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.     

An integrated study of die powder fill, transfer and compaction process using digital image correlation method

A major advantage of the powder metallurgical (P/M) manufacturing process is its ability to shape powder directly into a final component with a primary goal of a high quality, homogeneity of density and mechanical properties and productivity. In this research, powder die filling, powder transfer and powder compaction process have been studied in succession using a novel experimental set-up that utilizes a high strength transparent wall section to observe and record the particle movement and powder compaction during the entire sequence leading up to the formation of a green part. The natural powder pattern itself, as observed from the transparent wall section, is utilized for obtaining full-field displacement and strain measurement. The test set-up and the strain measurement technique offer a means of quickly obtaining density distribution data in select cases. In addition to the above, several powder flow characteristics during die filling, powder transfer and powder compaction under a range of test conditions have been noted through a series of high-speed photographic recordings.The observations reveal increased porosity in the die wall region due to friction and formation of shear bridges during powder transfer stages during suction filling. Spatial density data from optical strain measurements in the top, middle and bottom regions of the die are consistent with similar bulk density measurements from mass and volume of the 3 regions.     

A combined experimental-numerical study of the compaction behavior of NaCl

The compaction behavior of NaCl as a model substance is investigated by an integrated experimental and computational approach. The method for characterization of this granular material employs convenient experiments: load-displacement measurements of compaction; measurements of strain on outer circumference of an elastic tubular die; load on bottom and top of the powder compact, as well as compressive strength tests. Related equations for identification of material parameters are derived and are used to characterize powder behavior and powder-die friction. Subsequently, these material parameters are used in simulations with the Drucker-Prager-Cap (DPC) model. For the verification of the computations density distributions are determined based on micro X-ray computer tomography. Good agreement between the spatial density distributions from measurements and simulations is obtained. Restrictions of computer tomography in powder compaction applications are specified. While the study employs NaCl as a model substance, the approach is applicable to a wider array of granular substances.     

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.     

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.     

A small-angle X-ray scattering study of local variations within powder compacts

This work used two-dimensional small-angle X-ray scattering (2D-SAXS) to investigate the compaction behaviour of pre-gelatinised starch (PGS) and microcrystalline cellulose (MCC), which are commonly used as pharmaceutical excipients. By analysing azimuthal variations in scattering intensity, reproducible relationships were found between the compaction pressure, relative density and changes in the shapes of 2D-SAXS patterns for each material. These results indicated differences in the compaction mechanisms between PGS and MCC.The relationships also provided a means for investigating local variations in compaction behaviour within specimens prepared using different materials and compaction conditions. Relative density results from 2D-SAXS were consistent with expectations based on the effects of friction during compaction and appeared similar to data from other methods. In addition, however, 2D-SAXS measurements revealed local variations in the effective direction in which compaction occurred, with significant radial components observed near the die walls. This appeared to be consistent with the transfer of some compaction pressure to friction on the die wall. These observations represent an important advance, since other experimental methods do not easily reveal the direction of force transmission within the powder compact.     

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.     

Cold Compaction and Solid-State Sintering of WC-Co-Based Structures: Experiments and Modeling

Cold compaction (200-1900 MPa) and sintering (1250°-1350°C) of cermets based on WC-Co were experimentally studied using die compaction, cold isostatic pressing, sintering, and creep tests. Two different-sized WC powders were used. The cobalt content varied over a range of 10-30 wt%. Cold-compaction behavior has been described by using a Cam-Clay model. Die-wall friction was measured by using green powder compacts that had different aspect ratios. Friction coefficients were 0.28-0.85, depending on the WC particle size and cobalt content. Simple constitutive equations have been used to model the high-temperature behavior (sintering and creep). The constitutive equations were implemented in a finite-element program to model the compaction, ejection, and sintering of bilayer structures that had different cobalt contents. The model can represent the effect of die-wall friction on the average density, as well as deformation inside the green compact. Density gradients were generated; they were revealed during sintering, because the compact does not deform homogeneously. Simulation also can be used to evaluate deformations that are induced by sintering.     

