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.

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See the supplementary material at https://doi.org/10.1122/8.0000046 for the viscosity factor ϕη(ϕ)/η(ϕ) versus the volume fraction ϕ of fibers; the amplitude B(ϵ) of the deviation δR(z,t) versus strain ϵ for several values of the viscosity factor ϕ0η(ϕ0)/η(ϕ0); and derivation of approximate forms of amplitude B of deviation from uniform uniaxial stretching.

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