A bridging law and its application to the analysis of toughness of carbon nanotube-reinforced composites and pull-out of fibres grafted with nanotubes

Abstract

Bridging laws are essential in predicting the mechanical behaviour of conventional short-fibrereinforced composites and the emerging nanofibre-reinforced composites. In this paper, we first review some studies on the toughness of carbon nanotube-reinforced composites that is induced by the pull-out of the nanotubes from the matrix, and on the development of the corresponding bridging laws. A close examination of the available bridging laws for carbon nanotubes reveals that some fundamental issues need to be further addressed. We propose a simple nonlinear and smooth bridging law to describe the pull-out force-displacement behaviour of carbon nanotubes from a matrix. This law contains only two material parameters, reflects the basic features of the pull-out experiments, and is easy to use. We then use this bridging law to calculate the fracture toughness of carbon nanotube-reinforced nanocomposites and predict the pull-out force-displacement response of conventional short fibres that are grafted with carbon nanotubes. Some parametric studies are conducted to reveal the influence of various parameters at the nano-and micro-scale on these properties.

Synthesis and characterization of UHMWPE nanocomposite fibers containing carbon nanotubes coated with a PVP surfactant layer

“…The display of crack‐bridging behavior by the aligned nanotubes also supports the results of the tensile tests, which showed enhanced fracture strain and tensile strength compared to fibers with pristine SWCNTs. Wang et al showed that randomly oriented nanotubes can hinder efforts in forming crack bridging mechanisms . Pristine SWCNTs are associated with higher probability of aggregation in the polymer matrix and achieving uniform preferential alignment during extrusion of the fiber is difficult.…”

Dynamic Constitutive Model Analysis of High Parameter Steel Fiber Reinforced Concrete

“…The parameters a and b are related to the parameters of the matrix strength and the parameters of the steel fiber (3) Influence of steel fiber on damage After the micro cracks appear in the high parameter steel fiber reinforced concrete specimens, the strain release is first used for fiber debonding [29] instead of supporting the continuous expansion of cracks. Therefore, it has delayed the fracture process and played a toughening effect.…”

An Analytical Model of Interlaminar Fracture of Polymer Composite Reinforced by Carbon Fibres Grafted with Carbon Nanotubes

“…It is generally accepted that the toughness enhancement due to CNTs in the interlaminar region is attributed mainly to the CNT pullout process [18,19,20], involving (i) CNT pullout from polymer matrix; and (ii) CNT sword-in-sheath pullout. Thus, the various complex bridging laws, based on the Lawrence shear-lag theory [27] or nonlinear shear cohesive theory [28], have been continuously developed with the aim of good agreement with CNT pullout experimental curves [29]. The former bridging laws were established by the FE model [30], molecular dynamic model [20], and nonlinear theoretical model [29], and potentially increase computational cost or complicate the modelling process.…”

“…Thus, the various complex bridging laws, based on the Lawrence shear-lag theory [27] or nonlinear shear cohesive theory [28], have been continuously developed with the aim of good agreement with CNT pullout experimental curves [29]. The former bridging laws were established by the FE model [30], molecular dynamic model [20], and nonlinear theoretical model [29], and potentially increase computational cost or complicate the modelling process. However, in our concern to reduce the numerical computation to the minimum and facilitate application of the final proposed toughness model, linear analytical bridging laws with direct relationships and clear form can be established after a few assumptions are made: The CNTs are treated as unidirectional and straight multi-wall nanotubes without defects, and they are radially and uniformly grown on the surface of carbon fibres and then embedded into epoxy matrix to produce the CNTs@CFs hybrid structure.Based on assumption (1), the effects of any curvature [31], direction misalignment [32], stochastic failure [33], and bending [34] of individual CNTs on CNT pullout behaviour are minor.…”