Multiple Shock Compaction of Simple Type Powders by Punch Impact

1992 ◽  
Vol 114 (2) ◽  
pp. 117-138
Author(s):  
Yukio Sano
Keyword(s):  
Constitutive Relations ◽  
Wall Friction ◽  
Qualitative Behavior ◽  
Simple Type ◽  
Final Density ◽  
Shock Compaction ◽  
Powder Medium ◽  
Compaction Processes ◽  
Shock Fitting ◽  
Multiple Shock

Recently, we have elucidated some mechanical behaviors of powders during the compaction. The elucidation involves the constitutive relations of a powder medium under the multishock compaction, the qualitative behavior such as the similarities of the compaction processes, the die wall friction effect, and the uniformity of the final density distribution of the compact with a high density, and the quantitative behavior analyzed by the pseudo-viscosity method and the shock fitting. This review describes this behavior systematically.

Experimental Verification of the Similarity of Dynamic Compaction Processes of a Copper Powder Medium in Dies of Elementary Shapes

1987 ◽  
Vol 109 (4) ◽  
pp. 306-313
Author(s):  
Kiyohiro Miyagi ◽  
Yukio Sano ◽  
Takuo Hayashi
Keyword(s):  
Cross Section ◽  
Copper Powder ◽  
Similarity Theory ◽  
Rigid Bodies ◽  
Dynamic Compaction ◽  
Wall Friction ◽  
Simple Type ◽  
One Dimensional ◽  
Powder Medium ◽  
Compaction Processes

The similarity of dynamic compaction processes was investigated theoretically and predicted in our previous report, where powder media in a die were assumed to be of a simple type, and the punch and plug to be rigid bodies. The predictions were based on a set of one-dimensional equations and a set of nondimensionalized one-dimensional equations. The objective of this study is to examine the similarity experimentally and to present the results of compaction experiments in order to verify the existence predicted. The experiments were carried out on a copper powder medium in dies having inner cross-section in elementary shapes such as circle, square and triangle. The pressure of the medium at a point contacting the end of the plug, the density distribution and mean density of the green compacts were measured in the experiment. From the analysis of the experimental data the validity of the dynamic similarity theory was demonstrated and the similarity was verified to exist despite the differences in size and shape between the dies used, which implies that the copper powder medium in the dies of elementary shapes is of a simple type. Relations between the density and the shape coefficients showed that the density reached maximum as the coefficients decreased approaching a certain point with a decreasing influence of the die wall friction, while past that point, contrary to the prediction by the theory, it began to decrease due to an increasing influence of the elastic deformation of the punch and plug.

Dynamic Equilibrium Constitutive Relations of Copper Powder Within Dies Subjected to Mutliple Shock Compactions

1989 ◽  
Vol 111 (2) ◽  
pp. 183-191 ◽  
Author(s):  
Yukio Sano ◽  
Kiyohiro Miyagi ◽  
Koji Tokushima
Keyword(s):  
Copper Powder ◽  
Specific Volume ◽  
Dynamic Equilibrium ◽  
Constitutive Relations ◽  
Material Constant ◽  
Simple Type ◽  
Equilibrium Pressure ◽  
Material Constants ◽  
Shock Compaction ◽  
Compaction Processes

An approximate dynamic equilibrium pressure p-specific volume V relation exists for porous materials of a simple type undergoing mutliple shock compaction processes. A copper powder medium in dies is assumed to be of such a type, and the relation is constructed when the medium is compacted by a punch. It is given by an expression in the form of p=(V−Vi)/[b{Vi(1−a)−V}], where Vi, a and b are the material constants. These constants are estimated by matching the computational and experimental results obtained for the mean green density of the medium. Similarly, a dynamic equilibrium lateral pressure p1-specific volume V relation is also estimated for the medium after being given by p1=αp2+βp for ρ<3430 kg/m3, where α and β are the material constants and ρ is the density, while p1=0.5(Vsolid/V)νp+c for ρ≧3430 kg/m3, where Vsolid is the specific volume of solid copper, ν the material constant, and the contant c continuously connects the lateral pressures of the above two equations at ρ=3430 kg/m3. The compaction processes analyzed using the estimated relations agree favorably with the powder particle movement and shock wave front paths from experiments, suggesting the validity of the simple type assumption and that of the estimated relationships.

