Continuum modeling of mechanically-induced creep in dense granular materials

Recently, a new nonlocal granular rheology was successfully used to predict steady granular flows, including grain-size-dependent shear features, in a wide variety of flow configurations, including all variations of the split-bottom cell. A related problem in granular flow is that of mechanically-induced creep, in which shear deformation in one region of a granular medium fluidizes its entirety, including regions far from the sheared zone, effectively erasing the yield condition everywhere. This enables creep deformation when a force is applied in the nominally quiescent region through an intruder such as a cylindrical or spherical probe. We show that the nonlocal fluidity model is capable of capturing this phenomenology. Specifically, we explore creep of a circular intruder in a two-dimensional annular Couette cell and show that the model captures all salient features observed in experiments, including both the rate-independent nature of creep for sufficiently slow driving rates and the faster-than-linear increase in the creep speed with the force applied to the intruder

A finite element implementation of the nonlocal granular rheology

Inhomogeneous flows involving dense particulate media display clear size effects, in which the particle length scale has an important effect on flow fields. Hence, nonlocal constitutive relations must be used in order to predict these flows. Recently, a class of nonlocal fluidity models has been developed for emulsions and subsequently adapted to granular materials. These models have successfully provided a quantitative description of experimental flows in many different flow configurations. In this work, we present a finite element-based numerical approach for solving the nonlocal constitutive equations for granular materials, which involve an additional, non-standard nodal degree-of-freedom – the granular fluidity, which is a scalar state parameter describing the susceptibility of a granular element to flow. Our implementation is applied to three canonical inhomogeneous flow configurations: (1) linear shear with gravity, (2) annular shear flow without gravity, and (3) annular shear flow with gravity. We verify our implementation, demonstrate convergence, and show that our results are mesh independent.National Science Foundation (U.S.) (Grant NSF-CBET-1253228

Continuum modeling of size effects in dense granular flows: numerical solutions and comparison to experiments

Dense granular materials display complicated deformation phenomenology, which differentiate them from ordinary solids or fluids. For example, slowly flowing granular media form shear bands, which can have a variety of possible widths and which decay nontrivially into the surrounding quasi-rigid material. Furthermore, when a shear band exists at one point in a granular medium, creeping mechanical behavior is induced far outside the region of the shear band. Despite the ubiquity of granular flows, no model has been developed that captures or predicts these complexities, posing an obstacle in industry. We present a three-dimensional, continuum-level constitutive model and numerical simulation capability for well-developed, dense granular flows aimed at filling this need. The key ingredient of the theory is a grain-size-dependent nonlocal contribution, in which flow at a point is affected by both the local stress as well as the flow in neighboring material. With a single new material parameter, we show that the model is able to quantitatively predict experimental dense granular flows in an array of different geometries

Surface tension-driven shape-recovery of micro/nanometer-scale surface features in a Pt(57.5)Ni(5.3)Cu(14.7)P(22.5) 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, Pt57.5Ni5.3Cu14.7P22.5 [Pt subscript 57.5 Ni subscript 5.3 Cu subscript 14.7 P subscript 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 Pt57.5Ni5.3Cu14.7P22.5 [Pt subscript 57.5 Ni subscript 5.3 Cu subscript 14.7 P subscript 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 Pt57.5Ni5.3Cu14.7P22.5 [Pt subscript 57.5 Ni subscript 5.3 Cu subscript 14.7 P subscript 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.National Science Foundation (U.S.) (Grant CMS-0555614)Singapore-MIT Allianc

Continuum modeling of size-segregation and flow in dense, bidisperse granular media: Accounting for segregation driven by both pressure gradients and shear-strain-rate gradients

Dense mixtures of particles of varying size tend to segregate based on size during flow. Granular size-segregation plays an important role in many industrial and geophysical processes, but the development of coupled, continuum models capable of predicting the evolution of segregation dynamics and flow fields in dense granular media across different geometries has remained a longstanding challenge. One reason is because size-segregation stems from two driving forces: (1) pressure gradients and (2) shear-strain-rate gradients. Another reason is due to the challenge of integrating segregation models with rheological constitutive equations for dense granular flow. In this paper, we build upon our prior work, which combined a model for shear-strain-rate-gradient-driven segregation with a nonlocal continuum model for dense granular flow rheology, and append a model for pressure-gradient-driven segregation. We perform discrete element method (DEM) simulations of dense flow of bidisperse granular systems in two flow geometries, in which both segregation driving forces are present: namely, inclined plane flow and planar shear flow with gravity. Steady-state DEM data from inclined plane flow is used to determine the dimensionless material parameters in the pressure-gradient-driven segregation model for both spheres and disks. Then, predictions of the coupled, continuum model accounting for both driving forces are tested against DEM simulation results across different cases of both inclined plane flow and planar shear flow with gravity, while varying parameters such as the size of the flow geometry, the driving conditions of flow, and the initial conditions. Overall, we find that it is crucial to account for both driving forces to capture segregation dynamics in dense, bidisperse granular media across both flow geometries with a single set of parameters.Comment: 25 pages with 9 figure

