Dilatant double shearing theory applied to granular chute flow

Summary Although the steady flow of a granular material down a plane inclined slope has been exhaustively examined from both theoretical and experimental points of view, there is still no general agreement concerning the basic flow properties such as density and velocity profiles. The majority of studies assume that the velocity component of the material perpendicular to the inclined plane is sufficiently small to assume that it is everywhere zero. However, recent dynamical modelling of granular chute flow indicates that this component of velocity, although small, is actually non-zero. In this paper, we examine a dilatant double shearing theory for chute flow assuming that the perpendicular component of velocity is non-zero. An explicit analytical form for the perpendicular velocity profile is deduced which gives rise to an integral expression for the chute stream velocity. Assuming a linear decreasing density profile, numerical integration for the chute stream velocity predicts a non-linear profile which is concave in shape and which is in agreement with recent results from computer simulation and existing experimental data in the literature.     

Modeling plastic deformation and fracture of porous materials

Strain hardening of a porous material was numerically modeled. The corresponding stress-strain (σ-ε) curves, the ultimate strength, and the strain at break were calculated for iron with a relative porosity in the interval from 0 to 30%. Anomalous behavior of these characteristics is observed at a porosity corresponding to the percolation transition from isolated pores to the “infinite” pore cluster. The proposed model adequately describes the available experimental data.     

An entropy model for shear deformation of granular materials

A statistical mechanical analogy for characterization of granular materials is discussed by using such notions as the state of the material, the density of states, entropy, canonical distribution and the partition function. The transition law of states during shear deformations of the material is microscopically investigated in the case of two-dimensional model granular materials. The assumption of entropy growth is shown to characterize the dilatancy of the material. A rough proof is given by assuming the measure preserving property of the transition and showing its ergodicity.     

Multiscale constitutive modeling for plastic deformation of nanocrystalline materials

Macroscopic and microscopic constitutive modeling that can display large plastic deformation with shear band were presented for nanocrystalline materials subjected to uniaxial load over a wide strain rate range. The macroscopic model implemented with parameters microscopic meaning was established based on the theory of plastic dissipation energy. The microscopic model based on deformation mechanisms was composed of two parts: hardening and softening stages. In the hardening stage, the phase mixture model was used and a shear band deformation mechanism was proposed in the softening stage. Numerical simulations shown that the predications were in good agreement with experimental data. Finally, a parameter of normalized softening rate was proposed and its characteristics were evaluated quantitatively. It can be concluded that the failure strain could be prolonged when the normalized softening rate decrease through changing the softening path.     

Moisture influence on the resilient deformation behaviour of unbound granular materials

The influence of moisture on the resilient deformation properties of unbound granular materials was investigated based on repeated load triaxial tests. Results showed that the resilient modulus (M_R) decreased with increasing moisture for a relatively low number of load cycles (N) where the deformation behaviour was mostly resilient with a negligible amount of associated accumulated permanent deformation (PD). Modelling attempts on this behaviour were quite satisfactory. Furthermore, the M_R showed an increasing trend with increasing moisture, up to the optimum, when the N was relatively large with a significant amount of accumulated PD. Above the optimum, the M_R generally decreased. Further investigation suggested that moisture aided the post-compaction (PC) and possible particle rearrangement that resulted in the increased PD and increased M_R. The existing model did not work in this case indicating that the effect of PC on M_R should be considered in modelling.     

Tribological properties of ultrafine-grained materials processed by severe plastic deformation

Processing by severe plastic deformation (SPD) has been developed extensively over the last two decades in order to produce ultrafine-grained (UFG) materials having submicrometre or nanometre grain sizes. An important material property for UFG materials is good wear resistance so that they may be used in a range of structural applications. An examination of the published data shows that only limited reports are available to date on the wear behaviour of SPD-processed materials and, furthermore, many of these results appear to be conflicting. The correlation of hardness and wear is limited because the wear property is a system property that in practice is influenced by a range of factors. Accordingly, this review is designed to examine recent reports related to the wear resistance of materials processed by SPD with particular emphasis on alloys processed using equal-channel angular pressing (ECAP), high-pressure torsion (HPT) and accumulative roll-bonding (ARB).     

