## 5 Results
### Stress Distributions at Each Interface around the Hole Edge and the Periphery of Bolt Head  
According to our numerical calculations, interlaminar stress concentrations occurred at Position I, as well as the interior of the laminate near Position II. The interlaminar shear stress distributions at each interface around Position I with the tightened bolt (\(F_{0}\) = 2000 N) are shown in Figure 7. The interlaminar normal stress is not presented in this subsection, due to the assumption of that interlaminar compressive stress is able to delay delamination. This assumption is in agreement with the view of Reference [41]. In addition, shear stress distributions play a significant role in determining the mechanical behavior of multi-direction laminates. Therefore, we only present the shear stress distributions here. Furthermore, the data points of the stress distribution curve are the absolute values of the magnitude of the interlaminar shear stresses.  
As seen in Figure 7, the magnitude of interlaminar shear stresses at the 0/0 interface are lower than those of other interfaces in most of the area around Position I. These 0/0 interfaces not only refer to the middle interface, but also the outer interface. The value of the interlaminar shear stresses of these 0/0 interface do not exceed 2 MPa in most of the area around the hole edge. In contrast, the outer  
Figure 7: Interlaminar shear stress distributions around Position I: (**a**) \(\tau_{xz}\); (**b**) \(\tau_{yz}\). Outer interface—The interfaces located outside the filled-hole laminate, such as the 0/0 and 0/45 interface. Middle interface—The interfaces near the symmetry plane of laminate, such as the \(-45/0\) and 0/0 interface.  
0/45 interface or the middle \(-45/0\) interface exhibits a higher magnitude of interlaminar shear stresses. In general, a higher shear stresses occurs at all non 0/0 interface at Position I. This phenomenon is similar to the classical problems of interlaminar stress that exist at the free edge of laminate. The two classical problems of interlaminar stress are included in Reference [42]. [\(\pm 0\)] laminates exhibit only shear-extension coupling, and [0/90] laminates exhibit only a Poisson mismatch between layers. Both of these two problems exist at the 0/45 interface where adjacent layers of the laminate are subjected to an axial load, so the 0/45 interface exhibits obvious interlaminar shear stress concentrations. In addition, due to a match in the elastic properties between the 0/0 interface adjacent layers, the interlaminar shear stress at 0/0 interface is lower than at other interfaces.  
The interlaminar shear stress distributions curve at Position III is shown in Figure 8. As seen in Figure 8a, the magnitude of \(\tau_{xz}\) in the outer interface of the laminate is higher than that of the middle interfaces at Position III, except near \(\theta=90^{\circ}\) and \(-90^{\circ}\), and there is a decrease in thickness direction from outside to inside. \(\tau_{yz}\) shows a similar tendency excepted near \(\theta=0^{\circ}\). A larger magnitude of the interlaminar shear stress \(\tau_{yz}\) is also exhibited at the 0/45 interface. Therefore, the maximum value of \(\tau_{xz}\) or \(\tau_{yz}\) at the outer 0/0 and 0/45 interfaces are much higher than those of the middle \(-45/0\) and 0/0 interfaces. It is interesting to note that, at Position I (Figure 7), regardless of whether it is the outer interface or the middle, large interlaminar shear stresses at the 0/45 interface and small interlaminar shear stresses at 0/0 interface are found. However, at Position III, the magnitude of interlaminar stresses appears to have little relation to the elastic properties of adjacent layers and exhibit a higher value at the outer interfaces.  
Figure 8: Interlaminar shear stress distributions around Position III: (**a**) \(\tau_{xz}\); (**b**) \(\tau_{yz}\).