Atomic mechanisms of local structural rearrangements in strained crystalline titanium grain

The nucleation and development of plastic deformation in a crystalline grain of titanium (Ti) during uniaxial tension has been studied by molecular dynamics (MD) simulations with the interatomic interaction described using the embedded atom method. Specific features of the generation of local structural rearrangements in the grain at various straining rates are revealed. It is established that there is a threshold deformation level at which local structural rearrangements begin to nucleate in the crystal, which is accompanied by a jumplike decrease in the potential energy. Because of the inertial character of the accommodation processes, this threshold value increases with the loading velocity.     

Electrical surface perturbation of a piezoelectric acoustic plate mode by a conductive liquid loading

Surface loading of a piezoelectric crystal supporting acoustic plate modes (APMs) by a dilute conductive liquid is analyzed using a perturbation theory. The formulation of the problem is such that only the electrical loading is relevant, and the mass loading and viscous entrainment caused by the solute are ignored. The perturbation in the propagation characteristics is then obtained relative to the solvent and is described in terms of the coupling coefficient, the capacitive loading, and the conductivity of the liquid. The results are compared to measurements made on Z-cut X-propagating LiNbO(3 ) APM device loaded with various conductive liquids of different concentrations. While an interpretation of the results can be given on the use of the APM device as a detector of the liquid properties, it is shown that a conductive liquid loading of the piezoelectric surface can be used as a means of assessing the electromechanical coupling coefficient of APMs.     

Dynamic crack response to a localized shear pulse perturbation in brittle amorphous materials: on crack surface roughening

Linear Elastic Fracture Mechanics (LEFM) provides a coherent framework to evaluate quantitatively the energy flux released at the tip of a growing crack. However, the way in which the crack chooses its path in response to this energy flux remains far from completely understood: the growing crack creates a structure on its own as conveyed by crack surface roughening even in brittle amorphous materials such as glass. We report here experiments designed to uncover the primary cause of surface roughening in brittle amorphous materials. Therefore, we investigate the response of a growing crack to local perturbation introduced as a shear wave pulse of controlled duration, amplitude, frequency and polarization. This pulse is shown to induce a local mode III perturbation in the loading of the crack front, which makes it twist locally, without fragmenting. This response is linear both in amplitude and frequency with respect to the perturbation, and disappears with it. We also show that shear wave pulses are emitted when the propagating crack encounters the heterogeneity. Implications of these observations for possible sources of roughening are finally discussed.     

Topology optimization of continuum structures with stress constraints and uncertainties in loading

Topology optimization using stress constraints and considering uncertainties is a serious challenge, since a reliability problem has to be solved for each stress constraint, for each element in the mesh. In this paper, an alternative way of solving this problem is used, where uncertainty quantification is performed through the first‐order perturbation approach, with proper validation by Monte Carlo simulation. Uncertainties are considered in the loading magnitude and direction. The minimum volume problem subjected to local stress constraints is formulated as a robust problem, where the stress constraints are written as a weighted average between their expected value and standard deviation. The augmented Lagrangian method is used for handling the large set of local stress constraints, whereas a gradient‐based algorithm is used for handling the bounding constraints. It is shown that even in the presence of small uncertainties in loading direction, different topologies are obtained when compared to a deterministic approach. The effect of correlation between uncertainties in loading magnitude and direction on optimal topologies is also studied, where the main observed result is loss of symmetry in optimal topologies.     

Effect of irradiation by boron ions on the character of realization of twinning and slip under prolonged (more than 60 sec) loading of single crystals of bismuth

The twinning of single crystals of bismuth irradiated by boron ions with an energy of 25 keV and a dose of 10¹⁷ ion/cm², in the case of prolonged (more than 60 sec) loading of a crystal is studied. It is found that prolonged exposure of a crystal to a concentrated load promotes a decrease in the number of twins in the concentrator of external stresses. An increase of temperature up to 400 K stimulates the process of slip in the realization of plastic deformation of a crystal. Mozyr’ State Pedagogical Institute, Mozyr’, Belarus. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 72, No. 5, pp. 967–970.     

