Establishment of Fractal Approach in Metal Forming (Development of Simulator Predicting Surface Profiles of Press-Formed Products)

在金属成形作业中，存在许多表面现象和问题，这些现象和问题非常复杂，很难用通常的数学方法来定量描述。作为克服这些问题的一种措施，本文引入了一种分形方法。首先，提出了一种适用于各种表面现象的实用的分形方法。下一步，它的目标是开发一种模拟器，它可以预测任何冲压成形产品的自由表面轮廓，从而提供工艺设计所需的表面信息。最后，介绍了分形法的各种应用。取得的主要结果如下：1.研究成果。金属板材双向拉伸自由表面轮廓的分形特征给出了两种适用于金属板材和其他物体的分形分析方法。对不同应变比的金属板材进行了单轴拉伸和双向拉伸试验，并用e-…对其自由表面进行了观察。更多地利用这些分形学分析。发现了一个重要的规则，即表面的分维是由当量应变唯一确定的，与应变(或应力)比无关。板材自由表面轮廓预测模拟器的研制提出了一种模拟塑性变形引起的表面粗化现象的方法。模拟所需的分形参数与应变的关系可以用等效应变统一表示，而与应变比无关。在此基础上，提出了预测任意冲压成形产品表面轮廓的模拟器，并对其进行了验证。应用于锻造过程中刀具表面粘着颗粒的表征、低碳钢断口的定量估算和材料表面纳米裂纹结构的分析。因此，在本研究中发展的分形分析被证明是有用的。较少

In metal forming operations, there are many surface phenomena and problems which are very complicated and difficult to characterize quantitatively by the usual mathematical methods. As a measure to overcome such problems, a fractal approach was introduced in the present investigation. In the beginning, a practical fractal method applicable to various surface phenomena was proposed. Next, it was aimed to develop a simulator which can predict free surface profiles of any press-formed products and thus serves to provide such surface information as needed for process design. Finally, various applications of the fractal approach were presented. Main results obtained are as follows.1. Fractal Characteristics of Free Surface Profile of Sheet Metals under Biaxial TensionTwo fractal analyses applicable to metal sheets and other objects were presented. The uniaxial and biaxial tension test that caused various strain ratios were conducted on metal sheets, and their free surface were examined by e … More mploying those fractal analyses. An important rule was found that the fractal dimension of surfaces is uniquely determined from the equivalent strain independently of the strain (or stress) ratios.2. Development of Simulator for Prediction of Free Surface Profiles of Sheet-Formed ProductsA method for simulating the surface roughening phenomenon caused by plastic deformation is presented. The strain dependence of the fractal parameters required for simulation can be unifiably expressed with the equivalent strain, irrespective of the strain ratio. Based on the result, a simulator for predicting surface profiles of any press-formed products is proposed, and shown to be valid.3. Various Applications of Fractal ApproachThe fractal approach was applied to characterization of adhesion particles caused on the tool surface in forging, a quantitative estimation of fracture surfaces for mild steel and an analysis of the nanofractal structure of material surfaces. Thus, the fractal analyses developed in the present investigation was shown to be useful. Less