臺灣博碩士論文加值系統

本研究主旨在探討具不同摩擦係數及形狀的顆粒物質在壓克力罐體容器中受束制壓力負載之力學行為。利用廣義虎克定律將三個不同高度位置所量測的應變計算應力值，分析在不同高度下不同顆粒摩擦係數及形狀之力學行為。本研究選擇五種不同生鏽程度之鋼球探討顆粒摩擦係數對顆粒體與罐體間力學行為之影響；此外，選擇球形、二款橢圓形、藥丸型、雙球形共五種不同形狀之ABS顆粒進行束制壓力實驗，並將實驗結果分別依不同顆粒形狀、顆粒長寬比、顆粒角數進行比較分析以探討其在束制壓力條件下之力學響應。
實驗結果顯示，在束制壓力條件下，增加顆粒之摩擦係數會提升顆粒體內部的互鎖效應，導致顆粒不易水平側向位移或擠壓罐壁，也提升顆粒體與罐壁間的摩擦效應，而隨著顆粒摩擦係數增加，顆粒體內的孔隙率也會隨之增加。
將球形、橢圓形、藥丸形顆粒之實驗結果進行比較，藥丸形顆粒擁有較明顯之互鎖效應，使得整體顆粒體之剛性較大，同時接觸壁面的顆粒不易產生滑動，造成整體壁面與顆粒體摩擦力量降低。而相較於球形及藥丸形顆粒，橢圓形顆粒之側向壓力係數較大，代表橢圓形顆粒在束制壓力條件下較其他兩種顆粒形狀易側向移動。針對橢圓形顆粒增加其長寬比不僅提升整體顆粒體之初始填充密度及剛性同時也提升其側向壓力係數。另一方面，在束制壓力負載下，增加顆粒角數會提升顆粒體內部的互鎖效應，使得顆粒不易滑動及轉動，導致初始孔隙率較大且水平應力以及側向壓力係數較小，但由於增加顆粒角數使得初始孔隙率較大，造成其整體剛性只有些許提升。

The purpose of this study is to investigate the effects of particle friction and shape on the interaction between a granular assembly and an acrylic cylinder and the relevant mechanical responses at various positions under a confined compression condition. Variations of wall strains are measured through strain gages at three given axial positions and used to calculate the relevant stresses through a generalized Hooke’s law. Steel spheres of five rust levels are selected to characterize the effect of particle friction. In addition, the experimental results of five selected particle shapes, namely spherical, ellipsoidal I, ellipsoidal II, cylindrical, and paired ABS particles, are compared to characterize the effects of particle shape, aspect ratio, and particle angularity.
Experimental results show that an increase in particle friction causes a greater interlocking effect between particles, resulting in a greater difficulty for particles in the granular assembly to move and press laterally under a confined compression condition. In addition, the frictional force between particles and cylindrical wall also increases as the particle friction increases. The initial assembly height increases with increasing particle friction.
For spherical, ellipsoidal, and cylindrical particles, cylindrical particles have a greater interlocking effect, resulting in a greater stiffness of the granular assembly. In addition, a larger extent of decrease in the bulk wall friction is observed for the cylindrical particles indicating a smaller extent of mobilization of the particles beside the cylinder wall. Compared with spherical and cylindrical particles, ellipsoidal particles have a greater lateral pressure ratio. It indicates a greater extent of lateral movement for ellipsoidal particles under confined compression loading. An increase in the aspect ratio of ellipsoidal particles not only causes a higher packing density and a greater stiffness of the granular assembly, but also increases the extent of lateral movement of particles and induces a greater lateral pressure ratio. On the other hand, a higher particle angularity results in a greater interlocking and a greater difficulty for the particles in the granular assembly to slide and rotate. It increases the initial porosity of the assembly and lateral pressure ratio to a small extent under a confined compression condition. Due to a larger initial porosity in the particles of a greater angularity, the stiffness of the granular assembly of paired particles only increases slightly in comparison with the spherical particles

TABLE OF CONTENTS
LIST OF TABLES VII
LIST OF FIGURES VIII
NOMENCLATURE XIII
1. INTRODUCTION 1
1.1 Granular Materials 1
1.2 Confined Compression Test 2
1.3 Friction Effect of Granular Materials 3
1.4 Shape of Granular Materials 4
1.5 Purpose 6
2. EXPERIMENTAL PROCEDURES 8
2.1 Particles with Various Friction Coefficients 8
2.2 Non-Spherical Particles 9
2.3 Experimental Setup 10
2.4 Experimental Procedure 11
3. RESULTS AND DISCUSSION 19
3.1 Mechanical Response of Granular Solid 19
3.2 Effect of Material Stiffness 23
3.3 Effect of Friction Coefficient 25
3.4 Effect of Particle Shape 30
3.4.1 Shape effect 30
3.4.2 Aspect ratio 35
3.4.3 Spherical and paired particles 37
4. CONCLUSION 40
REFERENCES 42
TABLES 45
FIGURES 48

