Materials for engineering, 3rd Edition - (Malestrom)

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Materials for engineering
where G is the shear modulus, b the dislocation Burgers vector and α is a
constant of value about 0.2.
As plastic deformation continues, therefore, the increase in dislocation
density causes an increase in τ – the well-known effect of work hardening,
Fig. 2.3.
As a technical means of producing a strong material, work hardening can
only be employed in situations where large deformations are involved, such
as in wire drawing and in the cold-rolling of sheet. This form of hardening
is lost if the material is heated, because the additional thermal energy allows
the dislocations to rearrange themselves, relaxing their stress fields through
processes of recovery and being annihilated by recrystallization (see below).
3.1.2 Grain size strengthening
Metals are usually used in polycrystalline form and, thus, dislocations are
unable to move long distances without being held up at grain boundaries.
Metal grains are not uniform in shape and size – their three-dimensional
structure resembles that of a soap froth. There are two main methods of
measuring the grain size:
(a) the mean linear intercept method which defines the average chord length
intersected by the grains on a random straight line in the planar polished
and etched section, and
(b) the ASTM comparative method, in which standard charts of an idealized
network are compared with the microstructure. The ASTM grain size
number (N) is related to n, the number of grains per square inch in the
microsection observed at a magnification of 100×, by:
n
N = log
log 2 + 1.000
Thus, the smaller the average grain diameter (d ), the higher the ASTM
grain size number, N.
The tensile yield strength (σ y ) of polycrystals is higher the smaller the grain
size, these parameters being related through the Hall–Petch equation:
σ y = σ o + k y d –1/2 [3.2]
where k y is a material constant and σ o is the yield stress of a single crystal
of similar composition and dislocation density.
The control of grain-size in crystalline materials may be achieved in
several ways:
From the molten state
As discussed in Chapter 1, when molten metal is cast, the final grain size