多重分形在高温疲劳损伤中的应用

Application of Multifractal in High Temperature Fatigue Damage

基于多重分形谱的物理意义,将多重分形理论应用于材料疲劳损伤研究中。以高温低周疲劳表面裂纹为研究对象,对20钢缺口试样进行高温低周疲劳试验,获得疲劳损伤表面图像,通过Ostu阈值分割法进行图像处理,得到损伤演化的二值化图,采用多重分形谱理论对材料表面的损伤演化进行描述,并引入了描述疲劳裂纹分布复杂程度的多重分形谱的谱宽Δa及谱高Δf。试验结果表明,多重分形谱f(a)是一种有意义的表征参数,其中多重分形谱的谱宽和谱高随疲劳寿命按快速增加、缓慢增加、跳跃增加的趋势变化,能够从多分形角度对材料的损伤程度及疲劳裂纹演化过程的几个阶段进行定量化的分析与解释,为探索材料表面裂纹的分形特征与载荷条件及疲劳寿命之间的内在规律找到新的思路。

The multifractal spectrum theories are applied to the material fatigue damage based on the physical sense of multifractal spectrum. Surface cracks for low cycle at high temperature are studied, the notched specimens of 20 steel is experimentally studied. A series of binary images of the damage evolution are obtained by image processing. The multifractal spectrum theories are adopted to describe the damage evolution on material surface, and introduced the spectral width Aa and spectral height Alto describe the fatigue crack distribution complexity. The study indicates that the multifractal spectrum f（a） is a characteristic parameter which enables the quantitative analysis and explanation of material fatigue damage from multifractal perspective, and the spectral width Aa and spectral height Afwith the fatigue life by a certain trend development. In order to explore the inherent law between the fatigue life and the fractal characteristics on the crack surface figure of material, a new method is established.