PACKING OF PARTICLES
Particle packing is commonly divided into two types:
(1) regular (or ordered) packing .
(2) random packing.
The commonly used ceramic forming methods produce random packing arrangements. Several parameters can be used to characterize the
packing arrangement, but two of the most widely used are:
Packing density (also referred to as the packing fraction or the fractional solids content), defined as;
Packing density =(volume of solid)/(total volume of the(solids+voids))
2. Coordination number, which is the number of particles in contact
with any given particle.
The packing density is an easily measured parameter that provides much insight about the behavior of a powder.
Regular Packing of Monosize Spheres
In order to build up a three-dimensional packing pattern of particles we can begin conceptually by
(1) packing spheres in two dimensions to form layers
(2) stacking the layers on top of one another.
Where the angle of intersection between the rows has limiting values of 90? and 60?. Although other types of layers that have angles of intersection between these two values are possible, only the square layer and the simple rhombic layer will be considered here.
Random Packing of Particles
Two different states of random packing have been distinguished. If the particles are poured into a container that is then vibrated to settle the particles, the resulting packing arrangement reaches a state of highest packing density (or minimum porosity) referred to as dense random packing. On the other hand, if the particles are simply poured into the container so that they are not allowed to rearrange and settle into as favorable a position as possible, the resulting packing arrangement is
referred to as loose random packing. An infinite number of packing arrangements may exist between these two limits. The packing densities of a powder after pouring and after being vibrated are commonly referred to as the poured density and the tap density, respectively.
Factors Influencing the Compaction of Particles
A severe problem in die compaction is that the applied pressure is not transmitted uniformly to the powder due mainly to friction between the powder and the die wall.
The application of a uniaxial pressure pz to the powder leads to the generation of a radial stress pr and a shear) stress at the die wall. The radial and shear stresses vary with distance along the die, so the resultant stress in the compact is nonuniform.
The parameters investigated included the mean powder particle size dp, the roughness of the wall Rw, the hardness of the powder Hp, the hardness of the wall Hw, and the use of lubricants.
A layer of the fine particles sticks to the die wall so that there is no direct contact between the stationary powder compact and the moving wall in the friction coefficient apparatus. In this case, Rw and Hw have no effect on the powder particles. Failure occurs within the powder compact
and not at the die wall.
For particles larger than the wall roughness is dependent on both the powder parameters and the die wall parameters. reflection of the friction between the particles and the relatively smooth wall. Failure in this case occurs at the powder wall interface.
The higher friction coefficient, reduced uniformity of die filling, and greater tendency for agglomeration are largely responsible for the more severe density gradients obtained in die compaction of fine powders.
The friction coefficient between the powder and a rough wall is also dependent on the direction of the grooves in the wall. The friction is lower if the grooves run in the direction of relative motion between the powder and the die wall. The effect of die-wall lubricants (e.g., stearic acid) can be fairly complex.
For fine particles (dp/Rw ? 1), the coefficient of friction decreases gradually as the thickness of the lubricant increases, and the magnitude of the decrease can be fairly significant when the thickness of the lubricating layer becomes larger than the particle size. For coarse particles (dp/Rw > 1), the presence of a lubricant causes only a small reduction in the die-wall friction, and almost no dependence on the thickness of the lubricating layer is observed.
The type and amount of agglomerates in the powder influence its compaction behavior. The effect of the particle shape can sometimes be difficult to predict. The spherical (or equiaxial) shape is the commonly desired geometry, but flat particles with smooth surfaces can provide
a higher compact density if they become aligned.
Compaction Defects
After the completion of the die compaction process, we require that the green body be free of macroscopic defects and that density gradients be as low as possible. Density gradients lead to the development of crack like voids in the sintered body and can also lead to cracking and warping of the body during sintering.
Several factors can be controlled to reduce the extent of density gradients in the powder compact. Uniform die filling reduces the amount of internal movement of the powder during the compaction process. The use of lubricants to reduce the internal friction between the particles and die-wall friction can lead to significant improvements.
Stress gradients (and hence, density gradients) due to die-wall friction are enhanced with increasing ratio of the length to diameter (L/D) of the compact. For the single-action mode of die compaction, L/D should be less than 0.5, while for the double-action mode, it should be less than 1.
The use of a binder to increase the compact strength, reduction of the applied pressure to reduce the extent of the spring back, and the use of a lubricant to reduce die wall friction can significantly reduce the tendency for defect formation.
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