Size effects in the constrained deformation of metallic foams

The constrained deformation of an aluminium alloy foam sandwiched between steel substrates has been investigated. The sandwich plates are subjected to through-thickness shear and normal loading, and it is found that the face sheets constrain the foam against plastic deformation and result in a size effect: the yield strength increases with diminishing thickness of foam layer. The strain distribution across the foam core has been measured by a visual strain mapping technique, and a boundary layer of reduced straining was observed adjacent to the face sheets. The deformation response of the aluminium foam layer was modelled by the elastic-plastic finite element analysis of regular and irregular two dimensional honeycombs, bonded to rigid face sheets; in the simulations, the rotation of the boundary nodes of the cell-wall beam elements was set to zero to simulate full constraint from the rigid face sheets. It is found that the regular honeycomb under-estimates the size effect whereas the irregular honeycomb provides a faithful representation of both the observed size effect and the observed strain profile through the foam layer. Additionally, a compressible version of the Fleck-Hutchinson strain gradient theory was used to predict the size effect; by identifying the cell edge length as the relevant microstructural length scale the strain gradient model is able to reproduce the observed strain profiles across the layer and the thickness dependence of strength.     

Size effects on tensile and compressive strengths in metallic glass nanowires

Shear localization induced brittleness is the main drawback of metallic glasses which restricts their practical applications. Previous experiments have provided insights on how to suppress shear localization by reducing the sample size of metallic glasses to the order of 100 nm. In order to reveal the size effects and associated deformation mechanisms of metallic glasses in an even finer scale, we perform large-scale atomistic simulations for the uniaxial compression and tension of metallic glass nanowires. The simulation results show that, as the diameter of metallic glass samples decreases from 45 nm to 8 nm, the tensile yield strength increases while the compressive yield strength decreases. Homogeneous flow is observed as the governing deformation mechanism in all simulated metallic glass samples, where plastic shearing tends to initiate on the sample surface and propagate into the interior. To rationalize the size dependence of yield strengths, we propose a theoretical model based on the concept of surface stress and Mohr–Coulomb criterion. The theoretical predictions agree well with the simulation results, implying the important role of surface stress on the yielding of MGs below 100 nm. Finally, a discussion about the size effects of strength in metallic glasses at different length scales is provided. Our results suggest that the shear band energy and surface stress might be the two crucial parameters in determining the critical size required for the transition from shear localization to homogeneous deformation in MGs.     

Numerical simulation of progressive shear localization and scale effect in cohesionless soil media

Objective and methodsA multi-yield surface model of the total strain formulation, which takes into account the confinement dependency and has numerical consistency with the crack analysis of reinforced concrete, is presented to simulate the progressive failure and the shear band formation in a cohesionless soil media.ResultsFor experimental verification, a comparison of the numerical analysis results with the reality is carried out in view of the progressive failure. The scale effect on the nominal strength is discussed with regard to the shear localization.ConclusionIt is shown that by means of the proposed concept the scale effect of the static bearing capacity of foundation can be well simulated.     

Surface tension-driven shape-recovery of micro/nanometer-scale surface features in a Pt57.5Ni5.3Cu14.7P22.5 metallic glass in the supercooled liquid region: A numerical modeling capability

Recent experiments in the literature show that micro/nano-scale features imprinted in a Pt-based metallic glass, Pt_57.5Ni_5.3Cu_14.7P_22.5, using thermoplastic forming at a temperature above its glass transition temperature, may be erased by subsequent annealing at a slightly higher temperature in the supercooled liquid region (Kumar and Schroers, 2008). The mechanism of shape-recovery is believed to be surface tension-driven viscous flow of the metallic glass. We have developed an elastic-viscoplastic constitutive theory for metallic glasses in the supercooled liquid temperature range at low strain rates, and we have used existing experimental data in the literature for Pt_57.5Ni_5.3Cu_14.7P_22.5 (Harmon et al., 2007) to estimate the material parameters appearing in our constitutive equations. We have implemented our constitutive model for the bulk response of the glass in a finite element program, and we have also developed a numerical scheme for calculating surface curvatures and incorporating surface tension effects in finite element simulations. By carrying out full three-dimensional finite-element simulations of the shape-recovery experiments of Kumar and Schroers (2008), and using the independently determined material parameters for the bulk glass, we estimate the surface tension of Pt_57.5Ni_5.3Cu_14.7P_22.5 at the temperature at which the shape-recovery experiments were conducted. Finally, with the material parameters for the underlying elastic-viscoplastic bulk response as well as a value for the surface tension of the Pt-based metallic glass fixed, we validate our simulation capability by comparing predictions from our numerical simulations of shape-recovery experiments of Berkovich nanoindents, against corresponding recent experimental results of Packard et al. (2009) who reported shape-recovery data of nanoindents on the same Pt-based metallic glass.     

