Shear-lag model for discontinuous fiber-reinforced composites with a membrane-type imperfect interface
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O R I G I NA L PA P E R
J.-Y. Wang · C.-S. Gu · S.-T. Gu · X.-L. Gao
· H. Gu
Shear-lag model for discontinuous fiber-reinforced composites with a membrane-type imperfect interface
Received: 30 December 2019 / Revised: 18 May 2020 © Springer-Verlag GmbH Austria, part of Springer Nature 2020
Abstract A shear-lag model is developed for discontinuous fiber-reinforced composites with a membranetype imperfect interface, across which the displacement vector is continuous but the traction vector suffers a jump that is governed by the generalized Young–Laplace equation. Closed-form expressions are obtained for the stress fields in both the fiber-reinforced region and the pure matrix regions and for the shear stress on the interface from both the fiber and matrix sides. To illustrate the newly developed analytical model, a numerical analysis is provided by directly using the general formulas derived. The numerical results reveal that the fiber aspect ratio and the interface parameter can both have significant effects on the stress distributions in the composite.
1 Introduction Interfaces in composites are typically imperfect due to processing/manufacturing limitations. Such imperfect interfaces tend to negatively influence load transfer and other properties of composites, especially for nanocomposites that have a large interface-to-volume ratio. Thus, continuous efforts have been made to understand imperfect interfaces and their effects on composite properties (e.g., [1–8]). An imperfect interface is defined to be an interface across which the displacement vector or traction vector is discontinuous. Three models have been proposed to model imperfect interfaces. In the first model (e.g., [9– 12]), the traction vector is continuous and proportional to the displacement vector jump across the interface. The second model stipulates that the displacement vector is continuous, but there is a traction jump governed J.-Y. Wang · C.-S. Gu · H. Gu State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing 210098, China J.-Y. Wang · C.-S. Gu · H. Gu College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing 210098, China J.-Y. Wang · C.-S. Gu · H. Gu National Engineering Research Center of Water Resources Efficient Utilization and Engineering Safety, Hohai University, Nanjing 210098, China S.-T. Gu (B) School of Civil Engineering, Chongqing University, Chongqing 400044, China E-mail: [email protected] X.-L. Gao (B) Department of Mechanical Engineering, Southern Methodist University, Dallas, TX 75275-0337, USA E-mail: [email protected]
J.-Y. Wang et al.
by the Young–Laplace equation across the interface, which is widely used for nanocomposites (e.g., [4,6,13– 19]). The third one is a general interface model that treats an imperfect interface as a thin interphase (e.g., [1,2,20–22]). This model is characterized by two relations governing the traction and displacement jumps (e.g., [1,23]). The general imperfect interface model can be reduced to the spring-layer and memb
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