Materials for engineering, 3rd Edition - (Malestrom)

3
Metals and alloys
3.1 General strengthening mechanisms: the effect
of processing
The strength of a crystal may be assessed either by its resistance to cleavage,
by the application of normal stresses across the cleavage plane, or by its
resistance to shear under the action of shear stresses on the slip plane. It is
possible to make an estimate of these strengths for ideal, or perfect crystals,
but a large discrepancy is found between these values and those measured
experimentally. In pure materials, real strengths are several orders of magnitude
lower than their theoretical strengths – cleavage occurs due to the presence
of cracks in brittle solids and shear occurs due to the presence of mobile
dislocations in ductile solids. The local displacement (b) associated with a
given dislocation is known as its Burgers vector.
Dislocations are linear defects which are always present in technical
materials, usually in the form of a three-dimensional network. Dislocation
density (ρ) is usually expressed as the length of dislocation line per unit
volume of crystal or, its geometrical equivalent, the number of dislocations
intersecting the unit area. In a reasonably perfect crystal, the value of ρ
might be of the order 10 9 m –2 . Their number per unit length will therefore be
ρ 1/2 and their average separation will be the reciprocal of this quantity,
giving ~30 µm for the dislocation density considered.
3.1.1 Work hardening
As a crystal is deformed, dislocations multiply and the dislocation density
rises. The dislocations interact elastically with each other and the average
spacing of the dislocation network decreases. The shear yield strength (τ) of
a crystal containing a network of dislocations of density ρ is given by:
τ = αGb(ρ 1/2 ) [3.1]
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