本文採用顯性動態有限元素法，結合材料彈塑性理論，發展出一套三維有限元素分析程式，進行金屬板材擴孔成形與初始破裂分析，並探討擴孔發生破裂之位置、工件厚度變化、成形極限圖，及沖頭負荷與衝程關係，且設計一組圓柱形模具進行擴孔成形實驗，以驗證程式的可信度。 本文以材料單軸拉伸試驗所得應力－應變曲線下之應變能密度，作為數值模擬擴孔成形工件達初始破裂的判斷依據。由擴孔成形實驗結果得知，當料片初始孔徑小於4mm時，工件於沖頭圓弧角處發生初始破裂；若料片初始孔徑介於4mm到15mm 之間時，工件於沖頭平底部發生初始破裂；當料片初始孔徑大於15mm時，工件於內孔周緣處發生初始破裂。由初始孔徑4mm之料片於擴孔成形之數值模擬與實驗結果比較得知，沖頭負荷與衝程關係、內孔輪廓大小、應力與應變分佈、成形極限圖與工件厚度分佈等，皆顯示實驗與數值模擬間的一致性。 The objective of this study was to analyze the initial fracture in bore-expanding process of sheet metal by using the dynamic explicit finite element analysis program, which was based on the Updated Lagrangian Formulation and elasto-plastic theory. Simulation results included the deformation and the fracture position, the variation of the workpiece thickness, the forming limit diagram, and the relationship between punch load and punch stroke. A set of tools was designed for the bore-expanding experiment to verify the reliability of the program. The strain energy density under the stress-strain diagram by the uniaxial tensile tests was used to the criterion of the initial fracture in the simulation. According to the results of bore-expanding process, when the initial hole was less than 4mm, the workpiece was fractured near the punch corner. When the initial hole was between 4mm and 15mm, the workpiece was fractured around the punch flat-bottomed. If the initial hole was greater than 15mm, the workpiece was fractured around the hole. Simulation results of initial hole included the relationship of punch load and punch stroke, the hole profile, the distribution of stress and strain, the forming limit diagram, and the variation of the workpiece thickness. The simulation results showed good agreement with the experiments in the bore-expanding process.
