Mineralogy
"Hardness" is determined by comparison with other minerals. In the Mohs scale, a standard set of minerals are numbered in order of increasing hardness from 1 (talc) to 10 (diamond). A harder mineral will scratch a softer, so an unknown mineral can be placed in this scale by which minerals it scratches and which scratch it. A few minerals such as calcite and kyanite have a hardness that depends significantly on direction. Hardness can also be measured on an absolute scale using a sclerometer; compared to the absolute scale, the Mohs scale is nonlinear.
Fracture toughness
The problem can also be formulated in terms of stress instead of energy, leading to the terms stress intensity factor "K" (or "K" for mode I) and critical stress intensity factor "K" (and "K"). These "K" and "K" (etc.) quantities are commonly referred to as fracture toughness, though it is equivalent to use "G". Typical values for "K"are 150 MN/m for ductile (very tough) metals, 25 for brittle ones and 1–10 for glasses and brittle polymers. Notice the different units used by "G" and "K". Engineers tend to use the latter as an indication of toughness.