## 6 Comparison with Experiments  
The accuracy of the proposed FE simulation and analytical expressions in predicting the critical buckling stresses, nosing load, and limiting nosing ratio are verified through comparison with experimental observations. Three different materials, seamless mild steel tube, experimental results from [1], and hard and annealed aluminum tubes A1050 (experimental results from [22]) are used in this analysis. The tube specimen dimensions are as follows: seamless mild steel tubes (outside diameter: 47 mm; tube length: 60 mm, two wall thickness: 2 mm and 0.5 mm), hard and annealed aluminum tubes (outside diameter: 40 mm; wall thickness: 1.5 mm and tube length: 100 mm). The mechanical properties of these tube materials are given in Table 2. Molybdenum disulphide (MoS2) is used as a lubricant for the aluminum tube specimen and is coated on both the die and the specimen, while PTFE is used as a solid lubricant for the mild steel tube specimen. A thin film of PTFE is wrapped around the outer cylindrical surface of the test specimen.  
Figure 11: Load–displacement curves for tube nosing with different tube thickness for \(E=205\) GPa, \(Y=332\) MPa, \(v=0.33\), \(K=867\), \(n=0.241\), \(\mu=0.1\), \(D_{o}=47\) mm, \(L=60\) mm and \(\alpha=15^{\circ}\).  
Figure 12: Influence of the tube wall thickness on limiting nosing ratio for \(E=205\) GPa, \(Y=332\) MPa, \(v=0.33\), \(K=867\), \(n=0.241\), \(\mu=0.1\), \(D_{o}=47\) mm, \(L=60\) mm and \(\alpha=15^{\circ}\).  
Comparisons between the experimental, the theoretical and the FE predicted results of critical stresses \(\sigma_{cr2}\) for tube nosed specimen failed by axial buckling mode, see Figure 2b, are given in Table 3. Excellent alignment was achieved between the theoretical, FE, and experimental data. Notably, the critical buckling stress in mild steel tubes surpassed the initial yield stress due to the material's work-hardening under compressive loads. Conversely, the critical buckling stress in hard aluminum tubes was equivalent to the initial yield stress, representing nearly perfect plastic material. Additionally, we compared the experimental nosing load values with the outcomes of the FE simulations. Figure 13 gives comparison of nosing load-displacement curves of the mild steel tube specimen with 2 mm wall thickness and hard aluminum. It is clear from this figure that the FE predicted values match quite well with the experimental results. Experimental values of limiting nosing ratios are compared with that obtained from Equation (13) and FE simulations, as shown in Figure 14. It is clear from this figure that the FE predicted values match quite well with the experimental results. Also, we can observe satisfactory agreements between the theoretical, the finite elements, and the experimental results. Computed modes of failure for mild steel tubes with two different tube wall thickness, 0.5 mm and 2 mm, are also compared, as shown in Figure 15. The comparison of deformed shapes obtained from experimental and FE computational also match well. Usually, only one wrinkle forms on the partially deformed nose. The partially deformed nose has a wrinkle that extends across its entire length and becomes more prominent as the deformation progresses. As the ratio of the tube's outer diameter to its wall thickness decreases, the severity of this wrinkle diminishes. Generally, the occurrence of axisymmetric buckling and wrinkling during the tube nosing are successfully predicted.