Evaluation of force—displacement measurements during one-sided powder compaction in a die — the influence of friction with the die wall and of the diameter of punches and die on upper and lower punch pressure

On an instrumented single-punch press, working at an overall rate of 30 strokes per minute, the influence of diameter of punches and die on upper and lower punch pressure, measured during the densification of a powder with an initial height of 8.0 mm, has been investigated.The upper punch pressure necessary to effect a certain state of density, proved to decrease with increasing diameter, whereas the lower punch pressure proved to be independent of the diameter. The upper punch pressure differences, found for diameters ranging from 11 to 17 mm, could not be accounted for by differences in the actual speed of compaction between the individual force displacement measurements and it could be concluded that these pressure differences were exclusively due to an influence of the diameter on the process of compaction.By using a number of hyportheses concerning friction with the die wall, it was possible to derive a mathematical model for the pressure distribution on the upper punch which qualitatively agreed with the experimental results.     

Some studies in the displacements of powder material during compaction

On the basis of the results of tribological investigations during the compaction of iron powder type NC.100.24 and of the distribution of porosity in sintered compacts, the character of powder material displacements was described for the last stage of compaction, i.e. after establishment of a preset compacting pressure. In those investigations, the model used was of the compaction of a powder material in a rotary die. The choice of such a model results from the necessity of programming an experiment with a more complex state of stresses within the mixed powder being compacted than that in standard static compaction.In the paper decisive conditions are determined for depth of penetration of shearing stresses in the compacted material, as well as conditions of change of the state of friction of the compact against the stationary mandrel surface from static to kinetic friction.     

The importance of the amount/thickness of die wall lubricant for UO2 pellets pressing

External lubrication is often used to complete compaction process of powder materials. The main goal of this method is generally to reduce the amount of admixed internal lubricant (Zinc stearate powder) within the raw material. The application of external lubricants enhances the density uniformity and the mechanical strength of the resulting compacts. This study investigates the effects of the external lubricant amount for UO₂ powder compaction and the properties of the corresponding green pellets (corresponding to the compacts before sintering) without any admixed lubricant in the raw powder in order to evaluate the feasibility of this route in the case of nuclear powder. Results show that there is a quantity or number of layers from which the external lubricant applied on the die wall becomes detrimental to the friction index and the ejection force measured during the pressing cycle. The quality (surface defects, mechanical strength) of the green pellets can also be affected by the amount of lubricant. Thus the quantity and the thickness of the die wall lubricant must be optimized in order to assure an efficient mixed lubrication mode corresponding to the better lubrication mode in our study case.     

Stresses occurring during one-sided die compaction of powders

Die compaction of powders is related to the principles of powder mechanics. Measurements are reported of boundary normal stresses occuring during one-sided die compaction of a fine ferric oxide powder. One series of experiments is carried out with carefully cleaned die walls, another series is performed with lubricated dies. The powder yield locus and wall yield loci are determined respectively with the help of a triaxial cell and a powder/wall friction apparatus. For both series of experiments the powder yield locus lies above the wall yield locus. The experimental data give support to the assumption that the stresses at the die wall obey the wall yield locus. With respect to the internal stresses of the powder, evidence is obtained that the powder yield criterion is not fulfilled, at least not necessarily.     

An alternative to the conventional triaxial compression test

A new test for measurement of the mechanical properties of granular powders is proposed, consisting of upsetting the powder inside a metal tube. Varying the tube material as well as its wall thickness allows superimposing of a variable radial pressure. By pre-compacting the powder inside the tube in a closed die it is possible to test the powder at different densities. The radial pressure is found by correlating measurements of radial bulging of the tube with numerical analysis of tube bulging. Estimates of the error on the determination of the radial pressure are given and it is found that this error may be kept less than ± 4%. The coefficient of friction between powder and tube for a specific case is evaluated and found to be between 0.05 and 0.1 at p_c > 400 MPa. Data from the test with axial pressures up to 1100 MPa and radial pressures up to 500 MPa are presented. Data on the yield surface for BSCCO (ceramic powder (Bi,Pb)₂Sr₂Ca₂Cu₃O_x for manufacturing of superconductors) at 74% density are given and found to be in good agreement with previously published data determined by closed die compaction and fracture tests.The results obtained show that the new test may be a good alternative when high pressures are required or when pressurizing by fluid is impractical.     

The determination of the coefficient of dynamic friction of organic powder compacts on steel

A practical experimental model system has been successfully used to study the frictional response of organic powder compacts sliding across a polished steel plate, representative of the die bore of a production compaction system. This system offers a controlled approach to the study of frictional phenomena occurring during compaction and facilitates a more detailed investigation into the fundamental mechanisms of friction than a simple resolution of forces within a punch and die apparatus.For acetylsalicyclic acid sliding on steel, the dynamic friction coefficient was found to be dependent on the displacement and, to a lesser extent, the initial normal load, whereas for PTFE on steel, the dynamic friction coefficient was independent of displacement and load and estimated at 0.09. Thus, soft organic materials exhibit very different frictional characteristics to those of brittle materials. These differences reflect the differing importance and magnitude of the three frictional components, adhesion, shear and ploughing.     

