Computer simulation of morphology and packing behaviour of irregular particles, for predicting apparent powder densities

This paper describes a methodology for prediction of powder packing densities which employs a new approach, designated as random sphere construction (RSC), for modelling the shape of irregular particles such as those produced by water atomization of iron. The approach involves modelling an irregular particle as a sphere which incorporates smaller corner spheres located randomly at its surface. The RSC modelling technique has been combined with a previously developed particle packing algorithm (the random build algorithm), to provide a computer simulation of irregular particle packings. Analysis of the simulation output data has allowed relationships to be established between the particle modelling parameters employed by the RSC algorithm, and the density of the simulated packings. One such parameter is η, which is the number of corner spheres per particle. A relationship was established between η (which was found to have a profound influence on packing density), and the fractional density of the packing, fd. Vision system techniques were used to measure the irregularity of the simulated particles, and this was also related to η. These two relationships were then combined to provide a plot of fractional density for a simulated packing against irregularity of the simulated particles. A comparison was made of these simulated packing densities and observed particle packing densities for irregular particles, and a correlation coefficient of 0.96 was obtained. This relatively good correlation indicates that the models developed are able to realistically simulate packing densities for irregular particles. There are a considerable number of potential applications for such a model in powder metallurgy (PM), process control. In combination with on-line particle image analysis, the model could be used to automatically predict powder densities from particle morphology.     

Bond and interfacial properties of reinforcement in self-compacting concrete

This paper reports a study carried out to assess the impact of the use of self-compacting concrete (SCC) on bond and interfacial properties around steel reinforcement in practical concrete element. The pull-out tests were carried out to determine bond strength between reinforcing steel bar and concrete, and the depth-sensing nano-indentation technique was used to evaluate the elastic modulus and micro-strength of the interfacial transition zone (ITZ) around steel reinforcement. The bond and interfacial properties around deformed steel bars in different SCC mixes with strength grades of 35 MPa and 60 MPa (C35, C60) were examined together with those in conventional vibrated reference concrete with the same strength grades.The results showed that the maximum bond strength decreased when the diameter of the steel bar increased from 12 to 20 mm. The normalised bond strengths of the SCC mixes were found to be about 10–40% higher than those of the reference mixes for both bar diameters (12 and 20 mm). The study of the interfacial properties revealed that the elastic modulus and the micro-strength of the ITZ were lower on the bottom side of a horizontal steel bar than on the top side, particularly for the vibrated reference concrete. The difference of ITZ properties between top and bottom side of the horizontal steel bar appeared to be less pronounced for the SCC mixes than for the corresponding reference mixes.     

Effect of porosity on interfacial failure in steel-fibre-reinforced polymer-impregnated concrete

The interfacial bond between a steel fibre and concrete generally increases with the polymer content. Naphthalene used to generate new pores in order t increase the polymer loading and thus to increase the interfacial bond strength has a positive effect up to 3% by weight. Higher amounts weaken the cementitious phase and also decrease the amount of polymer incorporated. Drying of concrete before impregnation at 150°C rather than at 105°C increases the polymer loading and thus the interfacial bond strength. An increase in polymer loading without changing the original porosity, as in pressure or vacuum impregnation, increases the interfacial bond strength. Vacuum impregnation gives a higher interfacial bond strength than pressure impregnation. This could be due to the diffusion of monomer molecules into evacuated micro-pores. Thus, improved adhesion can be achieved between the polymer and the cemetiitious phase and steel fibre by means of vacuum impregnation.     

Aggregate packing and -void saturation in mortar and concrete proportioning

Proportioning was studied by measuring aggregate packing (C) and filling of aggregate void space (1?C) with varying volumes of cement paste (\(V_{\rm p}\)) or matrix (\(V_{\rm matrix}\)), i.e., all material <0.125 mm. Eleven widely different normal density aggregates with C = 0.57 to 0.71, i.e., aggregate void content (1?C) = 0.29 to 0.43, were used at constant w/c = 0.38 and flowing consistency and varying dosage of water reducer and paste- and matrix volume. Analysing plots of four excess phase volumes (paste with/without air, matrix with/without air) versus aggregate void space showed constant aggregate void saturation ratios. Both paste- and matrix-aggregate void saturation ratio can be used with the best estimate (\(V_{\rm p}-V_{\rm air})/{(1-C)}=1.15\) per \(\hbox{m}^{3}\). Including air voids in paste- or matrix volume improved correlation so air void content must be included in the normalized paste aggregate void saturation ratio (\(k=V_{\rm p}\)/[(1?C) \(V_{\rm tot}\)]). Simple measurements of aggregate packing are thus very useful. Cost per unit material, per unit fresh (slump, flow diameter) or hardened (compressive strength) property were used to show the cost efficiency of the mixes. The ranking of cost/MPa strength and cost/mm consistency is similar to ranking of total concrete cost for the 11 aggregates with a certain scatter though.     

