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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positions at the end of the loading and unloading stages are discussed in the following sections, providing valuable insights into the material's response during these stages.

(a) (b) Fig.12. Deformed geometry of contact surface for indentation depth of 0.78 nm: (a) At the end of loading and unloading stage with the variation of CNTs wall thickness when gradation parameter constant ( γ e =2) and (b) At the end of unloading and unloading stage with the variation of gradation parameter ( γ e =2, γ e =0, and γ e =-2) when CNTs wall thickness constant (0.102nm). In the modeling section, it was explained that the x-axis is positioned along the base of the model, while the y axis represents the line of symmetry. The x-coordinate of the nodes is used to indicate their distance from the line of symmetry. Fig.9 depicts the nodal displacements in the x-direction of the nodes situated on the top surface at the end of both the loading and unloading stages, with reference to their x-coordinate before loading. Specifically, Fig.12 (a) illustrates the variation of nodal displacements concerning the change in wall thickness of the CNTs. The figure clearly demonstrates that nodes near the tip of the CNTs exhibit positive displacement in the x-direction, with the highest displacement occurring at the middle of the contact zone. Subsequently, the displacement gradually decreases as one moves away from the contact zone. One could make an intriguing observation that while all the nodes situated at the contact surface experience a positive displacement, the lower wall thickness CNTs exhibit negative displacement in the x-direction. This is attributed to the fact, as previously discussed, that CNTs with a thickness of 0.034 nm have a lower stiffness compared to the matrix material. Consequently, the deformation occurs in the CNT beneath the contact zone, resulting in material movement towards the hollow section of the CNT. At the end of the loading stage, the nodal displacement in the x-direction is greater for CNTs with higher thickness and lower for CNTs with lower thickness. This difference is attributed to higher-thickness CNTs having lower chances of deformation, leading to minimal material flow toward the hollow section of the CNTs. A similar observation can be made at the end of the unloading stage, where only elastic recovery occurs. Fig.12.(b) illustrates the same scenario as in Fig.12.(a), but this time it focuses on equal-thickness CNTs with different gradation parameters (γ e =- 2, γ e =- 0, and γ e =-2). The graph displays a similar pattern to that observed in Fig.12.(a), where during the loading stage, negative displacement is seen near the presence of CNTs in the vicinity of the contact zone for γ e =-- 2 and γ e =-0 gradation parameters. This negative displacement occurs because the yield strength of the matrix material below the CNTs is lower compared to the gradation parameter γ e =-2. As a result, during the loading stage, the material flows towards the axis of symmetry, but in the case of parameter γ e =--2, the material undergoes plastic deformation, leading to negative displacement in the x-direction after unloading. In contrast, for the other cases, the displacements remain positive after unloading.