Materials for engineering, 3rd Edition - (Malestrom)

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Materials for engineering
the temperature of working, therefore, the grain size of the final product may
be controlled.
Hot working a material that may undergo a phase change on cooling, such
as steel, presents a further, powerful means of grain size control. Controlled
rolling of steel is an example of this, whereby the steel is deformed above
the γ transformation temperature: dynamic recrystallization produces a fine
γ grain size, which, on air-cooling, is transformed to an even finer α grain
size. Sophisticated process control is necessary to produce material consistently
with the desired microstructure, but, in principle, controlled rolling constitutes
a very attractive means of achieving this.
3.1.3 Alloy hardening
Work hardening and grain-size strengthening, which we have considered so
far, can be applied to a pure metal. The possibility of changing the composition
of the material by alloying presents further means of strengthening. We will
consider two ways in which alloying elements may be used to produce
strong materials: solute hardening and precipitation hardening.
Solute hardening
We have shown in Fig. 1.10(a) and 1.10(b) that two types of solid solution
may be formed, namely interstitial and substitutional solutions. The presence
of a ‘foreign’ atom in the lattice will give rise to local stresses which
will impede the movement of dislocations, hence raising the yield stress of
the solid.
This effect is known as solute hardening, and its magnitude will depend
on the concentration of solute atoms in the alloy and also upon the magnitude
of the local misfit strains associated with the individual solute atoms. It is
also recognized that the solubility of an element in a given crystal is itself
dependent upon the degree of misfit – indeed, if the atomic sizes of the
solute and solvent differ by more than about 14%, then only very limited
solid solubility occurs. There must thus be a compromise between these two
effects in a successful solution-hardened material – i.e. there must be sufficient
atomic misfit to give rise to local lattice strains, but there must also be
appreciable solubility.
A theoretical approach expresses the increase in shear yield stress, ∆τ y , in
terms of a solute atom mismatch parameter, ε, in the form:
∆τ y = Gε 3/2 bc 1/2 [3.3]
where G is the shear modulus, b the dislocation Burgers vector and c the
concentration of solute atoms.