An efficient method for fiber bridging traction identification based on the R-curve: Formulation and experimental validation

Fiber bridging is one of the main toughening mechanisms in mode I interlaminar and intralaminar fracture of laminated composites. Intact fibers exert closing forces on both faces of the crack, restraining crack propagation. An effective identification procedure is required to characterize bridging tractions and to develop accurate prediction models. The method proposed in this work is based on the resistance (R)-curve and assumes fiber bridging tractions decreasing non-linearly with respect to the crack opening displacement, following a parametric function. The distribution parameters are identified by a fixed-point iterative procedure where the energy release rate computed in a numerical model is matched with the values obtained experimentally in two points of the R -curve. The method is applied and validated through three cases, from low bridging intensity in thin-ply delamination to high bridging intensity in intralaminar fracture. (C) 2017 Elsevier Ltd. All rights reserved.

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John Botsis, Joël Cugnoni, Guillaume Frossard, Thomas Gmür
Elsevier, 2017
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https://infoscience.epfl.ch/record/229481?ln=fr

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Specimen thickness dependence of large scale fiber bridging in mode I interlaminar fracture of carbon epoxy composite

John Botsis, Joël Cugnoni, Ebrahim Farmand Ashtiani

Large scale bridging is an important toughening mechanism in composite laminates that depends on the specimen geometry as well as the constituent materials. In this work, an iterative approach is applied to identify the effect of specimen thickness on traction-separation behavior in the bridging zone. Double cantilever beam specimens (DCB) with embedded arrays of wavelength-multiplexed fiber Bragg grating (FBG) sensors are subjected to monotonic mode I fracture loading. As processed specimens with thicknesses h = 2, 4, 8 and 10 mm as well as specimens of h = 4 mm milled down from the 8 and 10 mm are tested. Non-homogeneous strain distributions in the vicinity of the interlaminar crack plane are locally monitored by means of embedded FBGs. The measured strain data are used to quantify the bridging tractions associated with each specimen thickness and consequently the energy release rate (ERR) due to the bridging. The results show that the bridging zone length and the ERR at the plateau level increase with specimen thickness while the results for all specimens with h = 4 are the same thus excluding any processing effects. Moreover, the maximum stress of traction-opening in the bridging zone and crack opening displacement at the end of the zone are independent of thickness. In contrast, the rate of tractions decay depends on the specimen thickness in that it decreases with thickness scaling. Thus the so-called bridging law is not a material parameter. The identified traction-separation relations are employed in a cohesive zone model to predict fracture of DCB specimens with different thicknesses. (C) 2014 Elsevier Ltd. All rights reserved.

Elsevier2015

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Studies of mode I delamination in monotonic and fatigue loading using FBG wavelength multiplexing and numerical analysis

John Botsis, Joël Cugnoni, Samuel Stutz

Bridging by intact fibers in composite materials is one of the most important toughening mechanisms. However, a direct experimental assessment of its contribution is not easy to achieve. In this work a semi-experimental method is proposed to quantify its contribution to fracture of unidirectional carbon fiber/epoxy double cantilever beam (DCB) specimens in mode I delamination under monotonic and 1 Hz fatigue loads. In each specimen, an embedded optical fiber with an array of eight wavelength-multiplexed fiber Bragg gratings is used to measure local strains close to the crack plane. The measured strain distribution serves in an inverse identification procedure to determine the tractions in the bridging zone in monotonic and fatigue loads. These tractions are used to calculate the energy release rate (ERR) associated with bridging fibers. The results indicate that the ERR due to bridging is about 40% higher in fatigue. The bridging tractions are further included in a cohesive element model which allows to predict precisely the complete load displacement curve of monotonic DCB tests. Using the principle of superposition and the identified tractions, the total stress intensity factor (SIF) is calculated. The results show that the SIF, at initiation, is very close to the one calculated at crack propagation and bridging by intact fibers is responsible for the entire increase in toughness seen in the DCB specimens used herein. (C) 2010 Elsevier Ltd. All rights reserved.

2011

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Identification of traction separation relations is at the forefront of damage and fracture mechanics of composite laminates. Such relations are of particular interest in fracture of laminates consisting of layers of different fiber orientations. In this study, an iterative method based on internal strain measurements and parametric numerical modeling is employed to identify a traction-separation relation in quasi-static mode I dominated delamination of a cross-ply carbon fiber epoxy laminate. The results demonstrate that crack propagation is accompanied by a large bridging zone which is smaller than the zone in a uniaxial composite specimen of the same materials and linear dimensions. While the initiation value of the energy release rate (ERR) is the same, the ERR at steady state propagation and the maximum stress in the bridging zone are respectively 1.7 and 3.1 times larger than the corresponding values of the unidirectional specimen. The obtained traction-separation relation is employed in a cohesive zone model to predict the loading response and crack growth. The adopted approach is a step towards a better understanding of delamination in cross-ply composites. (C) 2015 Elsevier Ltd. All rights reserved.

Elsevier2015

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