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A summarizing description of a statistical modeling method partly based on earlier publications is given to predict the total loading and breaking process of fiber bundles generated by tensile tests. This method uses some types of idealized fiber bundles, the so-called fiber bundle cells (basic types: E, EH, ES, and ET) to model the structure of real fibrous structures. Using one of these bundle cells or a composite bundle made of some bundle cells connected in parallel, the expected value and standard deviation of the whole damage process of this bundle can be calculated up to the breakage of the last intact fiber during a mechanical test. As a new application the fracture process of unidirectional composite beam is modeled during the 3P bending test considering the beam is built up of elementary embeddedfiber layers considered as E-type fiber bundle cells in the first step. Formulae for calculating the expected value and standard deviation processes of the bent specimen are elaborated assuming that the fiber breakages determined the failure of layers.

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In the fibrous structures such as textiles and composites there are fibre assemblies exhibiting statistical bundle like behaviour. This paper presents a modelling method and software FibreSpace, based on a system of structuralised statistical fibre bundles, so called fibre bundle cells. These fibre bundle cells introduced before represent different idealised and typified fibre properties such as fibre shape, state of deformation, gripping as a connection with the vicinity, and the characteristic of force-transmitting and damage. With the help of the weighted parallel connection of the fibre bundle cells the mechanical behaviour and the damage process of real fibrous systems can be modelled as well as some structural properties or the strength data of single fibres can be determined by a fibre bundle cells model identified on the basis of measurements. The applicability of the fibre bundle cells method and modelling program developed is demonstrated by modelling the load and damage process of real textile structures and unidirectional composites during tensile or flexural test.

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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.

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.

Unidirectional carbon fiber-epoxy composite specimens were produced and three-point bending tests were carried out at spans of 10 and 80 mm. During the tests images were taken using a CCD camera system and the type of damage was studied. The fracture process of unidirectional composite beams were modeled during the 3P bending test considering the beam built up of elementary embedded-fiber layers considered as E-type fiber bundle cells using the formulae developed in the first part of this paper. The fracture processes obtained by measurements were compared to the modeled expected value processes completed with deviation field or confidence interval.