Abstract
As part of an effort to predict wrinkling of carbon-fiber tows during automated fiber placement, the cohesive zone traction–separation relations for two carbon fiber epoxy prepreg tows are quantified for Mode I and Mode II loading using a rigid double cantilever beam (RDCB) specimen. An explicit expression for normal traction versus normal separation (\(\upsigma \hbox { vs }\updelta _\mathrm{n}\)) and tangential traction versus tangential separation \((\tau \hbox { vs }\updelta _\mathrm{t})\) are derived using static equilibrium equations for an RDCB considering a compressive zone ahead of the process zone. The traction–separation relationships are in term of quantities that can be measured using a full field measurement technique (StereoDIC). The baseline traction–separation relationships in this work are obtained using conditions representative of those experienced by an uncured tow undergoing automated fiber placement (AFP) onto a substrate of a similar material with layup temperature \(\hbox {T} = 40\,{^{\circ }}\hbox {C}\), pressure p = 1 MPa and contact time t = 1 s. The RDCB specimen is loaded in displacement control at a constant load line displacement rate of 0.3 mm/min. Speckle images for StereoDIC are captured using stereo vision systems equipped for capturing images of the RDCB specimen with a field of view of \(100\hbox { mm }\times 75\hbox { mm}\). Analysis of the data obtained for Mode I and Mode II loading shows that the Mode I energy release rate \({\varvec{\mathscr {{G}}}}_\mathrm{I }= 120\hbox { J}/\hbox {m}^{2}\) and Mode II energy release rate \({\varvec{\mathscr {{G}}}}_\mathrm{{II}} = 255\hbox { J}/\hbox {m}^{2}\), with the maximum normal traction \({\varvec{\upsigma }}_\mathrm{\mathrm{max}} = 0.50\hbox { MPa}\) and the maximum shear traction \({\varvec{\tau }}_\mathrm{\mathrm{max}} = 0.35\hbox { MPa}\).
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03 February 2020
This article was published with an erroneous author name.
03 February 2020
This article was published with an erroneous author name.
Notes
Though the interface traction is expected to be different at the ends of the beam, variations in the traction due to edge effects are not included in the analysis due to the limited size of the edge effect zones relative to the length of the adherent.
The spool is stored at \(-20\,^{^{\circ }}\hbox {C}\) inside vacuum sealed bags and it is thawed until the temperature of the tow reached ambient temperature).
The pneumatic loading system is calibrated to obtain the required pressure and the contact time using a pressure transducer mounted directly below the silicon rubber plate where the two tows contact each other.
Before applying the Loctite adhesive, the adherend faying surfaces are treated first using a coarse grit sandpaper (P50) to create a rough surface on both the adherends followed by cleaning the surfaces using water and acetone.
For tow specimens with different fiber orientation a lower energy release rate is expected due to higher number of airgaps at the epoxy rich interface; variation of the fracture properties with fiber orientation will be subject of our future publication.
The strain fields shown in Figs. 8 and 9 correspond to points 1 and 2, as marked on the \(\hbox {F}{-}\Delta \) curve in Fig. 7 (30 N load), respectively. The data for opening and shear strain fields shown in Figs. 8 and 9 are underestimates of the actual tow strains. The underestimates are due to the fact that the StereoDIC imaging system has a virtual strain gage size of \(\sim 880\,\upmu \hbox {m}\) whereas the entire adherent thickness is \(320\,\upmu \hbox {m}\). Thus, the virtual strain gage data includes a majority of information from the rigid adherends which have negligible strain during the loading process.
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Acknowledgements
Funding provided by Boeing Research Contract SSOWBRTW0915000 and associated matching funds provided by University of South Carolina Vice President for Finance Edward Walton via 15540 E250 is deeply appreciated. All materials and access to the \(\mathrm {Lynx}^{\textregistered }\) AFP facility provided by the McNair Aerospace Center, University of South Carolina is gratefully acknowledged. The technical support and assistance of the McNair technical staff, particularly Mr. Burton Rhodes, Jr., during operation of the AFP is also greatly appreciated. Finally, the support of Ms. Eileen Miller, Boeing Research and Technology in Charleston, SC, is gratefully acknowledged.
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Rajan, S., Sutton, M.A., McMakin, W. et al. Characterization of Mode I and Mode II traction–separation laws for cohesive separation of uncured thermoset tows. Int J Fract 221, 25–38 (2020). https://doi.org/10.1007/s10704-019-00399-1
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DOI: https://doi.org/10.1007/s10704-019-00399-1