Unconfined stress

The most complicated technique for the determination of powder flowability is that proposed by Jenike (Section 1.6.1), in which the ratio of the maximum compaction stress, <7, to an unconfined stress, /c, at a specified shear stress of 3 kPa - the flow function, ff- is calculated to predict the ease of powder flow. This Jenike flow function, = cti//c, has remained the main consensual parameter designated for mass flow hopper design and the flowability of powders. 

In order to achieve unique numbers for various and different degrees of flowability Jenike calculated the failure function at a specific value of the unconfined stress. The specific value of the ratio of the major consolidation stress to the unconfined stress was taken as 6.5 Ibf/ft (3.11 kPa) in the initial, Jenike designed, 4 inch diameter shear cell, because at this value the relationship between fa and a showed only small deviations from linearity. Currently a value of 3 kPa is generally used with a standard shear cell tester. 

Figure 1J12 Williams mould for the determination of unconfined stress (WiUiams et al. 1970/71).

Table 1.14 Comparison of the unconfined stress, /c, from the shear cells of Jenike and Peschl with the Johanson indicizer on BCR 116, a mineral oxide, com starch and flour.

Unconfined yield stress of powder kg/cm psf u,v Granule volumes 3 cm in ... 

Flow Property Tests Flowahility of the produc t granules can be charac terized by unconfined yield stress and angle of friction by... 

A powder s strength increases significantly with increasing previous compaction. The relationship between the unconfined yield stress/, or a powder s strength, and compaction pressure is described by the powder s flow function FE The flow function is the paramount characterization of powder strength and flow properties, and it is calculated from the yield loci determined from shear cell measurements. [Jenike, Storage and Flow of Solids, Univ. of Utah, Eng. Exp. Station Bulletin, no. 123, November (1964). See also Sec. 21 on storage bins, silos, and hoppers.]... 

The unconfined yield stress is a measure of the stress necessary to cause a material unsupported in two directions to fail in shear. This is what must happen when an arch fails within the powder or at the hopper opening. The effective... 

The behavior of confined flames differs considerably from that of unconfined flames. Acceleration of the gases, caused by confinement, results in the generation of shear stresses and turbulent motions, which decrease the influence of approach stream turbulence and the effect of chemical kinetic factors. How the implementation of the ABC and the PPDF method helps to obtain the experimentally observed flow patterns and to understand the mechanism of flame stabilization and blow-off is demonstrated in this section. 

It is convenient to introduce the concepts of material flow function, FF, and flow factor, ff. The material flow function, FF, relates the unconfined yield stress, To, to the corresponding major consolidating stress, cri, and is determined experimentally from the yield locus of the material, as shown in Fig. 8.9. The material flow function is presented as a plot of To versus flow factor, ff, is defined by... 

Considering the equilibrium of a stable arch, show that the minimum diameter of the orifice in a conical hopper, d,ma, which is defined to account for the arching, can be related to the unconfined yield stress of the bulk material by the relation... 

It is required to design a mass flow conical hopper with the volume capacity of 100 m3 to store a cohesionless material of bulk density 1,700 kg/m3 and an angle of internal friction 40°. Four sets of shear tests have been conducted on the material and results for the unconfined yield strength and the corresponding consolidating stress are as follows ... 

All the preceding particulate handling steps are affected by the unique properties of all particulates, including polymeric particulates while they may behave in a fluidlike fashion when they are dry, fluidized and above 100 pm, they also exhibit solidlike behavior, because of the solid-solid interparticle and particle-vessel friction coefficients. The simplest and most common example of the hermaphroditic solid/ fluidlike nature of particulates is the pouring of particulates out of a container (fluidlike behavior) onto a flat surface, whereupon they assume a stable-mount, solidlike behavior, shown in Fig. 4.2. This particulate mount supports shear stresses without flowing and, thus by definition, it is a solid. The angle of repose, shown below, reflects the static equilibrium between unconfined loose particulates. 

Fig. 5.17 Unconfined compression stress-strain curves and experimentally measured temperature increase ATa as a function of strain for PS (Dow 685), LDPE (Dow 640), and PP (LG H670). The initial test specimen was at 26°C and the crosshead speed of the compressing har with the load cell was 25.4 mm/min. The specimen dimensions were 101 mm diameter and 71 mm height. [Reprinted by permission from M. H. Kim, Ph.D Thesis, Department of Chemical Engineering, Stevens Institute of Technology, Hoboken, NJ (1999).]...

The unconfined yield strength of the powder,, is a powder characteristic which decides whether it can resist flow under gravity from a certain dipleg configuration, and is a function of the consolidating stress (c ) present during its preparation as shown in Fig. 25. 

Because the stress normal to the free bottom surface of the arch would have to be zero, the value of the unconfined yield strength fy, which is necessary for arching, can be obtained from Eq. (79) with the condition of d2 = 0, i.e.,... 

If, as stated above, Pcr = lOkbar, then the question arises how stresses of this magnitude can be generated by impact in explosive compacts whose compressive strengths are about 100 fold less than Pcr. For unconfined explosive compacts (in Kholevo No 2) this can only occur with thin explosive compacts, ie with explosive layers whose h/D l where h D are explosive thickness diameter. The relation between, Ou, the ultimate compressive strength of the explosive compact the average stress. Fu, at which the compact fails via brittle fracture (in compression) is ... 

Fig. 5 Mohr circle construction to obtain the major normal stress, (T v the unconfined field stress, fc. (From Ref. l)...

Flow Functions and Flowabilily Indices Consider a powder compacted in a mold at a compaction pressure Oi. When it is removed from the mold, we may measure the powder s strength, or unconflned miiaxial compressive yield stress L (Fig. 21-38). The unconfined yield and compaction stresses are dietermined directly from Mohr circle constructions to yield loci measurements (Fig. 21-36). This strength increases with increasing previous compaction, with this relationship referred to as the powder s flow function FF. 

One may compare the flowability of powders at similar pressures by comparing their unconfined yield stress at a single normal stress, or one point off a flow function. In this case one should clearly state the pressure of comparison. Flow indices have been defined to aid such one-point comparisons, given by the ratio of normal stress to strength, or... 

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