasmall crack initiating from the dislocation is quantitatively evaluated. This study reveals not only the role of dislocations in brittle fracture but also provides an in-depth understanding of the fracture mechanism of dislocations at the atomic scale.

Simultaneously Toughening and Stiffening Elastomers with Octuple Hydrogen Bonding.

Current synthetic elastomers suffer from the well-known trade-off between toughness and stiffness. By a combination of multiscale experiments and atomistic simulations, a transparent unfilled elastomer with simultaneously enhanced toughness and stiffness is demonstrated. The designed elastomer comprises homogeneous networks with ultrastrong, reversible, and sacrificial octuple hydrogen bonding (HB), which evenly distribute the stress to each polymer chain during loading, thus enhancing stretchability and delaying fracture. Strong HBs and corresponding nanodomains enhance the stiffness by restricting the network mobility, and at the same time improve the toughness by dissipating energy during the transformation between different configurations. In addition, the stiffness mismatch between the hard HB domain and the soft poly(dimethylsiloxane)-rich phase promotes crack deflection and branching, which can further dissipate energy and alleviate local stress. These cooperative mechanisms endow the elastomer with both high fracture toughness (17016 J m-2 ) and high Young's modulus (14.7 MPa), circumventing the trade-off between toughness and stiffness. This work is expected to impact many fields of engineering requiring elastomers with unprecedented mechanical performance.

Asynchronous cracking with dissimilar paths in multilayer graphene.

Multilayer graphene consists of a stack of single-atomic-thick monolayer graphene sheets bound with π-π interactions and is a fascinating model material opening up a new field of fracture mechanics. In this study, fracture behavior of single-crystalline multilayer graphene was investigated using an in situ mode I fracture test under a scanning electron microscope, and abnormal crack propagation in multilayer graphene was identified for the first time. The fracture toughness of graphene was determined from the measured load-displacement curves and the realistic finite element modelling of specimen geometries. Nonlinear fracture behavior of the multilayer graphene is discussed based on nonlinear elastic fracture mechanics. In situ scanning electron microscope images obtained during the fracture test showed asynchronous crack propagation along independent paths, causing interlayer shear stress and slippages. We also found that energy dissipation by interlayer slippages between the graphene layers is the reason for the enhanced fracture toughness of multilayer graphene. The asynchronous cracking with independent paths is a unique cracking and toughening mechanism for single-crystalline multilayer graphene, which is not observed for the monolayer graphene. This could provide a useful insight for the design and development of graphene-based composite materials for structural applications.

Griffith Criterion for Nanoscale Stress Singularity in Brittle Silicon.

Brittle materials such as silicon fail via the crack nucleation and propagation, which is characterized by the singular stress field formed near the crack tip according to Griffith or fracture mechanics theory. The applicability of these continuum-based theories is, however, uncertain and questionable in a nanoscale system due to its extremely small singular stress field of only a few nanometers. Here, we directly characterize the mechanical behavior of a nanocrack via the development of in situ nanomechanical testing using a transmission electron microscope and demonstrate that Griffith or fracture mechanics theory can be applied to even 4 nm stress singularity despite their continuum-based concept. We show that the fracture toughness in silicon nanocomponents is 0.95 ± 0.07 MPa√m and is independent of the dimension of materials and therefore inherent. Quantum mechanics/atomistic modeling explains and provides insight into these experimental results. This work therefore provides a fundamental understanding of fracture criterion and fracture properties in brittle nanomaterials.

Outstanding Elastic Limit of a Thin Film Composed of Nickel Nanosprings.

This paper presents experimental results of vertical loading using an atomic force microscope (AFM) performed on a thin film consisting of nickel helical nanoelements (nanosprings) formed by glancing angle deposition (GLAD) technique. As a helical element has large reversible deformation limit in general, a characteristic behavior is expected on the yielding of the film. From the load versus displacement curves, we find the outstanding elastic limit of nickel nanosprings film. The apparent yield strain is evaluated as ε' Y = 5.2˜6.2 × 10−2, which is around 200 times of that in bulk nickel (ε Y = 0.29˜0.44 × 10−3). However, comparing the maximum shear stress in the helical spring and the solid film, the shape effect (helical shape) is only around 10˜20 times stemmed from the difference in the stress condition (torsion). The origin of difference is attributed to the size effect of nanosprings, as nano-scale metals have higher yield strain than that of bulk counterpart because of the difference in the understructure morphology. The combination of shape effect and size effect brings about the giant elastic limit on the film.

Superior room-temperature ductility of typically brittle quasicrystals at small sizes.

The discovery of quasicrystals three decades ago unveiled a class of matter that exhibits long-range order but lacks translational periodicity. Owing to their unique structures, quasicrystals possess many unusual properties. However, a well-known bottleneck that impedes their widespread application is their intrinsic brittleness: plastic deformation has been found to only be possible at high temperatures or under hydrostatic pressures, and their deformation mechanism at low temperatures is still unclear. Here, we report that typically brittle quasicrystals can exhibit remarkable ductility of over 50% strains and high strengths of ∼4.5 GPa at room temperature and sub-micrometer scales. In contrast to the generally accepted dominant deformation mechanism in quasicrystals-dislocation climb, our observation suggests that dislocation glide may govern plasticity under high-stress and low-temperature conditions. The ability to plastically deform quasicrystals at room temperature should lead to an improved understanding of their deformation mechanism and application in small-scale devices.