Relationship between fracture toughness and fractal dimensional increment in two types of dental glass-ceramics with different fracture surface roughness

Objectives: Previous studies have reported the fractal dimensional increment of glass-ceramic fracture surfaces. The objective of this study was to determine the relationship between fracture toughness and fractal dimensional increment of two dental glass-ceramics with different volume fraction of crystals and different fracture surface roughness.

Methods: Bar-shaped specimens were prepared from lithium disilicate (LDS) and nanofluorapatite (NFA) glass-ceramics. One face of each specimen was indented using a Knoop diamond at 25 N (LDS) or 10 N (NFA) followed by loading in 4-point, or 3-point flexure, respectively, until failure. Fracture toughness (K_c) was calculated using the surface crack in flexure (SCF) technique (ASTM C1421). Epoxy replicas of the fracture surfaces were scanned using the atomic force microscope (AFM) followed by noise filtering. The FRACTALS software was used to determine the fractal dimensional increment (D*) by the Minkowski cover algorithm.

Results: Median (25%, 75% quartiles) fracture toughness of LDS bars were 1.62 (1.59, 1.69) MPa m^1/2 and NFA bars were 0.68 (0.66, 0.74) MPa m^1/2, respectively. The median fractal dimension (D) value (25%, 75% quartiles) before noise filtering were 2.16 (2.15, 2.17) and after noise filtering were 2.14 (2.14, 2.15) for LDS and before noise filtering were 2.29 (2.21, 2.38) and after noise filtering were 2.17 (2.17, 2.18) for NFA. Median (25%, 75% quartiles) surface roughness (Ra) before noise filtering were 139 (119, 188) nm and after noise filtering were 137 (118, 187) nm for LDS and before noise filtering were 7 (6, 15) nm and after noise filtering were 7 (6, 15) nm for NFA.

Significance: Noise filtering successfully eliminated noise from the material with smooth fracture surfaces (NFA), decreasing the measured fractal dimension. The NFA data fit a K_c vs. D*^1/2 statistical model for fused silica previously tested using a similar technique. The equation relating fracture toughness to the fractal dimension was modified, accounting for the toughening mechanisms. Fractal analysis with noise filtering can be used to estimate the fracture toughness of dental glass-ceramics that do not exhibit crack bridging.