Study of cold powder compaction by using the discrete element method

The discrete element method (DEM), based on a soft-sphere approach, is commonly used to simulate powder compaction. With these simulations a new macroscopic constitutive relation can be formulated. It is able to de-scribe accurately the constitutive material of powders during the cold compaction process. However, the force-law used in the classical DEM formulation does not reproduce correctly the stress evolution during the high density compaction of powder. To overcome this limitation at a relative density of about 0.85, the high density model is used. This contact model can reproduce incompressibility effects in granular media by implementing the local solid fraction into the DEM software, using Voronoi cells. The first DEM simulations using the open-source YADE software show a fairly good agreement with the multi-particle finite element simulations and experimental results.     

Compaction of aggregated ceramic powders: From contact laws to fracture and yield surfaces

This work describes a methodology based on Discrete Element Method (DEM) simulations to generate yield and fracture surfaces for aggregated ceramic powders. The DEM simulations, which consider the length scale of porous aggregates, are used as numerical triaxial experiments to obtain the behavior of a small volume element of powder under a given load. The experimental identification procedure, which relies on the Design Of Experiment method, is designed to limit the number of experiments and simulations needed to obtain the model material parameters. These material parameters, which model the interactions between aggregates in the DEM simulations are identified using two simple experiments on a Uranium diOxide powder: closed-die compaction and diametrical compression test. The yield and fracture surfaces obtained from the DEM simulations provide valuable information on the behavior of the powder for stress states that are difficult or impossible to attain in complex triaxial tests.     

Bulk density of solid polymer resins as a function of temperature and pressure

In a plasticating extruder, solid polymers are heated and are subjected to high pressures before they are melted and delivered to a die. In both the solids conveying and melting sections, these temperature and pressure increases will compact the unmelted polymer bed as it moves down the screw channel. Performance of the extruder depends in part on how well the screw design matches the compaction behavior of the resin for a given set of process conditions. The design of these screw sections, however, is often done based on past experience and with little knowledge of the resin compaction behavior. A much improved design would include screw performance prediction using variable bulk density and computer simulations. Computer simulations, however, are often performed using constant solid bulk density because of the lack of reliable density data as a function of both pressure and temperature. An instrument was developed for studying the compaction behavior of pellet and powder resins. Bulk densities and storage friction coefficients are reported for several important thermoplastic resins as a function of temperature and pressure. The bulk density data were fitted to a semi-empirical model.     

Wall friction in the compaction of pharmaceutical powders: measurement and effect on the density distribution

In this paper, the axial density profile of tablets of microcrystalline cellulose (MCC) powder compacted in nonlubricated die is investigated by finite element modelling (FEM). The Drucker-Prager/Cap model was adopted for the compaction behavior of powder. The material parameters of the model, including the die wall friction coefficient, were estimated from experimental data of die compaction where the initial density of powder is taken uniform. Changes of Young's modulus with density was measured with a four-point beam bending test. The results of the simulation of the compression and the decompression steps were used to calculate the axial density distribution. Comparison with the measured data presented in [A. Michrafy, M.S. Kadiri, J.A.D. Dodds, Wall friction and its effects on the density distri-bution in the compaction of pharmaceutical excipients, Chem. Eng. Research and Design, Vol. 81, Part A, September (2003)] is discussed.     

Bubble dynamics in a 3‐D gas–solid fluidized bed using ultrafast electron beam X‐ray tomography and two‐fluid model

Bubble characteristics in a three‐dimension gas‐fluidized bed (FB) have been measured using noninvasive ultrafast electron beam X‐ray tomography. The measurements are compared with predictions by a two‐fluid model (TFM) based on kinetic theory of granular flow. The effect of bed material (glass, alumina, and low linear density polyethylene (LLDPE), d_p ～1 mm), inlet gas velocity, and initial particle bed height on the bubble behavior is investigated in a cylindrical column of 0.1‐m diameter. The bubble rise velocity is determined by cross correlation of images from dual horizontal planes. The bubble characteristics depend highly upon the particle collisional properties. The bubble sizes obtained from experiments and simulations show good agreement. The LLDPE particles show high gas hold‐up and higher bubble rise velocity than predicted on basis of literature correlations. The bed expansion is relatively high for LLDPE particles. The X‐ray tomography and TFM results provide in‐depth understanding of bubble behavior in FBs containing different granular material types. © 2014 American Institute of Chemical Engineers AIChE J, 60: 1632–1644, 2014     

