中文摘要
複合包芯材是指由兩種或兩種以上不同材料所組成之複合材料，此種複合材料因其優異的機械特性，故廣泛的被應用於工業界中。但此種複合材料由於組成材料機械性質的差異，因此在材料進行擠製加工時，往往因不當的加工條件組合，造成擠製後的產品為非健全之擠製材。
本論文主要的研究對象是針對複合包芯材擠製時芯材的破斷條件。研究中使用極限解析（ Limit Analysis ）中的上界法（ Upper-Bound Method ），來分析複合包芯材於擠製加工過程中的種種變形現象。其中在運動可容許速度場的構築上，除了建構一一般正常變形之三維運動可容許速度場，再增設一偏差速度場模擬芯材破斷時之徑向流動之頸縮現象，此偏差速度場的存在與否取決於加工條件與材料特性的組合。藉由兩速度場的結合，可以得到此次解析所需之運動可容速度場，接著藉由簡單形搜尋（ Simplex Method ）的最佳化方法調整可變參數，求出滿足塑性變形消耗能量最小上界值，並從中判斷此運動可容許速度場中偏差速度場的存在與否。最後再利用此一判斷標準，探討在不同加工條件組合下，芯材的破壞界限。
ABSTRACT
The composite clad rod is a rod composed of two or more materials. It is applied extensively in industry because of its outstanding mechanical characteristics. However, when subject to extrusion the composite clad rod tend to develop non-uniform deformation because of these differences in materials' mechanical properties. In certain cases, core fracture appears.
The main object of this thesis is to investigate the criterion of core fracture for composite clad rod in extrusion. Upper-bound method was adopted for the analysis with a kinematically admissible velocity field to simulate the core and the sleeve's uniform deformation under sound process parameter combinations, while a deviation-velocity field simulates the radial flow of core material. These two velocity fields are combined together with a designed variable applied to the deviation velocity component. When the total minimized power of extrusion indicates an existence of deviation velocity component, the initiation of the core fracture is deemed positive to occur. With this criterion for core fracture established, the extrusion work designed variable combinations is systematically investigated, and the work limit diagram for the composite clad rod in extrusion can be constructed.