Mechanisms for acoustic emissions generation during granular shearing

Shear deformation of granular media leads to continual restructuring of particle contact network and mechanical interactions. These changes to the mechanical state include jamming of grains, collisions, and frictional slip of particles—all of which present abrupt perturbations of internal forces and release of strain energy. Such energy release events typically result in the generation of elastic waves in the kHz frequency range, termed acoustic emissions (AE). The close association between grain-scale mechanics and AE generation motivated the use of AE as surrogate observations to assess the mechanical state of complex materials and granular flows. The study characterizes AE generation mechanisms stemming from grain-scale mechanical interactions. Basic mechanisms are considered, including frictional slip between particles, and mechanical excitation of particle configurations during force network restructuring events. The intrinsic frequencies and energy content of generated AEs bear the signature of source mechanisms and of structural features of the grain network. Acoustic measurements in simple shear experiments of glass beads reveal distinct characteristics of AE associated with different source mechanisms. These findings offer new capabilities for non-invasive interrogation of micromechancial interactions and linkage to a stochastic model of shear zone mechanics. Certain statistical features of restructuring events and associated energy release during shearing were predicted with a conceptual fiber-bundle model (FBM). In the FBM the collective behavior of a large number of basic mechanical elements (representing e.g. grain contacts), termed fibers, reproduces the reaction of disordered materials to progressive loading. The failure of fibers at an individual threshold force corresponds to slipping of a particle contact or a single rearrangement event of the granular network. The energy release from model fiber breakage is the equivalent to elastic energy from abrupt grain rearrangement events and provides an estimate of the energy available for elastic wave generation. The coupled FBM–AE model was in reasonable agreement with direct shear experiments that were performed on large granular assemblies. The results underline the potential of using AE as a diagnostic tool to study micro-mechanical interactions, shear failure and mobilization in granular material.     

Fabric,force and strength anisotropies in granular materials: a micromechanical insight

In micromechanics, the stress–force–fabric (SFF) relationship is referred to as an analytical expression linking the stress state of a granular material with microparameters on contact forces and material fabric. This paper employs the SFF relationship and discrete element modelling to investigate the micromechanics of fabric, force and strength anisotropies in two-dimensional granular materials. The development of the SFF relationship is briefly summarized while more attention is placed on the strength anisotropy and deformation non-coaxiality. Due to the presence of initial anisotropy, a granular material demonstrates a different behaviour when the loading direction relative to the direction of the material fabric varies. Specimens may go through various paths to reach the same critical state at which the fabric and force anisotropies are coaxial with the loading direction. The critical state of anisotropic granular material has been found to be independent of the initial fabric. The fabric anisotropy and the force anisotropy approach their critical magnitudes at the critical state. The particle-scale data obtained from discrete element simulations of anisotropic materials show that in monotonic loading, the principal force direction quickly becomes coaxial with the loading direction (i.e. the strain increment direction as applied). However, material fabric directions differ from the loading direction and they only tend to be coaxial at a very large shear strain. The degree of force anisotropy is in general larger than that of fabric anisotropy. In comparison with the limited variation in the degree of force anisotropy with varying loading directions, the fabric anisotropy adapts in a much slower pace and demonstrates wider disparity in the evolution in the magnitude of fabric anisotropy. The difference in the fabric anisotropy evolution has a more significant contribution to strength anisotropy than that of force anisotropy. There are two key parameters that control the degree of deformation non-coaxiality in granular materials subjected to monotonic shearing: the ratio between the degrees of fabric anisotropy and that of force anisotropy and the angle between the principal fabric direction and the applied loading direction.     

Determining particulate–solid interphase strength using shear-induced anisotropy

The resistance to shear deformation developed by a granular material layer in contact with a topographically rough natural or manufactured solid material surface is critical to the stability of a variety of composite systems. By using discrete-element method numerical simulations, we show that evolution of fabric and contact force anisotropy at the boundary between the surface and the granular media controls shear behavior. Full mobilization of granular material strength occurs when the contact force anisotropy developed at the interface is equal to the maximum contact force anisotropy of the granular media.     

Stress-chain based micromechanics of sand with grain shape effect

The mechanical behaviors of granular media are controlled by grain properties and microstructure. The primary property of granular media is denoted by its grain shape, grain size distribution, stiffness, and interparticle friction. The grain shape itself is of particular importance. Microstructures are formed in the connection paths of contact points between grains. In this paper, the deformation of granular materials with different grain shapes was simulated using two-dimensional DEM under different stress-levels and densities. After analyzing the results, the authors investigated fabric changes. The evolution rule of stress-induced anisotropy and its limitation as well as the existence of a critical state of fabric are revealed.     

