CAE-Companion-2018-2019

Modeling of Materials & Connections WISSEN CAE

with:

(25)

(11)

(26)

(12)

(13)

(27)

(14)

(28)

(15)

(29)

(16)

(30)

(17)

(31)

(18)

(32)

(19)

with:

(20)

α

fibre aspect ratio (l/d)

(21)

λ f ,λ m ,µ f ,µ m Lamé constants of fibre and matrix The use of the models requires knowledge on the distribution of fiber orientations. These can be produced through injec- tion moulding simulations (see Figure 2). Software utilities then allow the automatic transfer of information on the local fibre structure into the structural simulation model. The described procedure requires, however, knowledge about the elastic characteristics of the plastics matrix. Their determination is problematic because for short-fibre-re- inforced plastics, the exact data of the matrix material are generally not known. One way to estimate these is the application of the Halpin-Tsai model. From tension test data the modulus E 11 of the fibre-reinforced plastics can be deter- mined. Once this is known, the matrix modulus E m follows from equation (1). For calculations reaching the plastic region very complex material models need to be applied, often by using the user interface of FEM software packages. The elastic material models described here reach their validity limit in this case.

(22)

(23) (24)

The parameters S in the equations (8) - (9) and (20) - (24) are the components of the so-called Eshelby tensor. They allow to explicitly take into account the geometry of the enclosure. In the case of a fiber, the components are defined as follows:

Figure 2: Screenshot of an injection moulding simulation for the determina- tion of the fibre orientation

CAEWissen by courtesy of the Chair of Plastics Processing Technology at TU Dortmund University

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