Strona 2_redak - Instytut Agrofizyki im. Bohdana DobrzaÅskiego ...

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8 Numerous granular materials when consolidated reveal cohesion that allows to maintain shape enforced under load. Ratholes or channels may be formed in granular materials but not in liquids. No fundamental mechanical model is currently available to describe behaviour of granular materials. The lack of precise description of material behaviour results in serious practical problems. Unpredictability leads to clogged chutes and catastrophic failures of industrial silos. Mechanical properties of materials stored in silos influence pressures exerted on the walls and flow patterns developing during discharge. Variation in raw material properties may result in a lack of reliability and repeatability of final product properties that may cause high costs in food industry, but may be disastrous in the case of pharmaceutical product. In pharmaceutical industry uniform mixing of medicinal components may be critical, as well. Considering that granular materials are so widespread and their use in industry increasing further understanding of how these media behave can have a profound impact on economy worldwide. Research in this area that has been intensively conducted in last 40 years had important implications for manufacturing and new processes. Background for the recent development in granular mechanics and technology has been given by results of investigations of Andrew Jenike presented in „Gravity flow of bulk solids” published in 1961 [74]. Although at that time it was clear that most of processing industries dealt with flow of granular materials Jenike’s book was the first comprehensive study of the subject. The fact that the work appeared at that time stemmed from the progress in theory of plasticity and in techniques of numerical calculations that had taken place in former fifteen years [74]. Jenike adopted testing technique and some concepts of soil mechanics but his creative input was substantial in that he analyzed granular material under 100 to 1000 lower load. In such conditions some effects that were never observed in soil mechanics got great importance. One example is curvature of the envelope of Mohr circles in (σ,τ) coordinates with no meaning in soil mechanics and of crucial importance for determination of flowability of granular material. For Jenike silo technique was natural field of application of the theory where he contributed significantly. After 40 years of work in numerous laboratories specialists achieved agreement in some questions and a set of national and international codes of practice as in the case of silo design: American ACI 313-91 [1] and ASAE EP433 [4]; Australian AS 3774 [10], Polish PN-B-03254 [135], and European Eurocode 1 [50]. Usually code of practice are contains standard procedures for determination of mechanical properties of stored granular materials. The earliest approach of scientists for predicting behaviours of bulk solids was continuum theory that looks at a volume of material as a whole, as a solid
9 body or a liquid. Continuum approach led to solutions numerous problems of technology but it failed in the cases where interactions of grains were important. Thus, the opposite extreme alternative is to model every single grain, which is what the discrete element method (DEM) does. This modelling technique requires extensive and costly computations so current solutions are limited to two-dimensional models of systems not exceeding 10000 particles. Other more popular approaches applied are: statistical mechanics, fluid mechanics, kinethic theory micropolar medium and finite element method. Specific questions in interest of science are, to quote several: granular flows, granular compaction, segregation, convection, avalanches, surface waves, collisions and friction, inelastic collapse, jamming and fluctuations, energy flows, strength properties, anisotropy of packing, stress fluctuation. The findings are published in journals like Powder Technology, Powder Handling and Processing, Geotechnique, Acta Mechanica, Granular Matter, International Journal for Analytical and Numerical Methods in Geomechanics, BIT Numerik Mathematik, and the International Journal of Solids and Structures. The presented work contains brief description of the most popular theoretical approaches, presents popular methods and equipment for determination of material parameters and typical or interesting examples of experimental results. 2. CONTINUUM MECHANICS APPROACH 2.1. The plastic flow rule The common feature of granular materials that distinguish them from other materials is the negligible value or total absence of tensile strength. Subjected to the isotropic stress, the materials are characterized by considerable compressibility and variable resistance to shearing related to precompaction applied. The high practical significance of mechanical effects taking place in granular materials resulted in the creation of numerous theoretical models and experimental methods for the investigation of yielding of such materials [32, 35, 39, 165]. Plastic strain of granular material can take place under the effect of both isotropic and deviatoric stress. Isotropic stress causes only the compaction of a material, while deviatoric stress can cause both compaction and dilation of the material, depending on the earlier stress path, as well as shear strain without volume change referred to as the critical states. The theory of plastic yielding is based on the assumption of the existence in space of the stress of plastic potential G(σ ij ). The existence of the potential has not been proven through deduction. Therefore, the assumption has to be treated as an axiom of the theory of plastic yielding, and its correctness has to be confirmed experimentally [15]. The plastic flow rule is a term applied to the relation between