Flow of branched polymer melts in a lubricated cross-slot channel: a combined computational and experimental study

Numerical simulations have been performed to evaluate the accuracy of the multimode Giesekus model in predicting the flow behavior of a rheologically well characterized low-density polyethylene melt in a lubricated cross-slot channel. Specifically, the fidelity of the numerical results is established by detailed comparison with flow-induced birefringence measurements in a new optical rheometer with lubricated side walls that allows the creation of ideal two-dimensional flow kinematics that lead to the elimination of end effects commonly encountered in flow birefringence measurements. Based on these comparisons, the ability of the multimode Giesekus model to capture the flow characteristics with reasonable accuracy in the experimentally available Wi range of 21 to 29 has been established. However, it should be noted that the model predictions are, at best, qualitative in the vicinity of the stagnation point. The discrepancy between numerically predicted and experimentally observed stresses in this region is mainly attributed to the inaccuracy of the experimental data that stem from the occurrence of multiple orders of retardation within the measurement volume. Overall, these studies have paved the way for the development of a hi-fidelity lubricated cross-slot channel rheometer.     

泡沫铝材料准静态本构关系的理论和实验研究

应用Chen和Lu提出的适用于可压缩弹塑性固体的唯象本构模型框架，建立了泡沫铝的准静态本构模型，推导了三维等比例加载和环向受约束轴向加载下的宏观应力-应变曲线. 对两种泡沫铝材料(开孔和闭孔)进行了4类准静态试验，即单轴压缩、三维静水压缩、三维等比例压缩和侧向受约束轴向压缩实验. 利用单轴压缩和三维静水压缩的实验结果得到了泡沫铝材料的本构参数曲线，并由此预测它在三维等比例压缩和侧向受约束轴向压缩情况下的响应. 理论预测与相应实验结果相比较，三维等比例压缩的结果比较吻合，但与侧向受约束轴向压缩的结果却相差很大. 分析表明，理论预测与侧向受约束轴向压缩实验结果的偏差是由于泡沫铝试件与约束筒之间的摩擦造成的. 研究结果说明, Chen-Lu模型能够很好地描述泡沫铝材料在压缩占主导的应力状态下的响应.     

Size effects in two-dimensional Voronoi foams: A comparison between generalized continua and discrete models

In view of size effects in cellular solids, we critically compare the analytical results of generalized continuum theories with the computational results of discrete models. Representatives are studied from two classes of generalized continuum theories: the strain divergence theory from the class of higher-grade continua and the micropolar theory from the class of higher-order continua. In the former, the divergence of strain is proposed as an additional deformation measure, while in the latter the microrotation gradients act as the source for extra internal energy. We analytically solve a range of basic boundary value problems (simple shear, pure bending and the strain concentration around a hole) and compare the results with discrete, numerical calculations that are based on a Voronoi representation of the cellular microstructure. By comparing both the local deformation fields and the overall elastic response, we critically assess the capabilities of both theories in capturing size effects in cellular solids.     

Size effects in indentation response of thin films at the nanoscale: A molecular dynamics study

The indentation response of Ni thin films of thicknesses in the nanoscale was studied using molecular dynamics simulations with embedded atom method (EAM) interatomic potentials. A series of simulations were performed in films in the [1 1 1] orientation with thicknesses varying from 4 to 12.8 nm. The study included both single crystal films and films containing low angle grain boundaries perpendicular to the film surface. The simulation results for single crystal films show that as film thickness decreases larger forces are required for similar indentation depths but the contact stress necessary to emit the first dislocation under the indenter is nearly independent of film thickness. The low angle grain boundaries can act as dislocation sources under indentation. The mechanism of preferred dislocation emission from these boundaries operates at stresses that are lower as the film thickness increases and is not active for the thinnest films tested. These results are interpreted in terms of a simple model.     

