PSI - Issue 60

Rakesh Bhadra et al. / Procedia Structural Integrity 60 (2024) 149–164 Bhadra et al. / Structural Integrity Procedia 00 (2023) 000 – 000

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The model comprises two distinct materials: a square block made of functionally graded material (FGM) and circular rings composed of carbon nanotubes (CNTs). The convergence analysis is performed separately for the FGM block and the CNTs using two different analyses. In the case of the FGM block, the number of divisions of the unmeshed lines is increased step by step during the meshing process with a spacing ratio of 0.02. Additionally, an indentation depth of 0.1 nm is applied using an indenter. At the end of each loading step, changes in contact force are measured and recorded. These changes are then plotted, as depicted in Fig. 4(a). It is observed that beyond 80 divisions, the variation in contact force becomes negligible. A subsequent analysis was conducted for the nanocomposite block using the division outcomes obtained from the previous convergence analysis. In a similar manner, the number of divisions in the lines in the circular rings, which model the CNTs, was changed in steps. The contact forces are extracted and plotted, as illustrated in Fig. 4(b). The results demonstrate that after 10 divisions, the changes in the outcome become negligible. As a result, all subsequent analyses have been performed using the mesh configuration established from the mesh convergence analysis. 3.2. Model Validation This section's objective is to compare the numerical findings (contact force vs. indentation depth) using the current method with those described in the established literature in order to visually demonstrate the validation of the method. In the absence of published results for validating the contact analysis of CNT-reinforced FGM matrix nanocomposites, the validation process focuses on two separate aspects.

(a) Validation of contact force with the results of Jana et al. (2020).

(b)Validation of the present model with the results of Ahmed et al. (2020).

Fig.5. Validation plots.

The first model is employed to validate the method used for modeling the FGM, while the second model is utilized to validate the CNT-based nanocomposite and the indentation method. In the first comparison, flattening contact analysis of a spherical substrate is done and the non-dimensional contact force versus non-dimensional interference is plotted during loading and unloading [Jana et al. (2020)]. In the second comparison, the findings of an indentation investigation on a carbon nanotube (CNT) reinforced nanocomposite [Ahmed et al. (2020)] are the main subject. The technique used to create the current model is the same one used to create and validate the two publications described above. Fig.5.(a) displays the comparison between the finite element (FE) results published by Jana et al. (2020) and the results obtained from the model developed using the present method. The model incorporates the same material properties and dimensions as those described in the published study. The figure clearly demonstrates a high level of agreement and good matching between the two sets of data. Fig.5.(b) illustrates the validation study conducted