Page 2 and 3: EC Centre of Excellence AGROPHYSICS
Page 4 and 5: 4 9.3. Factors influencing the coef
Page 6 and 7: 6 BASIC NOTATION c - cohesion [kPa]
Page 10 and 11: 10 the tensor of plastic strain inc
Page 12 and 13: 12 Fig. 2.1. Yield curves with comp
Page 14 and 15: 14 Stable or unstable behaviour of
Page 16 and 17: 16 In turn, the model of Lade, also
Page 18 and 19: 18 same porosity need not have iden
Page 20 and 21: 20 where: A = ∫ E( β) sin βdβ
Page 22 and 23: 22 (β = 0 o ), positioning the out
Page 24 and 25: 24 grain was poured into the mould
Page 26 and 27: 26 axes of the ellipse characterizi
Page 28 and 29: 28 [176] for the determination of p
Page 30 and 31: 30 A different approach to the desc
Page 32 and 33: 32 where: I - moment of inertia, k
Page 34 and 35: 34 a) b) f s f s m M f n f n Contac
Page 36 and 37: 36 The micropolar model yields resu
Page 38 and 39: 38 Fig. 3.17. Model of shear band f
Page 40 and 41: 40 In the case of agricultural mate
Page 42 and 43: 42 5.2. Density of consolidated mat
Page 44 and 45: 44 (cereal grain, sand, soil), the
Page 46 and 47: 46 Multiple wetting and drying of g
Page 48 and 49: 48 vertical pressure within the ran
Page 50 and 51: 50 of the curve defined by A, where
Page 52 and 53: 52 6. Vertical consolidation refere
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Page 56 and 57: 56 7.2.2. Bulk density Stress-strai
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58 near the box wall and lifted alo
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60 and the upper boundary was 18.5
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62 A -1 5 -1 0 -5 1 0 5 -5 5 1 0 1
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64 Fig. 8.2. Yield locus and effect
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66 in such a way that friction woul
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68 a) b) µ = tg ϕw ϕ w c) d) e)
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70 9.3. Factors influencing the coe
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72 galvanized steel received from d
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74 9.3.4. Velocity of sliding Becau
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76 1+ sinϕ k = . 1 − sinϕ (10.3
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78 N ϕ VLQϕ 3UHVVXUHUDWLRN
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80 10.4.1. Friction force mobilizat
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82 10.4.3. Moisture content With in
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84 Table 10.1. Measured (k s ) and
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86 conventional engineering analyse
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88 a, b - product-dependent coeffic
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90 also be performed as a function
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92 reliable processing and stable v
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94 unconfined yield strength to pow
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96 The Chute Index (CI) is recommen
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98 obtained the maximum deviation o
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100 efficient flow control using op
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102 In the field of experimental in
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104 22. Britton M.G., Moysey E.B.:
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106 69. Horabik J., Rusinek R.: Pre
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108 114. Morland L.W., Sawicki A.,
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110 158. 6WSQLHZVNL$ Influence of m
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112 16. APPENDIX - Physical Propert
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114 16.2. Density and porosity Tabl
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116 Table 16.7. Mean values (±St.
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126 Table 16.16. Cont. 1 2 3 4 Icin
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136 Table 16.25. Cont. 1 2 3 4 Icin
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140 Table 16.29. Cont. Table sugar
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144 Table 16.35. Mean values (± St
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