Density and plastic strain evaluations using small-angle X-ray scattering and finite element simulations for powder compacts of complex shape

Previous work suggested that two-dimensional small-angle X-ray scattering (2D-SAXS) could offer a new method for evaluating the local variations of density, strain and principal strain direction within powder compacts, which arise due to the effects of friction and die shape. In order to test this method further, this work compared results from 2D-SAXS with finite element (FE) simulations using a modified density-dependent Drucker–Prager Cap (DPC) model, for compacts of complex shape, prepared using a cylindrical die, a flat-faced upper punch and shaped lower punches with three different central protrusions. Variations in compaction behaviour were observed, which were due to friction against the die walls and the punch shape. Good agreement was obtained between SAXS measurements and FE simulation, supporting previous indications. Hence, this combination of experimental and computational techniques appeared particularly powerful for investigating powder compaction behaviour, in considerable accuracy and detail. Moreover, observations of the compaction behaviour in the vicinity of the central protrusion may be relevant to tablets with embossed features or compacted artefacts of more complex shape.     

Determination of large deformation and fracture behaviour of starch gels from conventional and wire cutting experiments

Large deformation and fracture properties of two types of starch gels were investigated through uniaxial compression, single edge-notched bend (SENB) and wire cutting experiments. Tests were performed at various loading rates and for various starch/powder concentrations (%w/w). It was found that starch gels exhibit rate independent stress–strain behaviour but show rate-dependent fracture behaviour, i.e. stress–strain curves at three loading rates are similar but fracture stress and fracture strain increase with increasing strain rate. This is rather unusual and interesting behaviour. SENB and wire cutting experiments also revealed rate-dependent fracture behaviour and that the true fracture toughness (G _c) values increase with loading/cutting speeds and starch powder concentration. In addition, the G _c values from wire cutting and SENB tests were in reasonable agreement. The wire cutting process was also studied numerically using finite element techniques. A non-linear elastic constitutive relationship based on Ogden was used to model the starch gels and a frictionless condition was assumed at the wire–starch gel contact interface. A fracture criterion based on maximum principal strain was assumed for the prediction of the steady state cutting force.     

Modeling and influence of shear retention parameter on the response of reinforced concrete structural elements

To obtain the complete solutions describing the balance of a reinforced concrete structure, it is necessary to introduce a behavioral law characterizing the physical properties of material. The goal of this work is to study the response of reinforced concrete elements by taking into account the variation of the shear retention parameter (aggregate interlock) and the mesh density. The concrete was assumed as elastic-plastic material and follow the Drucker–Prager failure criterion with associated flow rule, the steel reinforcements were assumed to be elastic-perfectly plastic. The numerical results obtained are compared with other results available in the literature. Translated from Problemy Prochnosti, No. 4, pp. 108–116, July–August, 2009.     

Analysis of the stressed state of a circular thin-walled cylinder under complex loading and with nonlinear hardening of the material

The generalized differential equations of plastic flow for a material with nonlinear hardening are derived using the Prager kinematic model. An example of numerical analysis for stress variation under elastoplastic deformation of a thin-walled cylinder of a structural carbon steel is given for different elastoplastic material models. Translated from Problemy Prochnosti, No. 3, pp. 58–65, May–June, 2009.     

Numerische und experimentelle Untersuchungen zum Pulverpressen von Aluminium

Numerical and Experimental Investigations of Aluminium Powder Compaction The FEM simulation is a powerful means which can drastically reduce the time to production and costs in the optimization of powder forming processes. The current paper investigates experimentally and numerically die compaction of aluminium powder. The plastic deformation is formulated by using the Drucker‐Prager‐Cap‐model. This yield criterion describes the compressibility of porous bodies and allows the prediction of crack formation in the green compact. Axial compaction tests have been performed to determine material parameters for hardening. Simulation examples are presented to demonstrate the ability of the model to compute the distribution of the relative density. Furthermore, the compaction of an axisymmetric workpiece was simulated in order to determine optimal tools kinematics and to avoid crack formation.     