DEM simulation of the packing of cylindrical particles

Granular Matter - Frustration arises for a broad class of physical systems where confinement (geometric) or the presence of a perturbation (kinematic) prevents equilibration to a minimum energy...     

Finite element simulation of interfacial segregation in dilute alloys

The finite element software Comsol is used to simulate surface or grain boundary segregation in dilute alloys. The model computes simultaneously the evolution of interfacial concentration and diffusion in the bulk. The solute exchange between bulk and interface is governed by Darken’s equation. The model is able to reproduce thermodynamic and kinetic aspects of the phenomenon, in particular the saturation segregation level and the short-time segregation kinetics expressed by the McLean approximation. It is also able to reproduce experimental trends in the case of surface segregation of sulphur in a Ni superalloy. In the case of the grain boundary segregation of impurities (P or S) in engineering alloys, the present approach provides a practical tool, as it can be coupled to other finite element simulations (heat transfer and/or mechanics). Thus, it becomes possible to predict the risk of synergetic segregation and thermomechanical damage during service or processing (forging, welding,...).     

Computer simulation-based method to predict packing density of aggregates mixture

A key theory in concrete mix design is maximizing aggregate packing density (PD) of aggregate mixture. Different methods have been presented by researchers to estimate PD of aggregate mixture. One such method is computer simulation that has become increasingly common over the last decade; however, it is usually a time-consuming procedure. In the current study, a method based on computer simulation is proposed for estimating aggregate PD. In this method, aggregates with specific shapes, grading and PDs are substituted by monosized spherical aggregates. An equation is also presented for determining the diameter of equivalent monosized aggregates. The coefficient of friction between the equivalent monosized aggregates is determined in a way that the monosized aggregates will have a PD equal to that of actual aggregates. The proposed method is also used to simulate laboratory experiments conducted by the present authors and other researchers. Comparisons reveal the high accuracy of the proposed simple method in predicting the PD of aggregate mixtures.     

Numerical simulation of quasibrittle fracture in concrete

A triangular unit, constructed from constant strain triangles with nodes along its sides and not at the vertex, is developed for the simulation of fracture in quasibrittle materials. Fracture is modelled through a constitutive softening-fracture law at the interface nodes, with the material within the triangular unit remaining linear elastic. The inelastic displacement at an interface node represents the crack opening, which is related to the conjugate inter-nodal force by the appropriate softening relationship. The path-dependent softening behaviour is solved in nonholonomic rate form within a quasiprescribed displacement formulation. At each event in the loading history, all equilibrium solutions for the prescribed mesh can be established and the critical equilibrium path with the minimum increment of external work adopted. The crack profile or trajectory is restricted in that it can only follow the interface boundaries of the defined mesh. No remeshing is carried out. Solutions to the nonholonomic rate formulation are obtained using a mathematical programming procedure based on the solution of an LCP. Several examples are given and compared, where possible, with published results. The advantage of this formulation is that branching and interacting cracks can be tracked subject to the limitations of the prescribed mesh.     

Properties of interfacial transition zones in recycled aggregate concrete tested by nanoindentation

The properties of new Interfacial Transition Zone (ITZ) and old ITZ in Recycled Aggregate Concrete (RAC) were investigated by Atomic Force Microscopy (AFM), Scanning Electron Microscopy (SEM) and nanoindentation. From the SEM images, obvious voids and high concentration of calcium hydroxide can be found in both old ITZ and new ITZ in RAC. Based on the nanoindentation study, it is indicated that the thicknesses of old and new ITZs are in the range 40–50 μm and in the range 55–65 μm, respectively. It is also found that the average indentation modulus of old ITZ is 70–80% of that of old paste matrix, while the average indentation modulus of new ITZ is 80–90% of that of new paste matrix. Additionally, the influences of mix proportion, aggregate types and hydration age on the properties of ITZs in RAC are discussed in this study.     

Computer simulation of serrated yielding

A model for serrated yielding based on the negative resistance characteristics of materials is discussed. An analog computer based on this model is described. The simulated curves show oscillations which are regular and uniform in amplitude. To simulate more realistic tensile test curves, a refined model which includes the effects of fluctuations in dislocation density and velocity is described. Some simulated curves using this refined model are presented. These results are close to observed tensile test curves.     

Computer simulation of iceberg instability

The possibility of an iceberg rolling to an orientation of deeper draft and colliding with the sea-bed has important implications for the offshore oil and gas industry on the Grand Banks of Newfoundland. In this paper that possibility is given substance. An interactive computer program was used to study a class of icebergs that increase their draft by as much as 50% on being perturbed from a position of near unstable equilibrium.     