Densification behavior of nanocrystalline titania powder under cold compaction

Densification behavior of nanocrystalline titania powder was investigated under cold compaction. Experimental data were obtained from triaxial compression with various loading conditions. Lee and Kim proposed the Cap model by employing the parameters involved in the yield function of sintered metal powder and volumetric strain evolution under cold isostatic pressing. The parameters in the Drucker/Prager Cap model and the proposed Cap model were obtained from experimental data under triaxial compression. Finite element results from the models were compared with experimental data for densification behavior of nanocrystalline ceramic powder under cold isostatic pressing and die compaction. The proposed model and the Drucker/Prager Cap model agreed well with experimental data under cold compaction. Finite element results and experimental data also, show that relative density distribution of nanocrystalline ceramic powder compacts is nonuniform compared to the conventional micron powder compacts at the same averaged relative density.     

Compaction behavior of Al6061 powder in the semi-solid state

Semi-solid powder processing involves compaction of metallic alloy powders in temperature ranges when both solid and liquid phases coexist. However, modeling of such process has been very scarce. In this study, compaction behavior of Al6061 powder in the presence of liquid phase was investigated. The relationship between compaction pressure and relative density of powder in the semi-solid state was modeled and verified against experimental measurements. The results showed that the powder compaction behavior can be accurately predicted by Shima-Oyane model when the liquid fraction was below 20%. In this range, all the normalized pressure-relative density curves merged into one, which could be expressed in a simple exponential form. When the liquid fraction was higher than 20%, the model failed to predict the compaction behavior because of the non-uniform distribution of the liquid phase. Squeezing-out of the liquid phase and interlocking of the irregular solid phase were speculated to occur during the compaction process.     

Analysis of pharmaceutical powder compaction using multiplicative hyperelasto-plastic theory

Single-ended compaction of lactose powder is investigated numerically within the framework of multiplicative hyperelasto-plastic theory. In keeping with previous work in the pharmaceutical field, a slightly modified Drucker-Prager Cap model is described and used in the simulations. Coulomb friction is included on all interfaces. Our results indicate that simulations of this type may be useful not only to determine density and stress distributions within tablets, as has been done hitherto, but also may provide indications of circumstances under which the tableting operation fails due to capping.     

Experimental calibration of density-dependent modified Drucker-Prager/Cap model using an instrumented cubic die for powder compact

Theory and experimental calibration of density dependent modified Drucker-Prager/Cap (DPC) model are presented by using a novel instrumented cubic die in powder compaction tests. The cubic die is designed for directly determining the loading and unloading forces and displacements of powder compact inside the die in compaction and transverse directions without any additional calibration. The cap surface parameters and elastic properties are characterized by fitting stress and strain curves recorded during loading and unloading at different green density values and the plastic material parameters for failure surface are obtained by additional radial and axial compressive tests. The experimental data is subsequently used in the simulation of cubic die compaction to verify the results from the density dependent modified DPC model.     

Elastoplastic coupling to model cold ceramic powder compaction

The simulation of industrial processes involving cold compaction of powders allows for the optimization of the production of both traditional and advanced ceramics. The capabilities of a constitutive model previously proposed by the authors are explored to simulate simple forming processes, both in the small and in the large strain formulation. The model is based on the concept of elastoplastic coupling – providing a relation between density changes and variation of elastic properties – and has been tailored to describe the transition between a granular ceramic powder and a dense green body. Finite element simulations have been compared with experiments on an alumina ready-to-press powder and an aluminum silicate spray-dried granulate. The simulations show that it is possible to take into account friction at the die wall and to predict the state of residual stress, density distribution and elastic properties in the green body at the end of the forming process.     