Fabric rates of elliptical particle assembly in monotonic and cyclic simple shear tests: a numerical study

This paper aims to investigate the evolutions of microscopic structures of elliptical particle assemblies in both monotonic and cyclic constant volume simple shear tests using the discrete element method. Microscopic structures, such as particle orientations, contact normals and contact forces, were obtained from the simulations. Elliptical particles with the same aspect ratio (1.4 and 1.7 respectively for the two specimens) were generated with random particle directions, compacted in layers, and then precompressed to a low pressure one-dimensionally to produce an inherently anisotropic specimen. The specimens were sheared in two perpendicular directions (shear mode I and II) in a strain-rate controlled way so that the effects of inherent anisotropy can be examined. The anisotropy of particle orientation increases and the principal direction of particle orientation rotates with the shearing of the specimen in the monotonic tests. The shear mode can affect the way fabric anisotropy rate of particle orientation responds to shear strain as a result of the initial anisotropy. The particle aspect ratio exhibits quantitative influence on some fabric rates, including particle orientation, contact normal and sliding contact normal. The fabric rates of contact normal, sliding contact normal, contact force, strong and weak contact forces fluctuate dramatically around zero after the shear strain exceeds 4 % in the monotonic tests and throughout the cyclic tests. Fabric rates of contact normals and forces are much larger than that of particle orientation. The particle orientation based fabric tensor is harder to evolve than the contact normal or contact force based because the reorientation of particles is more difficult than that of contacts.     

Effective properties of cemented granular materials

An analytical model is developed to describe the effective elastic properties of a cemented granular material that is modeled as a random packing of identical spheres. The elastic moduli of grains may differ from those of cement. The effective bulk and shear moduli of the packing are calculated from geometrical parameters (the average number of contacts per sphere and porosity), and from the normal and tangential stiffnesses of a two-grain combination. The latter are found by solving the problems of normal and tangential deformation of two elastic spherical grains cemented at their contact. A thin cement layer is approximated by an elastic foundation, and the grain-cement interaction problems are reduced to linear integral equations. The solution reveals a peculiar distribution pattern of normal and shear stresses at the cemented grain contacts: the stresses are maximum at the center of the contact region when the cement is soft relative to the grain, and are maximum at the periphery of the contact region when the cement is stiff. Stress distribution shape gradually varies between these two extremes as the cement's stiffness increases. The solution shows that it is mainly the amount of cement that influences the effective elastic properties of cemented granular materials. The radius of the cement layer affects the stiffness of a granular assembly much more strongly than the stiffness of the cement does. This theoretical model is supported by experimental results.     

Influence of particle shape on sheared dense granular media

We study by means of molecular dynamics simulations of periodic shear cells, the influence of particle shape on the global mechanical behavior of dense granular media. At large shear deformation samples with elongated particles, independent of their initial orientation, reach the same stationary value for both shear force and void ratio. At the micro-mechanical level the stress, the fabric and the inertia tensors of the particles are used to study the evolution of the media. In the case of isotropic particles the direction of the principal axis of the fabric tensor is aligned with the one of the principal stress, while for elongated particles the fabric orientation is strongly dependent on the orientation of the particles. The shear band width is shown to depend on the particle shape due to the tendency of elongated particles to preferential orientations and less rotation.     

On micromechanical characteristics of the critical state of two-dimensional granular materials