A constitutive theory for the mechanical response of amorphous metals at high temperatures spanning the glass transition temperature : application to microscale thermoplastic forming of Zr₄₁.₂Ti₁₃.₈Cu₁₂.₅Ni₁₀Be₂₂.₅

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2008.Includes bibliographical references.Bulk metallic glasses (BMGs) are a promising emerging engineering material distinguished by their unique mechanical properties and amorphous microstructure. In recent years, an extremely promising microscale processing method for bulk metallic glasses, called thermoplasticforming has emerged. As with any emerging technology, the scientific basis for this process is at present fragmented and limited. As a result their is no generally agreed upon theory to model the large-deformation, elastic-visco-plastic response of amorphous metals in the temperature range relevant to thermoplastic-forming. What is needed is a unified constitutive framework that is capable of capturing the transition from a elastic-visco-plastic solid-like response below the glass transition to a Newtonian fluid-like response above the glass transition. We have developed a finite-deformation constitutive theory aimed to fill this need. The material parameters appearing in the theory have been determined to reproduce the experimentally measured stress-strain response of Zr₄₁.₂Ti₁₃.₈Cu₁₂.₅Ni₁₀Be₂₂.₅ (Vitreloy-1) in a strain rate range of [10-5, 10-1] s-1, and in a temperature range [593, 683] K, which spans the glass transition temperature [nu]9 = 623K of this material. We have implemented our theory in the finite element program ABAQUS/Explicit. The numerical simulation capability of the theory is demonstrated with simulations of micron-scale hot-embossing processes for the manufacture of micro-patterned surfaces.by David Lee Henann.S.M

Aspects of the mechanics of metallic glasses

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2011.Cataloged from PDF version of thesis.Includes bibliographical references (p. 131-139).Metallic glasses are amorphous materials that possess unique mechanical properties, such as high tensile strengths and good fracture toughnesses. Also, since they are amorphous, metallic glasses exhibit a glass transition, and at temperatures above this glass transition, they soften dramatically and are therefore amenable to net-shape thermoplastic forming processes. This combination of superior properties and the ability to precisely form complex geometries makes metallic glasses attractive materials for structural applications. This thesis addresses several issues related to the mechanics of these materials: " Metallic glasses are near-"ideal" isotropic materials. We have conducted numerical experiments - using molecular dynamics simulations - to develop a continuum-level isotropic elastic free energy that accounts for volumetric-deviatoric coupling effects under circumstances involving large volumetric strains. " We have developed a large-deformation, elastic-plastic constitutive theory for metallic glasses that incorporates a cavitation mechanism to describe the onset of "brittle" failure. Using this theory, we have conducted finite element simulations of fracture initiation at notch tips in a representative metallic glass under Mode-I, plane strain, small-scale-yielding conditions. We show that our theory predicts important experimentally-observed, fracture-related phenomena in metallic glasses. " We have developed a large-deformation, elastic-viscoplastic constitutive theory in a temperature range, which spans the glass transition of these materials. The numerical simulation capability based on the theory is used to determine appropriate processing parameters in order to carry out a successful micron-scale hot-embossing operation for the thermoplastic forming of a Zr-based metallic glass tool for the manufacture of polymeric microfluidic devices. * The numerical simulation capability is also used to study surface tension-driven shape recovery of a Pt-based metallic glass and quantitatively determine the surface tension of this material above the glass transition.by David Lee Henann.Ph.D

RECUPERAÇÃO DE CHUMBO SECUNDÁRIO A PARTIR DE ENSAIOS DE DESSULFURIZAÇÃO EM LABORATÓRIO

O processo mais utilizado na reciclagem das baterias chumbo-ácidas é o pirometalurgico, o qual polui o meio ambiente devido a liberação de dióxido de enxofre, além de formar alto teor de escória durante a recuperação do chumbo. O processo hidrometalúrgico é uma rota alternativa, que a partir de reações de dessulfurização, garante um processo de reciclagem mais sustentável, sem as desvantagens citadas no processo tradicional. Para testar as melhores condições de dessulfurização em laboratório, utilizou-se pasta residual de bateria automotiva de uma empresa de reciclagem, a pasta foi lavada até pH 8,2,  homogeneizada, filtrada para separação de plástico e fibras, e seca. Testou-se a reação a temperatura ambiente, 40 e 60ºC; 1, 2 e 3h de reação e carbonato de sódio 26,5; 53; 106 e 159 g/L, como agente dessulfurizante. A pasta original e a dessulfurizada foram fundidas, obtendo-se 65% de recuperação do chumbo para os dois casos e 51% a menos de escória quando realizada a dessulfurização. Concluiu-se que a temperatura de 40ºC propiciou um maior aumento na % de conversão em relação à temperatura ambiente, para todas as concentrações testadas. A melhor concentração de carbonato de sódio  foi 106 g/L.  Houve um incremento médio de 15% na dessulfurização, quando dobrou-se o tempo de reação de 1h para 2h, mas somente aumento de mais 4% com 3h de reação. Conclui-se que a dessulfurização com carbonato de sódio é viável, podendo ser realizada industrialmente, devendo-se otimizar o processo para redução do teor de escória formada e aumento da % de recuperação do chumbo