Multi-scale analysis of the stress state in a granular slope in transition to failure

By means of contact dynamics simulations, we analyze the stress state in a granular bed slowly tilted toward its angle of repose. An increasingly large number of grains are overloaded in the sense that they are found to carry a stress ratio above the Coulomb yield threshold of the whole packing. Using this property, we introduce a coarse-graining length scale at which all stress ratios are below the packing yield threshold. We show that this length increases with the slope angle and jumps to a length comparable to the depth of the granular bed at an angle below the angle of repose. This transition coincides with the onset of dilation in the packing. We map this transition into a percolation transition of the overloaded grains, and discuss it in terms of long-range correlations and granular slope metastability.     

Constitutive description of primary and steady-state creep deformation behaviour of tempered martensitic 9Cr–1Mo steel

The model based on the coupled sine hyperbolic creep rate relation with the evolution of internal stress as a function of strain provides better understanding of primary and secondary creep behaviour of tempered martensitic 9Cr–1Mo steel. The predicted evolution of internal stress as an increase in the internal stress value (or, decrease in effective stress) with strain/time appropriately described the observed decrease in creep rate during primary creep in the steel. The applicability of the model has been demonstrated by comparing experimental and predicted creep strain–time and creep rate–strain/time data of 9Cr–1Mo steel at 793 and 873 K for quenched and tempered and simulated post-weld heat treatment conditions. Irrespective of prior heat treatment and test temperature, the optimised parameters associated with the internal stress values exhibited linear variations with applied stress. The influence of prior heat treatment on primary and secondary creep characteristics of the steel is reflected on the rate constant values associated with the model. At all temperatures and heat treatment conditions, good agreement between the experimental and predicted steady-state creep rates demonstrate the further applicability of the model.     

Granular medium under vertical tapping: change of compaction and convection dynamics around the liftoff threshold

A granular medium submitted to vertical tapping reveals simultaneously compaction and convection. The two phenomena are directly coupled and their dynamics can be quantified by a characteristic compaction time and by an estimation of the convective downhill speed along the wall. A remarkable change of behavior is observed around the liftoff acceleration threshold of the whole packing, with a drastic slowing down of both dynamics below this threshold. Above it, a collective shock wave densifies the packing at each tap, whereas, below it, cumulative localized rearrangements will compact the entire system in the long time range.     

Sheared force networks: anisotropies, yielding, and geometry

A scenario for the yielding of granular matter is presented by considering the ensemble of force networks for a given contact network and applied shear stress tau. As tau is increased, the probability distribution of contact forces becomes highly anisotropic, the difference between average contact forces along minor and major axes grows, and the allowed networks span a shrinking subspace of all force networks. Eventually, contacts start to break, and at the maximal shear stress the packing becomes effectively isostatic. The size of the allowed subspace exhibits simple scaling properties, which lead to a prediction for the yield stress for packings of an arbitrary contact number.     

Force Distributions near Jamming and Glass Transitions

We calculate the distribution of interparticle normal forces P(F) near the glass and jamming transitions in model supercooled liquids and foams, respectively. P(F) develops a peak that appears near the glass or jamming transitions, whose height increases with decreasing temperature, decreasing shear stress and increasing packing density. A similar shape of P(F) was observed in experiments on static granular packings. We propose that the appearance of this peak signals the development of a yield stress. The sensitivity of the peak to temperature, shear stress, and density lends credence to the recently proposed generalized jamming phase diagram.     

准静态颗粒介质的弹性势能弛豫分析

颗粒体系是典型的多体相互作用体系, 具有多重的能量亚稳态. 对于准静态颗粒体系, 引入构型颗粒温度T_c描述弹性势能涨落. 本文认为平衡的体系具有一定的构型颗粒温度T_a, 其量值反映了其结构特征. 当外界扰动激发的构型颗粒温度超出T_a时, 产生不可逆过程. 通过对应力松弛过程的分析, 发现(T_c-T_a)激发了弹性弛豫, 且(T_c-T_a)越大则松弛过程中应力变化越大, 最终构型颗粒温度T_c→T_a时,宏观应力松弛结束,体系达到新的能量亚稳态.     