In micromechanics of quasi-static deformation of granular materials, relationships are investigated between the macro-scale, continuum-mechanical characteristics, and the micro-scale characteristics at the particle and interparticle contact level. An important micromechanical quantity is the fabric tensor that reflects the distribution of contact orientations. It also contains information on the coordination number, i.e. the average number of contacts per particle. Here, the focus is on characteristics of the critical state in the two-dimensional case. Critical state soil mechanics is reviewed from the micromechanical viewpoint. Two-dimensional discrete element method (DEM) simulations have been performed with discs from a fairly narrow particle-size distribution. Various values for the interparticle friction coefficient and for the confining pressure have been considered to investigate the effect of these quantities on critical state characteristics (shear strength, packing fraction, coordination number and fabric anisotropy). Results from these DEM simulations show that a limiting fabric state exists at the critical state, which is geometrical in origin. The contact network tessellates the assembly into loops that are formed by contacts. For each loop, a symmetrical loop tensor is defined, based on its contact normals. This loop tensor reflects the shape of the loop. An orientation is associated with each loop, based on its loop tensor. At the critical state, the frequencies with which loops with different number of sides occur depend on the coordination number. At the critical state, these loops have, on average, the following universal characteristics, i.e. independent of the coordination number: (1) loops with the same number of sides and orientation have identical anisotropy of the loop tensor, (2) the anisotropy of the loop tensor depends linearly on the number of sides of the loop, (3) the distribution of loop orientations is identical, (4) Lewis’s law for the loop areas, which is a linear relation between the number of sides of loops and their area, is satisfied (not exclusively at the critical state) and (5) the areas of the loops do not depend on their orientation.     

Evolution of ultrasonic velocity and dynamic elastic moduli with shear strain in granular layers

Ultrasonic wave transmission has been used to investigate processes that influence frictional strength, strain localization, fabric development, porosity evolution, and friction constitutive properties in granular materials under a wide range of conditions. We present results from a novel technique using ultrasonic wave propagation to observe the evolution of elastic properties during shear in laboratory experiments conducted at stresses applicable to tectonic faults in Earth’s crust. Elastic properties were measured continuously during loading, compaction, and subsequent shear using piezoelectric transducers fixed within shear forcing blocks in the double-direct-shear configuration. We report high-fidelity measurements of elastic wave properties for normal stresses up to 20 MPa and shear strains up to 500 % in layers of granular quartz, smectite clay, and a quartz-clay mixture. Layers were 0.1–1 cm thick and had nominal contact area of $5 \mathrm{cm} \!\times \! 5 \mathrm{cm}$ . We investigate relationships among frictional strength, granular layer thickness, and ultrasonic wave velocity and amplitude as a function of shear strain and normal stress. For layers of granular quartz, P-wave velocity and amplitude decrease by 20–70 % after a shear strain of 0.5. We find that P-wave velocity increases upon application of shear load for layers of pure clay and for the quartz-clay mixture. The P-wave amplitude of pure clay and quart-clay mixtures first decreases by $\sim $ 50 and 30 %, respectively, and then increases with additional shear strain. Changes in P-wave speed and wave amplitude result from changes in grain contact stiffness, crack density and disruption of granular force chains. Our data indicate that sample dilation and shear localization influence acoustic velocity and amplitude during granular shear.     

DEM simulation of the shear behaviour of breakable granular materials with various angularities

Particle shape is an important factor that affects particle breakage and the mechanical behaviour of granular materials. This report explored the effect of angularity on the mechanical behaviour of breakable granular materials under triaxial tests. Various angular particles are generated using the quasi-spherical polyhedron method. The angularity α is defined as the mean exterior angle of touching faces in a particle model. A breakable particle is constructed as an aggregate composed of coplanar and glued Voronoi polyhedra. After being prepared under the densest conditions, all assemblies were subjected to triaxial compression until a critical state was reached. The macroscopic characteristics, including the shear strength and dilatancy response, were investigated. Then, particle breakage characteristics, including the extent of particle breakage, breakage pattern and correlation between the particle breakage and energy input, were evaluated. Furthermore, the microscopic characteristics, including the contact force and fabric anisotropy, were examined to probe the microscopic origins of the shear strength. As α increases, the peak shear strength increases first and then remains constant, while the critical shear strength generally increases. Assemblies with larger angularity tend to cause more serious particle breakage. The relative breakage is linearly correlated with α under shear loading. Compared with unbreakable particles, the peak shear strength and the critical volumetric strain decline, and the degree of decline linearly increases with increasing α.     

