Hardness, deformation and fracture

In the broadest sense, crystals deform by slipping, with hard crystals being more resistant to deformation. Typically, deformation occurs where the potential hollow to be crossed is shallowest.

A good parameter to estimate the resistance of a crystal plane to slipping is the following:

A low value for this ratio, that is, a high molecular density in the plane (low a) and a high interplanar distance dhkl, are the characteristics of soft materials. Graphite, talc and soap flakes deform readily, in a similar fashion to the MoS2 used as a lubricant in oils.

However, in most crystals, such a mechanism would require significant stress, which in reality is not the case. This contradiction is removed by observing that slips require the presence of local defects or corner or spiral dislocations, in which potential hollow crossing occurs more readily than it would in a perfect net [QUE 88].

The depth of the potential hollow to be crossed increases with the strength of the intermolecular bonds of the crystal. Hard crystals are crystals with strong bonds.

Therefore, the ionic bonds in ores and the covalent bonds in diamond and silicon are clearly stronger than the Van der Waals bonds present in crystals used by the pharmaceutics industry.

Typically, we observe two sorts of fracture:

  • - Ductile fracture, which follows an irreversible and often significant plastic displacement. The stress corresponding to traction is moderate in its value.
  • - Fragile fracture, where the two surfaces of the broken solid may be restored to contact with a near perfect alignment to the atomic level. The stress corresponding to fragile fracture is high in its value.

In reality, fragile fracture occurs earlier than perfect crystal theory would expect. Indeed, this fracture occurs due to existing microcracks and, where the crystal has none, they can be created by high stress, even short in duration (as in the case of glass shattering with an impact).

In practice, hardness can be measured in various ways:

- perforation pressure using an indenter of low cross-section. This is the Vickers hardness test measured in MPa [YOR 83] as follows:

Aspirin 85

KCl 174

NaCl 208

Sugar 624

- scratching a harder body and/or scratching a softer body with the body in question. In this way, Mohs developed a hardness scale going from 1 to 10 as follows:

Wax 0.02

Graphite 0.5-1

Talc 1

Organic Crystals 2 Glass 4.5-6.5

Alumina 9.25

Diamond 10

Both perforation and scratching correspond to a superficial fracture phenomenon that is:

  • - ductile for soft bodies;
  • - fragile for hard bodies.

There is a transition temperature T* between fragile fracture and, for T > T , ductile fracture. For example (in Kelvin), approximately:

Mild steel 160

NaCl 650

Silicon 750

In short, we can describe hardness as an increasing function of elasticity model E.

Hard particles E from 108 to 109Pa Soft particles E in the order of 105 Pa

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