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Simulation of the Mechanical Response of Thin-Ply Composites: From Computational Micro-Mechanics to Structural Analysis

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Abstract

This paper provides an overview of the current approaches to predict damage and failure of composite laminates at the micro-(constituent), meso-(ply), and macro-(structural) levels, and their application to understand the underlying physical phenomena that govern the mechanical response of thin-ply composites. In this context, computational micro-mechanics is used in the analysis of ply thickness effects, with focus on the prediction of in-situ strengths. At the mesoscale, to account for ply thickness effects, theoretical results are presented related with the implementation of failure criteria that account for the in-situ strengths. Finally, at the structural level, analytical and computational fracture approaches are proposed to predict the strength of composite structures made of thin plies. While computational mechanics models at the lower (micro- and meso-) length-scales already show a sufficient level of maturity, the strength prediction of thin-ply composite structures subjected to complex loading scenarios is still a challenge. The former (micro- and meso-models) provide already interesting bases for in-silico material design and virtual testing procedures, with most of current and future research focused on reducing the computational cost of such strategies. In the latter (structural level), analytical Finite Fracture Mechanics models—when closed-form solutions can be used, or the phase field approach to brittle fracture seem to be the most promising techniques to predict structural failure of thin-ply composite structures.

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Notes

  1. \(125\,\hbox {g/m}^2\) is typically regarded as the minimum dry ply areal weight of conventional low-grade CFRPs.

  2. The distinction between thin- and thick-ply behaviour in Eqs. (1) and (4), respectively, separates the cases of stable crack propagation in the longitudinal direction (crack tunnelling) after through-thickness propagation (thin-ply case), and unstable through-thickness propagation of the transverse crack without stable crack tunnelling, as longitudinal propagation occurs immediately after but at a lower applied stress (thick-ply case) [33, 67, 178]. The theory shows that the transverse stress level at which unstable though-thickness crack propagation occurs is independent of the ply thickness—thick-ply case, Eq. (4). However, stable propagation parallel to the fibres occurs at higher stress levels as the ply thickness decreases—thin-ply case, Eq. (1). Hence, for a ply thickness at which the stress level needed for stable propagation in the longitudinal direction is higher than for unstable through-thickness propagation, increasing strength with decreasing ply thickness is observed (Fig. 7).

  3. It is noted that, in the case of in-plane shear, Linear Elastic Fracture Mechanics alone is not able to accurately predict the in-situ strength, and the non-linear shear response typically observed in laminated composites must be included in the models [33].

  4. Although there is no direct experimental evidence of the in-situ effect for transverse compression, test results obtained in structural details indicate that ply thickness affects the ply compressive strengths [5, 8, 13, 14, 68, 101, 197].

  5. The use of strain space is justified by the fact that, in this case, failure envelopes are invariant [175]; in other words, in strain space, the shapes of the failure envelopes are independent of the presence of other plies.

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Acknowledgements

This work was funded by AIRBUS under project 2genComp—second generation Composites; the authors gratefully acknowledge the support provided by AIRBUS. The first author would also like to thank the financial support provided by FCT–Fundação para a Ciência e a Tecnologia through National Funds in the scope of project MITP-TB/PFM/0005/2013. The third author is grateful to the support of the research projects funded by the Spanish Ministry of Economy and Competitiveness/FEDER (Projects DPI2012-37187, MAT2015-71036-P and MAT2015-71309-P) and the Andalusian Government (Projects of Excellence No. P11-TEP-7093 and P12-TEP-1050), and to the financial support of the European Research Council (ERC), Grant No. 306622 through the ERC Starting Grant “Multi-field and multi-scale Computational Approach to Design and Durability of PhotoVoltaic Modules”—CA2PVM. The last author gratefully acknowledges 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), 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

    Albertino Arteiro & Pedro P. Camanho

  2. Advanced Composites Research Group (ACRG), School of Mechanical and Aerospace Engineering, Queen’s University Belfast, Belfast, BT9 5AH, UK

    Giuseppe Catalanotti

  3. Elasticity and Strength of Materials Group, School of Engineering, Universidad de Sevilla, Camino de los Descubrimientos s/n, 41092, Seville, Spain

    José Reinoso

  4. AIRBUS Operations GmbH, Kreetslag 10, 21129, Hamburg, Germany

    Peter Linde

  5. INEGI, Instituto de Ciência e Inovação em Engenharia Mecânica e Engenharia Industrial, Rua Dr. Roberto Frias, 400, 4200-465, Porto, Portugal

    Pedro P. Camanho

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Arteiro, A., Catalanotti, G., Reinoso, J. et al. Simulation of the Mechanical Response of Thin-Ply Composites: From Computational Micro-Mechanics to Structural Analysis. Arch Computat Methods Eng 26, 1445–1487 (2019). https://doi.org/10.1007/s11831-018-9291-2

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