PSI - Issue 8

A. Pantano et al. / Procedia Structural Integrity 8 (2018) 517–525 A. Pantano, B. Zuccarello / Structural Integrity Procedia 00 (2017) 000–000

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2. Numerical model

One of the most used techniques for predicting the mechanical behavior of a long fiber composite materials is to produce a micromechanical model that is based on the realization of a representative volume (RVE), a constitutive description of the fibers and the polymer matrix, a characterization of the interface between fiber and matrix, and appropriate boundary conditions on the RVE. In micromechanical models, fiber distribution in the matrix is often simplified as a regular distribution of staggered arrays or stacked arrays. The main problem of stacked arrays is the high non-uniformity; layers of pure matrix alternate with layers with high concentration of fibers, creating a microscopically more inhomogeneous composite than the real one. In the present study, after evaluating the possibility of using a micromechanical model based on a RVE of the type staggered arrays, we opted for a 1: 1 finite element model capable of reproducing a biocomposite specimen sufficiently faithfully; in particular it has been investigated the case of biocomposites reinforced by agave fibers, which typically exhibit the problem of natural fiber waviness, and for which the fiber form can be simulated with good approximation through a sine wave having amplitude a and wavelength l . Considering the case of biocomposites with layers of opposing waves, the numerical model was developed for a laminate consisting of only 2 layers (see Fig. 1 and 2) with volume concentration V f and waviness ratio a/l variables. In particular, by taking advantage of the symmetry of the system with respect to the transverse axis, the model reproduces only half of the specimen, thus allowing, with proper provision of constraints and load, significant savings in terms of calculation. A rectangular laminate specimen with 2 layers having length l = 375 mm, width w = 50 mm and thickness s = 1 mm, was simulated. In order to further simplify the model, the number of fibers was reduced compared to the real specimen of agave fibers, characterized by an average diameter of about 200 μm, increasing their diameter so as to keep constant the volume concentration V f .

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Single Fiber

Simmetry Plane

Fig. 1. Finite element model with ratio a/l = 0.05, length l = 350 mm, width w = 50 mm, thickness s = 1 mm and fiber concentration V f = 0.2; (a) three-dimensional view with indicated boundary conditions, (b) three-dimensional view where only a single fiber is visible, (c) frontal view of a single fiber where amplitude and wavelength are defined. A pure strain deformation is imposed, as in experimental traction tests, by an axial shift (direction 2 in Fig. 1a), applied to the entire surface of the upper edge. In Figures 1b and 1c, the generic sinusoidal fiber whose shape, as