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Materials Science in Additive Manufacturing Fast fiber orientation optimization

Figure 3. Flow chart of computation of the optimal stack’s fiber angles and of the number of reinforced layers.
divided into two steps: The first one is to define an optimal
fiber angle sequence for each stack of ten layers, and the
second one is to optimize the number of reinforced layers.
2.2.1. Optimized stack fiber angles
The first step of our proposed method is to determine the
optimal fiber angle based on the intuitive idea, considering
that the optimal fiber orientation of the material should
coincide with the absolute value of the dominant principal Figure 4. Computation of the stack’s fiber angles iteration by iteration.
stress direction . This method includes several substeps
[16]
as shown in the workflow (Figure 3): because the current commercial manufacturing
(i) A static analysis is first run on a whole part made of process does not allow printing continuous fibers in 3D
an isotropic material. This first calculation allows to orientations but only in 2D layers. The angle between
determine the location where the deposit of fibers is this projected direction and the X-axis (considered
needed to reinforce the stiffness of the part. After this parallel to a 0° fiber’s orientation) is computed at each
static analysis is performed, the Cauchy stress tensor node of the mesh. The optimal fiber angle of the stack
of each node is obtained. is the mean value of the node’s fiber angles, weighted
(ii) The diagonalization of the Cauchy stress tensor gives the by the dominant principal stress value of each node.
three principal stresses and the three principal directions. (iv) To account for a possible deviation around the mean
As the fibers in a composite are efficient for tensile or value calculated in step (iii), the algorithm determines
compressive loads, the first principal stress (tensile stress) which node has a fiber angle more than 10° degrees
is compared to the absolute value of the third principal greater or lower than this mean value. Note that the
stress (compressive if negative) to determine which of value of 10° can be decreased at will by the user, but
these two situations should be considered. it should not be increased, as it has been found that
(iii) The principal direction corresponding to the the strength and the stiffness fall quickly when the
dominant stress in absolute value between the first angle between the fibers and the load exceed 10°. The
and third principal stress is used to compute the fiber remaining nodes are divided into two areas (upper
orientation. The principal direction is projected on the and lower to the mean value), giving two new mean
xy-plane (perpendicular to the stacking direction z) angles (Figure 4). While node’s fiber angles are not in

Volume 2 Issue 1 (2023) 4 https://doi.org/10.36922/msam.49