THEORY OF YARN STRUCTURE by Prof. Bohuslav Neckář, Textile Department, IIT Delhi, New Delhi. Compression of fibrous assemblies

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1 THEORY OF YARN STRUCTURE by Prof. Bohuslav Neckář, Textle Department, IIT Delh, New Delh. Compresson of fbrous assembles Q1) What was the dea of fbre-to-fbre contact accordng to van Wyk? A1) Accordng to van Wyk, If 2 non-materal cylnders were penetrated mutually, then the materal fbers would create the contact. Q2) State the relatonshp between the densty of contacts and the packng densty of a fbrous assembly? A2) The densty of fbre-to-fbre contacts n a fbrous assembly s drectly proportonal to the square of the packng densty of the assembly. Q3) State the relatonshp between the mean dstance between adjacent contacts and the packng densty of a fbrous assembly? A3) The mean dstance between adjacent contacts n a fbrous assembly s nversely proportonal to the packng densty of the assembly. Q4) State the relatonshp between the compressve pressure and the packng densty of a fbrous assembly? A4) The compressve pressure s drectly proportonal to the cube of the packng densty of the fbrous assembly. Q5) What are the major problems of van Wyk s theory of compresson of fbrous assembly? A5) The two major problems of van Wyk s theory of compresson of fbrous assembly are 1) The packng densty cam be greater than one when the compressve pressure s greater than the coeffcent k p, whch s logcally non-sense and 2) The theory does not hold good for relatvely hgh values of packng densty. Q6) State the basc dea behnd generalzaton of C. M. van Wyk s theory. A6) C. M. van Wyk s theory assumes purely pont contact between fbres n a fbrous assembly, therefore, ts result could be accepted, but only for compressble 1

2 (deformable) part of volume. Ths compressble volume s the dfference between the total volume of the fbrous assembly and summaton of volumes of all noncompressble ( stones ) volumes. Pores among fbres Q1) State what are the parameters of pores n a fbrous assembly that are ndependent of the choce of fctve borders? A1) The three parameters are total pore volume, total pore surface area, and surface area per unt volume of pore Q2) Defne conventonal pore. A2) Conventonal pore has crcular cross-secton. Q3) Why conventonal pores are frequently used? A3) All parameters of conventonal pores are ndependent of the choce of fctve borders. Q4) What s the basc assumpton behnd dervng the expressons for pore parameters n terms of fbre parameters? A4) The basc assumpton s total pore surface area s equal to total fbre surface area n a fbrous assembly. Q5) What are the fbre parameters that decde the heght of wckng? A5) The fbre parameters are dameter of fbre and shape of fbre cross-secton. Orentaton of fbres Q1) What s the value of probablty densty functon of sotropc fbre orentaton n plane? A1) 1/ 2

3 Q2) What probablty dstrbuton does the tangent of fbre nclnaton angle follow? A2) Cauchy s dstrbuton. Q3) Defne coeffcent k n? A3) The coeffcent k n s defned by the rato of mean sectonal area of fbre to the cross-sectonal area of fbre. Q4) What s the value of mechancal utlzaton of fbre n a perfectly parallel fbre bundle? A4) 1 Mechancs of parallel fbre bundles Q1) Whch theory can explan the fact that after addton of fbers havng hgher tenacty, the tenacty of the resultng bundle can decrease? A1) Hamburger s theory of mechancs of blended fbre bundle can explan ths. Q2) Defne fbre strength utlzaton coeffcent. A2) The fbre strength utlzaton coeffcent s defned by the rato of the bundle strength related to one fbre to the mean fbre strength. Q3) Defne fbre breakng stran utlzaton coeffcent. A3) The fbre breakng stran utlzaton coeffcent s defned by the rato of the breakng stran of the bundle to the mean breakng stran of fbre. Q4) What s the fbre parameter that determnes both the fbre strength utlzaton coeffcent and fbre breakng stran utlzaton coeffcent? A4) The fbre parameter s the coeffcent of varaton of fbre breakng stran. Q1) Classfy yarn models as shown below. Modellng of nternal yarn geometry Functons m 0 m 0 z 0?? z const.?? z const.? 3?

