Asymmetry of plastic flow in a symmetrical convergent channel

1981

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Many investigations in the USSR and elsewhere have indicated that the discharge of loose materials from tall vessels {silos) is accompanied by local rises in the loads on the walls, pulsation of the loads, and nonuniform loading round the perimeter of the vessel [1][2][3]. Although much effort has been made to elucidate the mechanism of formation of these features, so far there are no satisfactory explanations of the development of the high peak loads or of the pulsations. The rise of pressure during discharge is associated with hanging (arch formation) [4][5][6], with changes in the coefficient of friction of the material on the wall [1], and even with the influence of acoustic shock waves [7]; the asymmetric pressures on the walls are associated with inhomogeneous stacking of the material and nonuniform rigidity of the structure round its perimeter [8].Experts consider that while calculations of the static pressures are rather indeterminate, calculations of the loads arising during discharge of the materials are even more so [9]. This is why there are relatively frequent cases of serious damage to structures for the storage and treatment of loose materials [8,9]. Many investigators have remarked that the solution to this problem will involve further detailed studies of the processes occurring during movement of materials in vessels [10].in [12,13] we showed that the principal disturbances in material flowing out of a vessel involve its motion in convergent channels, i.e., in the conditions of maximally confined deformation. Such channels are components of any bunkers, whether the latter have a convergent section or a fiat bottom; in the latter case the convergent channel is formed within the material itself. Let us therefore first consider experiments on the deformation of loose materials in convergent axisymmetric channels.The experimental methods and the characteristics of the materials used in our investigations were described in detail in [11,12]. To study the kinematics of motion of material in axisymmetric vessels, there is an additional method, ngelatin freezing, n which has proved to be more convenient and less troublesome than the ~paraffin coat freezing n method. Before forming the load, all the material (both light and black sand) was heated to 100*C. After a given portion of the loose material had been discharged through the outlet, the deformed material remaining in the vessel was filled with a heated gelatin solution {water and gelation in the proportions of 10 : 1 by weight). The specimen was then cooled, removed from the vessel, and cut up along various planes.As the convergent channels we used glass funnels and also funnels to which various grades of emery paper had been glued on the inside. The angles of divergence of the funnels were 45-90 ~ and the diameters of the outlets 5-16 ram. The use of glass funnels not only reduced the coefficient of friction between the material and the wall, but also had the advantage that it was possible to make direct observations on the kinematics near the wall...

Section: Institute Ofmentioning

confidence: 99%

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confidence: 99%

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confidence: 99%

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Deformation of loose materials in convergent axisymmetri channels

1981

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“…Without giving a detailed analysis, it is only noted that stress asymmetrty is still connected with kinematic deformation of loose materials in descending channels demonstrated in [13], and new features detected which are well illustrated in Fig. 7 (figures in one of the horizontal sections indicate the sequence of block separation during formation of a submerged descending channel).…”

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confidence: 92%

The second form of flow for loose materials in bunkers

1985

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The external manifestation of the so-called second (free) form of flow for loose materials in bunkers during discharge is descent of the charge surface parallel to itself, or as it is customary to assume, material movement as a whole column alon~ the wall.It is well known that this form of flow occurs, as a rule, in high silo bins (H = H/D ~ 3-4; H is silo height, D is diameter).The second form attracts most attention both from specialists in the field of loose body mechanics, and specialists in the field of design, planning, and operating silo structures. This interest is caused by the fact that with the second form of movement horizontal pressures on the silo walls increase by a factor of 2 to 2.5 compared with static pressures, and according to some data even by a factor of 5-7 [i]. Increased pressures develop at a certain characteristic height asymmetric relative to the bunker axis of symmetry and they have a pulsating character [2,3].The increase in pressure at the~closing surface during discharge, as already noted in [4], is connected with a freely formed change in flow and even with sonic shock waves.A number of researchers are inclined to explain this increase by dynamic phenomena [5] (whence the extensively used term "dynamic" loading).There is no single view on the nature of the rest of these facts.Standards set in most countries for determining static loads on silo el~ents recommend the method proposed in 1895 by Janssen [6] in spite of the existence of many other methods. This selection is dictated by the simplicity of relationships obtained in [6], and numerous verifications of calculated results by experiments.This situation is a weighty argument in favor taking the Janssen relationships as a basis for determining dynamic loads (in future we will call them peak or maximum loads). However, the difference in views on the mechanism of load formation, and, as a consequence of this ambiguity in estimates of absolute values of the latter, leads to the fact that the load curves for the same structure calculated by standards of different countries differ markedly.This paradoxical fact is illustrated in Fig.

“…1 in plane converging channels with a rigid wall inclination to the vertical 8 < 8* (8* is the angle atwhich in statics the condition T n > o n tan ~wa will be fulfilled alSng the walls, where T and o n are tangential and normal stresses at the wall). The discharge from converging c~annels has been considered previously [5][6][7]. We return to it only since it is possible to explain certain details of the process.…”

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Features of the stress-strain state of loose materials in converging channels and bunkers

1986

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624.074.7~042.8 I. We concentrate first on the strength properties of loose materials which are well described by three typical curves plotted on the coordinates "ratio of tangential to normal stresses-shear" (Fig. i). Materials with compact particle packing have peak and residual "strength" (~ = ~max, ~ " @in' respectively, curve i), and the limiting and residual "strength" of the same materials with the loosest packing coincide and they are determined by the internal friction angle ~in (curve 2) [i]. Curve 3 characterizes the material being considered independent of the original quality of packing with shears of relatively smooth surfaces. In this case "strength" is governed by the material friction angle ~w at the wall a whose value is alwasy less than the angle Smax, as also for angle ~in" The latter is easily explained if this property of loose materials is considered as dilation. Shear of loose materials for relatively smooth surfaces proceeds without dilation effects. Such changes in volume which may be observed here are only related to reorientation of individual particles and a changeover to a more stable state (shear at stress levels which lead to particle failure at points of contact are not considered). With loose material shear for a relatively smooth surface made of the same material as the particles themselves, angle ~wa takes on the sense of angle ~ ' for the contact friction of a group (aggregate) of particles. The latter differs from the contact friction angle for an individual particle ~ and it may be considered as the friction angle for a nondilating (u = 0, where ~ is dilation ~ngle) loose material (strictly speaking the angle ~' should possibly be called the internal friction angle).Taking account of this, the peak value of the friction angle (traditional terminology) 9 @max " ~' + ~max, and the internal friction angle ~in = ~min = @~' + @min"It follows from Fig. 1 that the contribution of dilation to the overall strength of loose materials and materials with a structure as a whole is greater, the more compact the original particle packing. As was shown in [2][3][4], dilation makes a decisive contribution to the stress-strained state of loose materials with loading under constrained conditions. 2. We now consider the flow of loose materials whose "stength" is characterized by curve 1 in Fig. 1 in plane converging channels with a rigid wall inclination to the vertical 8 < 8* (8* is the angle atwhich in statics the condition T n > o n tan ~wa will be fulfilled alSng the walls, where T and o n are tangential and normal stresses at the wall). The discharge from converging c~annels has been considered previously [5][6][7]. We return to it only since it is possible to explain certain details of the process. It was shown in [5] that flow in channels proceeds with formation of slip surfaces separating masses into individual "rigid" blocks, and it is characterized by deformation asymmetry. As in other cases of gravitational flow [3,4,8], the initial deformation paths during discharge from channel...