Faber–Evans model
[3] The effect is named after Katherine Faber and her mentor, Anthony G. Evans, who introduced the model in 1983.
[4] The Faber–Evans model is a principal strategy for tempering brittleness and creating effective ductility.
[5] Fracture toughness is a critical property of ceramic materials, determining their ability to resist crack propagation and failure.
[6] The Faber model considers the effects of different particle morphologies, including spherical, rod-shaped, and disc-shaped particles, and their influence on the driving force at the tip of a tilted and/or twisted crack.
The model first suggested that rod-shaped particles with high aspect ratios are the most effective morphology for deflecting propagating cracks and increasing fracture toughness, primarily due to the twist of the crack front between particles.
The findings provide a basis for designing high-toughness two-phase ceramic materials, with a focus on optimizing particle shape and volume fraction.
When the stress intensity factor reaches the material's fracture toughness, crack propagation becomes unstable, leading to failure.
In two-phase ceramic materials, the presence of a secondary phase can lead to crack deflection, a phenomenon where the crack path deviates from its original direction due to interactions with the second-phase particles.
The effectiveness of crack deflection in enhancing fracture toughness depends on several factors, including particle shape, size, volume fraction, and spatial distribution.
The study presents weighting functions, F(θ), for the three particle morphologies, which describe the distribution of tilt angles (θ) along the crack front: The weighting functions are used to determine the net driving force on the tilted crack for each morphology.
prescribes the strain energy release rate only for that portion of the crack front which tilts.
The resultant toughening increment, derived directly from the driving forces, is given by: where
represents the fracture toughness of the matrix material without the presence of any reinforcing particles,
The spatial location and orientation of adjacent particles play a crucial role in determining whether the inter-particle crack front will tilt or twist.
If adjacent particles produce tilt angles of opposite sign, twist of the crack front will result.
For spherical particles, the average twist angle is determined by the mean center-to-center nearest neighboring distance,
The maximum twist angle occurs when the particles are nearly co-planar with the crack, given by:
For rod-shaped particles, the analysis of crack front twist is more complex due to difficulties in describing the rod orientation with respect to the crack front and adjacent rods.
represents the dimensionless effective inter-particle spacing between two adjacent rod-shaped particles.
The analysis reveals that rod-shaped particles with high aspect ratios are the most effective morphology for deflecting propagating cracks, with the potential to increase fracture toughness by up to four times.
[4] This toughening arises primarily from the twist of the crack front between particles.
Disc-shaped particles and spheres are less effective in increasing fracture toughness.
For disc-shaped particles with high aspect ratios, initial crack front tilt can provide significant toughening, although the twist component still dominates.
In contrast, neither sphere nor rod particles derive substantial toughening from the initial tilting process.
For spherical particles, the interparticle spacing distribution has a significant impact on toughening, with greater enhancements when spheres are nearly contacting and twist angles approach π/2.
The Faber–Evans model suggests that rod-shaped particles with high aspect ratios are the most effective morphology for deflecting propagating cracks and increasing fracture toughness, primarily due to the twist of the crack front between particles.
In designing high-toughness two-phase ceramic materials, the focus should be on optimizing particle shape and volume fraction.
The model proved that ideal second phase should be chemically compatible and present in amounts of 10 to 20 volume percent, with particles having high aspect ratios, particularly those with rod-shaped morphologies, providing the maximum toughening effect.
[9] This model is often used in the development of advanced ceramic materials with improved performance when the factors that contribute to the increase in fracture toughness is a consideration.
