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Characterization of Mode I and Mode II traction–separation laws for cohesive separation of uncured thermoset tows

Authors
  • Rajan, Sreehari1
  • Sutton, Michael A.1
  • McMakin, William1
  • Compton, Elsa1
  • Kidane, Addis1
  • Gurdal, Zafer1
  • Wehbe, Roudy1
  • Farzana, Yasmeen1
  • 1 University of South Carolina, Columbia, SC, 29208, USA , Columbia (United States)
Type
Published Article
Journal
International Journal of Fracture
Publisher
Springer Netherlands
Publication Date
Dec 12, 2019
Volume
221
Issue
1
Pages
25–38
Identifiers
DOI: 10.1007/s10704-019-00399-1
Source
Springer Nature
Keywords
License
Yellow

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 (σvsδn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\upsigma \hbox { vs }\updelta _\mathrm{n}$$\end{document}) and tangential traction versus tangential separation (τvsδt)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\tau \hbox { vs }\updelta _\mathrm{t})$$\end{document} 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 T=40∘C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {T} = 40\,{^{\circ }}\hbox {C}$$\end{document}, 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 100mm×75mm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$100\hbox { mm }\times 75\hbox { mm}$$\end{document}. Analysis of the data obtained for Mode I and Mode II loading shows that the Mode I energy release rate GI=120J/m2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varvec{\mathscr {{G}}}}_\mathrm{I }= 120\hbox { J}/\hbox {m}^{2}$$\end{document} and Mode II energy release rate GII=255J/m2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varvec{\mathscr {{G}}}}_\mathrm{{II}} = 255\hbox { J}/\hbox {m}^{2}$$\end{document}, with the maximum normal traction σmax=0.50MPa\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varvec{\upsigma }}_\mathrm{\mathrm{max}} = 0.50\hbox { MPa}$$\end{document} and the maximum shear traction τmax=0.35MPa\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varvec{\tau }}_\mathrm{\mathrm{max}} = 0.35\hbox { MPa}$$\end{document}.

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