Biomechanics of the brain: A theoretical and numerical study of Biot's equations of consolidation theory with deformation-dependent permeability

Various mathematical models of hydrocephalus and other brain abnormalities have appeared in the literature over the past 2 decades. In this paper, we study a class of models based on Biot's theory of consolidation with boundary forcing. By simplifying the geometry, we derive a single non-linear parabolic equation for the unidirectional deformation of brain tissue and focus on the effects of variable permeability. Using the theory of semigroups, we prove the existence and uniqueness of weak solutions to a class of problems which includes our particular case under consideration. Numerical solutions of our problem are used to motivate a discussion as to whether it is reasonable to pursue the development and implementation of models that incorporate deformation dependent permeability for more complex geometric configurations that are of relevance for models of the clinical condition of hydrocephalus.     

A new crystal plasticity scheme for explicit time integration codes to simulate deformation in 3D microstructures: Effects of strain path,strain rate and thermal softening on localized deformation in the aluminum alloy 5754 during simple shear

The predominant deformation mode during material failure is shear. In this paper, a crystal plasticity scheme for explicit time integration codes is developed based on a forward Euler algorithm. The numerical model is incorporated in the UMAT subroutine for implementing rate-dependent crystal plasticity model in LS-DYNA/Explicit. The sheet is modeled as a face centered cubic (FCC) polycrystalline aggregate, and a finite element analysis based on rate-dependent crystal plasticity is implemented to analyze the effects of three different strain paths consisting predominantly of shear. Finite element meshes containing texture data are created with solid elements. The material model can incorporate information obtained from electron backscatter diffraction (EBSD) and apply crystal orientation to each element as well as account for texture evolution. Single elements or multiple elements are used to represent each grain within a microstructure. The three dimensional (3D) polycrystalline microstructure of the aluminum alloy AA5754 is modeled and subjected to three different strain rates for each strain path. The effects of strain paths, strain rates and thermal softening on the formation of localized deformation are investigated. Simulations show that strain path is the most dominant factor in localized deformation and texture evolution.     

A MICRO-MECHANICAL MODEL OF KNITTED FABRIC AND ITS APPLICATION TO THE ANALYSIS OF BUCKLING UNDER TENSION IN WALE DIRECTION： MICRO-MECHANICAL MODEL

The typical micro-knitting structure of knitted fabric, which makes it very different from woven fabric, is described. The tensile tests of knitted fabric are reported. The deformations of the micro-knitting structures are carefully studied. The study indicates that when a knitted fabric sheet is subjected to a tension along w-direction an extra compressive stress field inside loop in c-direction is induced. The extra stress field is also determined through analysis. Finally, a micro-mechanical model of knitted fabric is proposed. This work paves the way for the simulations of buckling modes of a knitted fabric sheet as are observed in experiments. The project supported by the National Natural Science Foundation of China (10272079)     

A fast non‐Fickian particle‐tracking diffusion simulator and the effect of shear on the pollutant diffusion process

This paper presents a fast method for the generation of non‐Fickian particle paths within a particle‐tracking pollutant diffusion model based on a Fourier spectral representation of fractional Brownian motion (fBm), a generalization of ordinary Brownian motion. Correlated diffusive components in a particle‐tracking algorithm are modelled using fBm increments that have long‐range correlations over numerous spatial and/or temporal scales; hence producing non‐Fickian diffusion. A fast algorithm to generate fBm and its increment by using its power spectral density S(f) in a fast Fourier transform algorithm is given. A general equation for the scaling of fBm within a velocity flow field with simple linear shear is presented. An initial numerical study of the nature of fBm shear dispersion has been conducted by incorporating fBm increments into a non‐Fickian particle‐tracking algorithm. It is shown that the effect of simple (i.e. linear) shear on the diffusion process is to produce enhanced diffusive phenomena with the longitudinal spreading of the plume scaling with exponent ∼1+H, where H is the Hurst exponent used to describe fBm. Finally, a more complex shear zone at the entrance of a coastal bay model is investigated using both a traditional particle‐tracking method and the fBm‐based method. Copyright © 2000 John Wiley & Sons, Ltd.     