颗粒介质弹性的弛豫

颗粒介质是复杂的多体相互作用体系, 其弹性源自内部的力链结构, 弹性能量处在亚稳态, 具有复杂的弛豫行为. 在常规作用下, 颗粒介质往往呈现明显的弹性弛豫. 应力松弛是应变恒定时应力的衰减现象, 弹性弛豫是应力松弛的主要原因. 在前期工作基础上, 从弹性势能面和双颗粒温度热力学角度分析了弹性弛豫的机理, 量化了弹性应力演化不可逆过程; 基于双颗粒温度热力学计算得到了弹性能、颗粒温度和应力的演化, 其中应力松弛的计算结果与实验结果基本一致, 讨论了颗粒温度初值和输运系数的影响. 指出, 开展力链结构及其动力学研究是揭示宏观弹性弛豫机理的关键.     

Stress fluctuations in monodisperse and bidisperse rapid granular shear flows

Local stress fluctuations are measured in annular rapid shear flows of granular medium made of steel spheres with 2 and 3 mm in diameter. Both monodisperse packing and bidisperse packing are investigated to reveal the influence of size diversity on intermittent features of granular materials. Experiments are conducted in an annulus that can contain up to 15 kg of the spherical steel balls. Shearing of granular medium takes place via the rotation of the upper plate which compresses the material loaded inside the annulus. Fluctuations of compressive force are locally measured at the bottom of the annulus based on piezoelectric phenomenon. Rapid shear flow experiments are pursued at different compressive forces and shear rates and the sensitivity of fluctuations is then investigated by different means through monodisperse and bidisperse packings.     

Experimental and computational creep characterization of Al–Mg solid-solution alloy through instrumented indentation

Carefully designed indentation creep experiments and detailed finite-element computations were carried out in order to establish a robust and systematic method to extract creep properties accurately during indentation creep tests. Samples made from an Al–5.3?mol%?Mg solid-solution alloy were tested at temperatures ranging from 573 to 773?K. Finite-element simulations confirmed that, for a power-law creep material, the indentation creep strain field is indeed self-similar in a constant-load indentation creep test, except during short transient periods at the initial loading stage and when there is a deformation mechanism change. Self-similar indentation creep leads to a constitutive equation from which the power-law creep exponent n, the activation energy Q _c for creep, the back or internal stress and so on can be evaluated robustly. The creep stress exponent n was found to change distinctively from 4.8 to 3.2 below a critical stress level, while this critical stress decreases rapidly with increasing temperature. The activation energy for creep in the stress range of n = 3.2 was evaluated to be 123?kJ?mol^?1, close to the activation energy for mutual diffusion of this alloy, 130?kJ?mol^?1. Experimental results suggest that, within the n = 3.2 regime, the creep is rate controlled by viscous glide of dislocations which drag solute atmosphere and the back or internal stress is proportional to the average applied stress. These results are in good agreement with those obtained from conventional uniaxial creep tests in the dislocation creep regime. It is thus confirmed that indentation creep tests of Al–5.3?mol%?Mg solid-solution alloy at temperatures ranging from 573 to 773?K can be effectively used to extract material parameters equivalent to those obtained from conventional uniaxial creep tests in the dislocation creep regime.     

静态堆积颗粒中的力链分布

颗粒物质是由众多离散颗粒组成的软凝聚态物质,涉及多个物理层次结构和机制,是多尺度问题. 首先阐述了颗粒物质多尺度力学的研究框架,指出颗粒间接触力链构成的细观尺度是核心,颗粒物质显示出的独特静态堆积特性和动态流变特性都与细观尺度力链的复杂演变规律直接相关. 围绕着定量描述力链特征这一目标,采用严格的球形颗粒Hertz法向接触理论和Mindlin-Deresiewicz切向接触理论,对重力作用下12000个球心共面的二维等径颗粒静态堆积进行了离散动力学模拟,对力链分布特征、接触力规律等做了量化分析,考察了颗粒 关键词： 颗粒物质 力链 离散模型 多尺度力学     

