Model Verification for Material Parameters of Titanium Alloy Ti-6AL-4V and Steel

. To carry out numerical simulation of TC4 titanium alloy blade impacted by foreign objects effectively, this paper takes the test results of steel ball and sandstone impacting titanium alloy flat blade inlet and blade surface as the benchmark, and uses ANSYS/LS-DYNA software to adopt kinematic hardening plasticity model to simulates the impact results and inverts the contact stiffness factor and the other three parameters were obtained by the way of inversion reasoning.


Introduction
The foreign object damage of the blade is of great significance for ensuring the reliability and flight safety of the aero-engine. The research methods are divided into experimental and simulation calculations. At present, there are many kinds of literature on simulation of blade impact damage [1][2][3][4][5][6][7][8][9][10]. And the material models used are also various. Different material models correspond to different material performance parameters, and kinematic hardening plasticity model proposed by Cowper-Symonds is one of the commonly used models. When this model is selected, a total of 1 calculation parameter and 9 material performance parameters are involved. On the one hand, for the same material, the material performance parameters of different materials are not only different but also far apart; on the other hand, most of the literature does not give all the material performance parameters and calculation parameters required for the full-stage simulation calculation, which reduces the reference value of the existing literature simulation results.

Experimental study 2.1 Scheme 1 analysis
According to the blade sample used in the steel ball impact test of the inlet vane of the flat blade in 1999 by Joseph L. Hamrick et al. [1] , the same flat blade geometry model is established here, as shown in Fig. 1. The steel ball has a diameter of 2 mm, and the flat blade has a thickness of 1.27 mm, a width of 4 mm, and a height of 6 mm.
The finite element discretization of the geometric model of the flat blade and the steel ball is performed In the ANSYS/LS-DYNA by using the SOLIDl64 unit. The grid element size of the flat blade is 0.05 mm, and the size of the steel ball mesh unit is 0.1 mm. Fixing the joints at one end of the flat blade, the steel ball impacts the intake side of the flat blade vertically at a speed of 305 m/s, and draws a dip with a depth D and a width W at the inlet side of the blade, as shown in Fig. 2.  The flat blade is Ti-6A1-4V material, and the kinematic hardening plasticity model is adopted; the steel ball adopts the piecewise linear constitutive model. The contact way of Erode nodes to the surface of point-toface is adopted, wherein the blade is a target body and the steel ball is a contact body. During the verification process, the hardening parameters, strain rate parameters C, P, and contact stiffness factors were repeatedly adjusted. Finally, it was found that only when the contact stiffness factor was 0.7 and the other three parameters were listed in Table 1, the calculation results were close to the test results. The specific calculation results are shown in Table 2 and Figure 3.   During the verification process, the hardening parameters, strain rate parameters C, P, and contact stiffness factors were repeatedly adjusted. Finally, it was found that only when the contact stiffness factor was 0.7 and the other three parameters were listed in Table 1, the calculation results were close to the test results. The specific calculation results are shown in Table 3.

Discussion
The depth of the impact dent calculated in the first scheme is smaller than the experimental value, and the depth of the impact dent calculated in the second scheme is larger than the experimental value. In order to make the calculated values of the dent depth in the two schemes close to the experimental values, a compromise method was adopted in the selection of the material parameters C, P and the contact stiffness factor of titanium alloy and steel. When the material parameters are as shown in Table 1, the calculated dent depth values for both solutions are close to the test values. When the material parameters are changed again, only the calculated dent depth of one of the solutions is closer to the experimental value, and the calculated value of the other scheme is far from the experimental value.

Conclusion
1. Using ANSYS/LS-DYNA software to adopt kinematic hardening plasticity model to simulates the impact results which helps to provides a viable method for testing residual stress and structural strength of materials.
2. By comparing the simulation value with the actual collision effect value, the material parameters are obtained by inversion reasoning, and the residual stress and the mechanical strength are calculated and predicted by using these parameters.