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Traction-Separation Relations in Delamination of Layered Carbon-Epoxy Composites Under Monotonic Loads: Experiments and Modeling

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Abstract

It is well known that large-scale bridging accompanying delamination and fracture in layered composites is among the most important toughening mechanisms. The resulting resistance to fracture, however, is dependent on the specimen geometry rendering its modeling difficult. As a consequence, characterization of the tractions on the wake of the crack, the so-called bridging zone, is very important in the efforts to predict the loading response of composite structures. In this chapter, experimental results and modeling of delamination and fracture in layered composite specimens are discussed. The experimental part consists of displacement-controlled monotonic tests of interlaminar and intralaminar fracture. Selected specimens are equipped with wavelength-multiplexed fiber Bragg grating (FBG) sensors to monitor crack propagation and strains over several millimeters in the wake of the crack. The modeling part involves an iterative scheme to calculate the traction-separation relation, due to bridging, using the strains from the FBG sensors, parametric finite elements, and optimization. The experimental results demonstrate an important effect of specimen thickness in interlaminar and intralaminar fracture: the bridging zone length at steady state linearly increases with specimen thickness, while the maximum bridging stress is independent of thickness in each case. Results of a similar study in cross ply specimens, limited to a selected specimen thickness, show important effects of specimen width on the extent of large-scale bridging. The obtained traction-separation relations for each investigated case are employed in cohesive zone simulations to predict the corresponding load-displacement curves. On the basis of the experimental results, a micromechanics model is used, based on an embedded-cell model, to predict the observed specimen thickness effects on large-scale bridging. The results of the reported studies demonstrate that the so-called bridging law is not a material parameter and the proposed methods of analysis, predict very well the load-displacement response.

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Abbreviations

α :

Vector of parameters of the bridging tractions profile

γ :

Traction profile exponent

Δ :

Applied displacement

δ :

Crack opening displacement

ε x,y,z :

Strains on directions x, y, and z

ε z (z):

Longitudinal experimental strain distribution

\( {\tilde{\varepsilon}}_z(z) \) :

Longitudinal numerical strain distribution

Λ 0 :

Period of the induced index modulation

λ B0, λ B :

Initial Bragg wavelength and current Bragg wavelength

ν f :

Poisson’s ratio of the optical fiber

σ max :

Maximum bridging traction

σ bf, max :

Fiber bundle strength

σ b (z):

Bridging tractions, over position

\( {\widehat{\sigma}}_b\left(\delta \right) \) :

Bridging tractions, over CODs

χ :

Crack length’s variation parameter

a :

Crack length

Β :

Specimen’s width

C :

Specimen’s compliance

D(δ):

Damage parameter, as linear stiffness degradation of the cohesive elements

F(α):

Objective function of the optimization scheme

f ε (z, α):

Error function, based on strains

f P (α):

Error function, based on forces

f J (α):

Error function, based ERRs

G IC, G IIC, G IIIC :

Critical energy release rates (ERRs) for each fracture mode

G I,i :

Initial fracture toughness, linear elastic, mode I

G I,b :

Energetic contribution of bridging, linear elastic, mode I

G II,i :

Initial fracture toughness, linear elastic, mode II

G total :

Total energy release rate, linear elastic

G ss :

Energy release rate at steady state, linear elastic

G weak :

Failure energy of weak connectors

G strong :

Failure energy of strong connectors

H :

Specimen’s thickness (or height)

J tip :

ERR by means of numerical J-integral

J I,b :

Energetic contribution of bridging, general case, mode I

J total :

Total ERR, general case

K c :

Stiffness of connectors

K 0 :

Initial stiffness of cohesive elements

n eff :

Mean core index of refraction

N weak :

Strength of weak connectors

N strong :

Strength of strong connectors

P :

Reaction force

p e :

Experimental optomechanical grating gage factor

w P , w J :

Weight factors of the error functions

z :

Bridging zone coordinates

z max :

Bridging zone length at steady state

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Acknowledgements

The authors acknowledge the partial financial support from the Swiss National Science Foundation under Grant 200020_149721.

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Authors and Affiliations

  1. Ecole Polytechnique Fédérale de Lausanne (EPFL), LMAF-STI, Lausanne, CH-1015, Switzerland

    J. Botsis, E. Farmand-Ashtiani, G. Pappas, J. Cugnoni & L. P. Canal

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  1. J. Botsis
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  2. E. Farmand-Ashtiani
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Correspondence to J. Botsis .

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Editors and Affiliations

  1. Department of Engineering, University of Cambridge, Cambridge, United Kingdom

    Peter W. R Beaumont

  2. Aerospace Research Institute, The University of Manchester, Manchester, United Kingdom

    Constantinos Soutis

  3. Department of Mechanical Engineering, The University of Sheffield, Sheffield, United Kingdom

    Alma Hodzic

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Botsis, J., Farmand-Ashtiani, E., Pappas, G., Cugnoni, J., Canal, L.P. (2017). Traction-Separation Relations in Delamination of Layered Carbon-Epoxy Composites Under Monotonic Loads: Experiments and Modeling. In: Beaumont, P., Soutis, C., Hodzic, A. (eds) The Structural Integrity of Carbon Fiber Composites. Springer, Cham. https://doi.org/10.1007/978-3-319-46120-5_20

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