From quantum to continuum mechanics: studying the fracture toughness of transition metal nitrides and oxynitrides

Figures & data

Figure 1. (a) Experimental setup and dimensions. (b) Simplified 2D model using the plane strain assumption and linear isotropic elastic material.

Figure 2. Finite element mesh of the structure as well as the traction-separation law for the CZ. CZ elements are shown in green and elastic solid elements in red.

Figure 3. (a) A comparison of the load–displacement curves for a 3D finite element model with no mesh refinement and the result from the 2D model used in this work, showing excellent agreement. (b) Variation of β with $t_0=3$ GPa, ${\lambda }_0={10}^{-5}\text{μ}\mathrm{m}$ and $G_c=26.3\mathrm{J}/{\mathrm{m}}^2$, showing the insensitivity of the model to the shear parameter.

Table 1. Elastic properties of MAlON.

		DFT prediction
Sample	Nanoindentation E (GPa)	E (GPa)	ν	B (GPa)	G (GPa)
VAlN	$428\pm 29$	492	0.212	285	203
VAlON	$390\pm 32$	442	0.221	264	181
TiAlN	$393\pm 12$	463	0.211	267	191
TiAlON	$289\pm 7$	330	0.215	193	136

Young's modulus (E) measured by nanoindentation and predicted by DFT. Moreover, calculated values of Poisson's ratio (ν), bulk modulus (B) and shear modulus (G) are provided.

Figure 4. (a) Three stress–strain curves from a beam tested to increasing values of strain. The overlapping curves indicate no plastic deformation nor stable crack growth before fracture occurs. (b) Fracture surface of a TiAlON micro-cantilever. Intercolumnar fracture can be seen running from the FIB-machined notch.

Figure 5. Experimental and simulated load–displacement data for (a) VAlN, (b) VAlON, (c) TiAlN, and (d) TiAlON. Experimental data shown in black, with the variation of $t_0$ for the four materials, with ${\lambda }_0={10}^{-5}\text{μ}$m, $\beta =1.0$. The best fit to the experimental data is given by the dashed line. Values of fracture energy are: 27.08, 26.3, 11.17 and $9.29\mathrm{J}/{\mathrm{m}}^2$ for VAlN, VAlON, TiAlN and TiAlON, respectively. The variation of $t_0$ is shown for VAlON to demonstrate the sensitivity of this parameter.

Table 2. Fracture properties as determined from micro-cantilever tests.

Sample	Fracture stress (GPa)	Fracture strain (%)	Fracture toughness (MPa$\sqrt{m}$)
VAlN	$5.5\pm 0.3$	$1.6\pm 0.5$	$4.5\pm 1.8$
VAlON	$2.3\pm 0.0$	$1.2\pm 0.1$	$3.1\pm 0.5$
TiAlN	$2.5\pm 0.3$	$1.4\pm 0.2$	$1.9\pm 0.3$
TiAlON	$1.3\pm 0.0$	$1.7\pm 0.1$	$1.1\pm 0.2$

Failure stresses and strains were calculated using simple (Euler–Bernoulli) beam theory. Two clear trends are present in the data: that oxynitride samples are more brittle than pure nitride samples, and that Ti-based materials are more brittle than V-based materials.

Table 3. CZ element parameters for the best fit to the experimental data for fracture in VAl(O)N and TiAl(O)N.

	VAlN	VAlON	TiAlN	TiAlON
Fracture energy $G_c$ ($\mathrm{J}/{\mathrm{m}}^2$)	27.1	26.3	11.2	9.3
Traction $t_0$ (GPa)	3.5	6.0	6.0	5.0
Separation ${\lambda }_0$ (µm)	${10}^{-5}$	${10}^{-5}$	${10}^{-5}$	${10}^{-5}$
Separation ${\lambda }_f$ (µm)	0.0155	0.0088	0.0037	0.0031