用内耗方法研究铜的蠕变断裂过程

在文献[1]关于工业纯铝研究的基础上,研究了工业纯铜在不同条件下蠕变过程中晶界内耗峰的变化,蠕变条件分为三类:(a)较高温度、较低应力;(b)中等温度、中等应力;(c)较低温度、较高应力;使试样分别发生晶间型、混合型和穿晶型的断裂。由晶界内耗峰的变化可以推知:在较高温度、较低应力的蠕变过程中,晶界强度变化不大;在中等温度、中等应力的蠕变过程中,晶界强度有一定程度的提高;在较低温度、较高应力的蠕变过程中,晶界强度则有比较显著的提高。这说明,在蠕变过程中,晶界强度是变化着的,在不同的蠕变条件下,晶界强化的程度不同,最终导致了不同类型的蠕变断裂。这对于“等强温度”概念是一个修正和补充。 关键词：     

X-ray tomography study on the structure of the granular random loose packing

Random loose packing is the minimum-density granular packing which can maintain mechanical stability. In this study, x-ray tomography is used to investigate the internal structure of an isotropically prepared random loose packing through a special apparatus to minimize the effect of gravity. It is found that the minimum packing density is around 0.587.The microscopic structural analysis of the packing is also carried out.     

剪切振动下湿颗粒的力学谱

在恒温25 ℃剪切振动条件下,测量不同水分含量的NaCl湿颗粒体系的力学谱（能量耗散tanφ和剪切模量G）.研究发现,随着剪切振幅增大,NaCl湿颗粒体系的剪切模量G和能量耗散tanφ都表现出类似于干颗粒体系的阻塞（Jamming）转变行为.随着体系中水含量的增大,湿颗粒体系的剪切模量G和能量耗散tanφ在质量分数约等于11%的临界水浓度下均出现一个峰值,且峰位与应变振幅无关,表明此时颗粒之间主要的作用力发生了变化.     

Fluctuations in granular media

Dense slowly evolving or static granular materials exhibit strong force fluctuations even though the spatial disorder of the grains is relatively weak. Typically, forces are carried preferentially along a network of "force chains." These consist of linearly aligned grains with larger-than-average force. A growing body of work has explored the nature of these fluctuations. We first briefly review recent work concerning stress fluctuations. We then focus on a series of experiments in both two- and three-dimension [(2D) and (3D)] to characterize force fluctuations in slowly sheared systems. Both sets of experiments show strong temporal fluctuations in the local stress/force; the length scales of these fluctuations extend up to 10(2) grains. In 2D, we use photoelastic disks that permit visualization of the internal force structure. From this we can make comparisons to recent models and calculations that predict the distributions of forces. Typically, these models indicate that the distributions should fall off exponentially at large force. We find in the experiments that the force distributions change systematically as we change the mean packing fraction, gamma. For gamma's typical of dense packings of nondeformable grains, we see distributions that are consistent with an exponential decrease at large forces. For both lower and higher gamma, the observed force distributions appear to differ from this prediction, with a more Gaussian distribution at larger gamma and perhaps a power law at lower gamma. For high gamma, the distributions differ from this prediction because the grains begin to deform, allowing more grains to carry the applied force, and causing the distributions to have a local maximum at nonzero force. It is less clear why the distributions differ from the models at lower gamma. An exploration in gamma has led to the discovery of an interesting continuous or "critical" transition (the strengthening/softening transition) in which the mean stress is the order parameter, and the mean packing fraction, gamma, must be adjusted to a value gamma(c) to reach the "critical point." We also follow the motion of individual disks and obtain detailed statistical information on the kinematics, including velocities and particle rotations or spin. Distributions for the azimuthal velocity, V(theta), and spin, S, of the particles are nearly rate invariant, which is consistent with conventional wisdom. Near gamma(c), the grain motion becomes intermittent causing the mean velocity of grains to slow down. Also, the length of stress chains grows as gamma-->gamma(c). The 3D experiments show statistical rate invariance for the stress in the sense that when the power spectra and spectral frequencies of the stress time series are appropriately scaled by the shear rate, Omega, all spectra collapse onto a single curve for given particle and sample sizes. The frequency dependence of the spectra can be characterized by two different power laws, P proportional, variant omega(-alpha), in the high and low frequency regimes: alpha approximately 2 at high omega; alpha<2 at low omega. The force distributions computed from the 3D stress time series are at least qualitatively consistent with exponential fall-off at large stresses. (c) 1999 American Institute of Physics.     