Effect of geometric work-hardening and matrix work-hardening on new constitutive relationship for aluminium–alumina P/M composite during cold upsetting

The densification and strain hardening behaviour during cold deformation of sintered aluminum–3.5% alumina powder metallurgy preforms were investigated by constitutive model and experimental data obtained with no and with subsequent annealing. The mechanisms most likely involved in the constitutive model, namely, densification and strain hardening were studied. The effect of geometric and matrix work hardening on the various constants involved in the constitutive model, namely, instantaneous density coefficient, instantaneous strain hardening index, instantaneous strain rate sensitivity and instantaneous strength coefficient were discussed in detail.     

Microstructural investigation of Bi–Sr–Ca–Cu–oxide thick films on alumina substrates

The microstructure of Bi–Sr–Ca–Cu–oxide (BSCCO) thick films on alumina substrates has been characterized using a combination of X-ray diffractometry, scanning electron microscopy, transmission electron microscopy of sections across the film/substrate interface and energy-dispersive X-ray spectrometry. A reaction layer formed between the BSCCO films and the alumina substrates. This chemical interaction is largely responsible for off-stoichiometry of the films and is more significant after partial melting of the films. A new phase with f c c structure, lattice parameter a = 2.45 nm and approximate composition Al₃Sr₂CaBi₂CuO _x has been identified as reaction product between BSCCO and Al₂O₃. This revised version was published online in November 2006 with corrections to the Cover Date.     

Construction of a constitutive model in calculations of pressure-dependent material

To make constitutive modeling of materials more approaching reality, a new theory is proposed, in which a corresponding constitutive model can be constructed and characterized experimentally via two steps, one relates to the characterization of yielding behavior of material, and the second relates to the characterization of plastic flow of material deformation. The constitutive model involves two functions, yield function and plastic potential. A relationship between two functions is suggested, therefore, a corresponding plastic potential can be easily created after we have an appropriate yield function. To consider the non-isotropic hardening feature of strength differential in the constitutive model, the concept of equivalent hardening state is introduced, and then, multi-experimental flow stresses can be addressed in the model. When pressure sensitive materials are taken as an example in discussions, the Drucker–Prager yield function is employed to express the yielding behavior of material and a differently experimental characterization of the model is created as the corresponding plastic potential to describe the feature of plastic flow of material. This simple constitutive model can reproduce three sets of experimental results; including two flow-stresses and the volumetric plastic strain. The constitutive model can also well predict stress–strain relations with different pressures loaded on the material. Study shows that the feature of plastic flow is not that sensitive to the pressure loaded on the material when the yielding stress is.     

Some aspects of workability studies on P/M sintered high strength 4% Titanium carbide composite steel preforms during cold upsetting

Workability is concerned with the extent to which a material can be deformed in a specific metal working process without the initiation of cracks. Ductile fracture is the most common failure in bulk forming process. The formability is a complicated phenomenon which depends on the friction between the preform and the die surface in cold upsetting. A complete experimental investigation on the workability behavior of the steel composite of 4%TiC was performed under different stress states, namely, plane and triaxial stress state conditions. Cold upsetting of the Fe–1.0%C–4%Ti steel composite preforms was carried out applying different lubricants, namely, graphite, zinc stearate and molybdenum disulphide, and without lubricant, and the formability behaviour of the same under plane and triaxial stress state conditions was determined. The curves plotted for different preforms were analysed and relationship was established between the axial strain and the formability stress index under plane and triaxial state conditions. A relationship between the relative density and the axial strain was also established. Various stress ratio parameters, namely, (σ_θ/σ_eff), (σ_m/σ_eff) and (σ_z/σ_eff), under plane and triaxial stress state conditions were determined empirically as a function of the relative density. An attempt is also made to study the variation of slope of the relative density versus stress ratio parameters under plane and triaxial stress conditions with respect to the relative density to identify the pore closure mechanism.     

