Nonwoven Fabric Studies

Abstract

IntroductionTheoretical analysis of the mechanics of a material structure may be based either on a consideration of the forces involved-resolving and compounding them and using the laws of equilibrium-or on a consideration of the energy relations.For instance, in studies of the mechanics of twisted yarns, the former approach has been extensively adopted [4,5,7,11,12] and has led to many useful , results. However, Treloar and Riding [13] have ' shown that some of these results can be obtained more easily by the energy method. In general, the analysis of forces has yielded more detailed information, especially on internal forces in the structure; but the energy method is simpler and, so, can be applied to more complicated problems. '' The mechanics of nonwoven fabrics, composed of fibers more or less randomly bonded together in sheets, has been analyzed in terms of the forces in elements of fibers between bonded points by Backer and Petterson [1] and Hearle and Stevenson [6} IThis has led to a satisfactory prediction of some of the mechanical properties of these fabrics. The -present paper derives equivalent relations by the energy method. The greater simplicity of the energy method leads, naturally, to a more rigorous .approach to the analysis, and a number of unnecessary assumptions and approximations are removed. The general equations which are derived can be applied to problems which would be difbcult to solve by the analysis of forces, thus, enabling many important practical features of the behavior of nonwoven fabrics to be explored and understood. Extension of the theory would lead to its use as a method of designing and developing new fabrics ' with particular properties.The brevity of the energy method will first be demonstrated in its application to the simplest treatment of the mechanics of a bonded fiber fabric, without any deep consideration of the assumptions made; then the full general analysis will be given and applied to special cases; finally, the wider implications of the method will be discussed. ' .Simple Treatment by the Energy Method We shall consider a fabric specimen deformed uniformly to a strain EL without transverse contraction, as illustrated in Figure 1 (a). The fabric is assumed to be made up of fiber elements of length I distributed at angles of orientation 0 deforming as in Figure 1 (b) so that their length parallel to the fabric length increases by the strain EL. If a is the projected fiber length parallel to the length of the fabric and b is the length at right angles, then Pythagoras' theorem gives .. p = az + b2 , .( 1 ) As b is constant during the deformation ' w If the fibers follow Hooke's law, then the elastic energy per unit mass' in a fiber is given by where Yf is the fiber modulus. , ' As 9 has a distribution of values, the average elastic energy per unit mass in the fabric specimen will be given by ~ _ where cos' 0 is the mean value of COS4 0. 1 Using moduli based on specific stresses. If the moduli are based on the conventional definition of stress, the energies will...

On the importance of fiber curvature to the elastic moduli of electrospun nonwoven fiber meshes

“…In accord with the earlier work of Hearle and coworkers [8,9] and Engelmayr and Sacks [15], the role of fiber curvature on the properties of nonwoven fabrics can be dramatic. In contrast with that work, where fiber curvature was introduced by mechanical crimping, fiber curvature is observed here to be a function of fiber diameter, increasing with decreasing fiber diameter solely as a consequence of the low flexural rigidity of the submicron diameter fibers formed by the electrospinning process.…”

“…Such fibers can respond to deformation by bending or unbending. Hearle and coworkers [8,9] defined the "curl"…”

“…Models of nonwoven fabrics can be categorized into four main approaches (Jearanaisilawong [6]): (i) idealized composite models of homogeneous continuum components that do not consider the structure of the material at the fiber level [7]; (ii) composite structures consisting of many continuum components to represent the idealized elements of the fabric structure [8][9][10]; (iii) complex fiber network structures that capture the macroscopic response of the fabric from the interactions between the components of the structure at the fiber and bond level [11]; and (iv) both continuum-and microstructually-based approaches that use a representative volume element of the material to homogenize the macroscopic response of nonwoven fabrics [12,13]. Our goal in this work is to understand how the fiber properties and mat microstructure translate to the elastic mechanical properties of the mat, for which purpose the microstructurallybased continuum approach is most appropriate to model the mat.…”

“…The importance of this feature was recognized already in the seminal work of Backer and Petterson [7]. Hearle and co-workers [8,9] were the first to account for this fiber "curl" in a microstructural model, using the approximation that only fully straightened fibers contribute to the elastic properties of a mat. Lee and Argon [10] studied the flexibility of crimped fibers in sinusoidal shape subjected to tension.…”

The Force-Elongation Curve of a Thin Fibrous Network

“…To this end Dodson [1]' has reviewed literature on the nature of bonds in paper and the behavior of paper under mechanical strain. The experimental and theoretical behavior of nonwoven fabrics subjected to tensile stress has been studied by Backer and Petterson [2,3] and by Hearle et al [4][5][6][7][8]. Dent [9] has reviewed existing theories for calculating Young's modulus of filament webs.…”