Localised formulations for thick “sandwich” laminated and composite structures

A “sandwich” panel under axial compressive loading is studied over its post-buckling range. Alternative formulations were developed to cover solutions other than the deflection shape given by the classical Rayleigh-Ritz analysis. General elasticity principles are used to derive the total potential energy function in terms of the displacement field. Given a constant modal amplitude displacement field, which is introduced in the total potential energy function, the results are discussed having as background models studied earlier. Techniques for the analysis of localized solutions are presented with reference to the study of the beam on nonlinear elastic foundation. The concepts of localization are introduced by using dynamical analogy and the double scale perturbation method and applied to the sandwich panel, to derive the governing amplitude modulation equations. The resulting formulations are discussed using some examples, and by solving analytical and numerically the amplitude differential equations.     

Theoretical and experimental study of mass sensitivity of PSAW-APMson ZX-LiNbO3

Acoustic plate mode (APM) devices have recently been used as sensing elements, both for the physical measurement of fluid properties and in biosensor applications. One of the primary interaction mechanisms in these devices is mass loading caused by the added mass bound to the layered crystal surface. However, the material properties of these thin composite layers are not well characterized or known as is required in order to accurately predict the sensor response. In the present work, perturbation theory is used to derive expressions for the sensitivity of the APM sensors to mass loading and viscoelastic stiffening. Mass sensitivity experiment was conducted on ZX-LiNbO₃ in a liquid environment to accurately reflect the sensitivity of an actual biosensor and the results are compared to theory. The measured data show a f² dependence for the mass sensitivity for APMs on ZX-LiNbO₃ in the measured frequency range, which indicates a SAW-like behavior. This behavior is due to the fact that the acoustic plate modes on ZX-LiNBO₃ are pseudo-SAW (PSAW) derived, and the acoustic energy is confined to the sensing surface. As a result, the APMs on ZX-LiNbO₃ are referred to as PSAW-APMs. Discussions are given in terms of the added mass which occurs in typical biosensor applications     

Contribution to the crystal free energy due to interacting quasiparticles

The new method of calculations for the contribution to the quantum crystal free energy, due to the quasiparticles interactions, is suggested. At rather low temperatures the pare scattering approximation of quasiparticles in the lattice space is used. The commonly used condition of the perturbation theory for the small value of the potential is not superimposed.     

Data science assisted cohesive finite element modelling of impact behaviour of AP-HTPB crystal binder composite

In this work, the response of an ammonium perchlorate (AP)-hydroxyl-terminated polybutadiene (HTPB) composite material under impact loading is presented, utilizing computational cohesive finite element method (CFEM) simulations that are validated with drop hammer experiments. This study examined the impact behaviour of AP crystal sizes between 200 and 400 μm by varying impact velocities between 3 and 10 m/s. Based on the outcome of CFEM simulations, analysis of variance (ANOVA) tests and a response surface method (RSM) were utilized to construct a mathematical model approximating the relationships between simulation inputs and outcomes. Both computational and experimental results show that the local strain rate has a considerable positive correlation with crystal size, and the rate of temperature change has positive correlations with both crystal size and impact velocity. Further, it was observed that stiffness and compression energy are the primary factors to variances in local strain rate and rate of change of temperature. RSM has been found to be an effective tool for modelling impact responses of materials under varying experimental conditions.     

Molecular-dynamics study of crystal structure defect formation by the thermal fluctuation mechanism during high-rate deformation

The possibility of structural defect generation in materials with the ideal crystal lattice under dynamic loading conditions in a broad temperature range has been studied by means of molecular dynamics using the embedded atom method with many-body interatomic interaction potentials. It is shown that thermal fluctuations can lead to a jumplike nucleation of defects in the ideal crystal under high-rate deformation conditions. Features of the defect nucleation via this mechanism are analyzed for various temperatures and loading regimes.     

On the complete extinction of selected imperfection wavelengths in dynamically expanded ductile rings

In this work the inception and development of multiple necks in dynamically expanded ductile rings with ab initio geometric imperfections has been addressed. Finite element simulations and linear perturbation analysis have been applied for that task. In the numerical calculations a selected wavelength is included into the model defining along the circumference of the ring an array of periodic geometric imperfections of predefined amplitude. In the stability analysis a perturbation of a given mode is added to the background solution and the growth rate of the perturbation is evaluated. The attention has been focused on the extinction of both long and short wavelength imperfections and the appearance of a dominant necking pattern which emerges when the geometric imperfections are vanished. The role played by the loading rate on the extinction of imperfections is also addressed. Moreover, the necking strain is found to be dependent on the imperfection pattern and the loading rate. Its maximum value is registered for the loading cases in which the initial imperfections distribution is completely extinguished.     

