Part III: Shearing and Buckling of Various Commercial Fabrics

Abstract

Load-deformation curves obtained by the methods for shearing and buckling de scribed in Part I and II are analyzed and discussed. Parameters obtained from these curves are given for 66 commercial fabrics covering an extreme range. Different fabrics show widely different values for the parameters obtained from both shearing and buck ling curves. It is further shown that there exist close relationships between simple de formations like shearing and plane buckling and complex deformations like buckling of corrugated fabric shells. The formability of a fabric is defined as the maximum com pression a fabric can take up before it buckles, given a certain geometric arrangement. The formability parity determines the tailorability and the crease pattern of fabrics. The formability is dependent on fabric direction, and it is shown that the integrated formability should be related to the product of buckling load and shear angle. A the oretical analysis of formability is given, and it is shown that it can be expressed as the product of an anisotropy ratio and the square of the fabric thickness. It is further shown that the shell buckling load depends on both the plane buckling load and the shear angle, in such a way that increasing shear angle leads to decreasing shell buckling load. It is shown that combination of high formability and low shell buckling load generally is attained by combining relatively high thickness with low bending modulus. It is also shown that wool fabrics generally have this combination of properties. A fabric map is given for all the commercial fabrics. Each fabric has a certain position on the map dependent on bending stiffness (which is closely related to buckling load) and shear angle. Attention is given to the relation between creasing behavior of fabrics and fabric prop erties. There is a certain relation between crease recovery angle and formability and a good relation between this angle and the noncyclical energy loss in shell buckling. The hypothesis that recovery properties depend mainly on the interaction within the fabric between frictional forces and elastic forces of the fibers is put forward. The energy loss following any fabric deformation depends mainly on friction. The permanent de formation is probably due to the fact that the elastic forces of the fibers cannot overcome the friction. By means of a rheological model it is shown how friction and fiber stiff ness may interact in a fabric. It is shown that the stiffness value should be that ob tained at infinitely slow loading of the fiber.