Geometrical and mechanical modelings of dry relaxed slack plain-knitted fabrics for the benefit of technical textile applications Part I: a geometrical model
Abstract:In the current literature, there is a lack of knowledge concerning which parameters are effective on relaxed slack plainknitted conventional fabrics, although slack fabrics (i.e. fabrics with no occurrence of jamming) are commonly used for technical applications. Thus, the present series of works are conducted as further investigation on relaxed slack plainknitted fabrics. In the present part, Part I, a geometrical model is created based on Kurbak's 1998 model. The created model is then applied to conventional… Show more
“…In the referenced works, 1,12 the model of relaxed fabric was investigated and the loop head was assumed to be circular in shape. In the present study, a relaxed fabric model with an elliptical loop head is assumed.…”
Section: Theoretical Calculations For Course-wise Extensionmentioning
confidence: 99%
“…Parameter η is about 4.5° in relaxed fabric (see Kurbak 1,12 ). It is thought that parameter η has a minor effect in the fabric plane when the fabric is extended in the course-wise or wale-wise directions; thus, the curve fitting equations for the fabric plane do not show any friction effects.…”
Section: Theoretical Calculations For Wale-wise Extensionmentioning
confidence: 99%
“…In this context, the load–extension properties of plain knitted glass fabrics are investigated experimentally and theoretically, especially for composite applications. The technical use of plain knitted fabrics is given by Kurbak; 1 therefore, they are not repeated here again. The work is conducted by loading the fabrics in both course-wise and wale-wise directions.…”
In this paper, the load–extension behavior of glass plain knitted fabrics is investigated both experimentally and theoretically. Experiments are carried out by preparing two sets of samples for two directions, namely for the course-wise and wale-wise directions. The load–extension properties are explored by attaching dead weights to the lower ends of the samples. Therefore, while obtaining the load–extension properties in the loading direction, the contraction properties of the samples in the lateral directions are also investigated. By observing the load–extension and load–contraction curves, three stages are distinguished. The first stage can be attributed to the fabric extension or contraction. The second stage can be attributed to the yarn extension or contraction as well as to the changes in the shapes of the samples. The third stage can be attributed to the extension or contraction of the fibers. After obtaining the dimensional properties of a single loop in the knitted fabric, curve fittings are carried out for the three stages.
In the rest of the work, a theoretical analysis is carried out to explain the first stage of extension and contraction that was explained above. In the theoretical work, the load–extension or the load–contraction behaviors of the arms of the loops are calculated by using the inflexional elastica theory. The extension behaviors of the loop heads, on the other hand, are calculated by using the extension of the circular ring, which was given in Part I. As a result of the theoretical analysis, some simple equations between the loads applied and the extensions or contractions are obtained. These equations for the extension or contraction rates depend on the initial dimensional properties of the loop, the bending rigidity of the material, frictional restraints and the Poisson ratio. The equations also show that an extension or contraction in the wale-wise direction follows Hooke’s Law, whereas an extension or contraction in the course-wise direction depends on the square root of the applied load.
Providing some simple equations about the relation between the load and extension in the loading direction as well as between the load and contraction in the lateral direction are suggested, determining the contractions in the lateral direction in addition to the extensions in the loading direction, which can be used in engineering software in simulating fabric load–extension behaviors under loadings.
Finally, the initial and the extended states of the fabric are drawn to scale by using 3DS Max computer software.
“…In the referenced works, 1,12 the model of relaxed fabric was investigated and the loop head was assumed to be circular in shape. In the present study, a relaxed fabric model with an elliptical loop head is assumed.…”
Section: Theoretical Calculations For Course-wise Extensionmentioning
confidence: 99%
“…Parameter η is about 4.5° in relaxed fabric (see Kurbak 1,12 ). It is thought that parameter η has a minor effect in the fabric plane when the fabric is extended in the course-wise or wale-wise directions; thus, the curve fitting equations for the fabric plane do not show any friction effects.…”
Section: Theoretical Calculations For Wale-wise Extensionmentioning
confidence: 99%
“…In this context, the load–extension properties of plain knitted glass fabrics are investigated experimentally and theoretically, especially for composite applications. The technical use of plain knitted fabrics is given by Kurbak; 1 therefore, they are not repeated here again. The work is conducted by loading the fabrics in both course-wise and wale-wise directions.…”
In this paper, the load–extension behavior of glass plain knitted fabrics is investigated both experimentally and theoretically. Experiments are carried out by preparing two sets of samples for two directions, namely for the course-wise and wale-wise directions. The load–extension properties are explored by attaching dead weights to the lower ends of the samples. Therefore, while obtaining the load–extension properties in the loading direction, the contraction properties of the samples in the lateral directions are also investigated. By observing the load–extension and load–contraction curves, three stages are distinguished. The first stage can be attributed to the fabric extension or contraction. The second stage can be attributed to the yarn extension or contraction as well as to the changes in the shapes of the samples. The third stage can be attributed to the extension or contraction of the fibers. After obtaining the dimensional properties of a single loop in the knitted fabric, curve fittings are carried out for the three stages.
In the rest of the work, a theoretical analysis is carried out to explain the first stage of extension and contraction that was explained above. In the theoretical work, the load–extension or the load–contraction behaviors of the arms of the loops are calculated by using the inflexional elastica theory. The extension behaviors of the loop heads, on the other hand, are calculated by using the extension of the circular ring, which was given in Part I. As a result of the theoretical analysis, some simple equations between the loads applied and the extensions or contractions are obtained. These equations for the extension or contraction rates depend on the initial dimensional properties of the loop, the bending rigidity of the material, frictional restraints and the Poisson ratio. The equations also show that an extension or contraction in the wale-wise direction follows Hooke’s Law, whereas an extension or contraction in the course-wise direction depends on the square root of the applied load.
Providing some simple equations about the relation between the load and extension in the loading direction as well as between the load and contraction in the lateral direction are suggested, determining the contractions in the lateral direction in addition to the extensions in the loading direction, which can be used in engineering software in simulating fabric load–extension behaviors under loadings.
Finally, the initial and the extended states of the fabric are drawn to scale by using 3DS Max computer software.
“…After extension, the circular shape changes in a way that is similar to the problem of an elastic ring extended by two opposite loads, as illustrated in Figure 1(b). Figure 1.(a) Plain knitted loop model (see Kurbak 1 ). (b) An extended elastic circular ring under a fixed load.…”
mentioning
confidence: 99%
“…(a) Plain knitted loop model (see Kurbak 1 ). (b) An extended elastic circular ring under a fixed load.…”
Pierce’s well-known solution to the problem of the load–extension behavior of a circular ring has been used as one of the measurement methods of bending rigidities of textile yarns. This paper provides some additions to Pierce’s solution to make it applicable for a knitted loop head curve. It is found that the load applied to a ring is equal to the bending rigidity multiplied by the difference between the squares of the major and minor curvatures of the extended ring. This equality gives way to apply the circular ring problem for obtaining the load–extension properties of a knitted loop head. It is also shown that, for the loop head curve, the elastica curve can be replaced by an elliptical curve for up to 30% of extension, as it is easier to apply.
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