Steels_ Metallurgy and Applications, Third Edition

8 Steels: Metallurgy and Applications

where T is the absolute temperature and the gas constant R = 1.987 cal.
degree -1 .mole -l.
As the carbon content of a steel is increased, the y to 7' + ct transformation
temperature is depressed and the ratio of pearlite to ferrite in the microstructure is
progressively increased, reaching 100% pearlite at about 0.8% carbon, the eutectic
composition. Whereas the above sequence of events relates to slow cooling and an
approach to equilibrium, faster cooling rates usually produce ferrite with globular
carbides within the grains. Lower-temperature transformation products such as
bainite or martensite may, however, be produced particularly when a suitable
alloy addition has been made. These will be discussed later.
The ferrite grain size has a very important effect on the properties of low-
carbon strip steels, as indicated by the Hall-Petch equation7'8:

Cry = tri + kyd -1/2

where try = yield stress

cri = the friction stress opposing dislocation movement

ky = a constant (dislocation locking term) and

d = the ferrite grain size

Thus the yield stress increases with decreasing ferrite grain size. Pickering 9 has
indicated that the value of ky often lies in the range 15-18 MPa mm 1/2.
The strength is also influenced by other factors such as solid solution and
precipitation strengthening. In the former, the strengthening is often related to
the square root of the atomic concentration of the solute atoms, but at low
concentrations, the strengthening effect may be regarded as linearly dependent.
The magnitude of the effect depends on the atomic size difference between the
iron and the solute element, the largest effects being produced by small elements
such as carbon and nitrogen which go into interstitial solid solution. Elements
such as phosphorus, manganese and silicon are often added to low-carbon strip
to provide solid solution strengthening.
Both strip and structural grades of steel may be precipitation strengthened
by the addition of elements such as titanium, niobium and vanadium and these
elements may have an additional effect on strength by leading to a finer grain size.
These elements are strong carbide and nitride formers which may be partially or
completely dissolved at the slab reheating stage prior to hot rolling and which may
then be reprecipitated into a fine form on subsequent cooling and transformation
to ferrite. The degree of strengthening is dependent on both the volume fraction
and size of the precipitates, finer precipitates producing the greater effect. Coarse
precipitates which are not dissolved at the slab reheating stage are ineffective
as strengthening agents. The solubility product for the precipitate is important,
therefore, since it determines the amount of precipitate that can be taken into
solution at any temperature and, consequently, the volume fraction that may be
subsequently reprecipitated in a fine form. The temperature dependence of the
solubility product is generally represented by an equation of the form:

log[X][Y] = -A/T q- B