Strength of Unidirectional Short Fiber Structures as a Function of Fiber Length

Abstract

The strength of super-oriented polymer fibers or unidirectional short fiber composites strongly depends on the length of the molecule chains or the reinforcing fibers, respectively. A simple statistical model is developed based on the theory of fiber flows and the strength of the structure and its dependence on fiber length are determined in case of fibers broken or damaged owing to parting rigidly from the environment simultaneously. Later, two new special and modified versions of the so-called ES-bundle and one of the idealized statistical fiber-bundlecells developed earlier, are introduced and applied to model the breaking process of the fibrous structure at different damage modes and its dependence on the fiber length is analyzed. In case of constant fiber length, a simple analytical relationship between the mean tensile strength and the fiber length is obtained which is valid for all the cases discussed. On the basis of the results, formulas are developed to estimate the strength of short fiber composites as a function of fiber length and fiber content, as well as to model the effect of the reduction in the fiber adhesion in case of a very small matrix content. The practical applicability of the results is demonstrated by identifying the relationship between tensile strength and molecule mass of PP fibers.

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 ):…”

Novel evaluation method of acoustic emission data based on statistical fiber bundle cells

“…This paper presents a statistical fiber-bundle-cells [55][56][57][58][59][60][61] based novel modeling and evaluating method for classifying and characterizing AE signals, which can manage overlaps in histograms or spectrums by the simultaneous decomposition of the stress-strain curve, the cumulative number of AE events and any cumulative statistics of AE descriptors. The fitted FBC model makes it possible to analyze the mechanical reliability of the material and construct a kind of damage map for characterizing the failure behavior.…”

“…The FBC modeling method is based on some idealized statistical fiber bundles called fiberbundle-cells (FBCs) which can be used as building elements of a model network created by parallel and/or serial connections. [55][56][57][58][59] Idealized fiber bundles are defined as fiber classes containing fibers of the same geometrical (shape, disposition) and mechanical properties (strain state, gripping by the surroundings) ( Figure 2). In the simplest case, the fibers are ideally elastic (E) with a linear or non-linear relationship between the strain and load, although they break at a random strain value.…”

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.…”

“…In addition to the classic one [1], L.M. Vas et al [4][5][6][7][8][9] have introduced some other idealized statistical fiber bundles called fiber-bundle-cells (FBC), and developed a modeling method as well as a software called FiberSpace [10][11][12][13][14][15][16], and shown that they can be applied to modeling some structural and strength properties of fibrous materials.…”