## 5 Results and Discussion
Figure 6: Influence of the strain hardening exponent on limiting nosing ratio for \(E=205\) GPa, \(Y=308\) MPa, \(v=0.33\), K = 1000, \(\mu=0.1\), \(D_{o}=47\) mm, \(L=60\) mm and \(t=2\) mm. Figure 7 shows the load-displacement curves during tube nosing for different values of the coefficient of friction \(\mu\). The experimental results (from [1]) for the same size of tube specimen are shown accompanied by the FE simulation results (see Figure 7). It can be noticed that the value of the maximum nosing load is not significantly affected by the friction coefficient. Also, the die penetration increases with the decrease in the friction coefficient, i.e., a higher limiting nosing ratio can be achieved. This result can also be seen from Figure 8, which indicates that the limiting nosing ratio decreases with the increase in the friction between the die and the tube. This is because the tube flows into the conical die more easily when there is a lower friction coefficient at the die-tube interface surface. Effects of the semi-die angle \(\alpha\) are analyzed by performing the FE simulation for four different values of \(\alpha\) = 10, 15, 20, and 25\({}^{\circ}\). The following parameters are kept constant: \(E\) = 205 GPa, \(Y\) = 332 MPa, \(v\) = 0.33, \(K\) = 867, \(n\) = 0.241, \(\mu\) = 0.1, \(D_{o}\) = 47 mm, \(L\) = 80 mm and \(t\) = 2 mm. Figure 9 shows the load-displacement curves during nosing for different values of the semi-die angle. It can be noticed that, the value of the maximum nosing load is not significantly affected by the variation in the semi-die angle. Also, the die penetration increases with the decrease in the semi-die angle. The quick reduction in the diameter of  
Figure 8: Influence of the friction coefficient on the limiting nosing ratio for \(E\) = 205 GPa, \(Y\) = 308 MPa, \(v\) = 0.33, \(K\) = 1000, \(\alpha\) = 10\({}^{\circ}\), \(D_{o}\) = 47 mm, \(L\) = 60 mm and \(t\) = 2 mm. Figure 7: Load–displacement curves for tube nosing with different values of friction coefficients for \(E\) = 205 GPa, \(Y\) = 332 MPa, \(v\) = 0.33, \(D_{o}\) = 47 mm, \(L\) = 60 mm, \(t\) = 2 mm, and \(\overline{v}\) = 867(0.00538 + \(\overline{x}\))\({}^{0.2411}\). the formed tube before buckling occurs is a result of a larger die angle. Effects of tube length on the required load for tube nosing are analyzed by performing the FE simulation for five different tube lengths; 60, 70, 80, 90, and 100 mm. The following parameters are kept constant; \(E=205\) GPa, \(Y=332\) MPa, \(v=0.33\), \(K=867\), \(n=0.241\), \(\mu=0.1\), \(D_{o}=47\) mm, \(\alpha=15^{\circ}\) and \(t=2\) mm. Figure 10 shows the load-displacement curves during nosing for different values of tube length. It can be noticed that both of the die penetrations and the values of the maximum nosing load are slightly affected by the variation in the tube length. The influence of the tube length ranging from 60 mm to 100 mm on the nosing load and LNR is not significant. This result is valid only if the chosen tube length is less than the critical tube length, which leads to Euler buckling. Effects of tube wall thickness on the required load for tube nosing are analyzed by performing the FE simulation for four different tube wall thicknesses: 1, 2, 3, and 4 mm. The process parameters \(E=205\) GPa, \(Y=332\) MPa, \(v=0.33\), \(K=867\), \(n=0.241\), \(\mu=0.1\), \(D_{o}=47\) mm, \(L=60\) mm and \(\alpha=15^{\circ}\) are kept constant throughout investigating the effect of the tube wall thickness. Figure 11 shows the load-displacement curves during nosing for different values of tube wall thickness. It can be noticed that both of the die penetrations and the values of maximum nosing load are strongly affected by the variation in the tube  
Figure 10: Load–displacement curves for tube nosing with different tube lengths for \(E=205\) GPa, \(Y=332\) MPa, \(v=0.33\), \(K=867\), \(n=0.241\), \(\mu=0.1\), \(D_{o}=47\) mm, \(\alpha=15^{\circ}\) and \(t=2\) mm.