Scaling of dislocation-based strain-gradient plasticity

By taking into account the dislocations that are geometrically necessary for producing a curvature or twist of the atomic lattice in crystals, Gao et al. recently developed a theory of strain-gradient plasticity on the micrometer scale and showed that it agrees relatively well with the tests of hardness, torsion and bending of copper on the micrometer scale. This paper subjects this theory to an asymptotic scaling analysis. It is shown that the small-size asymptotic limit of this theory exhibits (1) an unusually strong size effect in which the corresponding nominal stresses in geometrically similar structures of different sizes D vary as D^−5/2, and (2) an asymptotic approach to a load-deflection diagram whose tangent stiffness gradually increases, starting with an infinitely small initial stiffness at infinitely small stress. Although this peculiar small-size asymptotic behavior might not be attainable within the practical applicability range of a continuum theory, it renders questionable any efforts to construct approximations of an asymptotic matching character, with a two-sided asymptotic support, which have previously been proven effective for quasibrittle materials such as concrete, rock, ice and fiber composites. A possible simple modification of the existing theory with respect to the small-size asymptotic properties is suggested. However, the questions of experimental justification of such a modification and its compatibility with the dislocation theory will require further study. The small-size asymptotic properties of other strain gradient theories of plasticity have not been analyzed, except for those of the previous Fleck-Hutchinson theory, which have been found reasonable.     

Scaling impacted structures when the prototype and the model are made of different materials

By properly applying scaling laws, it is possible to infer the behaviour of a structure from the response of a similar model whose dimensions are scaled by a factor β. In some cases, however, e.g. in the case of strain rate sensitive structures under severe dynamic loads, these laws become distorted, severely limiting this approach. In this article, a methodology for the correction of this distortion is explored for the case when the structure and the model are made of different materials. It is shown that the behaviour of a structure, say, made of mild steel, can be forecast from the response of a model, say, made of aluminium. The technique here detailed is shown to be valid for simple structures subject to axial and transverse impact loads.     

Scaling law of resolved-scale isotropic turbulence and its application in large-eddy simulation

Eddy-damping quasinormal Markovian （EDQNM） theory is employed to calculate the resolved-scale spectrum and transfer spectrum, based on which we investigate the resolved-scale scaling law. Results show that the scaling law of the resolved-scale turbulence, which is affected by several factors, is far from that of the full-scale turbulence and should be corrected. These results are then applied to an existing subgrid model to improve its performance. A series of simulations are performed to verify the necessity of a fixed scaling law in the subgrid modeling.     

Scaling laws for gas-solid riser flow through two-fluid model simulation

Scale up of gas-solid circulating fluidized bed (CFB) risers poses many challenges to researchers.In this paper,CFD investigation of hydrodynamic scaling laws for gas-solid riser flow was attempted on the basis of two-fluid model simulations,in particular,the recently developed empirical scaling law of Qi,Zhu,and Huang (2008).A 3D computational model with periodic boundaries was used to perform numerical experiments and to study the effect of various system and operating parameters in hydrodynamic scaling o...     

Role of strain-rate sensitivity in the crystal plasticity of hexagonal structures

In the first part of this paper the stress and strain-rate response of hexagonal crystal structures are examined when slip is viscoplastic according to a power law. The stress and strain-rate equi-potential surfaces are constructed and discussed as a function of the strain-rate sensitivity index m. The second part of this paper deals with the case of linear viscous slip; i.e., for the case when m is equal to one. A simple analytic solution is presented to obtain the deviatoric stress state for a given strain-rate. It is shown that the plastic spin is not zero for m = 1 in hexagonal crystal structures, contrary to the cubic case where the plastic spin vanishes. In addition, the rate of texture evolution in simple shear of a magnesium polycrystal is examined as a function of m.     

Scaling behavior of coupled conservative weakly nonlinear oscillators

The scaling of the solution of coupled conservative weakly nonlinear oscillators is demonstrated and analyzed through evaluating the normal modes and their bifurcation with an equivalent linearization technique and calculating the general solutions with a method of multiple seales. The scaling law for coupled Duffing oscillators is that the coupling intensity should be proportional to the total energy of the system.Present address: Department of Chemistry and Chemistry and Chemical Engineering, Stevens Institute of Technology, Hoboken, New Jersey 07030, U.S.A.     

From lasers to the universe: Scaling laws in laboratory astrophysics

In this work scaling laws in laboratory astrophysics are studied. It is shown that mathematical models governing radiation hydrodynamics-driven phenomena are invariant under the homothetic group transformation and can be rescaled according to several types of scaling laws. This property is valid for both optically thick and optically thin materials and it allows a correct and rigorous connection between astrophysical objects or phenomena and laboratory experiments. This approach is applied to astrophysical jets and radiative shocks where advantages as well as difficulties are pointed out.     

