Abstract
Fracturing two-dimensional random fiber networks of different densities (porosities) were statistically analyzed using both high-resolution finite element models and image analysis algorithms. Under small strains, the finite element fracture models revealed that networks with high relative densities were able to localize evolving fractures to small cracks while surprisingly larger cracks were required to localize fractures in networks of lower density. Further, it is indicated that the pore size distribution in fiber networks is rather diverse and can be captured using two mixed Gamma distributions; one part describing the background size distribution containing the vast majority of pores, and a second part describing the size distribution of larger pores and open regions. The second part covers less than 5% of the total network area but seems to be of paramount importance for the network’s global fracture behavior. It seems as a fiber network’s crack sensitivity is related to the average pore size in the second part of the mixed Gamma distribution. The analysis is remarkably consistent with reported experiments.
Highlights
Fracture of randomly distributed fiber materials has been extensively studied during the past decades
Koh et al (2013) monitored fracture experiments on polymeric fiber networks to analyze the mechanical behavior in the vicinity of crack tips
Goutianos et al (2018) applied a finite element model to reveal the mechanical behavior of inter-fiber bonds in cellulose networks and how they influence a network’s
Summary
Fracture of randomly distributed fiber materials (e.g. paper or nonwoven fabrics) has been extensively studied during the past decades (among others Seth and Page, 1974; Niskanen, 1993; Considine et al, 2011; Mäkelä and Fellers, 2012; Hagman and Nygårds, 2012; Coffin et al, 2013; Isaksson and Hägglund, 2007; saksson and Hägglund, 2009; Hägglund and Isaksson, 2006). Carlsson and Isaksson (2020) obtained similar results in highly resolved numerical phase field fracture models of wood From both experimental and numerical studies it is clear that porous materials with a larger pore size have a relatively higher crack insensitivity than porous materials with smaller pores, because the pores act as naturally existing defects/cracks. Experimental and numerical studies concerning failures of fiber networks and other heterogeneous porous materials have been reported, the scientific question of how a network’s microstructural properties affect its global crack sensitivity is still open. It is hypothesized that the size distribution of larger pores and open regions in a fiber network governs the network’s global fracture behavior This seems to be physically sound since the larger the naturally existing pores are, the larger can a defect or crack be without notably affecting the mechanical behavior on the global scale.
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