Roll compaction of maize powder

This paper presents a study of a roll compaction process as a dry granulation method for typical food materials such as maize powder. This process is widely applied in industry as it can continuously produce large quantities of granular product at comparatively low cost. The objectives of this work were to predict the roll compaction performance from a simple measurement involving uniaxial die compaction using the classical Johanson model. This involved determination of the optimum operating conditions for the production of granules as evaluated by apparent density.In the current work, a smooth counter-rotating rolling mill with a roller diameter of 0.08 m and a roller width of 0.20 m was used. The operating conditions for the rolling mill are shown to be influenced by parameters such as the roll gap, the roll speed, the feed powder amount, and the friction ratio. Material properties such as the compressibility factor and the angle of wall friction were investigated using uniaxial die compaction. The angle of wall friction was analysed using both contact mechanical and continuum mechanical approaches.The results indicated that this simplified approach can be used to provide a quantitative prediction of the extent of the roll compaction performance, and can be used to design optimal roller geometries and operating conditions.     

High-pressure compaction modelling of calcite (CaCO3) powder compact

Numerical simulation of manufacturing processes with working conditions at high pressure (above 1 GPa) requires constitutive data of the powder for the whole range of pressure and density. Most of the test apparatuses commonly used to obtain such data are only working in the lower pressure regions. Because of the absence of high-pressure data, many parameters have to be guessed or extrapolated. A material used in high-pressure applications is Calcite (CaCO₃). The material can be used as an insulator in high-pressure capsules it is also a common material in the earth core. An apparatus often used to generate high pressure during compaction is the Bridgman anvil apparatus. In this work experimental tests with a Bridgman anvil set-up using Calcite powder discs with different thicknesses were done. A nonlinear elastic-plastic cap model was developed to model the behaviour of powder material from low pressure and loose state to high pressure and solid state. The constitutive model was implemented in a finite element code. The constitutive data were identified by optimization of experimental data. Validation was done by numerically reproduce the mechanical behaviour of uni-axially pressing Calcite to different pressure (up to 5 GPa) including unloading. The load-displacement curves, density distribution and the surface displacement were measured and compared to the finite element results. The results of the compaction simulations agree reasonably well with the experimental results.     

The effect of processing parameters on pharmaceutical tablet properties

The preferred drug delivery system today is represented by tablets, which are manufactured using high speed rotary presses where the powder material is compressed in a die between rigid punches. Compression represents one of the most important unit operations because the shape, strength and other important properties of the tablets are determined at this time. These properties are dictated not only by the characteristics of the powder constituents (which are determined by the properties of the constituents, mixing and granulation), but also by the selection of process parameters imposed by production machinery. This paper focuses on the die fill and the compaction parameters.Die fill on high speed rotary tablet production presses is a complex phenomenon. On most presses the powder is deposited into the die under the effect of the gravity. Die fill is facilitated by the paddle wheels operating in the feed frame and the suction effect, whereby the lower punch is withdrawn while the die opening is exposed to powder in the feed frame. An experimental shoe-die system was developed to examine the effect of the contributing factors. High speed video observations enabled a detailed examination of the die fill process. The flowability of powders was quantified using the concept of critical velocity. It was illustrated that a detailed understanding of die fill could contribute to the design of feed frames as well as optimisation of press parameters in order to ensure consistent and efficient die fill, thus maximising the productivity of the presses.The compaction parameters are discussed with reference to tablet strength. Results generated using a compaction simulator as well as a number of rotary tablet presses are presented for a range of pharmaceutical excipients and placebo formulations.As a result of combined interactions between the material behaviour during compaction, powder-die wall friction and process parameters during die fill and compaction, the resulting tablets are in general non-homogeneous. X-ray computed tomography is employed to characterise the internal density distribution in tablets. The effect of tablet structure on friability, erosion and disintegration behaviour is examined.     

