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，必须严格控制材料的温度和工作速度，特别是非延展性材料的成形，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在模具设计阶段的工作。然而，传统的有限元方法仍然存在着同样的困难。在本研究中，提出了一种新的分析方法。首先，根据模型试验得到的应变分布，将变形区域划分为细的子区域；其次，采用有限元法对各子区域进行了变形分析。最后，将这些解结合起来，估计出三维变形的解。以非轴对称反挤压为例。由于除法的方式可能会使解产生误差，因此讨论了以下两种除法方法。第一种方法是在挤压后零件的横截面上进行应变测量，得到主应变线，主应变线近似呈径向分布；然后，用包含主应变线的水流面进行划分；这些表面上的剪切应变相当小，相邻子区域之间的变形干扰似乎很小。在第二种方法中，划分面被假设为平面，这次没有应用实验信息。这种方法比较粗糙，但在有许多对称曲面的情况下，如用方截面冲头挤压时，得到了合理的解。因此，后一种划分方法适用于离轴对称变形不远的变形，而前一种方法应适用于发生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.