顆粒物質受自由落體衝擊之力學分析

Mechanical Response of Granular Bed Subjected to Impact of a Free-drop Projectile

陳宇家(Yu-Chia Chen)

指導教授 ： 林志光

國立中央大學/工學院/機械工程學系/碩士(2014年)

摘要

本研究主旨在探討不同剛性及形狀的顆粒物質在透明壓克力罐體容器中受一自由落體衝擊作用之力學行為。利用加速規黏貼於自由落體上，記錄衝擊過程中的加速度值進而得知速度、灌入深度及顆粒對落體之阻力，並利用高速攝影機拍攝衝擊過程。透過廣義虎克定律將罐體上三個不同高度位置所量測的應變值計算應力，藉以分析罐壁在顆粒受衝擊過程中應力隨高度變化之情形。本研究選擇兩種不同材質探討不同剛性顆粒受衝擊下，顆粒與罐體間力學行為之差異 ; 此外，選擇球形、二款橢圓形、藥丸形、雙球形共五種不同形狀之ABS顆粒進行衝擊實驗，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受自由落體衝擊之力學響應。對於高剛性之顆粒則選擇球形及藥丸形兩種形狀之不銹鋼顆粒來探討高剛性顆粒的形狀效應。
實驗結果顯示，球形ABS顆粒及不銹鋼顆粒對罐壁產生之環向應力皆為張應力並隨高度減少而減少，而軸向應力在上層會因為顆粒濺出而對罐體造成張應力，其下層為壓應力並隨高度減少而增加。剛性大之顆粒會增加顆粒對落體之阻力，造成灌入深度遠小於剛性小之顆粒，其罐壁應力值也遠大於剛性小之顆粒，顯示在鋼性較大的顆粒床中應力較容易傳遞。而由於硬質顆粒床之灌入深度較淺，罐體大半部分內壁屬於受壓力的狀態。
將球形、橢圓形、藥丸形 ABS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，使得整體顆粒床之剛性較大，進而增加阻力導致灌入深度較淺，且不易側向移動，產生較小的環向及軸向應力比。圓球則是體積較小使得接觸落體面積較多且易側向移動，產生較大阻力，也產生較深的灌入深度，因此有較大的環向與軸向應力比。而橢圓形顆粒，由於互鎖效應較不明顯，橢圓形顆粒的環向及軸向應力比介於兩種形狀之間。針對橢圓形顆粒增加其長寬比會提升整體顆粒床的剛性，但整體之間的形狀效應差異不明顯。而長寬比小的顆粒接觸落體數目較多，產生較大阻力。另一方面，增加顆粒角數會提升顆粒體內部的互鎖效應，使得雙球形顆粒不易滑動，導致灌入深度淺及側向移動皆小，其阻力及環向與軸向應力比皆小於圓球顆粒。
採用球形、藥丸形之不銹鋼顆粒進行衝擊實驗，其環向應力與ABS顆粒趨勢一致，而在藥丸形之不銹鋼顆粒的軸向應力在底部呈現與ABS顆粒相反趨勢，進而顯示藥丸形之不銹鋼顆粒由於互鎖效應大而幾乎不滑動的現象，導致在底部的軸向應力減小，也顯示剛性大之顆粒的形狀效應較為明顯。

關鍵字

顆粒 ； 衝擊 ； 顆粒床 ； 拋射體

並列摘要

The purpose of this study is to investigate the effects of particle stiffness and shape on the interactions between a granular bed and an acrylic container and the relevant mechanical responses at various positions during impact by a free-drop projectile. The acceleration data recorded by an accelerometer are used to calculate the penetration depth and velocity of the projectile and vertical drag force. Variations of strains in the container wall are measured through strain gages attached at three heights and used to calculate the relevant stresses through a generalized Hooke’s law. Two kinds of particle material, namely steel and ABS, are selected to characterize the effect of particle stiffness. 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. For the high-stiffness particle, the experimental results for steel particles of spherical and cylindrical shapes are also compared to characterize the shape effect.
Experimental results of the spherical ABS particles and steel particles show the peak hoop stress in the container wall is of tensile stress and decreases gradually from the top of the container to the bottom. The peak axial stress is of compressive stress except for the top position and decreases gradually from middle to bottom due to various types of particle movement. For the high-stiffness particles, a greater vertical force leads to a shallow penetration and the container wall is subjected to a greater force during impact. It indicates that particles of a larger stiffness are easy to transmit force and dissipate less energy on deformation. The projectile does not completely penetrate into the steel granular bed leading to a greater extent of confined compression for the particles located at the bottom of the container.
For spherical, ellipsoidal, and cylindrical particles, cylindrical particles have a greater interlocking effect, resulting in a greater stiffness of the granular bed. Therefore, a greater vertical drag force is generated by the cylindrical particles and leads to a smaller penetration depth. A less extent of particle movement in the granular bed of cylindrical particles results in a lower hoop and axial ratio. For the spherical particles, interactions between particles are intensified for their smaller size and exert more drag force on the projectile. The hoop and axial stress ratio is greater due to a greater extent of particle movement and a deeper penetration depth. An increase in the aspect ratio of ellipsoidal particles causes a greater stiffness of the granular bed, but the interlocking effect of the ellipsoidal particle is insignificant. For a smaller aspect ratio, as the size is smaller than that of a larger aspect ratio, the interactions between particles are intensified and exert more drag force on the projectile. On the other hand, a higher particle angularity results in a greater interlocking effect and a less extent of particle movement in the granular bed of paired particles. The vertical drag force, hoop stress ratio, and axial stress ratio of the paired particles are smaller than those of the spherical particles.
For spherical and cylindrical steel particles, the variation of peak hoop stress in the container wall shows a similar trend to that of ABS particles. For cylindrical steel particles, the axial stress shows an opposite trend to that of ABS particles at the bottom position. It indicates a less extent of particle movement in the granular bed of cylindrical steel particles due to a greater interlocking effect, resulting in a decrease in the axial stress at the bottom position. Apparently, the shape effect is more pronounced for hard particles.

並列關鍵字

particle ； impact ； granular bed ； projectile

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