Powder Yield Loci

Powder Yield Loci For a given shear step, as the applied shear stress is increased, the powder will reach a maximum sustainable shear stress "U, at which point it yields or flows. The functional relationship between this limit of shear stress "U and applied normal load a is referred to as a yield locus, i.e., a locus of yield stresses that may result in powder failure beyond its elastic limit. This functional relationship can be quite complex for powders, as illustrated in both principal stress space and shear versus normal stress in Fig. 21-36. See Nadia (loc. cit.), Stanley-Wood (loc. cit.), and Nedderman (loc. cit.) for details. Only the most basic features for isotropic hardening of the yield surface are mentioned here. 

Hong, G.-H. and Watanabe, K. 2000. Powder bed tester. An instrument for measuring the powder yield locus. In Processing. Part IV, Wohlbier, R. H. (ed.). Clausthal-Zellerfeld, Germany Trans Tech Publications. 

If the wall shear stress line is curved, a Mohr circle may be drawn in contact with the powder yield locus of a separate shear test obtained at a pre-shear normal stress identical or similar to that of the wall friction test (Akers 1992). The intersection of the curved WYL with the superimposed Mohr circle is then extrapolated to the origin to give the angle of wall friction. 

Here, [L is the coefficient of internal friction, ( ) is the internal angle of friction, andc is the shear strength of the powder in the absence of any applied normal load. The yield locus of a powder may be determined from a shear cell, which typically consists of a cell composed of an upper and lower ring. The normal load is applied to the powder vertically while shear stresses are measured while the lower half of the cell is either translated or rotated [Carson Marinelli, loc. cit.]. Over-... 

This line represents the critical shear stress that a powder can withstand which has not been over or underconsolidated, i.e., the stress typically experienced by a powder which is in a constant state of shear, when sheared powders also experience fiiciion along a wall, this relationship is described by the wall yield locus, or... 

In general, a yield locus is obtained that relates the shear strength of the powder bed to the consolidation load and reduced load. The yield locus has been found to take the following form [71] ... 

A rigid-plastic powder which has a linear yield locus is called a Coulomb powder. Most powders have linear yield loci, although, in some cases, nonlinearity appears at low compressive stresses. A relation between the principal stresses in a Coulomb powder at failure can be found from the Mohr circle in Fig. 8.4 as... 

Figure 16(a). The term Cohesionless was therefore used to describe materials which have a negligible shear strength under zero normal load (an = 0). On the other hand, Jenike found that the yield loci of cohesive materials differ significantly from a straight line and have a nonzero intercept, indicated by C. Moreover, the position of the locus for a cohesive powder is a strong function of the interstitial voidage of the material. Fig 16(b) shows the typical yield locus for cohesive materials. 

Construction of the Dynamic Internal Yield Locus. The dynamic yield locus represents the steady state deformation, as opposed to the static yield locus which represents the incipient failure. The dynamic yield locus is constructed by plotting on a (a, t) plane the principal Mohr circles obtained for various consolidation stresses. The dynamic yield locus will be the curve or straight line tangent to all circles, as shown in Figure 17. The dynamic angle of internal friction S and cohesion C are independent of the consolidation stress. S and Q are obtained as the slope and the intercept at er=0 of the dynamic yield locus of the powder. 

Jenike developed the idea that no single line represents the yield but rather a curve called the yield locus. The yield behavior depends on the packing density of the powder when it is caused to flow under the action of normal and shear stress. Figure 12.36 shows a yield locus for a given porosity, e. A Mohr circle for the stage when yielding starts is characterized by the principal stresses i and 2-The points at the end of the yield locus lies on the Mohr circle pertains to... 

In general, this Ck)ulomb yield criterion can be used to determine what stress will be required to cause a ceramic powder to flow or deform. All that is needed are the two characteristics of the ceramic powder the angle of friction, 8, and the cohesion stress, c, for each particular void fraction. With these data, the effective yield locus can be determined, from which the force required to deform the powder to a particular void fraction (or density) can be determined. This Coulomb yield criterion, however, gives no information on how fast the deformation will take place. To determine the velocity that occurs durii flow or deformation of a dry ceramic powder, we need to solve the equation of motion. The equation of motion requires a constitutive equation for the powder. The constitutive equation gives the shear and normal states of stress in terms of the time derivative of the displacement of the material. This information is unavailable for ceramic powders, and the measurements are particularly difficult [76, p. 93]. 

Eq. (5) describes the yield locus. As early as 1965, Eq. (5) was established empirically from a study of the shapes of yield loci for more than 30 powders ... 

As with the Jenike cell, this process is time-consuming. Amidon and Houghton, " however, used a single yield locus with this cell for comparative purposes. Hiestand et al., ° in comparing this apparatus to the Jenike cell, claimed that this simple shear cell can be used to provide characterization of the unconfined yield strengths of powders. The results from the two devices are not identical. However, as much as the Hiestand device requires less powder and the consolidation step is more automated and consistent, it provides an inexpensive alternative to the Jenike-type cell to characterize pharmaceutical powders. Amidon and Houghton used the cell to examine the effect of moisture on the powder flow properties of microcrystalline cellulose. ... 

Heistand, E.N. Poet, C.B. Tensile strength and compressed powders and an example of incompahbihty as end-point and shear yield locus. J. Pharm. Sci. 1974, 63 (4), 605-612. 

Flowability If we re considering particles, powders, and other products that are intended to flow, then this is a very important consideration. These materials need to easily flow from bins, hoppers, and out of boxes for consumer products. Powder flowability is a measure-able characteristic using rotational shear cells (Peschl) or translational shear cells (lenike) in which the powder is consolidated under various normal loads, and then the shear force is measured, enabling a complete yield locus curve to be constructed. This can be done at various powder moistures to create a curve of flowability versus moisture content. Some minimal value is necessary to ensure free flow. Additional information on these devices and this measure can be found in Sec. 21, Sohd-Solid Operations and Processing. ... 

There exists a critical state line, also referred to as the effective yield locus. The effective yield locus represents the relationship between shear stress and applied normal stress for powders always in a critically consolidated state. That is, the powder is not over- or undercompacted but rather has obtained a steady-state density. This density increases along the line with increases in normal stress, and bed porosity decreases. 

When sheared powders also experience friction along a wall, this relationship is described by the wall yield locus, or... 

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