不同因素下镍铜双层膜表面摩擦行为的研究

材料在摩擦接触过程中的弹塑性变形对基体的力学性能具有重要影响。为研究镍铜双层膜在接触过程中的变形行为和力学特性,本文从原子轨迹、原子晶格结构变化、接触力和基体内部位错等方面,详细研究了表面纹理密度、纹理方向、晶体学方向、磨粒半径和接触深度等因素对摩擦接触过程的影响。结果表明：纳观纹理表面以及镀层的引入对接触力产生影响。镍膜晶体学方向对滑动接触过程影响显著,存在接触力最小的晶体学方向;凸体的分布角度对摩擦过程的影响较小;在界面作用下,特定纹理密度表现出一定的减摩作用;基体材料的接触力随着磨粒半径和接触深度的增大而增大;在不同因素及水平下,基体表现出不同的位错缺陷程度和原子堆积现象。     

Isostaticity in Cosserat continuum

Under conditions of isostaticity in granular media, the contact forces for all particles are statically determinate and forces can be computed without recourse to deformation equations or constitutive relationships. Given that stresses represent spatial averages of inter-particle forces, the stress-equilibrium equations for the isostatic state form a hyperbolic system of partial differential equations that describe the internal stress state using only boundary tractions. In this paper, we consider a Cosserat medium and propose closure relationships in terms of stresses and couple stresses from observations of stress variations in the critical state regime from discrete element simulations and experiments on sand, even though the isostatic condition is only satisfied in an average sense. It is shown that the governing equations are hyperbolic, which can be solved using the method of characteristics. Examples of both analytic and numerical solutions are presented. These examples clearly demonstrate that stress chains (characteristic lines) form oblique angles with the assumed direction of the force chains.     

A flow rule incorporating the fabric and non-coaxiality in granular materials

Deficiencies of constitutive models in prediction of dilatancy are often attributed to simplifications associated with flow rules such as assumptions of isotropy and coaxiality. It is thus proposed here to develop a comprehensive flow rule for granular materials by including the effect of fabric and without the assumption of coaxiality. A second-order tensor is introduced as a fabric for the distribution of contact normals and contact forces. By using the energy principle in micro-mechanical scale and a suitable dissipation mechanism in granular materials, a stress-dilatancy relation is obtained. Fabric plays a “bridge-like” role in the dilatancy and non-coaxiality. Non-coaxialities between stress-strain-fabric are attributed to the non-coaxiality between stress-fabric and strain-fabric. In this formulation the constants for modeling fabric depend on non-coaxiality of the system rather than the history that determines such a state. Ability of this stress-fabric-dilatancy for modeling the non-coaxiality shows that this relation can predict the behavior of granular materials in the presence of the rotation of principal stress axes.     

DEM simulations of stiff and soft materials with crushable particles: an application of expanded perlite as a soft granular material

The mechanical behavior of granular materials is largely affected by particle breakage. Physical and mechanical properties of granular materials, such as grain size distribution, deviatoric and volumetric behavior, compressibility and mobilized friction angle are affected by particle crushing. This paper focuses on the evolution of the above mentioned characteristics using the Discrete Element Method (DEM). Behaviors of stiff and soft materials are studied using well established crushing criteria. Results from simulations indicate that stiff materials, have a typical fractal distribution of particle size, which is dominant when confining pressure increases. The fractal characteristic parameter of grain size effect is discussed. Evolution of shear stresses and volumetric strains during shearing are also predicted and analyzed. Expanded perlite, selected as a soft material, is investigated in terms of shear and volumetric behavior. For perlite, triaxial compression tests and corresponding DEM simulations are also performed. Results show good agreement between experiments and simulations and support the fact that the DEM can be considered as a useful tool to predict the behavior of crushable granular materials.     

Discrete element method investigation on thermally-induced shakedown of granular materials

Temperature change, as a common kind of internal perturbation performed on granular materials, has a significant effect on the bulk properties of granular materials. However, few studies on thermally-induced shakedown under a long-term thermal cycling were reported. In this work, the discrete element method was used to give insight into the thermally-induced shakedown on the fabric and stress states within non-cohesive, frictional granular assemblies. Assemblies were submitted to thermal cycling at a stationary boundary condition after experiencing a one-dimensional compression. Evolution of coordination number, entropy and anisotropy was investigated as well as boundary forces and contact forces. At the same time, effects of the heating rate, the initial vertical load and the magnitude of temperature change were examined. It demonstrates that thermal cycling induces a significant force relaxation within granular materials, while the corresponding granular fabric has a small change. In addition, the entropy and anisotropy decreases with thermal cycling. Moreover, the initial vertical load can constrain the development of thermally-induced fabric change, thereby limiting force relaxation to some degree. Both high heating rate and larger magnitudes of temperature change contribute to more significant force relaxation. However, they cause smaller fabric changes even though they provide larger perturbations.     