A Theoretical Derivation of the Similarity of Dynamic Compaction Processes of Powder Media in Dies

1986 ◽  
Vol 108 (2) ◽  
pp. 147-152
Author(s):  
Yukio Sano
Keyword(s):  
Cross Sections ◽  
Dynamic Compaction ◽  
Simple Type ◽  
Theoretical Derivation ◽  
Cross Sectional ◽  
Density Distributions ◽  
Powder Medium ◽  
Compaction Energy ◽  
The Mean ◽  
Compaction Processes

Multiple shock compactions of powder media within a die with a rigid punch are theoretically investigated. First, similarity of dynamic compaction processes for a powder medium of a simple type is exhibited through nondimensionalized one-dimensional equations. The similarity is established after determination of three parameters, i.e., the ratio S* of the lateral surface to the cross-sectional area of the medium, the ratio M* of the mass of the punch to that of the powder medium filled in the die, and the compaction energy per unit powder volume e. The similarity indicates that the particle velocity, specific volume and pressure have the same variation with respect to nondimensional time at all points in the medium with various cross-sections and initial lengths so long as S* is kept fixed at a certain value, i.e., at the same proportional nondimensional point in the medium. The density distributions of the green compacts are necessarily identical, and so is the mean density in all compactions. Second, it is shown in one of the nondimensionalized equations that wall frictional influence in a compaction where S* → 0 is not present, while the wall frictional influence is extremely large when S* is very large, which implies that the mean densities of the compacts are larger in compactions with smaller S*. Two types of compactions can be obtained for any powder medium because the equation used is applicable to any medium.

General-Form Solution of Shock Fitting Equation Including Die Wall Friction for the Multishock Powder Compaction

1993 ◽  
Vol 115 (4) ◽  
pp. 424-432
Author(s):  
Y. Sano ◽  
K. Tokushima ◽  
M. Yamashita
Keyword(s):  
Friction Force ◽  
Form Solution ◽  
Wall Friction ◽  
Friction Effect ◽  
Medium Length ◽  
Powder Medium ◽  
Different Types ◽  
The One ◽  
Initial Medium ◽  
Shock Fitting

In this paper, shock fitting equations including wall friction force for predicting the one-dimensional compaction process of a powder medium caused by punch impact are first derived. The medium is assumed to be discontinuously compressed only at a shock wave front both when the front propagates toward an assumed rigid plug and when it propagates back to an assumed rigid punch. The equations suggest that the effect of the friction force on the process becomes large as the front propagates toward the plug. This friction effect suggests that a continuous compression will occur in the medium between the impacted surface and the front if the effect is large. Next, the general-form solution of the shock fitting equations is obtained. This solution is compared with the solution by the pseudo-viscosity method without using the assumption that the medium is compressed only at the front. Both the solutions agree well for the compaction with a short initial medium length where the effect is not remarkable. For the compaction with a long initial medium length where the effect is remarkable, however, the solutions predict different types of the process, especially in its earlier stage. Explicitly, the former predicts the discontinuous compression only at the front, as is clear from the assumption made, while the latter predicts not only the discontinuous compaction at the front but also the continuous compression between the impacted surface and the front due to the remarkable friction effect. In its later stage, they predict the compression only at the front. Thus, the general-form solution is valid for the compaction with short initial medium lengths, but results in errors in the earlier stage for long initial medium lengths.

Multishock Compactions of a Die-Contained Copper Powder Medium Analyzed by Improved Theory

1991 ◽  
Vol 113 (4) ◽  
pp. 560-569
Author(s):  
Yukio Sano ◽  
Koji Tokushima ◽  
Tokujiro Inoue
Keyword(s):  
Copper Powder ◽  
Elastic Waves ◽  
Common Factor ◽  
Wall Friction ◽  
Compaction Process ◽  
Medium Length ◽  
Powder Medium ◽  
Compaction Processes ◽  
Initial Medium ◽  
The Waves

