本文採用Hill的異向性降伏理論及Updated Lagrangian Formulation (ULF)的觀念，建立一增量型彈塑性大變形三維有限元素分析程式，以模擬方杯深引伸成形製程。由於流線法在預測初始料片輪廓曲線時，並未考慮沖頭底部圓弧角，因此在方杯引伸貫穿成形後，方杯的實際杯高將會高於所給定的設定杯高。因此本文利用流線法及其補正公式預測固定杯高之初始料片外形，根據不同杯高的假設來預測各料片之初始輪廓，再進行方杯深引伸成形分析，進而判斷出方杯深引伸成形極限之最佳化初始料片之輪廓曲線。 本文並設計一組方形模具，進行方杯深引伸成形實驗，以探討方杯深引伸之杯高之分佈、厚度變化情形與破裂情況，進而得到方杯深引伸成形最佳化料片之成形極限，此數值分析所得之結果均可合理的預測實驗成果。 經由數值分析與實驗結果比較得知，固定杯高47.5mm的初始料片外形是方杯深引伸貫穿達成形極限之最佳化料片，並且與圓形料片經直接貫穿成形後之方杯在外形上做比較，經流線法及補正公式計算之方杯在平行邊處較為平整，而圓形料片其方杯平行邊之中點附近仍為曲線外形，可知由流線法及補正公式所預測之料片經深引伸成形後之工件具有較佳的外形。最後利用極限引伸比(LDR)之定義可知，其極限引伸比為2.56。 A methodology for formulating an elasto-plastic finite element model was developed to analyze the deep drawing process of the square cup. The model was based on the Updated Lagrangian Formulation and Hill’s yield criterion. Because the stream line didn’t consider the effect of punch radius when predicting the initial contour of optimum blank, hence the actual height of square cup would be higher than the fixed height of square cup after deep drawing. Therefore, stream line and its modified formula were used in this study. According to the assumption of the different cup height, the prediction of the optimum contour profile would be achieved. Also, the simulation of the deep drawing of square cup was proceeded to determine the initial contour profile of optimal blank to the forming limit. A set of tools was designed to perform the deep drawing experiment of the square cup. A good agreement was obtained from the comparison of the results between the simulation and experiment, such as the distribution of cup height and the distribution of the workpiece thickness. In addition, the forming limit could be gained from the deep drawing experiment of the optimum blank of the square cup. Therefore, the elasto-plastic finite element program simulation result could predict the experiment result reasonably. From the comparison of the results between the simulation and experiment, the square cup height was 47.5mm of the initial contour profile of optimal blank to the forming limit. The appearance of the square cup of the optimum blank after deep drawing was better than the circular blank. Finally, the limiting drawing ratio of the optimal blank was 2.56 in the deep drawing process of square cup.
