Multiscale analysis of short fiber reinforced polymers through an anisotropic phase-field model
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Short fiber reinforced polymer (SFRP) components, typically manufactured via injection moulding, exhibit locally varying microstructural configurations \cite{Schneider2017} e.g., fiber orientations, fiber volume contents, and fiber length distributions, which render fracture modeling a challenging task. The strong heterogeneity induced by the manufacturing process causes a tight coupling of the material microstructure with the effective response on the component scale. In this work, we attempt to perform macroscale fracture modeling while accounting for this microstructural complexity in a simplified way, We model fracture macroscopically using a phase-field model and we extend the well-established isotropic phase-field model of brittle fracture \cite{Bourdin2000,Pham2011, Miehe2010} towards anisotropic behavior making use of the fiber orientation interpolation concept \cite{Koebler2019}.To create the database, the anisotropic elastic coefficients are obtained from micromechanical simulations on realistic microstructures \cite{Schneider2017} executed in an “offline” stage. Also, the local microstructure of the component to be studied must be known in order to obtain the relevant properties from the database; for this purpose microstructural information stemming from either X-ray micro computed tomography \cite{Hessman2019} or from injection moulding process simulation is mapped into the finite element mesh of the component prior to the execution of the macroscopic simulations. The performance of the resulting approach is demonstrated by means of several numerical examples. The limitations of the approach stemming from the underlying assumptions are quantified and further development needs are identified.