Semi-Experimental Analysis of Three-Dimensional Plastic Deformation in Backward Extrusion

挤压、锻造等产品的形状和材料种类繁多，材料的温度和加工速度必须严格控制，特别是在非韧性材料的成形中，例如，钛合金在这种情况下，数值分析似乎是有效的估计应变或温度的工作在设计阶段的模具。然而，常规的有限元法（FEM）仍然存在同样的困难，本研究提出了一种新的分析方法。首先，参照模型试验得到的应变分布，将变形区划分为薄的子区。其次，利用有限元法分析了这些子区域的变形。最后，将这些解结合起来，估计了三维变形的解，并以非轴对称反挤压为例进行了计算。这种划分方式可能会引起解的误差，因此讨论了两种划分方法：第一种方法是在挤压后的截面上进行应变测量，得到近似沿径向分布的主应变线;然后，流面，包含主应变线，用于划分，这些表面上的剪切应变是相当小的，相邻的子区域之间的变形干扰似乎是小的。这种方法比较粗糙，但在有许多对称面的情况下，如在方形凸模挤压中，得到了合理的解，因此，后一种分割方法适用于离轴对称变形不远的变形，而前一种方法则适用于有大量周向流动的变形。

There are many kinds in shapes and materials in products of extrusion, forging, etc., and temperature of material and working speed must be controlled rigorously, especially in forming of non-ductile materials, eg. titanium alloys. In such situation, numerical analysis seems to be effective for estimation of strain or temperature of a work at the stage of designing dies. However, same difficulties remain yet in usual finite element method (FEM).In this research, a new method of analysis is proposed. First, a deforming region is devided into thin sub-regions, by referring to strain distribution obtained by a model experiment. Secondly, deformations of these sub-regions are analysed by the use of FEM. Finally, those solutions are combined and the solution of 3-D deformation is estimated.Non-axisymmetric, backward extrusion is dealt with as an example. The pattern of division possibly causes some errors in the solution, so the following two methods of division are discussed.In the first method, strain measurement is done in the cross section at the part after extrusion and principal strain lines, distributed approximately in radial direction, are obtained. Then, stream surfaces, containing principal strain lines, are used for division; shear strain across these surfaces is rather small and interference of deformation between neighboring sub-regions seems to be small.In the second method, deviding surfaces are assumed to be planes and no experimental information is applied to, this time. This method is rather rough but it was found that a reasonable solution is obtained in the situation that there are many symmetric surfaces as in the extrusion with a punch of square section.Consequently, the latter method of division is useful in the deformation not far from axi-symmetric one, whereas the former method should be applied to, when considerable circumferential flow occurs.