Extended Isogeometric Analysis for Fracture Behaviour of CNT Reinforced Materials Subjected to Thermo-Mechanical Loading

Abstract

The significant advantage of composites over other pure materials has made a definite rise in the use of composites by several industries. Designs that aim to have lightweight and high-strength structures often make use of composites. These composites also offer a more comprehensive range of design options. The composites involve the reinforcement of various materials for property enhancement purposes, and one such well-known reinforcement material is the carbon nanotube (CNT). It then becomes important for the researchers to focus on examining the deformation, fracture, and other related issues that arise in structures made from nanocomposites. This is especially important because these materials may contain defects, discontinuities, or foreign inclusions that can impact their performance. Particularly noteworthy is the vulnerability of these materials to temperature-dependent failures due to prolonged exposure to mechanical or thermo-mechanical loads. In this context, our study endeavors to surmount these challenges by harnessing an advanced numerical technique known as extended isogeometric analysis (XIGA). This method has demonstrated its effectiveness in handling intricate real-world problems specifically in the presence of flaws. This method also aligns with the conventional fracture mechanics framework. This investigation seeks to elucidate the fracture characteristics of cracked CNT reinforced structures that also include: uncertainties the geometry of crack may inherit (e.g., strong and weak discontinuities), the properties of the material (e.g., fracture toughness, Young’s modulus etc.), the loading conditions (e.g., mechanical, thermal, thermo-mechanical, etc.), etc. A comparative assessment of fracture analysis is conducted on a center crack within a homogeneous matrix, a carbon nanotube (CNT) reinforced metal-matrix composite (specifically, Ti–6Al–4V), and a CNT-reinforced functionally graded material (FGM) comprising both metal (Ti–6Al–4V) and ceramic (ZrO2) components. Both mechanical and thermo-mechanical loading conditions are scrutinized, with results rigorously validated against existing research, leveraging the prowess of the XIGA method. Firstly, the vital properties such as equivalent mechanical and thermal properties (elastic modulus, Poisson’s ratio, fracture energy, fracture toughness, coefficient of thermal expansion, and thermal conductivity) are evaluated with a varying volume percentage of CNTs in the matrix. Multi-walled carbon nanotubes (MWCNT) and single-walled carbon nanotubes (SWCNT) are the two types of CNTs used to strengthen the composite. The exponential rule is supposed to regulate the material property gradation in FG structures. A suite of micromechanics models is harnessed to ascertain the equivalent properties of these CNT-reinforced composites/FG structures. Several micromechanics models are utilized for evaluating the equivalent mechanical, and thermal properties of CNTs (SWCNT and MWCNT) reinforced FG structure. The discontinuous and singular fields, i.e., temperature and displacement near the crack, are illustrated by suitable enrichment functions. Adiabatic crack is considered for the computational simulation for thermal loading conditions. A modified domain-based interaction integral approach has been used to extract the stress intensity factor (SIFs) for the aforementioned crack problem. This work also includes the fracture study of horizontal and inclined center cracks. Investigations are performed to estimate the effects of inclusions and holes on the SIFs of metal-matrix/FG structures reinforced with CNT. Also, the impact of mechanical properties (Young’s modulus) of inclusion and percentage content of CNTs (SWCNT & MWCNT) on SIFs is explored. Furthermore, various loading conditions (mechanical and thermo-mechanical loading) are scrutinized for their influence on the SIFs. The authenticated results deduce that the fracture toughness and fracture energy enhance with the hike in the percentage of the volume of CNTs in the matrix. Moreover, SIF values experience a significant upswing under thermo-mechanical loading compared to purely mechanical loading. Intriguingly, greater CNT content leads to delayed fracture in CNT-reinforced composites. Notably, SWCNTs exhibit more pronounced reinforcement effects in metal-matrix composites than MWCNTs. The results underscore the more substantial influence of holes on SIFs compared to inclusions.