Statistical Modeling of Unidirectional Fibrous Structures

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.