The Upper Bound Approach to Plane Strain Problems Using Linear and Rotational Velocity Fields—Part I: Basic Concepts
The Upper Bound Approach to Plane Strain Problems Using Linear and Rotational Velocity Fields—Part I: Basic Concepts
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使用线性和旋转速度场解决平面应变问题的上限方法 - 第一部分：基本概念
DOI：
10.1115/1.3187080
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发表时间：
1986
期刊：
影响因子：
--
通讯作者：
W. Pachla
中科院分区：
文献类型：
--
作者：
B. Avitzur;W. Pachla
本文研究了理想塑性刚性材料平面应变变形的上限法。在这种方法中，变形区域被划分成有限数量的刚性三角形体，相对于彼此滑动。在特定情况下分析相邻刚体区域，其中区域（1）都处于旋转运动，（2）一个处于线性运动，另一个处于旋转运动，以及（3）都处于线性运动。具体的方程，描述表面的速度不连续（剪切边界）之间的移动机构，和速度不连续性和剪切功率损失的三种情况下。速度不连续表面的形状由相邻物体的速度比、它们的相对运动方向以及它们的旋转中心的位置（如果适用）唯一地确定。当一个或两个相邻的物体都有旋转运动时，速度不连续的表面是一个柱面。在两个相邻的机构，每个线性运动的情况下，速度不连续的表面被发现是平面。发现速度间断沿整个速度间断面沿着为常数。研究了平面应变变形中速度间断面的特征。平面应变问题的上限方法可以成功地适用于真实的金属成形过程，包括板带拉拔、挤压、锻造、轧制、校平、熨烫和机加工。
This paper investigates an upper bound approach to plane strain deformation of a rigid, perfectly plastic material. In this approach the deformation region is divided into a finite number of rigid triangular bodies that slide with respect to one another. Neighboring rigid body zones are analyzed in specific cases where the zones are (1) both in rotational motion, (2) one in linear, the other in rotational motion and (3) both in linear motion. Specific equations are presented that describe surfaces of velocity discontinuity (shear boundaries) between the moving bodies, and the velocity discontinuities and shear power losses for each of the three cases. The shape of the surface of velocity discontinuity is uniquely determined by the velocity ratios of neighboring bodies, their relative directions of motion and, where applicable, the positions of their centers of rotation. Where one or both neighboring bodies exhibit rotational motion, the surface of velocity discontinuity is found to be a cylindrical surface. In the case of two neighboring bodies, each with linear motion, the surface of velocity discontinuity is found to be planar. The velocity discontinuity is found to be constant along the entire surface of velocity discontinuity. The characteristics of the surfaces of velocity discontinuity in plane strain deformation are investigated. The upper-bound approach to plane strain problems can be successfully adapted to real metal forming processes, including sheet and strip drawing, extrusion, forging, rolling, leveling, ironing, and machining.