<< Click to Display Table of Contents >>
## Fiber Function Overview |

Fiber analyses are integrated with Flow, Pack and Warp modules. As the result of flow, the fiber effect will have a big impact on warpage; However, users do need dedicated license codes to run fiber analysis.

Moldex3D Fiber calculates fiber orientation by using the Folgar-Tucker model and its modification for long fiber reinforcement. Users can get successful analysis results with Moldex3D Material Wizard or provide their own appropriate material parameters. In the hierarchical structure of all material grades in Moldex3D Material Wizard menu, the sign next to a material grade entry indicates that fiber related parameters are included. Alternatively, the user can assign appropriate fiber related parameters to any grade in the User Bank.

The fiber-orientation calculation in Moldex3D is done using the Folgar-Tucker equation throughout the whole filling and packing processes. Therefore, it must be performed with Flow and Pack analyses for keeping accurate flow history for orientation calculation. Moreover, analyses with fiber-orientation calculation function will take longer computation time.

Definition of Fiber Orientation

The orientation of a single fiber is defined by the orientation vector p. The probability function is defined so that the probability of finding a fiber between (q, f) and (q+dq, f+df) is given by. The probability distribution function must satisfy two physical conditions. That is, one end of the fiber is indistinguishable from the other, so

And, every fiber must has a definite direction, so the normalization requirement is,

Definition of orientation vector

Since the direct computation of probability function is extremely time-consuming from the engineering’s viewpoint, the second order fiber orientation tensor Aij defined below is used,

Then it’s obvious to find that Aij is a symmetric tensor with

Aij = Aji

A11+ A22+ A33=1

Since orientation tensor is real and symmetric, it has three orthogonal eigenvectors e1, e2, e3 and three eigenvalues l1, l2, l3. Each eigenvalue ranges between 0 and 1. In the post-processing of fiber orientation, the biggest eigenvalue and its corresponding eigenvector are plotted together to show the complex fiber orientation phenomena. The orientation of the vector shows the most favorable orientation direction, while the magnitude of it (displayed in color) shows the degree of orientation.

In summary, for a random orientation, the maximum eigenvalue would be 1/3; for a fully aligned orientation, the maximum eigenvalue would be approximately 1.

The first approach is the 4th orientation tensor closure. It includes three methods: Hybrid (Original Moldex3D fiber orientation calculation solver model), ORE (Orthotropic closure approximation model), and IBOF (Modified orthotropic closure approximation model). The properties of the three models are listed below.

Hybrid |
Short computation time Fiber orientation tensor over-estimates at skin Moderate fiber orientation prediction accuracy |
---|---|

ORE |
Improvement of fiber orientation tensor over-estimating problem High fiber orientation prediction accuracy Long computation time |

IBOF |
Improvement of fiber orientation tensor over-estimating problem High fiber orientation prediction accuracy Short computation time |

The second approach is the Rotary Diffusion, which is to describe the fiber-fiber interaction. It includes three methods: Folgar-Tucker (Original Moldex3D fiber orientation calculation solver model), ARD (Anisotropic Rotary Diffusion Model) and iARD (Improved Anisotropic Rotary Diffusion Model). The properties of these models are listed below.

Folgar-Tucker |
Account for the fiber-fiber interactions with isotropic rotary diffusion which can help users to capture the short-fiber orientation distribution profile. |
---|---|

ARD |
Account for the fiber-fiber interactions with anisotropic rotary diffusion which can help users to better capture the long-fiber orientation distribution profile. The drawback is there are five parameters to set. |

iARD |
Account for the fiber-fiber interactions with anisotropic rotary diffusion which can help users to better capture the long-fiber orientation distribution profile. Only two parameters are needed. |

The third approach uses the Retard Principal Rate (RPR) to consider the Fiber-Matrix interation, and hence improve the original Folgar-Tucker model’s approach, which over-estimates the changing rate of the orientation tensor in concentrated suspensions. The RPR model alpha factor is suggested to be from 0 to 1 (the larger factor value is, the more obvious RPR effect is).