分形及分维在单轴向三维编织复合材料拉伸实验中的应用

基于分形几何的计盒维数研究了三维编织复合材料拉伸实验的断裂样照,结果表明,该材料的断裂曲线具有统计自相似性,在不同的尺度范围内具有不同的空间分布格局;而计盒维数定量地表征了其尺度变化规律;准静态和低应变率加载条件下材料的分维数较大,表明其空间占据程度较大,曲线弯曲结构复杂,这是因为低应变率加载时材料内部结构断裂时间不同造成;而高应变率加载时,断裂曲线分维数较小,曲线空间占据小,弯曲结构比较简单,这是由高应变率加载时材料内部结构断裂时间差异缩小造成。

Application of Fractal and Fractal Dimension in the Tensile Test of Uniaxial 3-D Braided Fabric Composite

Based on the idea of box dimension of fractal geometry,we study the broken picture of the tensile test of 3-D braided composite materials.The result shows that the broken curve exhibits the statistical self-similarity with scale dependency and box-counting dimension of the curve quantifies with the scale variation range.The fractal dimension of sub-static state and the low strain rate loading environment is big and the curve structure is complex.The reason is that the broken time of the fiber and resin is different in low strain rate loading process.On the contrary,the fractal dimension is smaller in the high strain rate loading and the broken curve is simpler than that of low strain rate loading.It is caused by the little difference of the broken time in the internal structure of the material in high strain rate loading process.