本研究利用離散元素法(Discrete Element Method, DEM)模擬具有傾斜開槽之正方薄平板在單軸拉力作用下的力學性質及破壞過程。本研究主旨在於藉由改變平板的晶體結構和開槽的傾斜角度來觀察此兩種因素對於平板中的力學行為、裂縫的生成與傳播及裂縫路徑的影響，而研究的內容可分成三個部分:(1)比較離散元素法與有限元素法在平板中的應力分布情形;(2)分析平板在裂縫即將生成前的四種力學行為：應力集中因子、破壞力、邊界位移及應變能;(3)探討平板在裂縫生成後的裂縫發展及路徑。在第一部分的研究結果顯示，在離散元素法中，平板在裂縫生成前的應力分布狀態與有限元素法的結果非常一致，而在第二部分中的研究結果顯示：(1)在全部四種晶體結構中，應力集中因子先隨著角度的增加而上升，到達最大值(此時對應的開槽傾角皆為30度)，接著隨著角度增加而逐漸下降，最後到達最小值(此時對應的開槽傾角皆為90度);(2)在同一種晶體結構中，破壞力與應力集中因子呈現負相關，即當應力集中因子越大時其對應的破壞力越小;(3)裂縫生成前的邊界位移在所有的晶體結構中，皆在開槽傾角為90度時呈現最大值，而最小值則會因晶體結構而異，若在相同開槽傾斜角度條件下，晶體結構的位移量由大到小依序為:體心立方、簡單立方、面心立方、六方緊密堆積;(4)裂縫生成前的應變能在所有的晶體結構中，同樣都在開槽傾角為90度時呈現最大值，且最小值亦會因晶體結構而異，最後在第三部分中的研究結果顯示，在不同晶體結構及開槽傾角條件下，裂縫皆會沿著垂直拉力的方向發展直到試體完全斷裂並在裂縫附近殘留部分壓力區，且因為在面心立方及六方緊密堆積晶體結構中，顆粒及接觸鍵接的排列皆具有不對稱性，此情形會使得結構中的力量產生偏集中的現象，並造成該集中處的裂縫較其它力量集中處快發生，而在裂縫的破壞型態上，簡單立方、體心立方和六方緊密堆積晶體結構的正向鍵接破壞數分別占了各自整體鍵接破壞數的100%、83%和78%，而面心立方晶體結構則是46%，由此顯示，此四種晶體結構在承受單軸拉力作用時，主要是由拉力模式所控制，雖然在面心立方晶體結構中，剪向鍵接破壞數略多於正向鍵接破壞數。;This thesis studies mechanical behavior and failure process of a thin notched plate subjected to uniaxial tension using the discrete element method (DEM). The purpose of this study is to investigate the effects of crystal structure and notch inclination angle on the mechanical responses, crack initiation and propagation process, and crack paths. The proposed DEM model has been verified by the corresponding FEM calculation. The main findings are highlighted as follows: (1) The force-displacement curves for each crystal structure all exhibit wavy profiles and the loading stiffnesses of the curves follow the sequence of hexagonal close-packed (HCP) > face-centered cubic (FCC) > simple cubic (SC) > body-centered cubic (BCC); (2) The stress concentration factor first increases with notch inclination angle, reaches the maximum value (at the notch inclination angle of 30 degrees) and then decreases to the minimum value (at the notch inclination angle of 90 degrees); (3) In general, for the same crystal structure, the larger the stress concentration factor is, the smaller the fracture force is; (4) For the same notch inclination angle, the magnitude order of the boundary displacement is as follows: BCC>SC>FCC>HCP; (5) For all the four crystal structures, the maximum stored strain energy occurs at the notch inclination angle of 90 degrees but the minimum is at the different angle for each crystal structure; (6) The crack generally developed and propagated along the horizontal direction, and the region behind the crack tip shows the compressive contact forces; (7) The SC and BCC crystal structures show a symmetric feature of crack propagation, whereas the FCC and HCP crystal structures exhibit asymmetric characteristics; (8) In such a loading scenario, a plate with an inclined notch subjected to uniaxial tension, the crack initiation and propagation in all the four crystal structures are mainly dominated by the tension mode.
