PSI - Issue 28

Stylianos Anastopoulos et al. / Procedia Structural Integrity 28 (2020) 2132–2141 S. Anastopoulos et al. / Structural Integrity Procedia 00 (2019) 000–000

2137

a

b

Fig. 7 Fixed Angle Fiber Orientation: (a) result presented with ANSA and (b) geometry

The 16 phi theta angle combinations shown in Table 1 were used for the inclusions, each for equal volume fractions, representing a kind of “ideal” dispersion.

Table 1 Fixed Phi Theta Angle combinations ( o )

φ 0 0 0 0

θ 0

45 90

-45

45 45 45 45 90 90 90 90

0

45 90

-45

0

45 90

-45

-45 -45

0

45 90

45

The orientation tensor, borrowed from fluid mechanics, provides an efficient description of fiber orientation, using a probability curve. The tensor has nine components, with the suffixes for the tensor terms being in the flow direction, in the transverse to the flow direction and in the thickness direction. Typically, these axes are mentioned as the X-Y (or 1-2) for the flow plane and as the Z-axis for the thickness direction, out of the 1-2 flow plane. The original nine components reduce to five independent components, due to tensor symmetry and a normalization condition. These three major orientation components have been included in the orientation considerations:  fiber orientation in the flow direction, varying from 0 to 1.0.  fiber orientation transverse to flow, varying from 0 to 1.0.  tilt of orientation in the 1-3 plane, varying from -0.5 to 0.5.