4 A1) The yarn models are classfed as follows. Functons m 0 m 0 z 0 Parallel fbre bundle Entangled fbre bundle z const. Helcal model Radal mgraton z const. Twsted mgraton General mgraton Q2) State the assumptons of deal helcal model of fbres n yarn. A2) The assumptons are: 1) The fbres follow helcal path n yarn, 2) All helxes have the same sense of rotaton, 3) All helxes have the common axs, that s, yarn axs, 4) All fbres have the same col heght, and 5) The packng densty s constant at all places nsde the yarn. Q3) State whether t s true that the coeffcent k n ncreases wth the ncrease n twst angle of surface fbres. A3) False, the coeffcent k n decreases wth the ncrease n twst angle of surface fbres. Q4) What s the lmt value of yarn retracton accordng to deal helcal model under the assumpton that the fbre volume does not change wth twst? A4) 0.5 Q5) What s the lmt value of angle of twst of surface fbres accordng to deal helcal model under the assumpton that the fbre volume does not change wth twst? A5) 70.5 degree Q6) What are the parameters that determne the tensle force utlzaton coeffcent n twsted yarn? A6) Angle of twst of surface fbres and yarn contracton rato. Q7) Why Treloar s model of radal fbre mgraton n not consdered to be enough precse? 4

5 A7) Treloar s dea of regular path of fbres n yarn s not precse. The fbre path s n fact random. Hence the number of fbre elements ntersectng the yarn cylnder at any radus on one fber per unt length of yarn s not constant. Relaton between yarn count, twst, packng densty and dameter Q1) State the assumpton of Koechln s model? A1) Koechln studed the yarns produced from same fbrous materal usng same technology for analogcal end-uses. He assumed that 1) the packng densty s a functon of twst ntensty only and 2) the twst ntensty of yarns of dfferent fnenesses (counts) shall be same. Q2) Whch of the assumptons s consdered not to be enough precse? A2) Koechln s frst assumpton s not enough precse. The twst ntensty s not a functon of packng densty only, t depends on yarn count too. A stochastc model of yarn harness Q1) Why the sngle exponental model of yarn harness does not correspond well wth the results of experments? A1) In realty, there are two types of hars n yarn. One type of hars s composed of shorter fbers and s concentrated manly round the yarn surface (body); ths can be magned as moos on the yarn. Second type of hars s composed of longer flyng fbers. Ths ntutvely suggested dea would make the double exponental model of yarn harness closer to the realty. Bundle theory of yarn unevenness Q1) State the general assmptons of Martndale s model of slver unevenness. A1) The general assumptons are: 1) The fbres are straght and parallel to the slver axs, 2) They have the same length, and 3) They are postoned along the slver ndvdually and randomly. 5

6 Q2) Whch s hgher: coeffcent of varaton of fbre fneness or coeffcent of varaton of fbre dameter? A2) The coeffcent of varaton of fbre fneness s two tmes hgher than the coeffcent of varaton of fbre dameter. Q3) Why the model of Martndale s consdererd not to be enough correct? A3) The ndex of rregularty n actual slver s much hgher than that calculated from Martndale s model. The reason s that the assumpton of ndvdual postonng of fbres n slver s not correct. Yarn strength as a stochastc process Q1) What s the prncple of the weakest lnk theory? A1) Let us assume that a longer secton of yarn s dvded nto n number of smaller sectons. The prncple of the weakest lnk theory states that the longer secton must not break untl any of n shorter sectons breaks. Q2) State the assumptons of Perce s model of strength versus length of yarn. A2) Perce s model s based on the consderaton that a longer yarn secton s composed of many shorter sectons of equal length. The three assumptons are: 1) The probablty of breakage of one secton of length s ndependent of the probablty of breakage of any other secton, 2) The longer secton must not break untl any of the shorter sectons breaks, and 3) The strength of shorter secton follows normal dstrbuton. Q3) Why Perce s model s not consdered to be enough precse? A3) The strength versus length relaton n actual yarn does not correspond well to that of Perce s model. Ths s because the assumpton of strength ndependency s not true n realty. 6