Fractal Analysis of Branched Structures on Fractured Surfaces of Crosslinked Polymers and Model Systems

本研究旨在研究分形几何在表征交联热固性聚合物断口表面裂纹模式中的应用。断裂实验将在一系列表征良好的树脂（从橡胶到脆性）和不同粘度的非牛顿流体上进行。然后将开发数值方法来分析这些系统中的模式形成，以更好地理解导致断裂行为的物理和化学过程。将分析表征树状裂纹几何和拓扑特征的分形维数和其他标度指数，以确定这些指数与材料性能之间是否存在关系。

The research is to study the application of fractal geometry to characterize crack patterns formed on the fracture surfaces of cross-linked thermoset polymers. Fracture experiments will be performed on a series of well characterized resins (ranging from rubbery to brittle) and on non-Newtonian fluids of varying viscosity. Numerical methods will then be developed for analyzing pattern formation in these systems to better understand the physical and chemical processes which contribute to the fracture behavior. The fractal dimensions and other scaling exponents characterizing the geometrical and topological features of the tree-like cracks will be analyzed to determine whether there is a relationship between these exponents and the material properties.