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Analysis Models for Polymer Composites Across Different Length Scales

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Book cover The Structural Integrity of Carbon Fiber Composites

Abstract

This chapter presents the analysis models, developed at different length scales, for the prediction of inelastic deformation and fracture of polymer composite materials reinforced by unidirectional fibers. Three different length scales are covered. Micro-mechanical models are used to understand in detail the effects of the constituents on the response of the composite material, and to support the development of analysis models based on homogenized representations of composite materials. Meso-mechanical models are used to predict the strength of composite structural components under general loading conditions. Finally, macro-mechanical models based on Finite Fracture Mechanics, which enable fast strength predictions of simple structural details, are discussed.

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Notes

  1. 1.

    In a region with a set of points, it is possible to define a Voronoi polygon as the sub-region that is closer to a given point than to any other. The set of Voronoi polygons defines a subdivision of this region, known as Dirichlet tessellation [29]. The standard deviation of the areas of the Voronoi polygons can be used as a measure of the periodicity of the distribution of fibers [13]—in a periodic distribution all Voronoi polygons are equal, and the standard deviation of the areas is zero.

  2. 2.

    The neighboring fibers are defined as the fibers that share the sides of the Voronoi polygon of the fiber of interest [13]. The standard deviation of the distances to neighboring fibers provide a measure of how separate from each other the fibers are [13]. Like the standard deviation of the areas of the Voronoi polygons, the standard deviation of the distances to neighboring fibers in a periodic distribution is zero.

  3. 3.

    The Cumulative Distribution Function of the orientation of the nearest neighbor represents the total number of fibers that have the nearest neighbor oriented along a certain direction. For a perfectly random spatial arrangement, given by the Poisson distribution, this statistical descriptor follows a straight diagonal line meaning that a given orientation has the same probability of occurring as any other orientation. Deviations from this line correspond to the existence of preferred orientations, as in periodic distributions.

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Acknowledgements

The authors gratefully acknowledge the funding of Project NORTE-01-0145-FEDER-000022—SciTech—Science and Technology for Competitive and Sustainable Industries, co-financed by Programa Operacional Regional do Norte (NORTE2020), through Fundo Europeu de Desenvolvimento Regional (FEDER).

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Authors and Affiliations

  1. DEMec, Faculdade de Engenharia, Universidade do Porto, Rua Dr. Roberto Frias, s/n,, 4200-465, Porto, Portugal

    Pedro P. Camanho

  2. INEGI, Universidade do Porto, Rua Dr. Roberto Frias, 400, 4200-465, Porto, Portugal

    Albertino Arteiro

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  1. Pedro P. Camanho
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Correspondence to Pedro P. Camanho .

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  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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Camanho, P.P., Arteiro, A. (2017). Analysis Models for Polymer Composites Across Different Length Scales. 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_9

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