Effects of dark soliton on self-deflection of bright soliton in a separate bright-dark soliton pair

Abstract

Based on the theory of one-dimensional separate soliton pairs formed in a serial photorefractive crystal circuit, the effects of the dark soliton on the self-deflection of the bright one in one separate bright-dark soliton pair are investigated by taking the diffusion term into account. The numerical results obtained by solving the nonlinear propagation equation show that the bright soliton moves on a parabolic trajectory in the crystal and its spatial shift changes with the input intensity of the dark soliton. These effects are further studied using perturbation analysis and the characteristics of the spatial shift of the bright soliton varying with the input maximum intensity of the dark soltion are analysed. The position of the bright soliton at the output surface of the crystal can be determined accurately according to the formula obtained from perturbation method.     

Coupled thermomechanical analysis of transformation-induced plasticity in multiphase steels

The thermomechanical response of low-alloyed multiphase steels assisted by transformation-induced plasticity (TRIP steels) is analyzed taking into account the coupling between the thermal and mechanical fields. The thermomechanical coupling is particularly relevant since in TRIP steels the phase transformation that occurs during mechanical loading is accompanied by the release of a considerable amount of energy (latent heat) that, in turn, affects the mechanical response of the material. The internal generation of heat associated with the martensitic phase transformation and the plastic deformation are modeled explicitly in the balance of energy. The momentum and energy equations are solved simultaneously by using a fully-implicit numerical scheme. The simulations are conducted using a micromechanical formulation for single crystals of austenite and ferrite. The characteristics of the model are illustrated by means of simulations for a single crystal of austenite and an aggregate of austenitic and ferritic grains. For a single crystal of austenite, it is found that the increase in local temperature due to transformation actually hinders further transformation and, instead, promotes plastic deformation. However, for an aggregate of austenitic and ferritic grains in a multiphase steel, the increase in temperature due to transformation is limited since the heat generated in the austenite is conducted to the ferritic matrix, effectively lowering the temperature in the austenitic phase.     

Micromechanical modelling of switching phenomena in polycrystalline piezoceramics: application of a polygonal finite element approach

A micromechanically motivated model is proposed to capture nonlinear effects and switching phenomena present in ferroelectric polycrystalline materials. The changing remnant state of the ferroelectric crystal is accounted for by means of so-called back fields—such as back stresses—to resist or assist further switching processes in the crystal depending on the local loading history. To model intergranular effects present in ferroelectric polycrystals, the computational model elaborated is embedded into a mixed polygonal finite element approach, whereby an individual ferroelectric grain is represented by one single irregular polygonal finite element. This computationally efficient coupled simulation framework is shown to reproduce the specific characteristics of the responses of ferroelectric polycrystals under complex electromechanical loading conditions in good agreement with experimental observations.     

Cellular automata simulation of the phenomenon of multiple crystallization

The phenomenon of multiple crystallization from supersaturated solutions was simulated. For this simulation the model used is based on partitioning cellular automata (CA) with probabilistic table lookup for the implementation of diffusion and interaction according to diffusion and crystal growth basic equations. Such an approach, which takes into account temperature, crystallographic indexes of crystal surface and local fluctuations describes the problem at a mesoscopic level. This simulates the physical processes of diffusion, nucleation, and aggregation of particles. Results were obtained that are in qualitative agreement with the behavior of the majority of real situation for the: (i) temperature dependence of the crystal solubility; (ii) temperature dependence of the concentration of beginning of crystallization from supersaturated solutions. It was also studied the processes of crystallization at different temperatures and analyzed the behavior of the different parameters involved in crystallization systems: concentration of solution, interfacial energy, mass of crystals and average size of crystal. Finally, the process of crystallization was modeled at several conditions of temperature gradient.     

