模具钢电渣重熔铸坯凝固组织形貌的分形特征

为了更为精细化地表达及控制铸坯质量，以H13模具钢电渣重熔铸坯凝固组织为研究对象，引入分形维数对其主体形貌特征进行定量描述。结果表明，基于数盒子法计算得到的分形维数可定量表征凝固组织形貌的自相似复杂程度，其值从柱状晶向中心等轴晶先减小后增大；凝固组织分形维数可作为衡量铸坯偏析程度（偏析率大小）的指标，且分形维数越大，对应区域偏析率越小，偏析越轻；通过凝固组织分形维数、偏析率和偏析点平均面积与二次枝晶间距关系的研究发现，使用二次枝晶间距表征铸坯凝固组织形貌差异并由此反映偏析程度的方法存在局限性。

Fractal morphology characteristics of solidification structure in electroslag remelting billet of die steel by ESR#br#

In order to describe and control the quality of casting billet more delicately，solidification macrostructure of H13 die steel electroslag remelting billet was researched based on fractal dimension calculated by box counting method，and the overall morphology of solidification structure was described quantitatively. Meanwhile，the relationship between solidification characteristics and segregation characteristics was also studied. The results show that the fractal dimension can be used to quantitatively characterize the degree of self similarity of solidification structure，which decreases firstly and then increases from columnar grain to equiaxed grain. The fractal dimension of solidification structure can be used as an index to measure the segregation degree（segregation rate）of the billet. The larger the fractal dimension，the smaller is the corresponding region segregation rate and the lighter is the segregation. The relationship of the fractal dimension of solidification structure，segregation ratio and the average area of segregation point with secondary dendrite spacing was studied, respectively. Based on the results， limitations exist through using secondary dendrite spacing to describe the billet morphology difference of solidification macrostructure and to reflect the segregation extent.