Plastic deformation behaviour of pavement granular materials under low traffic loading

This paper analyses the permanent deformation performance of an unbound granular material for base layers of low traffic roads. The material has been subjected to repeated triaxial loads. Three models were fitted to express the cumulative permanent strain as a function of the number of load cycles. In general, the predictions of two models previously studied by other researchers proved to be good but in the long-term, they tended to underestimate the measured values. In contrast, a third new model-the sum of two well known models-offered excellent predictions, which in the long term did not tend to either underestimate or overestimate the measured values. The granular material did not give satisfactory results to be used in low traffic volume road pavements.     

A large deformation breakage model of granular materials including porosity and inelastic distortional deformation rate

A general constitutive model of crushable granular materials is developed within the context of large deformations. The time evolution equations for breakage, inelastic porous compaction and dilation, and distortional deformations are coupled by a yield surface and restrictions are imposed to ensure that these inelastic processes are dissipative. Some of the most salient mechanisms of such materials are described, including: (1) stiffness dependent on the breakage (a variable index of grading), porosity, and pressure; (2) critical comminution pressure and isotropic hardening, also dependent on the breakage and porosity; (3) jamming transition between solid and gaseous states; (4) a dilation law that embodies competition between porous compaction (due to the rate of breakage) and bulking (porous dilation at positive pressure due to the rate of inelastic distortional deformation); and finally, (5) the non-unique critical state relation between stress and porosity, in terms of the loading history and grading changes.     

Simple shear deformation of rate type plastic materials with combined work-hardening

The simple shear deformations of the rate type plastic materials are theoretically analyzed and numerically calculated. The materials are endowed with the combined work-hardening which is analytically represented by a scalar and a tensor internal state variable. Two types of materials are treated, that is, the Prandtl-Reuss material with a generalized Huber-von Mises yield condition and the $\text{T}$ material with a generalized Tresca yield condition. The numerically evaluated loading-unloading phenomena of the materials are very similar with those of actual metal or plastics.     

Severe plastic deformation (SPD) and nanostructured materials by machining

Large plastic strains between 1 and 15 can be imposed in chips formed by plane-strain (2-D) machining of metals and alloys. This approach has been used to examine microstructure changes induced by large strain deformation in model systems—copper and its alloys, precipitation-hardenable aluminum alloys, high-strength materials such as titanium, Inconel 718 and 52100 steel, and an amorphous alloy. It is shown that materials with average grain sizes in the range of 60 nm–1 μm can be created by varying the parameters of machining, which in turn affects the deformation processes. Furthermore, a switch-over from an elongated subgrain microstructure to an equi-axed nanocrystalline microstructure, with a preponderance of large-angle grain boundaries, has been demonstrated at the higher levels of strain in several of these materials. This switch-over can be readily controlled by varying the deformation conditions. Dynamic recrystallization has been demonstrated in select material systems under particular conditions of strain and temperature. This study may be seen as providing an important bridge between furthering the understanding of microstructural refinement by large strain deformation and the practical utilization of nanostructured materials in structural and mechanical applications. Conventional plane-strain machining has been shown to be a viable SPD method for examining the underlying processes of very large strain deformation.     

The processing of ultrafine-grained materials through the application of severe plastic deformation

The application of severe plastic deformation (SPD) to bulk metals provides the opportunity of achieving grain sizes in the submicrometer and nanometer range. Several different SPD processing techniques are now available including Equal-Channel Angular Pressing (ECAP), High-Pressure Torsion (HPT) and Accumulative Roll-Bonding (ARB). This paper examines the principles of grain refinement using ECAP and gives examples of the advantageous properties that may be achieved including increased strength at ambient temperatures and a superplastic forming capability at elevated temperatures. Invited paper presented in Symposium C at 5th Brazilian MRS Meeting, Florianópolis, Brazil.     