In the present paper, the multishock compaction process of a die-contained copper powder medium supported by an elastic plug at one end and impacted by an elastic punch at the other end, is analyzed by means of an improved theory having the effect of elasticity of the punch and plug. The compactions computed first have a constant sum of lengths of the medium and plug S0*=110, a constant ratio of punch mass to powder mass filled in the die M*=20, and an initial punch velocity ν0=50m/s. The computations of the compactions for the medium with very short lengths and the plug with long lengths confirm the existence of the medium length Scr1* corresponding to the first critical plug-length found in the previous study, and support the compaction process and the final mean density ρmean*-initial medium length S* relation of the medium shorter than the length Scr1* which were inferred in the study. Furthermore, the effect of elastic waves in the punch and plug on the process of the medium longer than Scr1* are examined. There are one common factor and one significant different factor in the processes. Explicitly, the waves in the plug exert different influence on compaction processes of the medium with different lengths, whereas the waves in the punch have similar influence on the processes. The elastic waves in the plug and die wall friction cause the medium length Scr2* corresponding to the second critical plug-length inferred in the previous study. Moreover, the waves in the plug make the form of the computed relation curve more complicated than the inferred one. The computed curve has the lengths Scr3* and Scr4* at which the density has an extreme value, respectively. Approximate similarity conditions for the compactions with various values of S0* are given by two fixed parameters M* and ν0 in region S*<Scr1*, three fixed parameters S*/S0*, M*, and ν0 in region from Scr1* to small S* where the wall friction effect can be neglected, and three fixed parameters S*, M*, and ν0 in region S*>(1/2)S0*. The computed ρmean*–S* and ρmean*–S*/S0* relations support these conditions. Furthermore, the computations of the compactions reveal that the waves in the punch, medium, and plug behave in similar manner during the processes, though they have different strengths.

Lyon-Type Integral Forms of Wall Friction, Heat- and Mass Transfer Closure Relationships for Non-Equilibrium Two-Phase Flows: Generalization for Annular and Rod Cluster Geometries

2013 ◽  
Author(s):  
Yuri Kornienko
Keyword(s):  
Boundary Layer ◽  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Constitutive Relations ◽  
Wall Friction ◽  
Transfer Coefficients ◽  
Two Phase ◽  
Friction Heat ◽  
Integral Forms ◽  
Substance Transfer

The main goal of this paper is to describe new approach to constructing generalized closure relationships for pipe, annular and sub-channel transfer coefficients for wall friction, heat and mass transfer. The novelty of this approach is that it takes into account not only axial and transversal parameter distributions, but also an azimuthal substance transfer effects. These constitutive relations, which are primordial in the description of single- and two-phase one-dimensional (1D) flow models, can be derived from the initial 3D drift flux formulation. The approach is based on the Reynolds flow, boundary layer, and substance transfer generalized coefficient concepts. Another aim is to illustrate the validity of the “conformity principle” for the limiting cases. The method proposed in this paper is founded on the similarity theory, boundary layer model, and a phenomenological description of the regularity of the substance transfer (momentum, heat, and mass) as well as on an adequate simulation of the flow structures. With the proposed generalized approach it becomes possible to develop an integrated in form and semi-empirical in maintenance structure analytical relationships for wall friction, heat and mass transfer coefficients.

Multishock Compactions of Powder Media Influenced by Elastic Waves in Punch and Plug

1991 ◽  
Vol 113 (4) ◽  
pp. 372-381
Author(s):  
Yukio Sano ◽  
Koji Tokushima ◽  
Kiyohiro Miyagi
Keyword(s):  
Experimental Data ◽  
Elastic Waves ◽  
Critical Length ◽  
Wall Friction ◽  
Initial Powder ◽  
Green Density ◽  
Previous Experimental Data ◽  
Powder Medium ◽  
Theoretical Predictions ◽  
The Mean

The previous theoretical predictions of the compaction of a copper powder medium, based on the assumption that the punch and plug were both a rigid body, did not satisfactorily agree with the experimental results obtained for short initial powder lengths and long plug lengths. This type of compaction amounts to cases when the plug length exceeds the second critical length which will be described below. Shock waves in a powder medium and elastic waves in the elastic punch and plug, schematically shown in space coordinate-time diagrams, suggest that the elastic wave in the plug is the probable cause of the inconsistency between the theoretical and experimental data of the previous investigation. In fact, the diagrams indicate that the shock wave transmitted in the medium across the medium-plug interface exerts an effect on the compaction process when the plug length does not exceed what is termed the first critical length. In cases when the effect of die wall friction is neglected, the mean green density-initial powder length relation of the copper medium is obtained from a theoretical approximation based on energy of the medium for the compaction with the sum of the initial powder length and the plug length being constant. This relation indicates that the effect of elasticity of the plug is large as the plug length becomes large. The second critical plug length at which the effect of elasticity becomes balanced with the effect of die wall friction is established by this relation and by the previously computed density-length relation with the effect of die wall friction taken into account. More specifically, these two relations provide a relation involving the first and second critical-plug lengths. The relation inferred as such agrees qualitatively with the previous experimental data in the examined region of the initial powder length. This qualitative agreement suggests that if the effects of elasticity and die wall friction are considered, a satisfactory theoretical and experimental agreement could be obtained. Therefore, the mean green density-initial powder length relation is computed taking into account both the effects. The computed relation agrees quantitatively with the previous experimental data even for short initial powder lengths and long plug lengths.

