PSI - Issue 71

Ritesh Kumar et al. / Procedia Structural Integrity 71 (2025) 364–371

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3.2 Validation

Fig.7. Stress ̅̅̅ versus ̅

Fig.8. Stress ̅̅̅̅ versus ̅

Figure 7-9 compares the displacement and stresses with the benchmark results available in [33]. When an FG orthotropic annular circular disk rotates with = 1000 rps and a temperature field (0 to 100 ℃ ) is applied on the disk, the effects of the material grading parameter on stresses: radial, tangential, displacement, and von Mises ( ̅̅̅ , ̅̅̅ , ̅ , ) are evaluated for free-free boundary conditions considering an exponential law is shown in Fig 10-13 respectively. Figure 10 shows that the normalized radial stresses ( ̅̅̅ ) of a disk, which perfectly satisfies the free-free boundary conditions. With an increase in material grading parameter ( ) the induced ̅̅̅ stress decreases. It can be seen that the magnitude of ̅̅̅ is higher for the variable temperature fields as compared to the constant

temperature field. But for = −1, ̅̅̅ is higher for the variable temperature field up to r =0.6 (approx.) beyond this the magnitude of ̅̅̅ is superior for the constant temperature field. Figure 11 shows the variation of normalized tangential stress ( ̅̅̅ ) for radius ( ̅ ) for an exponential profile under free-free boundary conditions. It is evident from the figure that the magnitude of ̅̅̅ is higher at the inner radius and it is maximum for =−1, followed by 0, 1, and 2 and decreases along the radius and minimum at the outer radius. For =1, the ̅̅̅̅ becomes constant throughout the radius and for = 2, the magnitude of ̅̅̅̅̅ is lowest at the inner radius and increasing along the radius. Figure 12 represents the normalized radial displacement ( ̅ ) with respect to the radius of the disk for free-free boundary conditions. In the case of a constant temperature field, the magnitude of ̅ is higher for > 0 . Also, the magnitude of ̅ is higher at the inner radius and continually reduces along the radius for all values of grading parameters. In the case of a variable temperature field, the magnitude of ̅ is higher at the inner radius than for > 0 and reduces along the radius. But for ≤ 0 , the radial displacements are increasing from the inner to outer radius. Figure 13 represents the normalized von Mises stress ( )̅̅̅̅̅̅̅̅ distribution with respect to the normalized radial coordinate. The ̅̅̅̅̅̅ decreases along the radius upto radius 0.9 (approx.) the stress is maximum for =−1 , followed by = 0, 1 and 2, beyond this range a reverse trend is seen where the stress is maximum for =2 , followed by = 1, 0 and −1 at the tip of the disk. In Fig 11 and Fig 13 the stress variation at a normalized radius of 0.9 is due to the transition in the trend of normalized tangential stress and normalized von Mises stress ( σ̅ _von) respectively. The stresses decreases along the radius up to r̅ = 0.9, where it reaches its minimum, and then exhibits a reverse trend beyond this point. This indicates that r̅ = 0.9 is a critical point where stress redistribution occurs, likely due to material property variations controlled by the parameter β and the influence of boundary conditions. Additionally, for different values of β, the stress behavior changes, suggesting that the material grading affects how stress is distributed across the disk. This transition at r̅ = 0.9 could be attributed to the interplay between material composition, load distribution, and stress gradients in the structure. The parameter β plays a key role in controlling material property variations, especially in metal-ceramic composites, where metals contribute to toughness and ceramics enhance wear resistance and thermal stability. Depending on the application, material combinations can include metal-metal or ceramic ceramic. Functionally graded materials (FGMs) are particularly useful in such systems, as they provide a gradual transition between different materials, reducing stress concentrations and improving overall durability. FGMs help optimize mechanical strength, thermal resistance, and wear performance by integrating the benefits of both metal and ceramic properties. While ceramics excel in high-temperature and wear-resistant environments, most metals except for steel and nickel have lower melting points. However, ceramics are brittle and less effective in absorbing shock loads, whereas Fig. 9. Displacement ̅ versus ̅