论文部分内容阅读
一、引言分形几何学的创立为人们认识自然界广泛存在的不规则的几何形貌及复杂的物理现象提供了强有力的数学工具。在短短的20年内,分形几何在自然科学的各个领域得到了十分普遍的应用。分形几何学的一个重要概念是分形维数(D_f)。目前,对材料断裂面的研究主要是关于断面分维数的测量。分维数的测量方法主要有:小岛法(Slit—island analysis,简称为SIA法)、侧面轮廓线法(Fracture profile method,简称为FPM法)、谱分析法、二次电子线法、相关函数法等,这些方法的一个共同特点都是间接地通过剖面(降低一维)来测量断面分维数,其中最常用的是小岛法和侧面轮廓线法。
I. INTRODUCTION The establishment of fractal geometry has provided a powerful mathematical tool for people to recognize the irregular geometric shapes and complex physical phenomena that exist widely in nature. In just 20 years, fractal geometry has been widely used in various fields of the natural sciences. An important concept of fractal geometry is the fractal dimension (D_f). At present, the research on the fracture surface of the material is mainly about the measurement of the fractal dimension of the section. The fractal dimensions are mainly measured by the Slit-island analysis (SIA) method, the Fracture profile method (FPM method), the spectral analysis method, the secondary electron beam method, the correlation Function method, etc. One of the common features of these methods is that the fractal dimensions of sections are measured indirectly through the profile (one-dimensional reduction). The most common ones are the islet method and the side contour method.