One-Dimensional Density Distributions of Powder Media in Dies Subjected to Multishock Compactions

1988 ◽  
Vol 110 (4) ◽  
pp. 355-360 ◽  
Author(s):  
Y. Sano
Keyword(s):  
Shock Wave ◽  
Density Distribution ◽  
Friction Force ◽  
The Other ◽  
Wall Friction ◽  
Uniform Density ◽  
Simple Type ◽  
One Dimensional ◽  
Density Distributions ◽  
The One

A theoretical attempt to clarify the reason why the compacts of powder media have uniform density distributions as the density of the compacts becomes high, is made for the compaction of the copper powder medium of a simple type by punch impaction. Based on the one-dimensional equation of motion including the effect of die wall friction force, there are two main factors which influence the density distribution of the medium during the compaction process; one is the propagation of the shock wave passing through the medium, while the other is the friction force between the circumferential surface of the medium and the die wall. The equation reveals that the effect of the force increases little as the density becomes high as a result of the repetitive traveling of the shock wave between the punch and plug. The propagation or more definitely the repetitive traveling, on the other hand, increasingly unformalizes the density distribution during the process as the number of the traveling increases. Owing to the aforementioned effects of the two factors on the density distribution during the process, the high density compacts become uniform.

Al2O3-ZrO2 Ceramics with Submicron Microstructures Obtained through Microwave Sintering, Plasma Sintering and Shock Compaction

1992 ◽  
Vol 274 ◽  
Author(s):  
J. McKittrick ◽  
B. Tunaboylu ◽  
J. D. Katz ◽  
W. Nellis
Keyword(s):  
Liquid Phase ◽  
Eutectic Composition ◽  
Microwave Sintering ◽  
Liquid Phase Sintering ◽  
Fine Grained ◽  
Grain Sizes ◽  
Final Density ◽  
Plasma Sintering ◽  
Shock Compaction ◽  
Rapidly Solidified

ABSTRACTSubmicron and nanocrystalline grain sizes were achieved in the Al2O3-ZrO2 eutectic composition through conventional, microwave and plasma sintering of rapidly solidified starting powders and through shock compaction of commercial powders. Post sintering studies revealed nanocrystalline intragranular ZrO2 in the 1–2 μm Al2O3 grains, which is thought to be a result of the solidification synthesis. Additions of B2O3 greatly increased the final density through liquid phase sintering. Shock compression of commercial powders produced dense, crack-free, fine grained ceramics with loading pressures up to 9.1 GPa and a metastable ZrO2 phase under higher pressures.

Gravity flow of cohesionless granular materials in chutes and channels

1979 ◽  
Vol 92 (1) ◽  
pp. 53-96 ◽  
Author(s):  
Stuart B. Savage
Keyword(s):  
Granular Materials ◽  
Constitutive Relations ◽  
Side Wall ◽  
Wall Friction ◽  
Hydraulic Jumps ◽  
Two Dimensional ◽  
High Deformation ◽  
Gravity Flows ◽  
Theoretical Predictions ◽  
Set Up

A constitutive equation appropriate for flow of cohesionless granular materials at high deformation rates and low stress levels is proposed. It consists of an extension and a reinterpretation of the theory of Goodman & Cowin (1972), and accounts for the non-Newtonian nature of the flow as evidenced by Bagnold's (1954) experiments. The theory is applied to analyses of gravity flows in inclined chutes and vertical channels. Experiments were set up in an attempt to generate two-dimensional shear flows corresponding to these analyses. Velocity profiles measured by a technique which makes use of fibre optic probes agree qualitatively with the theoretical predictions, but direct comparison is inappropriate because of unavoidable side-wall friction effects in the experiments. The existing measure of agreement suggests that the most prominent effects have been included in the proposed constitutive relations. Tests in the inclined chute revealed the possible existence of surge waves and granular jumps analogous to hydraulic jumps.

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