A rate-dependent constitutive model for brittle granular materials based on breakage mechanics

Modeling the rate-dependent mechanical behavior of brittle granular materials is of interest to defense applications, civil and mining engineering, geology, and geophysics. In particular, granulated ceramics in armor systems play a significant role in the overall dynamic material response of ceramics, particularly in their penetration resistance. This paper presents a rate-dependent constitutive model for brittle granular materials based on a recent reformulation of breakage mechanics theory. The rate-dependency is introduced via the overstress theory of viscoplasticity. The proposed formulation incorporates the effects of relative density and particle grading on strength and porous compaction/dilation, and is capable of tracking their evolution. The model is devised with internal variables linked to underlying dissipative micromechanisms including configurational reorganization, particle breakage and frictional dissipation. A strategy for calibrating model parameters and required experiments are described. The impact of loading rate on shear strength and grading evolution are explored through a sensitivity analysis. The presented model is capable of capturing several key features of the experimentally observed behavior of brittle granular materials including stress-, rate- and density-dependent stress-strain and volume change responses, the competition between dilation and breakage-induced compaction, the evolving particle grading due to particle breakage, and the evolution toward a critical (steady) state under shearing. A possible application of this micromechanics-inspired modeling framework involves integrating it into rate-dependent models for ceramics to assist in improving the impact performance of next-generation ceramics.     

A study on the sensitivity of Drucker-Prager Cap model parameters during the decompression phase of powder compaction simulations

The compaction of pharmaceutical powders can be simulated using phenomenological elasto-plastic continuum models adopted from soil mechanics. These models are typically implemented in finite element codes and have been used recently to investigate the macroscopic property distributions in powders during compaction.The present study demonstrates the importance of obtaining accurate yield surface parameters for use in such models. A commercial finite element code implementing the Drucker-Prager Cap (DPC) model was used to model the compression and decompression stages of powder compaction in a tabletting operation. The parameters used in the DPC model were obtained from the literature. Although the compression stage of the process gave expected behavior, the decompression response was unrealistic for at least one set of published data. Small values for the friction and cohesion parameters resulted in a significant elastic recovery during decompression. This study demonstrates the need to obtain accurate parameter data in order to model the decompression stage of powder compaction.     

Experimental characterization of CaCO3 powder for use in compressible gaskets up to ultra-high pressure

High Pressure High Temperature (HPHT) equipment is used for commercially produce synthetic diamond and other polycrystalline products. The common denominator for almost all high-pressure systems is to use capsules where a powder material encloses the core material. In this work, the properties of CaCO₃ powder up to ultra-high pressure have been studied using an instrumented Bridgman anvil apparatus. Bismuth phase transformations were used as fix point calibrant. Three different parameters were studied, density, moisture and diametral support dependence on the load–thickness and pressure build-up. The experiments are done such as they can be used as validation and calibration of constitutive models for finite element simulations of the HPHT-process. The results show that increasing the density of the powder compact increases the load needed to reach maximum pressure. In addition, the residual stresses in the compact seem to delay the phase transition on the down-ramp. Moisture content within 0.5%–1.2% does not significantly influence the compaction properties of the discs. Diametral support increases the phase transition load.     

Texturing unsaturated granular media submitted to compaction and kneading processes

The aim of this study is to characterise the mass and volume of wet unsaturated granular media for an equilibrium state obtained after a compaction or kneading process. For two mixing processes for powder and water, under constant operating conditions, the dry density is correlated to water content by a characteristic relation. As observed in the dynamic compaction of soils, this phenomenon exists also for the kneading and static compaction of different raw materials. An analytical expression is suggested for modelling the relation between these two parameters.     

A validation procedure for numerical models of ceramic powder pressing

This paper describes an experimental procedure to validate numerical models used to simulate powder pressing. It consists mainly of two steps: closed die uniaxial pressing followed by isostatic pressing. The uniaxial pressing causes a non-homogeneous density distribution in the pressing direction as a consequence of friction between die walls and powder. In the isostatic pressing, less compacted regions have a larger volumetric strain, resulting in a non-trivial shape of the re-compacted part, which computes indirectly the previous density distribution. Experimental data from both steps are compared to the results from finite element models. The Drucker-Prager/Cap constitutive model was used to represent the compaction of alumina powder. Several simulations covering a range of parameters obtained from the literature were performed to calibrate the model, through an inverse analysis. The developed procedure sheds a light in the methods to calibrate and/or validate constitutive models used for powder pressing.