Quantitative description of the microstructure of composites. Part I: Morphology of unidirectional composite systems

A combined experimental–numerical approach for generating statistically equivalent fibre distributions for high strength laminated composite materials

“…The second order intensity function, also known as Ripley's K-function, is widely used to distinguish between different types of point patterns [11,12]. The function K(r) is defined as the number of further points expected to lie within a radial distance, r, of an arbitrary point, as shown in Fig.…”

“…However, Pyrz [11] showed that for three different curing conditions applied to a glass/epoxy composite, the resulting spatial patterns in each microstructure differed considerably. It was concluded that the previous assumptions regarding complete randomness or perfect regularity in the microstructure may be in error and the patterns produced are highly dependant on the manufacturing process and conditions.…”

Statistics of microstructure, peak stress and interface damage in fiber reinforced composites

“…The latter, in turn, can be characterized by several parameters, including coordination number, particle cage, interparticle spacing, second-order intensity (Ripley's) function, radial distribution function, nearest neighbor distribution function, two-point cluster function, etc. (see, for example, [Pyrz 1994b;Babuška et al 1999;Torquato 2002;Buryachenko et al 2003]). At the same time, a very few publications are known to the authors where the relationships between the statistics of structure and local fields were established.…”

“…The papers [Pyrz 1994a;1994b;Pyrz and Bochenek 1998] address the problems encountered in the quantitative description of arrangements and correlations in unidirectional fiber reinforced composite materials. It has been indicated there that both topological and second-order statistics are related to the local stress variability under transverse loading conditions.…”

“…(see, for example, [Pyrz 1994b;Buryachenko et al 2003]). The structure parameters we focus on are the normalized nearest-neighbor distance,…”