The effects of plastic deformation on stress wave propagation in multi-layer materials

The behavior of a multi-layer material at high strain rate and the effect of plastic deformation on stress wave propagation were investigated by a combination of experimental and numerical techniques. Plastic deformation effects were studied in multi-layer materials consisting of ceramic, copper and aluminum subjected to large strains under high strain rate loading. First, stress wave propagation behavior for the monolithic metals was studied, and then extended to multilayer combinations of these metals with each other and with a ceramic layer. The axial stress distributions were found to be non-uniform in the elastic deformation range of the specimen. The degree of non-uniformity was much more pronounced in the multi-layer samples consisting of different materials. The presence of a ceramic layer increased the magnitudes of stress gradients at the interfaces. It was also found that a major effect of plastic deformation is a tendency to produce a more homogeneous stress distribution within the components. The implications of these observations for practical systems are discussed.     

Local migration of grain boundaries in polycrystalline materials under plastic deformation conditions

We propose a theoretical model describing the local migration of grain boundaries (GBs) near triple junctions according to the new mechanism stimulated by the GB slip. Within the framework of this model, a driving force for the local migration is due to the interaction between sliding and structural GB dislocations responsible for the GB slip and misorientation, respectively.     

Localised deformation patterning in 2D granular materials revealed by digital image correlation

Tests have been performed on an analogue two-dimensional granular material in a special laboratory apparatus that allows the application of general stress or strain conditions. Digital image correlation of pairs of consecutive photographs taken during the tests has enabled fields of displacement and hence strain to be determined. Thus direct observation of internal displacements and strains has been possible for a series of general strain increments with different orientations of principal strain and different imposed angles of dilation. This analysis has successfully provided clear evidence of evolving internal structures of deformation. The observed evolving structures consist of bands of localised deformation and ‘cells’ of low deformation between the bands. The orientations of the identified localised features and cells are seen to depend on the applied strain path. The characteristic features and dimensions of the bands have been approximately identified.     

Creep of granular materials

This paper examines the creep of brittle granular materials subjected to one-dimensional compression. One-dimensional creep tests were performed on aggregates of brittle pasta and compared with the behaviour of sand at much higher stress levels. It was found that for both materials, creep strain is proportional to the logarithm of time. One possible mechanism for creep is particle crushing. However, it is usually difficult to measure changes in the particle size distribution during creep because the fines produced are so small, and the mass of fines is too small to measure accurately unless creep is permitted for a very long time. However, for pasta, the particle fragments produced are large, and it is found that particle crushing does occur during creep for 24 hours. This is consistent with the proposition that the behaviour of all brittle granular materials is essentially the same. A micro mechanical argument is then summarised which predicts that creep strain should be proportional to log time.     

Mixtures of granular materials

Balance laws are given for a mixture of granular materials of a type described by Goodman and Cowin. Constitutive equations are given for the case of two dry granular constituents, and consequences of the entropy principle are found.     

On the effects of plastic rotation in the finite deformation of anisotropic elastoplastic materials

Using the notions of intermediate configuration firstly introduced by Eckart (1948) and of vector directors due to E. and F. Cosserat (1909), we obtain constitutive equations for an anisotropic solid subject to finite strains. This study closely follows Mandel's ideas (1971, 1982) although it differs in presentation and in the way of deriving the final equations. In a second part we establish the form of constitutive equations for some particular anisotropic materials by applying representation theorems. As an application, we show that the introduction of plastically induced rotations suppresses oscillations of Cauchy stress for a material with kinematic hardening submitted to simple shear test: in fact our method consists in defining a new stress rate which is physically motivated. It provides an alternative to the more phenomenological approach of Nagtegaal and de Jong (1980/1982). Furthermore, in contrast to other recent methods, it can be applied to a wide range of anisotropic materials.