Kinematics and dynamics of small-scale vorticity and strain-rate structures in the transition from isotropic to shear turbulence

We applied a technique that defines and extracts “structures” from a DNS dataset of a turbulence variable in a way that allows concurrent quantitative and visual analysis. Local topological and statistical measures of enstrophy and strain-rate structures were compared with global statistics to determine the role of mean shear in the dynamical interactions between fluctuating vorticity and strain-rate during transition from isotropic to shear-dominated turbulence. We find that mean shear adjusts the alignment of fluctuating vorticity, fluctuating strain-rate in principal axes, and mean strain-rate in a way that (1) enhances both global and local alignments between vorticity and the second eigenvector of fluctuating strain-rate, (2) two-dimensionalizes fluctuating strain-rate, and (3) aligns the compressional components of fluctuating and mean strain-rate. Shear causes amalgamation of enstrophy and strain-rate structures, and suppresses the existence of strain-rate structures in low-vorticity regions between enstrophy structures. A primary effect of shear is to enhance “passive” strain-rate fluctuations, strain-rate kinematically induced by local vorticity concentrations with negligible enstrophy production, relative to “active,” or vorticity-generating strain-rate fluctuations. Enstrophy structures separate into “active” and “passive” based on the level of the second eigenvalue of fluctuating strain-rate. We embedded the structure-extraction algorithm into an interactive visualization-based analysis system from which the time evolution of a shear-induced hairpin enstrophy structure was visually and quantitatively analyzed. The structure originated in the initial isotropic state as a vortex sheet, evolved into a vortex tube during a transitional period, and developed into a well-defined horseshoe vortex in the shear-dominated asymptotic state.     

Scaling group transformation on fluid flow with variable stream conditions

Thermophoresis particle deposition with chemical reaction on Magnetohydrodynamic flow of an electrically conducting fluid over a porous stretching sheet in the presence of a uniform transverse magnetic field with variable stream conditions is investigated using scaling group transformation. Starting from Navier-Stokes equations and using scaling group transformations, the governing equations are obtained in the form of differential equations. The fluid viscosity is assumed to vary as a linear function of temperature. It is found that the decrease in the temperature-dependent fluid viscosity makes the velocity to decrease with the increasing distance of the stretching sheet. At a particular point of the sheet the fluid velocity decreases with the decreasing viscosity but the temperature increases in this case. Impact of thermophoresis particle deposition in the presence of chemical reaction plays an important role on the concentration boundary layer. The results thus obtained are presented graphically and discussed.     

Scaling function, anisotropy and the size of RVE in elastic random polycrystals

This article is focused on the identification of the size of the representative volume element (RVE) in linear elastic randomly structured polycrystals made up of cubic single crystals. The RVE is approached by setting up stochastic Dirichlet and Neumann boundary value problems consistent with the Hill(-Mandel) macrohomogeneity condition. Within this framework we introduce a scaling function that relates the single crystal anisotropy to the scale of observation. We derive certain exact characteristics of the scaling function and postulate others based on detailed calculations on copper, lithium, tantalum, magnesium oxide and antimony-yttrium. In deriving the above, we make use of the fact that cubic crystals and polycrystals have a uniquely determined scale-independent bulk modulus. It turns out that the scaling function is exact in the single crystal anisotropy. A methodology to develop a material selection diagram that clearly separates the microscale from the macroscale is proposed. The proposed scaling function not only bridges the length scales but also unifies the treatment of a wide spectrum of cubic crystals. Although the scope of this article is restricted to aggregates made up of cubic-shaped and cubic-symmetry single crystals, the concept of the scaling function can be generalized to other crystal shapes and classes as well as to scaling of other elastic/inelastic properties.     

论工程地质模型——涵义、意义、建模与应用

本文重点论述了工程地质模型。阐明了工程地质模型的概念与涵义、阐述了建模的依据与方法；探讨了其应用的范畴与要点；尤其充分论述了工程地质模型的学科意义与深远影响。工程地质模型是条件研究的归宿, 是分析、计算与评论的基础。     

Fast approximations of dynamic stability boundaries of slender curved structures

Curved beams and panels can often be found as structural components in aerospace, mechanical and civil engineering systems. When curved structures are subjected to dynamic loads, they are susceptible to dynamic instabilities especially dynamic snap-through buckling. The identification of the dynamic stability boundary that separate the non-snap and post-snap responses is hence necessary for the safe design of such structures, but typically requires extensive transient simulations that may lead to high computation cost. This paper proposes a scaling approach that reveals the similarities between dynamic snap-through boundaries of different structures. Such identified features can be directly used for fast approximations of dynamic stability boundaries of slender curved structures when their geometric parameters or boundary conditions are varied. The scaled dynamic stability boundaries of half-sine arches, parabolic arches and cylindrical panels are studied.     

