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.

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.

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.

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.

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.

Effect of Shock and Elastic Waves on Dynamic Compaction Process of Two-Layer Powder Media

1987 ◽  
Vol 109 (4) ◽  
pp. 266-271
Author(s):  
K. Miyagi ◽  
Y. Sano
Keyword(s):  
Elastic Waves ◽  
High Speed ◽  
Lower Layer ◽  
Initial Density ◽  
Dynamic Compaction ◽  
Compaction Process ◽  
Density Distributions ◽  
Layer Arrangement ◽  
Powder Medium ◽  
Compaction Processes

The dynamic compaction processes of copper powder which was filled in two layers into a die and subjected to solid punch impaction were investigated experimentally in order to assess the effect of different initial density distributions of the powder on the compaction process. The compaction experiments were performed for two situations of layer arrangement: in the first situation the upper layer had a lower uniform initial density distribution than the lower layer and in the second this order was reversed. The processes were photographed for the two situations of layer arrangement using a high speed camera in order to analyze the movement of powder medium and punch, the propagation of shock and elastic waves in the powder medium and density distributions. The pressure on the plug supporting the medium in the die was also measured so that the analysis of the photograph would be facilitated. The two compaction processes observed and analyzed differed considerably, but the green density distributions had only a slight difference. The compaction process obtained for the first situation of layer arrangement agreed well with the theoretical prediction reported previously by the authors. The compaction process for the second situation also agreed with the theoretical result, indicating that the amounts of internal energy dissipation during the two processes differ only slight.

An Analysis Method for the Dynamic Compaction Processes of Powder Media Within a Die

1988 ◽  
Vol 110 (1) ◽  
pp. 28-34
Author(s):  
Yukio Sano
Keyword(s):  
Equations Of Motion ◽  
Approximate Solutions ◽  
Rigid Bodies ◽  
Jump Conditions ◽  
Rigid Plastic ◽  
Von Neumann ◽  
Powder Medium ◽  
Plastic Type ◽  
Particle Velocities ◽  
Compaction Processes

A method of analysis for the multishock compaction process of die-contained powder media with a plug at one end and an impacting punch at the other end is presented. In the method assumptions are made that the media are of a simple rigid-plastic type, and compressed only at the fronts of the shock waves passing through, and furthermore the punch and plug are rigid bodies. Based on the assumptions, particle velocities of elements between the punch surface and a shock wave front are the same and equal to the punch velocity, while velocities of elements between the front and the plug surface are equal to a velocity of the plug surface, i.e., zero. Therefore, it is possible to use jump conditions at the front and equations of motion for the punch and medium moving with the same velocity as it, instead of partial differential equations, i.e., conservation equations which were used in other methods. The equations of motion, together with the jump conditions and rigid-plastic constitutive relation equations provide two sets of equations governing the process. It is shown that there exist unique solutions of the equations of motion, and the equations are analyzed for a copper powder medium. Exact solutions obtained are compared with approximate solutions analyzed previously by the von Neumann and Richtmyer method. A fairly good agreement of the solutions by both the methods indicates that the approximate solutions are effective.

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.

The Exact One-Dimensional Theory for End-Loaded Fully Anisotropic Beams of Narrow Rectangular Cross Section

2001 ◽  
Vol 68 (6) ◽  
pp. 865-868 ◽  
Author(s):  
P. Ladeve`ze ◽  
J. G. Simmonds
Keyword(s):  
Cross Section ◽  
Plane Stress ◽  
Rectangular Cross Section ◽  
Dimensional Theory ◽  
Explicit Formulas ◽  
Cross Sectional ◽  
Rectangular Shape ◽  
One Dimensional ◽  
Anisotropic Elastic ◽  
Derivatives Of

The exact theory of linearly elastic beams developed by Ladeve`ze and Ladeve`ze and Simmonds is illustrated using the equations of plane stress for a fully anisotropic elastic body of rectangular shape. Explicit formulas are given for the cross-sectional material operators that appear in the special Saint-Venant solutions of Ladeve`ze and Simmonds and in the overall beamlike stress-strain relations between forces and a moment (the generalized stress) and derivatives of certain one-dimensional displacements and a rotation (the generalized displacement). A new definition is proposed for built-in boundary conditions in which the generalized displacement vanishes rather than pointwise displacements or geometric averages.

