CAE-Companion-2018-2019

Modeling of Materials & Connections WISSEN CAE

Material Models for FEMAnalysis of Short Fibre Reinforced Plastics

The analysis and design of parts by structural and crash simulations is often performed with the material parameters Young’s modulus E, Poisson’s ratio ν and a plasticity model. This procedure however is insufficient to select and design short-fibre-reinforced plastics. As shown in Figure 1, short-fi- bre-reinforced plastics exhibit a strong anisotropy, which is due to the different local fibre orientations. This causes strongly direction-dependent mechanical properties.

(4)

(5)

with:

E m , ν m

Young’s Modulus, Poisson’s Ratio of the matrix Young’s Modulus, Poisson’s Ratio of the fibre e.g. Glass Fibre: E f = 72000MPa; ν f = 0.22 Length and diameter of the fibre (l/d ≈ 20 ...30) Fibre volume fraction, to be calculated from the

E f , ν f

l,d

Φ

fibre

weight fraction:

Figure 1: Electron microscopic picture of a polished specimen (PA-GF50)

ρ m ,ρ f Density of the plastics matrix and the fibre Studies in the past have shown that the model of Halpin and Tsai is suitable to estimate the mechanical properties. More accurate, but much more expensive, is the micromechanical model approach of Tandon andWeng. In this model the five transversely isotropic engineering constants are calculated as follows:

For technical applications it is sufficient to know the me- chanical properties in and transverse to the fibre orientation. For these so-called transversely isotropic materials the implementation of the material in FEM analysis still requires five material parameters. These can be determined experi- mentally or calculated using the mechanical properties of the fibres and the polymer matrix, the fibre dimensions and ori- entation. For this, the empirical Halpin-Tsai model, is a widely used method. The five required engineering constants of a transversely isotropic elastic material are defined as follows:

(6)

(1)

(7)

(2)

(8)

(3)

(9)

(10)

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