Strain-rate history effects and microstructural aspects in lithium fluoride and aluminium single crystals after dynamic loading

Single crystals of LiF and Al are deformed in shear at a number of constant strain-rates in the range 10^–4 to 1600 s^–1. These constant rate tests are supplemented by a series of jump tests in which a sharp increment in strain rate is imposed during the quasi-static straining. Dislocation arrangements are observed by etch-pits technique for LiF crystals and by TEM for Al crystals. It is shown that cell sizes vary inversely with flow stress and strain-rate sensitivity.     

Influence of partial constrained layer damping on the bending wave propagation in an impacted viscoelastic sandwich

This paper presents a parametric model to study the transient bending wave propagation in a viscoelastic sandwich plate due to impact loading. The effect of partial constrained layer damping (PCLD) geometry on wave propagation is investigated by comparing with propagation in single layer elastic plate. Several boundary conditions are also considered, and their effect on wave propagation is highlighted.The equation of motion is obtained from Lagrange’s equations. For the single layer plate, the governing equation is solved in time domain using Newman and Wilson method. For the plate with PCLD, the frequency dependant viscoelastic behavior of the core is represented by Prony series; the equation of motion is converted into frequency domain using Fourier transform the displacement is obtained in the frequency domain and is converted into time domain with the Inverse Fast Fourier Transform.The model was validated in our previous paper (Khalfi and Ross (2013)) with experimental results, additional validation is carried in this paper with literature, and good agreement is recorded. The results show that the plate covered with PCLD remains a dispersive medium. The shape of the wave is mainly related to the sandwich stiffness while the viscoelastic layer contributes in reducing the amplitude and speed of propagation. The particularity of this transient model lies in its ability to follow the shape of the bending wave at all times to observe formation, propagation and disappearance. With this model, the influence of any structural input parameters on the bending wave can be studied. The findings presented will also serve as a research base for more advanced horizons.     

Modelling the dynamics of large block structures

This paper summarizes the main critical points that arise when the problem of modelling the dynamics of block structures is tackled. In the first sections, a rigorous formulation of dynamics and impact problem is presented for a single rigid block freely supported on rigid ground, in order to illustrate the basic difficulties concerning the modelling of more complicated structures. Then, a critical review is presented on the numerous researches performed on this subject and the results achieved, and the problems still open, are put in evidence.

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Sommario In questo lavoro, si illustrano i punti salienti e critici che devono essere affrontati nella modellazione del comportamento dinamico di structture costituite da grandi blocchi assemblati a secco. Nei primi paragrafi, viene presentato e discusso il problema generale della dinamica e dell' urto del blocco singolo semplicemente appoggiato su suolo rigido: è questa la base necessaria per affrontare in modo rigoroso la modellazione di strutture più complesse. Viene quindi presentata una rassegna critica di vari modelli proposti in letteratura, evidenziando i problemi risolti e quelli ancora aperti.

     

Scaling theory of adsorption-induced stresses in polymer brushes grafted onto compliant structures

The lateral forces exerted on a substrate by a layer of end-grafted polymer molecules are calculated on the basis of simple scaling arguments. The results are cast in terms of an equilibrium surface stress and an elastic constant, which describes the rate of change of the surface stress upon deformation of the substrate. This allows for straightforward integration of the present results into a continuum framework describing the response of a compliant structure, which facilitates device design and analysis. The results are illustrated with calculations for end-grafted poly(styrene) and poly(ethylene oxide), and the implications for building micromechanical devices based on adsorption-induced deformation are discussed.     

Development of testing systems for dynamic assessment of sheet metal specimens

The work presented herein regards the analysis of an experimental technique for the execution of dynamic tensile tests on structural material sheet specimens. Dynamic tensile testing of sheet is becoming more important due to the need for more optimized vehicle crashworthiness analysis in the automotive industry. Positive strain-rate sensitivity, i.e. the strength increases with strain-rate, offers a potential for improved energy absorption during a crash event. Tests have been carried out in the Reliability and Safety Laboratory of the 2^nd Engineering Faculty of the Politecnico di Torino. Different types of testing techniques have been used to generate data under dynamic conditions. However, no guidelines are available for the testing method, specimen dimensions, measurement devices, and other important issues which are critical for the quality of the results. Accurate signal processing and curve smoothing are often necessary to make the testing data usable.     