LIST OF TABLES
Table 1 Material properties of as-received AISI 1012 steel sphere 45
Table 2 Friction coefficients of AISI 1012 steel spheres with different rust levels 45
Table 3 Dimensions of spherical and non-spherical ABS particles 46
Table 4 Material properties of spherical and non-spherical ABS particles 46
Table 5 Friction coefficients of spherical and non-spherical ABS particles 46
Table 6 Material properties of acrylic cylinder [32,33] 47
Table 7 Initial assembly state for various types of particles. 47

LIST OF FIGURES

Fig. 1 A confined compression test apparatus for bulk solid. [9] 48
Fig. 2 6-mm-diameter steel spheres of various rust levels: (a) W0; (b) W2; (c) W6; (d) W8; (e) W12; (f) W24; (g) W42; (h) W186; (i) W186+SW5; (j) W186+SW10; (k) W186+SW20. 49
Fig. 3 Nominal dimensions of various particle shapes: (a) spherical,  = 1; (b) ellipsoidal I,  = 1.5; (c) ellipsoidal II,  = 2; (d) cylindrical,  = 2; (e) paired,  = 2. (Dimensions in mm) 50
Fig. 4 Schematic of an experimental setup of confined compression test. [31] 51
Fig. 5 Photograph of the experimental setup. [31] 52
Fig. 6 Top and side views of a 260-mm-long acrylic cylinder. [31] 53
Fig. 7 Free body diagram of the granular assembly and cylinder sectioned at a given height. 54
Fig. 8 Mechanical responses at different heights of the granular assembly during confined compression for steel spheres of rust level W0: (a) vertical force; (b) average vertical stress; (c) average horizontal stress; (d) average shear stress; (e) lateral pressure ratio; (f) bulk wall friction. 55
Fig. 9 Mechanical responses at different heights of the granular assembly during confined compression for spherical ABS particle ( = 1): (a) vertical force; (b) average vertical stress; (c) average horizontal stress; (d) average shear stress; (e) lateral pressure ratio; (f) bulk wall friction. 59
Fig. 10 Mechanical responses at different heights of the granular assembly during confined compression for ellipsoidal I ABS particle ( = 1.5): (a) vertical force; (b) average vertical stress; (c) average horizontal stress; (d) average shear stress; (e) lateral pressure ratio; (f) bulk wall friction. 63
Fig. 11 Mechanical responses at different heights of the granular assembly during confined compression for ellipsoidal II ABS particle ( = 2): (a) vertical force; (b) average vertical stress; (c) average horizontal stress; (d) average shear stress; (e) lateral pressure ratio; (f) bulk wall friction. 67
Fig. 12 Mechanical responses at different heights of the granular assembly during confined compression for cylindrical ABS particle ( = 2): (a) vertical force; (b) average vertical stress; (c) average horizontal stress; (d) average shear stress; (e) lateral pressure ratio; (f) bulk wall friction. 71
Fig. 13 Mechanical responses at different heights of the granular assembly during confined compression for paired ABS particle ( = 2): (a) vertical force; (b) average vertical stress; (c) average horizontal stress; (d) average shear stress; (e) lateral pressure ratio; (f) bulk wall friction. 75
Fig. 14 Free body diagram of a portion of granular assembly at a given height. 79
Fig. 15 Vertical force at different heights of the granular assembly during confined compression for steel spheres of rust level W0 and polystyrene spheres. (Data for the polystyrene spheres are taken from Ref. [31]) 80
Fig. 16 Average vertical stress at various heights for steel spheres of rust level W0 and polystyrene spheres: (a) top strain gages; (b) middle strain gages; (c) bottom strain gages. (Data for the polystyrene spheres are taken from Ref. [31]) 81
Fig. 17 Average horizontal stress at various heights for steel spheres of rust level W0 and polystyrene spheres: (a) top strain gages; (b) middle strain gages; (c) bottom strain gages. (Data for the polystyrene spheres are taken from Ref. [31]) 83
Fig. 18 Average shear stress at various heights for steel spheres of rust level W0 and polystyrene spheres: (a) top strain gages; (b) middle strain gages; (c) bottom strain gages. (Data for the polystyrene spheres are taken from Ref. [31]) 85
Fig. 19 Lateral pressure ratio at various heights for steel spheres of rust level W0 and polystyrene spheres: (a) top strain gages; (b) middle strain gages; (c) bottom strain gages. (Data for the polystyrene spheres are taken from Ref. [31]) 87
Fig. 20 Vertical force at various heights for steel spheres of rust level W0, W6, W42, W186+SW10, and W186+SW20: (a) top platen; (b) top strain gages; (c) middle strain gages; (d) bottom strain gages; (e) bottom platen. 89
