Statistical Modeling of Unidirectional Fibrous Structures

Abstract

Some textiles such as slivers, rovings, yarns, and highly oriented polymer fibers as well as the reinforcing structure of unidirectional composites have a kind of unidirectional or quasi‐unidirectional fibrous structures. The statistical properties of their structure and strength can be modeled by using idealized fiber bundles as model elements. In this study the tensile test process of unidirectional short fiber structures is modeled for different damage types using the instantaneous fracture model and special idealized fiber bundles for gradual damages such as fiber breakage and fiber slippage. Constant fiber length and exponential fiber length distribution as extreme cases of the Erlang distributions were used for analysis. In case of exponential fiber length distribution and constant fiber breaking strain simple analytical relationships between the mean tensile strength and the fiber length were derived and compared to those for constant fiber length and written in a general form which is valid for all the damage modes discussed. The convex linear combination of the solutions for exponential fiber length distribution and constant fiber length was proposed to use for cases when the variation coefficient of the fiber length is between 0 and 1. The practical applicability of the results was demonstrated by identifying the relationship between the mean tensile strength and the average molecule mass of polypropylene fibers that made it possible to estimate the critical molecule mass and the tensile strength of the molecules without further measurements.

Theoretical and experimental study of the effect of fiber heads on the mechanical properties of non-continuous basalt fiber reinforced composites

“…The volume ratio between the fiber heads and the other parts of the composite (containing no such kind of defect site) is assumed to determine the decrease in strength. In order to handle this problem, a statistical fiber mat model of Poisson type [12,13] used also for describing the so called fiber flows [12][13][14][15][16] was adapted by substituting the fibers by spheres where a sphere G(r,P) (1) was defined as a spherical volume around point P with r radius in the three dimensional real space (R 3 ):…”

“…The total volume of spheres intersecting B is given by (14): (14) Equation (14) is a sum containing a random number of terms where ξ B and ρ are not independent of each other since the vicinity of B -once ξ B is known -depends on ρ (15).…”

Modelling method based on idealised fibre bundles

“…1). [8][9][10] These FBCs represent different idealised and typified fibre properties such as fibre shape, state of deformation, gripping as a connection with vicinity (stiff or frictional grip) and force transmitting characteristics. Figure 1 shows the structural scheme of the FBCs and the relationship between the bundle (u) and the fibre (e) strains which includes the character of the fibre gripping, that is to say, the connection between the fibre and its vicinity as well.…”

“…[8][9][10] As an example for the structural-mechanical application, the 3P bending test with l560 mm span length (Fig. 11a) …”

Modeling and Analysing the Tensile Behavior of Fabric Samples

“…Fibrous structures such as textile materials, fiber reinforced composites, and linear polymers are built up of discrete fiber-like elements such as textile or reinforcing fibers or yarns. The adjoining fibers or those intersecting a cross section of a fibrous sample create certain small assemblies that are fiber bundles in which the fibers show collective group-behavior [1][2][3][4][5][6][7][8][9]. The fiber bundle can be treated as intermediate elements of a fibrous structure, which can represent the statistical properties of the geometry or the strength.…”