金屬成形技術，其具有許多優點，例如生產效率高、成本低和產品
可具複雜之幾何外形等。不過，當成品尺寸縮小之微米等級時，如摩
擦、材料機械性質等對成形有影響之因素，其效應與巨觀下有所差異
的現象將其稱之為尺寸效應。
本文採用Prandtl-Reuss 塑流法則和Hill 的降伏條件，結合有限變
形理論及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，並應用四邊形四節點退化殼元
素(Degenerated Shell Element)所推導之形狀函數偶合入剛性矩陣中，
組成三維有限元素之分析模式，以及使用廣義min r 法處理板材成形
時，元素降伏之判斷、最大容許應變增量、最大容許旋轉增量、料片
與模具間節點之接觸或分離等問題，分析結果包括衝頭負荷與衝程關
係圖、工件之應力分佈圖和工件之成形履歷。
本研究之研究重點在於討論grain size effect 對於銅箔微深引伸之成
形極限之影響，選取厚度0.1mm、0.075mm、0.05 mm 之銅箔並且利
用熱處理方法改變試片內部之晶粒大小進行實驗，以求得晶粒尺寸的
改變對銅箔微深引伸之成形極限之影響，以作為日後在微深引伸測試
的參考。

The metal forming technology, it has many merits, for example the
production efficiency is high, the cost is low and the product may have
the complex geometry contour and so on. However, when finished size
reduction micron rank, like the friction, the material mechanical property
and so on to form the influential factor, under its effect and the great view
has the difference phenomenon to call it the size effect.
A methodology of formulating an elasto-plastic three-dimensional finite
element model, which is based on Prandtl-Reuss flow rule and Hill’s
yield criterion respectively, combined with an updated Lagrangian
formulation, is developed to simulation sheet metal forming processes.
An extended r-min algorithm is proposed to formulate the boundary
conditions, such as the yield of the elements, maximum allowable strain
increment, maximum allowable rotation increment, maximum allowable
equivalent stress increment, and tolerance for nodes getting out of contact
with tool.
The simulation results include relationships between punch load and
punch stroke, distribution of the thickness, distribution of the stress, ,
deformation history.
Research of this research key lies in discusses grain size effect influence
of forming of limit regarding the copper foil micro deep extension,
copper foil of selection thickness 0.1mm, 0.075mm, the 0.05 mm, and
carries on the experiment of grain size using the heat treatment method
change preview interior, obtains the grain size the change to influence of
forming of limit the copper foil micro deep drawing, by will take in the
future in the micro deep drawing test reference

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