Elasto-viscoplastic model for rayon yarns

Abstract

In this paper we develop a new model for the simulation of the mechanical behavior of rayon twisted yarns, at macroscopic level. A yarn with its continuous filaments is represented by an equivalent three-dimensional solid of cylindrical shape, discretized by finite elements, with properly defined local anisotropic material properties. The new constitutive model, inspired by experimental results on rayon untwisted yarns, is formulated in the framework of the thermodynamics of irreversible processes and includes visco-elastic and visco-plastic dissipation mechanisms. The effect of twist is taken into account by including the direction of the fibers in the free energy definition. The overall model is validated comparing numerical and experimental results on twisted rayon yarns.

Geometrical and Mechanical Modeling of Polymeric Multi-Ply Yarns

“…The transversal isotropic elasto-viscoplastic model developed in [13] is here assumed. Isotropic hardening is also included in the present work.…”

“…The stiffness matrix depends on five material parameters: µ L , µ P are the shear moduli, respectively, along the fiber direction a (index L) and in the plane of isotropy (orthogonal to a, index P), and λ, α and β are three material constants that can be derived from the more usual engineering elastic constants E L , E P , ν P and ν PL , as shown in [13]. The material parameter h governs the isotropic hardening, assumed linear for simplicity, while H ℓ and H nℓ define the linear and non-linear kinematic hardening.…”

“…Similarly, Ξ is a fourth-order tensor, depending on five retardation times (cp. [13]). Here, a single retardation time is considered for simplicity, hence assuming…”

“…In [13], the present authors, in the framework of the thermodynamics of irreversible processes [14], developed a new transversely isotropic viscoelastic-viscoplastic constitutive law intended to model fibrous materials. The model was applied to describe the mechanical behavior of single-ply yarns, replacing their real geometry with an equivalent three-dimensional continuum of cylindrical shape.…”

“…Section 2 first introduces the model employed to describe the fiber direction inside a multi-ply yarn and the approach here proposed to define a mean direction in each point of a homogenized equivalent solid. Then, the model formulated in [13] for rayon filaments is summarized and extended to include isotropic hardening and different elastic behavior in tension and compression. In Section 3, the model parameters are first identified on the basis of experimental results obtained in tension tests on untwisted and twisted yarns; then, the model and the proposed approach are validated by simulating uniaxial tension test on two-ply cords.…”