# Recent Advances in Additive Manufacturing of Fibre-Reinforced Materials: A Comprehensive Review
## 3 Evaluation
### Anisotropy  
Anisotropy in 3D-printed reinforced materials is a critical factor influencing their mechanical performance and structural integrity. Unlike isotropic materials, which exhibit uniform properties in all directions, anisotropic materials show variation in properties depending on the direction of measurement. This directional dependence is observed in 3D-printed composites, where factors such as print orientation, layer adhesion, fibre alignment [103], or thermal properties [104] introduce significant anisotropy. Quantifying this anisotropy often involves metrics like the Zener ratio or the anisotropy ratio. The Zener ratio assesses elastic anisotropy, with deviations from unity indicating the extent of anisotropy in stiffness, while the anisotropy ratio compares mechanical properties, such as tensile strength or modulus, in different directions. \[\underline{\mathsf{C}}= \begin{bmatrix}\mathrm{C}_{11}&\mathrm{C}_{12}&\mathrm{C }_{12}&0&0&0\\ \mathrm{C}_{12}&\mathrm{C}_{11}&\mathrm{C}_{12}&0&0&0\\ \mathrm{C}_{12}&\mathrm{C}_{12}&\mathrm{C}_{11}&0&0&0\\ 0&0&0&\mathrm{C}_{44}&0&0\\ 0&0&0&0&\mathrm{C}_{44}&0\\ 0&0&0&0&0&\mathrm{C}_{44}\end{bmatrix}  \tag{3}\]  
\[\mathrm{A}_{\mathrm{z}}=\frac{2\cdot\mathrm{C}_{44}}{\mathrm{C}_{11}-\mathrm{ C}_{12}} \tag{4}\]  
The Zener ratio \(\mathrm{A}_{\mathrm{z}}\) is a dimensionless number that is used to quantify the elastic anisotropy for cubic crystals, where \(\mathrm{C}_{\mathrm{ij}}\) are the stiffness coefficients. A Zener ratio equal to \(1\) indicates an isotropic material, while a deviation from \(1\) signifies anisotropy [105; 106]. For 3D-printed composites, this ratio is taken under consideration during the printing process, where fibre orientation may affect material stiffness and overall mechanical performance. As mentioned, the anisotropy ratio, or degree of anisotropy (DA), compares mechanical properties like tensile strength or modulus. The translation of this could be in the form of  
\[\mathrm{DA}=1-\frac{\sigma_{90^{\circ}}}{\sigma_{0^{\circ}}} \tag{5}\]  
where \(\sigma_{90^{\circ}}\) is the strength with a fiber direction perpendicular to the load, and \(\sigma_{0^{\circ}}\) is the strength with fibre direction parallel to the force. Carbon fibre is known for its anisotropic behaviour under stress loads, and the only force it can withstand is tensile force. To overcome this problem, common carbon fibre manufacturing methods accumulate twill, plain, or unidirectional weaves in the carbon fabric [107]. AM is adopting the same principles to overcome the same drawback, but instead of using a fabric with a different knitting pattern, the slicing software is programmed by the designer to lay down the fibres in different raster angles for each layer. The most common patterns are with raster angles of \(0^{\circ}\), \(45^{\circ}\), \(90^{\circ}\), or a combination of those. Figure 9 provides an example of the raster angle, where Figure 9a shows a \(45^{\circ}\) raster angle, Figure 9b a combination of external shells with a \(45^{\circ}\) raster angle, and Figure 9c a \(0^{\circ}\) raster angle. Experimental studies have revealed that there is a direct dependence between the mechanical properties and the raster angle. In more depth, studies [108; 109; 110] investigated the tensile and flexural properties of specimens with raster angles of \(0^{\circ}\), \(15^{\circ}\), \(30^{\circ}\), \(45^{\circ}\), \(60^{\circ}\), \(75^{\circ}\) and \(90^{\circ}\), and the results revealed that the ultimate tensile and flexural strengths were achieved at \(0^{\circ}\), while the lower started to appear at \(60^{\circ}\) until the ultimate low at \(90^{\circ}\). In addition, [PERSON] et al. [111] conducted experiments with raster angles of \(90^{\circ}\), \(45^{\circ}/-45^{\circ}\), \(90^{\circ}/0^{\circ}\), and \(0^{\circ}\), where the tensile strength was the highest at the \(0^{\circ}\) raster angle and the lowest at \(90^{\circ}\).