Long waves in a straight channel with non-uniform cross-section

2015 ◽  
Vol 770 ◽  
pp. 156-188 ◽  
Author(s):  
Patricio Winckler ◽  
Philip L.-F. Liu
Keyword(s):  
Boundary Layer ◽  
Wave Propagation ◽  
Cross Section ◽  
Three Dimensional ◽  
Channel Cross Section ◽  
Cross Sectional ◽  
New Model ◽  
One Dimensional ◽  
Uniform Channel ◽  
The Cross

A cross-sectionally averaged one-dimensional long-wave model is developed. Three-dimensional equations of motion for inviscid and incompressible fluid are first integrated over a channel cross-section. To express the resulting one-dimensional equations in terms of the cross-sectional-averaged longitudinal velocity and spanwise-averaged free-surface elevation, the characteristic depth and width of the channel cross-section are assumed to be smaller than the typical wavelength, resulting in Boussinesq-type equations. Viscous effects are also considered. The new model is, therefore, adequate for describing weakly nonlinear and weakly dispersive wave propagation along a non-uniform channel with arbitrary cross-section. More specifically, the new model has the following new properties: (i) the arbitrary channel cross-section can be asymmetric with respect to the direction of wave propagation, (ii) the channel cross-section can change appreciably within a wavelength, (iii) the effects of viscosity inside the bottom boundary layer can be considered, and (iv) the three-dimensional flow features can be recovered from the perturbation solutions. Analytical and numerical examples for uniform channels, channels where the cross-sectional geometry changes slowly and channels where the depth and width variation is appreciable within the wavelength scale are discussed to illustrate the validity and capability of the present model. With the consideration of viscous boundary layer effects, the present theory agrees reasonably well with experimental results presented by Chang et al. (J. Fluid Mech., vol. 95, 1979, pp. 401–414) for converging/diverging channels and those of Liu et al. (Coast. Engng, vol. 53, 2006, pp. 181–190) for a uniform channel with a sloping beach. The numerical results for a solitary wave propagating in a channel where the width variation is appreciable within a wavelength are discussed.

Model Approach for Displaying Dynamic Filament Displacement during Impregnation of Continuous Fibres Based on the Theory of Similarity – Theory and Modelling

2021 ◽  
Vol 36 (4) ◽  
pp. 423-434
Author(s):  
F. Schulte-Hubbert ◽  
D. Drummer ◽  
L. Hoffmann
Keyword(s):  
Process Parameters ◽  
Similarity Theory ◽  
Dynamic Compaction ◽  
Experimental Investigations ◽  
Process Conditions ◽  
Scaled Model ◽  
Compaction Behavior ◽  
Thermoplastic Matrix ◽  
Analytical Foundation ◽  
Reinforced Thermoplastics

Abstract The underlying process for the production of textile reinforced thermoplastics is the impregnation of dry textile reinforcements with a thermoplastic matrix. The process parameters such as temperature, time and pressure of the impregnation are mainly determined by the permeability of the reinforcement. This results from a complex interaction of hydrodynamic compaction and relaxation behavior caused by textile and process parameters. The foundation for the description and optimization of impregnation progresses is therefore the determination of the pressure-dependent permeability of fibre textiles. Previous experimental investigations have shown that the dynamic compaction behavior during the impregnation of fibre reinforcements with thermoplastics or thermosets can be successfully characterized. However, for most cases, an analytical representation has not been possible due to the complexity of the process. Although it may be possible to reproduce this behavior by numerical calculations, the results need to be confirmed by experiments. This paper lays the analytical foundation for building a scaled model system, based on the theory of similarity, to observe, measure, and evaluate the dynamic compaction behavior of textile reinforcements under controlled process conditions.

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