战斗部壳体爆炸破片体/线分形维数研究

为研究爆炸瞬时情况下金属壳体破碎形成破片的形状特征规律，设计了壳体爆炸破碎形成破片回收试验，来研究瞬时破碎条件下破片分布及内在关系。通过借鉴体/线分形维数测定数学模型，并应用MATLAB软件中数学算法对描述破片质量或大小分布特征的体分形维数D₃以及描述破片迎风面投影轮廓特征的线分形维数D₁进行了计算。研究结果表明：爆炸条件下壳体破碎形成破片质量分布和形貌特征均满足统计自相似性，可以用分形维数来表征；计算获得破片平均体分形维数为2.385 9，平均线分形维数为1.298 7，二者之间满足D₃+2D₁=5.

Research on the Volume and Line Fractal Dimensions of Fragments from the Explosion of Warhead Shell

The fragment characteristics and inherent features of metal shells under instantaneous explosion loading are presented. An experiment is designed to measure the fragmentation of a steel cylinder shell filled with high explosives. The expressions for the volume and line fractal dimensions of the fragments are obtained by using fractal mathematical models. The volume fractal dimension D₃, which is used to describe the mass or size distribution of the fragments, and the line fractal dimension D₁, which is used to describe the projected contour of fragments, are measured by using a MATLAB mathematical model. The results reveal that the characteristic mass distribution and morphology of the fragments are statistically self-similar and can be characterized by the fractal dimension. The line fractal dimension D₁ is 1.298 7, the volume fractal dimension D₃ is 2.385 9, and the resulting volume and line fractal dimensions meet the relationship D₃+2D₁=5.