Fig. 21 Average vertical stress at various heights for steel spheres of rust level W0, W6, W42, W186+SW10, and W186+SW20: (a) top strain gages; (b) middle strain gages; (c) bottom strain gages. 92
Fig. 22 Average horizontal stress at various heights for steel spheres of rust level W0, W6, W42, W186+SW10, and W186+SW20: (a) top strain gages; (b) middle strain gages; (c) bottom strain gages. 94
Fig. 23 Average shear stress at various heights for steel spheres of rust level W0, W6, W42, W186+SW10, and W186+SW20: (a) top strain gages; (b) middle strain gages; (c) bottom strain gages. 96
Fig. 24 Lateral pressure ratio at various heights for steel spheres of rust level W0, W6, W42, W186+SW10, and W186+SW20: (a) top strain gages; (b) middle strain gages; (c) bottom strain gages. 98
Fig. 25 Bulk wall friction at various heights for steel spheres of rust level W0, W6, W42, W186+SW10, and W186+SW20: (a) top strain gages; (b) middle strain gages; (c) bottom strain gages. 100
Fig. 26 Vertical force at various heights for spherical (= 1), ellipsoidal II (= 2), and cylindrical (= 2) ABS particles: (a) top platen; (b) top strain gages; (c) middle strain gages; (d) bottom strain gages; (e) bottom platen. 102
Fig. 27 Average vertical stress at various heights for spherical (= 1), ellipsoidal II (= 2), and cylindrical (= 2) ABS particles: (a) top strain gages; (b) middle strain gages; (c) bottom strain gages. 105
Fig. 28 Average horizontal stress at various heights for spherical (= 1), ellipsoidal II (= 2), and cylindrical (= 2) ABS particles: (a) top strain gages; (b) middle strain gages; (c) bottom strain gages. 107
Fig. 29 Average shear stress at various heights for spherical (= 1), ellipsoidal II (= 2), and cylindrical (= 2) ABS particles: (a) top strain gages; (b) middle strain gages; (c) bottom strain gages. 109
Fig. 30 Lateral pressure ratio at various heights for spherical (= 1), ellipsoidal II (= strain gages; (c) bottom strain gages. 111
Fig. 31 Bulk wall friction at various heights for spherical (= 1), ellipsoidal II (= 2), and cylindrical (= 2) ABS particles: (a) top strain gages; (b) middle strain gages; (c) bottom strain gages. 113
Fig. 32 Vertical force at various heights for ellipsoidal I (= 1.5) and ellipsoidal II (= 2) ABS particles: (a) top platen; (b) top strain gages; (c) middle strain gages; (d) bottom strain gages; (e) bottom platen. 115
Fig. 33 Average vertical stress at various heights for ellipsoidal I (= 1.5) and ellipsoidal II (= 2) ABS particles: (a) top strain gages; (b) middle strain gages; (c) bottom strain gages. 118
Fig. 34 Average horizontal stress at various heights for ellipsoidal I (= 1.5) and ellipsoidal II (= 2) ABS particles: (a) top strain gages; (b) middle strain gages; (c) bottom strain gages. 120
Fig. 35 Average shear stress at various heights for ellipsoidal I (= 1.5) and ellipsoidal II (= 2) ABS particles: (a) top strain gages; (b) middle strain gages; (c) bottom strain gages. 122
Fig. 36 Lateral pressure ratio at various heights for ellipsoidal I (= 1.5) and ellipsoidal II (= 2) ABS particles: (a) top strain gages; (b) middle strain gages; (c) bottom strain gages. 124
Fig. 37 Bulk wall friction at various heights for ellipsoidal I (= 1.5) and ellipsoidal II (= 2) ABS particles: (a) top strain gages; (b) middle strain gages; (c) bottom strain gages. 126
Fig. 38 Vertical force at various heights for spherical (= 1) and paired (= 2) ABS particles: (a) top platen; (b) top strain gages; (c) middle strain gages; (d) bottom strain gages; (e) bottom platen. 128
Fig. 39 Average vertical stress at various heights for spherical (= 1) and paired (= 2) ABS particles: (a) top strain gages; (b) middle strain gages; (c) bottom strain gages. 131
Fig. 40 Average horizontal stress at various heights for spherical (= 1) and paired (= 2) ABS particles: (a) top strain gages; (b) middle strain gages; (c) bottom strain gages. 133
Fig. 41 Lateral pressure ratio at various heights for spherical (= 1) and paired (= 2) ABS particles: (a) top strain gages; (b) middle strain gages; (c) bottom strain gages. 135
Fig. 42 Average shear stress at various heights for spherical (= 1) and paired (= 2) ABS particles: (a) top strain gages; (b) middle strain gages; (c) bottom strain gages. 137
Fig. 43 Bulk wall friction at various heights for spherical (= 1) and paired (= 2) ABS particles: (a) top strain gages; (b) middle strain gages; (c) bottom strain gages. 139

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