# Effect of Impact and Bearing Parameters on Bird Strike with Aero-Engine Fan Blades
## 2 Bird and Fan Modeling
### Geometric Model and Meshing  
The bird strike often occurs at the fan of a turbofan engine [1]. To simulate this situation, a real aero-engine fan was used as the impact target in this paper. The geometry of all parts of the fan was extracted from real aircraft engines, and they were discretized, as can be seen in Figure 3. The fan was composed of 24 equally spaced (15\({}^{\circ}\)) narrow chord blades connected to the hub. The form of connection between the blades and the disk was ignored, and they were considered as a single body. The initial twist angle of the blades was 61.3\({}^{\circ}\) with a measuring height of 603.2 mm. In some studies [9; 30], only a few blades were considered for numerical simulation to increase the computational speed. However, because the rotation of the fan and the debris generated by the impact can affect most of the blades, this paper has considered the whole fan for the numerical simulation. Due to the focus of this study on the impact of the blades, the structure of the wheel was simplified. The fan was discretized using the Lagrangian method. Although the shell element helps to improve the computational speed, as the blades did not have uniform thicknesses and they had obvious vibrational characteristics in the thickness direction, this research used solid elements to discretize the blades. The fan was composed of 1,520,213 elements, each blade containing 54,086 elements: 4 elements in thickness, 194 elements in length, and 104 elements in the width directions. The type of finite element is a hexahedral solid element.  
When a bird strike occurs, the aero-engine fan blades deform under the high-velocity impact. The blades may even fail if the situation is detrimental. To simulate and reproduce the impact phenomenon and truly reflect the relationship between impact loads and structural response, the Johnson-Cook material model was chosen to simulate the material behavior of the fan. In the Johnson-Cook material model, the flow stress is expressed by [31]:  
\[\sigma_{y}=(A+B\hat{z}^{p^{n}})(1+c\ln\hat{z}^{*})(1-T^{*m}) \tag{5}\]  
Figure 3: The aero-engine fan model used in simulations: (**a**) geometrical model; (**b**) finite element model.  
where \(A\), \(B\), \(n\), \(c\) and \(m\) are the constants of the material; \(\tilde{e}^{p}\) is the effective plastic strain; \(\tilde{e}^{*}\) is a unitless rate which can be obtained by dividing the quasi-static threshold rate by effective plastic strain rate; \(T^{*}=\frac{T-T_{r}}{T_{m}-T_{r}}\) is the homologous temperature, \(T\) is the current temperature, \(T_{m}\) is the melt temperature of the material, and \(T_{r}\) is the room temperature.  
Since the Johnson-Cook model simulates the fracture process by calculating the failure of elements, it is necessary to obtain its strain at failure, which is defined as follows [31]:  
\[\varepsilon^{f}=[D_{1}+D_{2}\exp D_{3}\sigma^{*}][1+D_{4}\ln\tilde{e}^{*}][1+ D_{5}T^{*}] \tag{6}\]  
where \(\varepsilon^{f}\) is the strain at fracture; \(D_{1},\ D_{2},\ D_{3},\ D_{4},D_{5}\) are the failure parameters depending on the material; and \(\sigma^{*}\) is the stress triaxiality.  
Since the stress state, strain rate, and temperature are changing during the failure process, the failure of the material is determined by the following equation:  
\[D=\sum\frac{\Delta\tilde{e}^{p}}{e^{f}} \tag{7}\]  
where \(D\) is the damage parameter and \(\Delta\tilde{e}^{p}\) is incremental changes in the effective plastic strain. The \(\sum\) is a summation notation. When the value of \(D\) reaches 1, the material can be considered as failed. Titanium alloy Ti-6 Al-4V material properties were assigned to aero-engine fan blades (Table 3).  
In this paper, solid elements are used in the simulation, so the Johnson-Cook material model should be accompanied by an EOS [19]. The Gruneisen EOS, which was introduced above, also works for this model. The parameters are given in Table 4.