A model to evaluate dynamic stability of imperfection sensitive shells

The paper deals with the perturbation energy concept and its application to stability of imperfection sensitive structures under time-dependent loads. The evaluation of the stability is based on energy norms, which may be used for investigation of safety against buckling. Starting from a stable state of equilibrium the presented procedure allows to decide whether the structure stays for a certain load history within critical bounds, which separate the motion round the prebuckling state from a motion in the postbuckling region. The stability is proved by comparing the critical energy calculated by a static analysis and the load induced energy. Applications to a truss and a spherical shell illustrate the variety of the phenomena in dynamic buckling behaviour of elastic structures in case of impulsive loading and the accuracy of the proposed method.     

Infrared and Raman spectra and the band structure of yttrium trifluoride YF3

The infrared and nonresonant Raman spectra of YF₃ have been studied within the framework of density functional perturbation theory. We report the calculated frequencies of three Raman active modes and one IR active mode that could not be detected experimentally. The valence and conduction band structure of YF₃ have been calculated, using density functional theory. A good agreement between the calculated valence band width and experimental result was obtained, and an indirect energy gap of 7.58 eV is estimated in the local density approximation.     

Analysis of strain error sources in micro-beam Laue diffraction

Micro-beam Laue diffraction is an experimental method that allows the measurement of local lattice orientation and elastic strain within individual grains of engineering alloys, ceramics, and other polycrystalline materials. Unlike other analytical techniques, e.g. based on electron microscopy, it is not limited to surface characterisation or thin sections, but rather allows non-destructive measurements in the material bulk. This is of particular importance for in situ loading experiments where the mechanical response of a material volume (rather than just surface) is studied and it is vital that no perturbation/disturbance is introduced by the measurement technique. Whilst the technique allows lattice orientation to be determined to a high level of precision, accurate measurement of elastic strains and estimating the errors involved is a significant challenge. We propose a simulation-based approach to assess the elastic strain errors that arise from geometrical perturbations of the experimental setup. Using an empirical combination rule, the contributions of different geometrical uncertainties to the overall experimental strain error are estimated. This approach was applied to the micro-beam Laue diffraction setup at beamline BM32 at the European Synchrotron Radiation Facility (ESRF). Using a highly perfect germanium single crystal, the mechanical stability of the instrument was determined and hence the expected strain errors predicted. Comparison with the actual strain errors found in a silicon four-point beam bending test showed good agreement. The simulation-based error analysis approach makes it possible to understand the origins of the experimental strain errors and thus allows a directed improvement of the experimental geometry to maximise the benefit in terms of strain accuracy.     

A global energy analysis of impact loaded bi-material strips

A global energy analysis is given of both the static and dynamic energy release rates for a bi-material strip loaded in tension. A steady state crack propagation speed is identified which is determined by the mode II fracture toughness, modulus ratios and thickness of the strips. Initiation times are also found as a function of loading velocity and both these and the steady state speeds are found to compare well with experiments. The initiation phase is also examined using a perturbation analysis and this is found to predict the observed accelerations. Solutions for combined shear and axial loads are also given.     

Microstress estimate of stochastically heterogeneous structures by the functional perturbation method: A one dimensional example

A new functional perturbation method (FPM) for calculating the probabilistic response of stochastically heterogeneous, linear elastic structures is developed. The method is based on treating the governing differential operator as well as the unknown displacement function as a functional of material modulus field. By executing a functional perturbation around the homogeneous case, a set of successive differential equations is obtained and solved, from which the average and variance of any local parameter (displacements, stresses, strains) can be found. For a linear problem, the equations to be solved in each approximation order differ from the one for the homogeneous case by a pseudo external loading (right hand side) part only. Thus, only the Green function for the homogeneous case is needed for an analytical solution of the corresponding heterogeneous problem. A one dimensional stochastically heterogeneous rod embedded in a uniform shear resistant elastic medium is solved as an example. The statistical variance of displacements and stresses are found analytically, including the edge regions. Morphological (grain size) and material (modulus) effects on the stochastic response are demonstrated. The above results are essential for estimating the stochastic features of local stress concentrations, which are the source for many strength-related macro properties of materials. Extensive usage of generalized functions (Dirac operator and its derivatives) is needed for the analysis.