Structural and Physical Properties of Nd Substituted Bismuth Cuprates Bi1.7 Pb0.3−x Nd x Sr2Ca3Cu4O12+y

BiPb-2234 bulk samples with nominal composition of the compound Bi_1.7Pb_0.3−x Nd _x Sr₂Ca₃Cu₄O_12+y (BSCCO) (0.025≤x≤0.10) have been prepared by the melt-quenching method. The effects of Nd substitution on the BSCCO system have been investigated by electrical resistance (R–T), scanning electron microscopy (SEM), X-ray diffraction (XRD) and magnetic hysteresis measurements. It has been the BSCCO (2212) low-T _c phase is formed for all the substitution levels, together with the BSCCO (2223) high-T _c phase. The results obtained suggest that with increasing Nd³⁺ doping for Pb²⁺ the (2223) phase existing in undoped BSCCO gradually transforms into the (2212) phase and hence all of the samples have a mixed phase formation. The R–T result of the samples show two-step resistance transition; first transition occurs at 100 K and second in an interval of 80–90 K, depending on the Nd concentration. We have found that the magnetization decreases with increasing temperature in agreement with the general characteristic of the high-T _c materials. The samples exhibit weak field dependence particularly after 2 T and changes on the magnetic hysteresis, M–H curve rather small compared to the conventional superconducting materials. The maximum critical current density, J _c, value was calculated to be 8.51×10⁵ at 4.2 K and J _c decreases with increasing temperature and the substitution level.      

Rate-dependent deformation of Sn–3.5Ag lead-free solder

Compression experiments on bulk Sn-3.5Ag lead-free solder specimens have been carried out to help formulate the material constitutive behaviour of this alloy using the concept of an evolving internal stress. Tests covered the temperature range 0–125 °C and fixed strain rates between 3 × 10⁻⁷–3 × 10⁻³ s⁻¹. Flow behaviour was found to be compatible with that for a deforming a tin-rich matrix (stress exponent n = 7, activation energy Q = 46.7 kJ/mol) in which the external applied stress is reduced by an internal back stress due to the presence of precipitate phase particles. Stress–strain curves have been satisfactorily modelled using rate equations incorporating linear hardening and diffusion-controlled recovery. Comparison with supplementary tension and creep experiments, and with data from other researchers, indicates that inconsistencies in reported flow behaviour is most likely to be due to variations in initial microstructure rather than the nature of the applied loading.     

Yield stress of SiC reinforced aluminum alloy composites

This article develops a constitutive model for the yield stress of SiC reinforced aluminum alloy composites based on the modified shear lag model, Eshelby’s equivalent inclusion approach, and Weibull statistics. The SiC particle debonding and cracking during deformation have been incorporated into the model. It has been shown that the yield stress of the composites increases as the volume fraction and aspect ratio of the SiC particles increase, while it decreases as the size of the SiC particles increases. Four types of aluminum alloys, including pure aluminum, Al–Mg–Si alloy, Al–Cu–Mg alloy, and Al–Zn–Mg alloy, have been chosen as the matrix materials to verify the model accuracy. The comparisons between the model predictions and the experimental counterparts indicate that the present model predictions agree much better with the experimental data than the traditional modified shear lag model predictions. The present model indicates that particle failure has important effect on the yield stress of the SiC reinforced aluminum alloy composites.     

A multi-field coupled FEM model for one-step-forming process of spark plasma sintering considering local densification of powder material

A mechanical constitutive model of powder material is introduced to a fully coupled thermal–electric–mechanical finite element model to simulate the one-step-forming spark plasma sintering (SPS) process of metal powders. The effects of displacement field and local density distribution on sintering are considered in this article, which are generally neglected in the existing SPS models. The mechanical, thermal, and electrical parameters of powders are assumed as functions of local relative density and temperature. The simulated varying displacement field remodels the distributions of temperature and electric potential by changing the contact thermoelectric resistances. For the 20, 40, and 60 MPa external pressures, the simulation indicates that the sintering temperature and the temperature gradient within powders are decreased by enhancing the external pressure, and the comprehensive effect of stress promotes the densification of the colder regions. Thus, the interrelationship between the temperature gradient and the intrinsic stress distribution plays an important role in the densification mechanism of SPS powders.     