碳纤维织物力学性能和冲压成形实验研究

在实际成形过程中,碳纤维复合材料往往处于复杂的应力状态,开展近于真实载荷环境下的力学试验分析,能够更准确地认识实际应用中材料的成形性能和变形机理.为获得碳纤维织物的基本力学特性,设计了平纹碳纤维织物拉伸试样及成形试样,进行了单轴拉伸、双轴拉伸、镜框剪切试验和方盒冲压成形实验研究,对比了不同双拉比及纱线取向对力学性能及成形性能的影响.研究结果表明:碳纤维织物具有高度的非线性、各向异性和双拉耦合特性,即经纬向纤维的力学性能会相互影响;剪切变形是成形过程中的主要变形模式,当剪切角达到临界锁死角时,织物发生起皱现象;同种织物不同纱线取向试样表现出不同的成形性能,因此可以根据零件几何形状选择合适纤维取向的织物,从而减少缺陷,优化成形零件的力学性能.研究结果为后续建立碳纤维织物本构模型和成形仿真奠定了基础.     

Grain-scale mechanics of geologic materials and lunar simulants under normal loading

A realistic characterization of contact behavior is crucially important to the development of discrete element models of naturally occurring granular media. Although contact behavior can be inferred by adjusting the numerical simulations to agree with results from geotechnical laboratory tests, it is preferable to establish the contact laws directly with grain-scale experiments. Moreover, such an approach provides an objective way to establish the influence of characteristics such as mineralogy, microstructure, hardness, grain size, shape and surface roughness on contact behavior, and thus opens the door to a more fundamental understanding of granular media mechanics. With this motivation, we are conducting an integrated experimental/DEM modeling program with a focus on naturally occurring geologic materials. The goals of this work are to improve the physical basis of this powerful numerical modeling method, and to develop a broader understanding of the contact behavior of naturally occurring materials of interest to the geotechnical engineering community. This paper describes equipment and methods that we have developed to conduct normal contact experiments on pairs of unbonded grains of crushed and ball-milled gneiss, Ottawa sand, and lunar simulants. Contact curvatures ranged from 0.05 to 8.2 mm for the grains examined. The computer-controlled testing system applied normal forces ranging up to 10 N, and both monotonically increasing (ramp) and cyclic loading waveforms were employed. A laser proximity gauge with 100 μm resolution provided direct grain-to-grain deformation readings. The resulting force–displacement relationships showed that Hertzian behavior emerged above a normal force threshold ranging from several tenths of a Newton to several Newtons, depending on surface roughness, and approximately linear behavior was observed below the threshold for Hertzian behavior. Normal contact stiffness ranged from 0.2 to over 2 MN m⁻¹ for forces up to 10 N, and depended on material type, local radius of curvature and surface roughness. Hysteresis was generally observed under cyclic loading and calculated values of the apparent internal friction ranged from 0.01 to 0.16, depending on material type, contact geometry and force level. The test system was capable of inducing damage in some contacts with a low radius of curvature, and it was observed that minor levels of damage typically increased stiffness and frictional loss of the contact. Engineer Research and Development Center U.S. Army Corps of Engineers.     

Macroscopic model with anisotropy based on micro–macro information

Physical experiments can characterize the elastic response of granular materials in terms of macroscopic state variables, namely volume (packing) fraction and stress, while the microstructure is not accessible and thus neglected. Here, by means of numerical simulations, we analyze dense, frictionless granular assemblies with the final goal to relate the elastic moduli to the fabric state, i.e., to microstructural averaged contact network features as contact number density and anisotropy. The particle samples are first isotropically compressed and then quasi-statically sheared under constant volume (undrained conditions). From various static, relaxed configurations at different shear strains, infinitesimal strain steps are applied to “measure” the effective elastic response; we quantify the strain needed so that no contact and structure rearrangements, i.e. plasticity, happen. Because of the anisotropy induced by shear, volumetric and deviatoric stresses and strains are cross-coupled via a single anisotropy modulus, which is proportional to the product of deviatoric fabric and bulk modulus (i.e., the isotropic fabric). Interestingly, the shear modulus of the material depends also on the actual deviatoric stress state, along with the contact configuration anisotropy. Finally, a constitutive model based on incremental evolution equations for stress and fabric is introduced. By using the previously measured dependence of the stiffness tensor (elastic moduli) on the microstructure, the theory is able to predict with good agreement the evolution of pressure, shear stress and deviatoric fabric (anisotropy) for an independent undrained cyclic shear test, including the response to reversal of strain.