Fiber shape curvature

Textile fibers must be flexible to be useful. The flexural rigidity or stiffness of a fiber is defined as the couple required to bend the fiber to unit curvature (3). The stiffness of an ideal cylindrical rod is proportional to the square of the linear density. Because the linear density is proportional to the square of the diameter, stiffness increases in proportion to the fourth power of the filament diameter. In addition, the shape of the filament cross-section must be considered also. For textile purposes and when flexibiUty is requisite, shear and torsional stresses are relatively minor factors compared to tensile stresses. Techniques for measuring flexural rigidity of fibers have been given in the Hterature (67—73). 

In the past, filament-wound parts consisted primarily of axisymmetric cylinders, spheres and domed vessels. Several manufacturing techniques have been developed that allow more complex shapes and curvatures while maintaining the cost effectiveness associated with process automation [52], These methods have emerged because of advances in programming software. These advances enable precise positioning of the moving head and allow real-time simulation of fiber paths. 

Variation in Fiber Curvature, Cross-Sectional Shape, and Dimensions... 

There are several process requirements for the preparation of polypropylene staple with permanent three-dimensional helical curvature. Specifically, a rectangular spinneret-pack assembly is used to produce flow perturbation and to impart high internal stress. A specially designed cooling device cools the fiber quickly to form a paracrystalline structure in the fiber. The process principle is that the flow perturbed in the polypropylene melt creates internal stress on one side of the fiber section. Because of the stress memory of polypropylene, the internal stress difference at the interface of streamlined and perturbed flows can sustain in the fiber after it has been cooled and solidified. This leads to different crystal structures and shrink properties, and thus a fiber in the shape of a three-dimensional helix. 

Cross bow is a condition that generally results from the process of correcting coil set. It is the condition where the strip exhibits a curvature across its width. Both coil set and crossbow are examples of shape defects where the fiber length difference from one surface to the other is consistent across the width of the strip. 

Fig. 31. Seven axes of motion on fiber-placement system can steer prepreg tow or slit tape around compound-curvature shapes to make highly contoured parts. Courtesy of Cincinnati Machine.

Consider a drop of radius R deposited on a fiber of radius b b is typically 10 to 100 J-m). Assume that the liquid is able to wet the fiber, which means that the two media will connect smoothly at an angle equal to zero. The fiber may be a strand of hair, a textile thread, or a thin glass fiber. The shape taken on by the drop is sketched in Figure 1.10. Since its radius R is very much greater than b, the overpressure within the drop remains low (Ap 2 y/R), At the outer point of contact between the drop and the fiber, one of the radii of curvature becomes very small (equal to b). Therefore, the other radius of curvature must become negative (of the order of —b) in order for the total radius of curvature to remain small. 

One generally cannot wind reverse curvature. To wind a reverse curvature, wind the exact shape on a positive dummy mandrel insert and then remove the insert and place the fiber. 

In the bent strip test according to ISO 22088, Part 3 [272] the entire test region of the specimen is under a defined, constant peripheral fiber strain. The strip-shaped specimen is clamped on a forming plate with constant radius of curvature and exposed to flexural load. The peripheral fiber strain in the specimen depends on its thickness and the radius of curvature of the forming plate ... 

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