# Off-Axis Tension Behaviour of Unidirectional PEEK/AS4 Thermoplastic Composites
## 2 Materials and Methods
### End-Tab Design  
[PERSON] and [PERSON] [25] have proposed using oblique end-tabs in off-axis tension tests to counterbalance bending moment and eliminate stress concentration areas. The concept is to use a slant rigid connection between the loading point and the specimen to generate a uniformly distributed stress field. The end-tab oblique angle \(\varphi\) depends on the compliance of the off-axis lamina \(\overline{S}_{ij}\):  
\[cot\varphi=-\frac{\overline{S}_{16}}{\overline{S}_{11}} \tag{1}\]  
For unidirectional laminate under plane-stress conditions, the off-axis compliance \(\overline{S}_{ij}\) can be derived from the transformation of the on-axis compliance \(S_{ij}\):  
\[\left\{ \begin{matrix}\overline{S}_{11}=S_{11}cos^{4}\theta+(2S_{12}+S_{16}) sin^{2}\theta cos^{2}\theta+S_{22}sin^{4}\theta\\ \overline{S}_{16}=(2S_{11}-2S_{12}-S_{66})sin\theta cos^{3}\theta-(2S_{22}-2S_ {12}-S_{66})sin^{3}\theta cos\theta\end{matrix} \right. \tag{2}\] \begin{table}
\begin{tabular}{c c} \hline \hline  & **PEEK/AS4** \\ \hline Matrix system & Polyetheretherketone (PEEK) \\ Fibre & AS4 carbon fibre \\ Fibre volume fraction & 34\% \\ Overall density & 1.46 g/cm\({}^{3}\) \\ Moulding & Hot press moulding \\ Thickness & 0.14 mm \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The properties of the PEEK/AS4 prepreg. Figure 2: Off-axis tension specimen with oblique end-tabs. The compliance coefficients can be expressed by material constants:  
\[ \begin{split} S_{11}&=\frac{1}{E_{1}}\\ S_{22}&=\frac{1}{E_{2}}\\ S_{66}&=\frac{1}{G_{12}}\\ S_{12}&=-\frac{-\
u_{21}}{E_{1}}\end{split}  \tag{3}\]  
Therefore, the corresponding oblique angles are calculated and listed in Table 2.  
Oblique end-tabs are manufactured using glass fibre epoxy composite in the dimension of 25 mm \(\times\) 10 mm. The nominal thickness of the end-tab is 1.5 mm. The effect of this end-tab design on the failure mechanisms of thermoplastic composites is not analysed by any researcher. Hence finite element (FE) analysis and experimental investigation are carried out in this study. A comparative study on rectangle and oblique end-tabs is carried out using the FE method. Three-Dimensional models of the specimen with two types of end-tabs were built in ABAQUS using an eight-node brick element with reduced integration (C3D8R). The properties of the thermoplastic composite lamina and end tab is listed in Table 3. A displacement loading of 0.2 mm was applied on the end-tab surfaces to simulate the experimental loading condition. Representative deformation contour plots of 15\({}^{\circ}\) off-axis tension models are illustrated in Figure 3. Significant in-plane bending deformation was induced by the off-axis loading in the specimen with regular end-tabs. The oblique end-tab neutralized the bending moment and produced a uniform displacement field. Figure 3(a,b) is the FE simulated stress contour plots of the 15\({}^{\circ}\) off-axis tension specimen. For the specimen with rectangle end-tabs, clear stress concentration points can be observed at the upper right and bottom left area of the specimen assessment area. The stress values are also not evenly distributed along the width direction. The application of oblique end-tabs eliminates stress concentration points, and the largest values are located along the hypotenuse of the end-tabs. The stresses are homogeneously distributed over the specimen length and width. Figure 3(c,d) illustrates the simulated shear stress contour plots of the 15\({}^{\circ}\) off-axis tension specimen. A highly inhomogeneous shear stress field was generated in the specimen with rectangle end-tabs. Shear stress concentration points are located in the same corners as the axial stress field shows. The highest values are detected along the centre of the specimen width. The shear stresses of specimens with oblique end-tabs show uniform distribution. FE analysis results have shown that the use of oblique end-tabs in a 15\({}^{\circ}\) off-axis tension specimen alleviates stress concentration and bending moment.