A numerical study of the effect of free surface and water depth on the stability of wakes: use of GDQ formulation

The instability character of a wake in the presence of a free surface is examined by a recently developed GDQ (generalized differential quadrature) numerical method. It is shown that at low Froude number the wake near a free surface is convectively unstable, but when the Froude number is increased further it becomes absolutely unstable. The effect of water depth on the stability property of the wake flow is also investigated. It is found that the influence of water depth on the critical point of instability is limited to at most 20% variation in the complex frequency, while the change in temporal growth rate is also limited to about 20%. © 1997 John Wiley & Sons, Ltd.     

The effects of the rock bridge ligament angle and the confinement on crack coalescence in rock bridges: An experimental study and discrete element method

The present article investigates the influences of the rock bridge ligament angle, β, and the confinement on crack coalescence patterns by conducting laboratory and numerical tests on rock-like specimens. Laboratory tests show that no coalescence in the rock bridge occurred for low β. With an increase of β, tensile-shear coalescence and tensile coalescences subsequently occurred. In addition, the increase in the confinement first promoted shear coalescence and then restrained crack coalescence for low β, whereas the tensile coalescence was restrained by the increase in confinement for high β. The numerical results corroborate the laboratory tests in the coalescence patterns. In addition, the numerical study shows that tensile and shear cracks subsequently initiated near crack tips because of the concentrated tensile and shear stresses, respectively. Regarding the influence of β on crack coalescence, tensile or shear stress failed to concentrate in rock bridges for low β. Therefore, the cracks failed to coalesce, whereas with the increase in β, tensile and shear stress concentrations occurred in the bridge and led to either tensile shear or tensile coalescence. Regarding the influence of confinement on crack coalescence, the increase in confinement restrained the tensile stress concentrations and further hindered tensile crack coalescence in rock bridges for high values of β.     

On the coupling of plastic slip and deformation-induced twinning in magnesium: A variationally consistent approach based on energy minimization

The present paper is concerned with the analysis of the deformation systems in single crystal magnesium at the micro-scale and with the resulting texture evolution in a polycrystal representing the macroscopic mechanical response. For that purpose, a variationally consistent approach based on energy minimization is proposed. It is suitable for the modeling of crystal plasticity at finite strains including the phase transition associated with deformation-induced twinning. The method relies strongly on the variational structure of crystal plasticity theory, i.e., an incremental minimization principle can be derived which allows to determine the unknown slip rates by computing the stationarity conditions of a (pseudo) potential. Phase transition associated with twinning is modeled in a similar fashion. More precisely, a solid-solid phase transition corresponding to twinning is assumed, if this is energetically favorable. Mathematically speaking, the aforementioned transition can be interpreted as a certain rank-one convexification. Since such a scheme is computationally very expensive and thus, it cannot be applied to the analysis of a polycrystal, a computationally more efficient approximation is elaborated. Within this approximation, the deformation induced by twinning is decomposed into the reorientation of the crystal lattice and simple shear. The latter is assumed to be governed by means of a standard Schmid-type plasticity law (pseudo-dislocation), while the reorientation of the crystal lattice is considered, when the respective plastic shear strain reaches a certain threshold value. The underlying idea is in line with experimental observations, where dislocation slip within the twinned domain is most frequently seen, if the twin laminate reaches a critical volume. The resulting model predicts a stress-strain response in good agreement with that of a rank-one convexification method, while showing the same numerical efficiency as a classical Taylor-type approximation. Consequently, it combines the advantages of both limiting cases. The model is calibrated for single crystal magnesium by means of the channel die test and finally applied to the analysis of texture evolution in a polycrystal. Comparisons of the predicted numerical results to their experimental counterparts show that the novel model is able to capture the characteristic mechanical response of magnesium very well.