Fractal model for estimating fracture toughness of carbon nanotube reinforced aluminum oxide

Abstract

The current work focuses on predicting the fracture toughness of Al2O3 ceramic matrix composites using a modified Mandelbrot’s fractal approach. The first step confirms that the experimental fracture toughness values fluctuate within the fracture toughness range predicted as per the modified fractal approach. Additionally, the secondary reinforcements [such as carbon nanotubes (CNTs)] have shown to enhance the fracture toughness of Al2O3. Conventional fractural toughness evaluation via fractal approach underestimates the fracture toughness by considering the shortest crack path. Hence, the modified Mandelbrot’s fractal approach considers the crack propagation along the CNT semicircumferential surface (three-dimensional crack path propagation) for achieving an improved fracture toughness estimation of Al2O3-CNT composite. The estimations obtained in the current approach range within 4% error regime of the experimentally measured fracture toughness values of the Al2O3-CNT composite.

Hydroxyapatite‐titanium bulk composites for bone tissue engineering applications

“…Recently, Rishabh et al have also used the Mandelbrot's modified model to estimate the fracture toughness of monolithic alumina with equiaxed grains. The fracture toughness of alumina reinforced with elongated alumina grains as well as with single wall carbon nanotubes was calculated.…”

“…A self-similar object (fractal curve) can be broken into arbitrary small elements with each small element being a replica of the entire object; N is calculated from fractal curve and equal to the number of patterns generated for a ratio "'r." 119,120 Recently, Rishabh et al 121 have also used the Mandelbrot's modified model to estimate the fracture toughness of monolithic alumina with equiaxed grains. The fracture toughness of alumina reinforced with elongated alumina grains as well as with single wall carbon nanotubes was calculated.…”

Crack Propagation Resistance of α-Al2O3 Reinforced Pulsed Laser-Deposited Hydroxyapatite Coating on 316 Stainless Steel

“…However, only a marginal increase of 8.0% was observed in the elastic modulus for the HA-50 wt.% Al 2 O 3 PLD coating (Fig. 5c) 54 It is a general trend that incorporating a second hard phase in a matrix increases the overall hardness. However, issues in achieving theoretical hardness and level of uniformity across the microstructure are major concerns in the composite coatings.…”

Restriction of Phase Transformation in Carbon Nanotube-Reinforced Yttria-Stabilized Zirconia

“…Since their discovery, carbon nanotubes have been considered one of the most ideal reinforcement agents, due to high stiffness, high modulus, and superior thermal and electrical properties. [14,15] While the extensive use of ceramics in various applications is hindered owing to their brittleness, incorporation of MWNTs has the potential to offer an effective solution by enhancing the fracture toughness. [2,16] Moreover, low density (1.5 to 2.1 g/cm 3 ), high aspect ratio (~500 to 1000), and high tensile strength (~150 GPa) of MWNTs further encourage their usage in ceramic composites.…”

“…[2,31] Hence, even though Vickers' indentation is not very suitable for measuring absolute toughness values, the values so obtained can be useful for qualitative comparisons between samples in the same study. [15,27,[32][33][34][35] Spark plasma sintering (SPS) has, over the past decade, emerged as an effective technique to achieve high densification and better mechanical properties in ceramic-matrix composites. SPS is advantageous with respect to other methods, such as conventional sintering and hot pressing as the shorter soaking time and relatively rapid method of sintering prevent damage to MWNTs while also leading to homogenous densification of the composites.…”