In a previous paper, we proposed a theoretical equation to predict the breaking behaviour of the yarn and discussed the effect of the breaking behaviour of the filaments on that of the yarn. Since this proposed equation has many parameters, the application of the equation to an actual yarn is very difficult. Therefore, an approximate equation is proposed in this work.
By using this new equation, the breaking behaviour of the yarn is discussed theoretically. Furthermore, the Monte Carlo Method was applied for the breaking behaviour of the yarn.
Following conclusions were obtained from the calculation by the approximation and simulation method.
1) The breaking stress and strain of the multi-filament yarn are proportional to the averages of those of the single filament in the yarn, respectively.
2) The breaking stress of the multi-filament yarn is inversely proportional to the coefficient of strain variation for the single filament.
3) The variation of strain at yield point for the single filament gives a negligible effect on the breaking stress and strain of the multi-filament yarn.
4) The breaking stress of the multi-filament yarn is directly proportional to the yield stress of the single filament, and the breaking stress of the multi-filament yarn is inversely proportional to the yield stress of the single filament.
5) The variations of stress at yield point for the single filament and initial Young's modulus give a negligible effect on the breaking stress and strain of the multi-filament yarn.
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