Simulation of the supersonic turbulent flow around a cylinder with coaxial disks

The turbulent axisymmetric flow around a stepped body — a cylinder with coaxial front and rear disks — has been calculated with the aid of a VP2/3 package based on multiblock computational technologies and the generalized procedure of pressure correction. The computational model has been tested with the example of a supersonic flow around a sphere. The numerical forecasts made with the use of Spalart–Allmares shear stress transfer and eddy viscosity transfer models have been compared with the data of the aeroballistic experiment, wind tunnel tests, and the results of the calculation of the flow around the disk–cylinder arrangement by a simplified zonal model in a wide range of variation of the incident flow Mach number (from 1.5 to 4). We have obtained a good agreement between the calculated transverse flow density distributions in the front stalling zone and those determined from the interferograms for the wave-drag-rational disk–cylinder arrangement. The influence of the rear disk on the drag of the disk–cylinder–disk arrangement has been estimated.     

Processing of BSCCO 2212 and 2223 Superconductor Compounds

High-T_c BSCCO superconductor tapes were prepared by the conventional powder-in-tube method. Some tapes involved partial melting, while the others involved solid-state processing only. Bulk samples were prepared by powder metallurgy. X-ray diffraction (XRD) showed the presence of both BSCCO 2223 (T_c = 105 K) and BSCCO 2212 (T_c = 80 K) phases in all the materials. For the mostly BSCCO 2212 phase samples, x-ray studies indicated that tape #1 which involved partial melting at 850^°C for 0.3 h had a higher degree of basal orientation than either a tape #2 sample which involved partial melting at 855^°C for 0.5 h, or a bulk (#2) sample. For the mostly BSCCO 2223 phase samples, however, a comparison of bulk (#1.), tape #3 (solid state processing at 840^°C) and tape #4 (partial melting at 865^°C for 0.5 h) samples, showed that the solid-state processed tape (#3) had the highest degree of basal orientation. Direct current magnetic susceptibility measurements were used to follow the transition at T_c. Critical current density, J_c, values were estimated from DC magnetic hysteresis loops for all bulk and tape samples.     

pH controlled dispersion and slip casting of Si3N4 in aqueous media

The dispersion characteristics of commercial Si₃N₄ powder in aqueous media (deionized water) was studied as a function of pH in the range 2–11. The slip was characterized for its dispersion quality by various experimental techniques like particle size analysis, sedimentation phenomena, viscosity and flow behaviour and zeta potential analysis. The optimum dispersion was found to be in the pH region 9–11 wherein the slurry displayed minimum sedimentation height, minimum viscosity, near Newtonian flow behaviour and maximum zeta potential. The slip is highly agglomerated in the pH range 2–8 as manifested by higher sedimentation height, higher viscosity, lower zeta potential and thixotropic non-Newtonian flow behaviour. The 72 wt% (44 vol.%) Si₃N₄ slips made at pH = 10 resulted in green bodies having 53–59% of theoretical density after casting into plaster molds.     

Consolidation of ultrafine-grained Cu powder and nanostructured Cu–(2.5–10) vol%Al<Subscript>2</Subscript>O<Subscript>3</Subscript> composite powders by powder compact forging

An as-received ultrafine-grained Cu powder and four nanostructured Cu–(2.5–10) vol%Al₂O₃ composite powders produced by high-energy mechanical milling of mixtures of the Cu powder and an Al₂O₃ nanopowder were consolidated using warm powder compaction followed by open die powder compact forging. The circular discs produced in the experiments achieved full densification. Tensile testing of the specimens cut from the forged discs showed that the Cu-forged disc had a fairly high yield strength of 330 MPa, UTS of 340 MPa and a plastic strain to fracture of 15%, but the Cu–Al₂O₃ composite-forged discs did not show any macroscopic plastic yielding. The fracture strength of the composite-forged discs decreased almost linearly with the increase of the volume fraction of Al₂O₃ nanoparticles. This study shows that a high level of consolidation of the ultrafine-grained Cu powder and the nanostructured Cu–2.5 vol%Al₂O₃ composite powder has been achieved by warm powder compacting at 350 °C and powder compact forging at 500 and 700 °C. However, this is not true for the nanostructured Cu–(5, 7.5 and 10) vol%Al₂O₃ composite powders, possibly due to their higher powder particle hardness at elevated temperatures in the range of 350–800 °C.