It is not straightforward to prepare a fiber reinforced composite in which reinforcing fibers are dispersed uniformly. The nonuniform distribution of the reinforcing fibers produces nonuniform viscosity of the composite and thus drives the breakup of the filament upon extension. However, this breakup is suppressed when the fiber length is large. By using Bachelor’s theory for the viscosity of fiber suspensions, we here theoretically analyze the dynamics of the breakup of a fluid filament due to the nonuniform distribution of reinforcing fibers under uniaxial stretching by the linear order term with respect to the nonuniform component of the number density of centers of gravity of fibers. Our theory predicts that the fracture strain increases logarithmically with increasing the fiber length, corresponding to the linear dependence of the extension ratio at the fracture on the fiber length.

中文翻译：

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非均匀分布增强纤维复合材料的断裂应变

制备其中增强纤维均匀分散的纤维增强复合材料并不简单。增强纤维的不均匀分布会导致复合材料的粘度不均匀，从而导致长丝在拉伸时断裂。然而，当纤维长度大时，这种断裂被抑制。通过使用关于纤维悬浮液粘度的学士理论，我们在这里理论上分析了由于增强纤维在单轴拉伸下的非均匀分布而导致的流体长丝断裂动力学，通过相对于数密度的非均匀分量的线性阶项纤维的重心。我们的理论预测断裂应变随着纤维长度的增加呈对数增加，