A viscoplasticity model with an invariant-based non-Newtonian flow rule for unidirectional thermoplastic composites

TL;DR

This work develops an invariant-based, transversely isotropic viscoplasticity model for unidirectional thermoplastic composites, extending the isotropic EGP framework with an Eyring-type, rate-dependent flow rule. Through a multimode relaxation spectrum and a fully implicit integration scheme with a consistent tangent modulus, the model captures direction-, rate-, and pressure-dependent plasticity and creep while excluding plastic flow in the fiber direction. Parameter identification relies on a minimal set of off-axis tests and micromechanical homogenization, enabling accurate mesoscale predictions with modest input data. The approach is validated against micromodel results and off-axis ply experiments, demonstrating good agreement and paving the way for efficient virtual testing of thermoplastic composite laminates with potential extensions to multiple relaxation processes and temperature effects.

Abstract

A three-dimensional mesoscopic viscoplasticity model for simulating rate-dependent plasticity and creep in unidirectional thermoplastic composites is presented. The constitutive model is a transversely isotropic extension of an isotropic finite strain viscoplasticity model for neat polymers. Rate-dependent plasticity and creep are described by a non-Newtonian flow rule where the viscosity of the material depends on an equivalent stress measure through an Eyring-type relation. In the present formulation, transverse isotropy is incorporated by defining the equivalent stress measure and flow rule as functions of transversely isotropic stress invariants. In addition, the Eyring-type viscosity function is extended with anisotropic pressure dependence. As a result of the formulation, plastic flow in fiber direction is effectively excluded and pressure dependence of the polymer matrix is accounted for. The re-orientation of the transversely isotropic plane during plastic deformations is incorporated in the constitutive equations, allowing for an accurate large deformation response. The formulation is fully implicit and a consistent linearization of the algorithmic constitutive equations is performed to derive the consistent tangent modulus. The performance of the mesoscopic constitutive model is assessed through a comparison with a micromechanical model for carbon/PEEK, with the original isotropic viscoplastic version for the polymer matrix and with hyperelastic fibers. The micromodel is first used to determine the material parameters of the mesoscale model with a few stress-strain curves. It is demonstrated that the mesoscale model gives a similar response to the micromodel under various loading conditions. Finally, the mesoscale model is validated against off-axis experiments on unidirectional thermoplastic composite plies.

Figures (20)

• Figure 1: Rheological model of the driving stress.
• Figure 2: Decomposition of total deformation in elastic and plastic deformation for each mode $i$, with the corresponding initial$\Omega_0$, intermediate$\Omega_i$ and current configuration $\Omega$.
• Figure 3: The transversely isotropic stress invariants are related to transverse shear (left), longitudinal shear (middle) and biaxial tension or compression (right).
• Figure 4: Stress-strain response with a single mode and with multiple modes.
• Figure 5: Nested external-internal solution scheme. At every external iteration (left), $N$ internal schemes are solved, one for each mode $i$ (right).