Randomization algorithm for the micromechanical modeling of fiber-reinforced Polymer Matrix Composites
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Abstract
Polymer Matrix Composites (PMCs) are replacing metallic materials in many engineering fields such as aerospace, naval and mechanical engineering. Failure in PMCs can happen due to matrix cracking, fiber failure, fiber/matrix debonding and delamination. Performing damage and failure analysis requires advanced computational tools; micromechanical studies are fundamental to fully understand mechanisms triggered at the fiber and matrix scale. Perfectly packed Representative Unite Cells (RUCs), as square or hexagonal arrays, are often used to characterize macromechanical properties of composites1 within the Finite Element Method (FEM) where periodicity constraints are enforced2. Understanding composites failure requires the modelling of a realistic microstructure that accounts for variability within composites3. This work provides a randomization algorithm developed in Matlab environment. Different randomization methods have been studied4,5; an optimized algorithm is then proposed in terms of efficiency in fiber placing and run time. Giving the fiber volume fraction, “vf”, fiber diameter, “d”, and the number of fibers modeled, “nf” as inputs, the algorithm generates a square domain of length, “l”, in which fibers are randomly placed. The number of RUCs generated is also defined by the user. The algorithm prevents overlapping between fibers to occur. Outputs are fiber coordinates listed in a text file that can be imported in any Finite Element (FE) commercial code as Abaqus, Ansys or Nastran for RUC meshes generation as shown in Figure 1 that depicts ten 20-fiber randomly packed RUCs. This code is developed within the Integrated Computational Materials Engineering (ICME) framework as a pre-processor for FE analysis.
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