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A novel transversely-isotropic 3D elastic-viscoplastic constitutive law for modeling fiber matrix composites

A transversely isotropic elastic-viscoplastic constitutive law with a novel 3D failure criterion is presented, addressing high pressure effects, strain rate sensitivity in yielding and failure and volumetric plastic strain. The constitutive equations are derived in the framework of transversely-isotropic invariants, which allow for a coordinate system independent formulation and an easy parameter identification. Triaxiality dependent non-linearities are taken into account and entirely different yielding behavior under uniaxial/biaxial compression, uniaxial/biaxial tension and under in-plane/transverse shear stress states is addressed. Hardening curves for each loading state can easily be input either via tabulated data or optionally by use of a three parameter power law. Lateral plastic straining due to volumetric plastic compression and dilatation is load path dependent as well. In order to control the lateral plastic straining in each stress state, a non-associated flow rule, assuming a plastic potential which gives the direction of the plastic flow is introduced. The applicability of this novel material law is shown by two examples.The first one is a short fiber reinforced thermoplastic PA6GF60, the second one adresses off-axis tensile and compression tests of a unidirectional carbon-epoxy IM7-8552, which is widely used in aircraft industry. For PA6GF60, a complete test setup for characterizing the novel transversely isotropic yield surface is used for validation. All test cases are simulated and compared with these experiments. The sensitivity of the plastic Poisson coefficient and the influence on the simulated load displacement curves are discussed. Strain rate effects are obtained from dynamic uniaxial tensile tests and are considered by a viscoplastic approach. Unidirectional carbon-epoxy IM7-8552 reveal pronounced yielding under combined shear- compression loadings as it is observed in off-axis compression tests. Furthermore, the glass transition temperature of epoxy resin drops from above 200◦ C to operating temperature in the presence of high pressures. This results in a change of mechanical properties, effecting the elastic parameters as well as the yielding behavior.This change of mechanical properties and the pronounced non-linear behavior in the presence of high pressure due to matrix yielding can be modeled properly with this new approach.