Computer simulation of martensitic textures

We consider a Ginzburg-Landau model free energy F(ε, e₁, e₂) for a (2D) martensitic transition, that provides a unified understanding of varied twin/tweed textures. Here F is a triple well potential in the rectangular strain (ε) order parameter and quadratic e₁², e₂² in the compressional and shear strains, respectively. Random compositional fluctuations η(r) (e.g. in an alloy) are gradient-coupled to ε, ˜ − ∑_rε(r)[(Δ_x² − Δ_y²)η(r)] in a “local-stress” model. We find that the compatibility condition (linking tensor components ε(r) and e₁(r), e₂(r)), together with local variations such as interfaces or η(r) fluctuations, can drive the formation of global elastic textures, through long-range and anisotropic effective ε-ε interactions. We have carried out extensive relaxational computer simulations using the time-dependent Ginzburg-Landau (TDGL) equation that supports our analytic work and shows the spontaneous formation of parallel twins, and chequer-board tweed. The observed microstructure in NiAl and Fe_xPd_{1 − x} alloys can be explained on the basis of our analysis and simulations.     

Computer simulation of tensile testing

A brief overview of the molecular dynamics method, with emphasis on the work of Parrinello and Rahman, is presented. Molecular dynamics is a method for studying classical statistical mechanics of well-defined systems through a numerical solution of Newton’s equations. A set ofN particles with coordinatesr _i (i=1, …,N) and confined in a cell are allowed to interact through a potential. The bulk is usually simulated by periodically repeating the cell in space. Newton’s equations are then solved numerically and the statistical averages of dynamical properties are calculated as temporal averages over the trajectory of the phase space. This method has already been used to simulate a liquid. Now, based on a Lagrangian formulation, it is possible to study systems under the most general conditions of externally applied stress. Unlike the earlier calculations, in this procedure, shape and size are governed by equations of motion obtained from the Lagrangian. Thus it allows us to study structural transformations which may be brought about by an interplay of external and internal stresses. By applying this technique to a single crystal of Ni, Parrinello and Rahman observe that the stress-strain relations obtained confirm with reported results. Under compressive loading it is found that Ni shows a bifurcation in its stress-strain relation and the system changes from cubic to hexagonal close packing. Such a transformation could perhaps be observed under extreme conditions of shock. Finally the scope of computer simulation is highlighted and the limitations of employing such a method are pointed out. only summary of the talk     

Computer simulation of pressure sintering

The densification process during pressure sintering has been analyzed using finite element analysis. This analysis uses an iterative solution algorithm. With this the densification process in complex geometries with complex boundary conditions can be analyzed and this technique is particularly suited for tackling material nonlinearity. Evolution of dense structures with gradual closure of pores is described for two typical geometries.     

Computer simulation of liquid zinc

An embedded atom model potential for zinc has been developed, which makes it possible to calculate liquid zinc properties both under normal pressure and in strongly compressed states using the molecular dynamics method. In order to calculate the potential, the data on density, energy, and compressibility of liquid zinc and the data on shock compression of zinc were used. Pair contribution to the potential and the embedding potential are represented by analytical functions. Liquid zinc properties are calculated at temperatures up to 1500 K. The values of energy, bulk compression modulus, and self-diffusion coefficient, as well as pair correlation functions at T < 1000 K, agree well with the experiment. The electron contribution to the thermal capacity at those temperatures is not high. Zinc models are constructed for densities up to 15.86 g/cm³ and pressures up to 773 GPa. Zinc models melt in the case of shock compression at compression rates of V/V ₀ < 0.7 and temperatures above 1900 K. A significant contribution of electron excitation energy to the zinc energy is observed at temperatures above 20000 K. The estimated average surplus thermal capacity of electrons at 30000–50000 K is ∼12 J/mole K. Discrepancies between the molecular dynamic calculation and the Gruneisen model at low temperatures are relatively low; however, they rise as temperature increases. A series of zinc nanocluster models with magic sizes of 55 and 147 atoms is constructed. The clusters have an amorphous structure with slightly lower energy than that of icosahedral or cuboctahedral configuration, after cooling from 600 to 10 K. The surface energy of zinc at T = 0 calculated based on the dependence of energy of clusters on size is 1.3 J/m².     

Computer simulation of bias recording

The technique of AC bias recording is explained by a newly developed theoretical approach. It is demonstrated that the model can explain the physical background of the linearization of the remanence curve and be used to determine the dependence of the maximum output level (MOL) on various technical and media parameters. The merits and drawbacks of changes in the different media data are evaluated quantitatively by computer simulation. All theoretical results are compared with corresponding experimental data and thus verified