Hard water
Water's hardness is determined by the concentration of multivalent cations in the water. Multivalent cations are positively charged metal complexes with a charge greater than 1+. Usually, the cations have the charge of 2+. Common cations found in hard water include Ca and Mg. These ions enter a water supply by leaching from minerals within an aquifer. Common calcium-containing minerals are calcite and gypsum. A common magnesium mineral is dolomite (which also contains calcium). Rainwater and distilled water are soft, because they contain few ions.
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.