Abstract
We report the effect of a variable frictional shear force distribution along a slipping broken fiber on the stress concentration (SCF) in blended yarns. Our micromechanical model leads to a system of second order differential equations, which we solve using a convenient eigenvector expansion approach. The results for an exponential variation of frictional shear on a slipping fiber, starting from zero at the broken end, are compared to those for a constant friction force. While the extent of the slip region increases by as much as 50% for the exponential variation compared to the constant friction case, the SCF changes only slightly, generally decreasing less than 6%. Decreases are smaller when a high elongation fiber is broken than when a low elongation fiber is broken. The hybrid effect in blended yarns, established in previous work, continues to be supported by these new results.
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