Dynamic response of shallow buried structures associated with landmine clearing operations

The development of mechanical means of landmine clearing using flail machines requires a good knowledge of load transfer and tool-soil-landmine interaction. Recent research have provided a good understanding of the soil-tool interaction, but load transfer and responses of buried landmines due to loading from the flails remains undefined. Buried landmines act as unsupported buried structures and loads from the flailing motion are considered as impact loading on the soil surface. A 4 degree-of-freedom mechanical model is constructed and corresponding experiments are conducted to better understand the load transfer and dynamic responses of buried structures due to surface impact loading. The model and experiment is limited to a single impact load directly above the structure, and the buried structure is assumed to move only in the vertical direction. Experiments are conducted for various load magnitude and depth of burial for buried structure in two types of soil. The minimum surface impact forces needed to trigger a landmine in prescribed conditions for two different types of soils have been found. This information could be useful in the design optimization of a mine flail. A correction factor to account for nonlinearity in the form of the ratio of Burgers model and Kelvin stiffness and damping constants is introduced. Considering an appropriate correction factor, the response behavior of the model compares well with the experimental results. The model, while simple, is deemed adequate to represent and predict the behavior of a buried landmine in a mine clearing condition - or any other unsupported buried structure - in soil and sand medium subjected to surface impact loads.     

Mechanics of very fine-grained nanocrystalline materials with contributions from grain interior, GB zone, and grain-boundary sliding

In this paper, we formulated an atomically-equivalent continuum model to study the viscoplastic behavior of nanocrystalline materials with special reference to the low end of grain size that is typically examined by molecular dynamic (MD) simulations. Based on the morphology disclosed in MD simulations, a two-phase composite model is construed, in which three distinct inelastic deformation mechanisms disclosed from MD simulations are incorporated to build a general micromechanics-based homogenization scheme. These three mechanisms include the dislocation-related plastic flow inside the grain interior, the uncorrelated atomic motions inside the grain-boundary region (the GB zone), and the grain-boundary sliding at the interface between the grain and GB zone. The viscoplastic behavior of the grain interior is modeled by a grain-size dependent unified constitutive equation whereas the GB zone is modeled by a size-independent unified law. The GB sliding at the interface is represented by the Newtonian flow. The development of the rate-dependent, work-hardening homogenization scheme is based on a unified approach starting from elasticity to viscoelasticity through the correspondence principle, and then from viscoelasticity to viscoplasticity through replacement of the Maxwell viscosity of the constituent phases by their respective secant viscosity. The developed theory is then applied to examine the grain size- and strain rate-dependent behavior of nanocrystalline Cu over a wide range of grain size. Within the grain-size range from 5.21 to 3.28 nm, and the strain rate range from 2.5 × 10⁸ to 1.0 × 10⁹/s, the calculated results show significant grain-size softening as well as strain-rate hardening that are in quantitative accord with MD simulations [Schiotz, J., Vegge, T., Di Tolla, F.D., Jacobsen, K.W., 1999. Atomic-scale simulations of the mechanical deformation of nanocrystalline metals. Phys. Rev. B 60, 11971–11983]. We have also applied the theory to investigate the flow stress, strain-rate sensitivity, and activation volume over the wider grain size range from 40 nm to as low as 2 nm under these high strain rate loading, and found that the flow stress initially displays a positive slope and then a negative one in the Hall–Petch plot, that the strain-rate sensitivity first increases and then decreases, and that the activation volume first decreases and then increases. This suggests that the maximum strain rate sensitivity and the lowest activation volume do not occur at the smallest grain size but, like the maximum yield strength (or hardness), they occur at a finite grain size. These calculated results also confirm the theoretical prediction of Rodriguez and Armstrong [Rodriguez, P., Armstrong, R.W., 2006. Strength and strain rate sensitivity for hcp and fcc nanopolycrystal metals. Bull. Mater. Sci. 29, 717–720] on the basis of grain boundary weakening and the report of Trelewicz and Schuh [Trelewicz, J.R., Schuh, C.A., 2007. The Hall–Petch breakdown in nanocrystalline metals: a crossover to glass-like deformation. Acta Mater. 55, 5948–5958] on the basis of hardness tests. In general the higher yield strength, higher strain rate sensitivity, and lower activation volume on the positive side of the Hall–Petch plot are associated with the improved yield strength of the grain interior, but the opposite trends displayed on the negative side of the plot are associated with the characteristics of the GB zone which is close to the amorphous state.