MECHANICAL BEHAVIOR OF CRIMPED SYNTHETIC YARN (2)

Abstract

Load-elongation curve of a crimped synthetic yarn is divided into three regions. At the 1st region the crimps of filaments are only stretched. At the 2nd region, because the yarn is consisted of crimped filaments and filaments crimps are stretched to the true length, the filaments themselves are stretched. At the 3rd region, the filaments are themselves stretched.In this paper the load-elongtion behavior and stress relaxation at the 2nd region only will be investigated.The distribution of true length of the crimped filaments is a normal distribution. Their standard deviation ρ and mean value μ are dependent on the kinds of crimped yarns.It is easily understood that theoretical load-elongation curve is formed of standard normal distribution and stress curves of a crimped monofilament. Investigating the stress of crimped yarn theoretically, following equation may be derived;(1)where σi=stress of crimped monofilament at the 1st region.σi=stress of crimped monofilament at the 3rd region.f(εi)=probability density of distribution of true length at εi.f(εj)=probability density of distribution of true length at εj.The range of distribution of the true length for each crimped yarns is to be determined by their values of ρ max., ρ min., μ max., and μ min. Therefore by comparison of the theoretical curve and experimental curves, the identification of these curves are proved.At the second region relaxation stress is also divided into two parts, as in load-elongation behavior. One part is relaxation stress at crimp region, and the other part is at the true lengthed region. Stress relaxation may be expessed by the equation;(2)where σRi=relaxation stress for a monofilament at 1st region.σRj=relaxation stress for a monofilament at the 3rd regionRelation of quantity of relaxation stress up to a difinite time (such as 10sec) and elongation is non-linear.Because it is reasonable that difference of relaxation modulus is also non-linear to elongation, at the 1st region of elongation, relaxation modulus exhibits mainly linear property. But at the 2nd region, it is non-linear. At the third region it is also linear.