Universal slow dynamics in granular solids

Experimental properties of a new form of creep dynamics are reported, as manifest in a variety of sandstones, limestone, and concrete. The creep is a recovery behavior, following the sharp drop in elastic modulus induced either by nonlinear acoustic straining or rapid temperature change. The extent of modulus recovery is universally proportional to the logarithm of the time after source discontinuation in all samples studied, over a scaling regime covering at least 10(3) s. Comparison of acoustically and thermally induced creep suggests a single origin based on internal strain, which breaks the symmetry of the inducing source.     

Shear- and vibration-induced order-disorder transitions in granular media

By molecular dynamics simulations we investigate the order-disorder transitions induced in granular media by an applied drive combining vibrations and shear. As the steady state is attained, the pack is found in disordered configurations for comparatively high intensities of the drive; conversely, ordering and packing fractions exceeding the random close packing are found when vibrations and shear are weak. As forcing amplitudes get smaller, we find diverging time scales in the dynamics, as the system enters a jamming region. Under this perspective, our picture supports the intuition that externally applied forcing has, in driven granular media, a role similar to temperature in thermal systems.     

Internal stress and heterogeneous dislocation structure in creep

The present work deals with the problem of microstructural interpretation of internal stress measured in high-temperature creep by the strain-transient dip-test technique. The development of microstructure in the course of creep is considered a transition from uniformly distributed dislocations to a well-developed substructure. The substructure is supposed to have a composite character that consists of cell or subgrain boundaries with few dislocations in cell or subgrain interiors. Model equations for the relation of internal stress to the parameters of the dislocation structure are discussed and examined with reference to experimental data. The evolution of internal stress in creep, evaluated using different formulae, is compared with the evolution of macroscopically measured internal stress. The use of applied-stress dependences of microstructure parameters permits quite realistic estimates of the values of internal stress in steady-state creep.     

Physics of compaction of fine cohesive particles

Fluidized fractal clusters of fine particles display critical-like dynamics at the jamming transition, characterized by a power law relating consolidation stress with volume fraction increment [sigma--(c) proportional, variant(Deltaphi)(beta)]. At a critical stress clusters are disrupted and there is a crossover to a logarithmic law (Deltaphi = nu logsigma--(c)) resembling the phenomenology of soils. We measure lambda identical with- partial differentialDelta(1/phi)/ partial log(sigma--(c) proportional, variant Bo(0.2)(g), where Bo(g) is the ratio of interparticle attractive force (in the fluidlike regime) to particle weight. This law suggests that compaction is ruled by the internal packing structure of the jammed clusters at nearly zero consolidation.     

Upward penetration of grains through a granular medium

We study experimentally the creeping penetration of guest (percolating) grains through densely packed granular media in two dimensions. The evolution of the system of the guest grains during the penetration is studied by image analysis. To quantify the changes in the internal structure of the packing, we use Voronoï tessellation and a certain shape factor which is a clear indicator of the presence of different underlying substructures (domains). We first consider the impact of the effective gravitational acceleration on upward penetration of grains. It is found that the higher effective gravity increases the resistance to upward penetration and enhances structural organization in the system of the percolating grains. We also focus our attention on the dependence of the structural rearrangements of percolating grains on some parameters like polydispersity and the initial packing fraction of the host granular system. It is found that the anisotropy of penetration is larger in the monodisperse case than in the bidisperse one, for the same value of the packing fraction of the host medium. Compaction of initial host granular packing also increases anisotropy of penetration of guest grains. When a binary mixture of large and small guest grains is penetrated into the host granular medium, we observe size segregation patterns.     

Strain stiffening in random packings of entangled granular chains

Random packings of granular chains are presented as a model system to investigate the contribution of entanglements to strain stiffening. The chain packings are sheared in uniaxial compression experiments. For short chain lengths, these packings yield when the shear stress exceeds the scale of the confining pressure, similar to granular packings of unconnected particles. In contrast, packings of chains which are long enough to form loops exhibit strain stiffening, in which the effective stiffness of the material increases with strain, similar to many polymer materials. The latter packings can sustain stresses orders-of-magnitude greater than the confining pressure, and do not yield until the chain links break. X-ray tomography measurements reveal that the strain-stiffening packings contain system-spanning clusters of entangled chains.