Industrial Quantitative Control of the Pressing Behavior of Spray-Dried MnZn-Ferrite Granules

In the first stage of a broad factory stabilization program, the compaction properties of spray-dried granulated powders are investigated. Certain compaction process parameters are identified and include (i) the slide coefficient between powder material and die wall during compaction, which mainly affects the pressing tool life time, (ii) the ratio of the pressure drop over the compact to the axial mechanical strength of the compact, basically related to the chance of chipping and crack occurrence upon ejection, and (iii) the homogeneity of the density profile along the compact, basically related to the chance of crack development and product deformation during sintering. The effect of important factors, such as binder and lubricant content, granulate storage humidity, and compaction temperature, on those parameters is investigated. Based on factory data, specification values for the previously mentioned parameters are derived and used to control the compaction quality of the industrially spray-dried powders with satisfactory results.     

Stress Transmission During the Compaction of a Spray-Dried Alumina Powder in a Steel Die

Stress transmission through the compact, die wall friction, and the radial/axial stress ratio were investigated using a spray-dried alumina powder containing 2.3% polyvinyl alcohol binder, stored at 15, 55, or 92% rh, and an unlubricated/lubricated steel die for pressing. Stress transmission was enhanced by lubricating the die and decreasing the thickness/ diameter of the compact. Increasing the punch velocity in the range 0.006 to 0.6 cm/min improved the stress transmission for powder stored at the highest humidity, but only in the intermediate range of pressures. Radial stress at the highest pressures (>10⁷ Pa) was essentially independent of the properties of the binder phase and the radial/axial stress ratio was ∼0.4. At high pressures, the product of (die wall friction) (radial/axial stress ratio) decreased with lubrication of the die and storage of the granulated powder at a higher percent relative humidity (softer granules).     

Evaluation of Force-Displacement Measurements during one-sided powder compaction in a Die. The quantitative evaluation of a model of die-wall friction from experiments with various diameters,with a critical examination of the influence of various other machine variables

With a microgranulation of lactose, experiments at various diameters of punches and die, namely from 7 to 17 mm, have been performed in order to determine the influence of the diameter on the pressure required to achieve a given state of density during compaction.These measurements have been performed under strictly standardised conditions, but small alterations in the experimental conditions are unavoidable as, for example, the depth o f penetration of the upper punch in the die, the state of die-wall lubrication, the precision with which punches fit in the die, the amount of powder in the die, etc- The influence of a number of 'machine variables' of this kind as well as the influence of the diameter on the pressures required for compaction have been investigated and their magnitude was established. Finally, it could be concluded that the upper punch pressure required to effect equal states of density decreased with an increase of the diameter, whereas the lower punch pressure proved to be independent o f the diameter- The experimentally obtained results could be accounted for quantitatively with an earlier published model o f die-wall friction.     

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.     

Modelling and numerical investigation of the residual stress state in a green metal powder body

Die pressing of metal powder results in a green body. After release from the die, the green body must have enough strength to be handled, to endure transport to a sintering furnace and heating to the sintering temperature. Drilling, turning and milling, which are common operations in the green state, require a green body of high strength, with no defects and excellent mechanical properties. A plane strain finite element model is used to analyse pressing of metal powder into a rectangular bar. The powder behavior is described by a “cap” model, which is implemented as a user material subroutine in the non-linear finite element program LS-DYNA. To improve modelling of strength in the green state a new non-linear density dependent failure envelope has been used. The model is adjusted to the properties of a water atomised metal powder from Höganäs AB. To resolve the severe stress gradient at the side surface of the green body, the smallest element size was chosen to be 65 μm. The aim of this work is to numerically capture and understand the development of the residual axial stress in particular at the side surface. The influence of kinematics, friction, compacting pressure and die taper are studied. Results from the numerical study show that the thickness of the compressive stress region close to the side surface of the green body varies between 50 μm and 600 μm along the surface. Compacting pressure, “upper punch hold down” and die taper geometry all have a significant influence on the residual stress state while die wall friction has only a small influence. The numerical results are in agreement with results from X-ray and neutron diffraction measurements.     

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.