3.1 General strengthening mechanisms: the effect of processing
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 (σy) of polycrystals is higher the smaller the grain size, these parameters being related through the Hall–Petch equation:
σy = σo + kyd–1/2 [3.2]
where ky is a material constant and σo 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
Metals and alloys 73 depends upon the rate of nucleation of solid crystals within the melt. Equation [1.6] shows that the critical nucleus size decreases with increasing degree of supercooling of the liquid, so that rapidly cooled liquids will form solids of finer grain size than slowly cooled liquids. For example, when large bronze sand castings are made (e.g. a ship’s propeller), the cooling rate and degree of supercooling of the melt are low, so the product has a coarse grain-size – typically tens of millimetres in dimension. Conversely, when die-cast objects are formed by injecting molten metal into a water-cooled metal die, the high supercooling leads to a high nucleation-rate and, thus, a fine grain-size – typically tens of micrometres in dimension.
Fine-grained castings can be produced if an inoculant is added to the molten metal before it is introduced into the mould. For example, the addition of a small quantity of zirconium to molten magnesium alloys results in a dramatic refinement of the grain size in the casting.
In recent years, ultrafine (sub-micrometre) grain-size material has been produced by rapid-solidification processing (RSP), whereby molten metal is sprayed in fine droplet form onto a water-cooled substrate, thus achieving extremely high supercoolings. The high cost of this process limits its wide application, however.
Solid state phase changes
In the case of those materials which undergo a phase change in the solid state, it is possible to refine the grain size by thermal treatment. The most important example of this process is that of normalizing steel, whereby a fine-grained microstructure can be developed in (say) a coarse-grained steel casting by subjecting it to an appropriate heating and cooling cycle.
Pure iron (α-iron, or ‘ferrite’) undergoes a change in crystal structure when heated above 910°C, forming γ-iron, or ‘austenite’. Most ferritic steels exhibit a similar transformation and, if such a steel is heated just above its γ transformation temperature, a new (γ) grain structure will form. When the material is allowed to undergo normal air-cooling, the γ structure will transform to new α-grains by a process of nucleation and growth. Air-cooling permits sufficient supercooling to encourage prolific nucleation of the α phase, so the original grain structure is refined. If the normalizing cycle is repeated, an even finer grain-size can be achieved. This effect is illustrated in Fig. 3.1 for a steel specimen of initial grain size 50 µm (ASTM 6). If the specimen is immersed in a molten lead bath at 815°C and then allowed to air cool to room temperature, a structure of grain size 11 µm (ASTM 10) is formed. If the cycle is repeated, grain sizes of 8 µm (ASTM 11) and 5 µm (ASTM 12) are formed.
Materials for engineering 74
Recrystallization
If work-hardened metals are annealed at a suitable temperature, a set of new, undeformed grains will grow by a process of nucleation and growth – consuming the so-called cold-worked microstructure. The process, known as recrystallization, is illustrated in Fig. 3.2. If the temperature is raised, or the annealing prolonged, these new grains grow at the expense of their neighbours – a phenomenon known as grain growth.
815
Temperature (°C)
Grain size 50 µm 11 µm 8 µm 5 µm
Time
3.1 Change in grain size with normalizing for a ferritic steel.
3.2 Recrystallization; new strain-free grains progressively replacing a cold-worked structure.
Metals and alloys 75 A minimum degree of prior cold work is necessary before a material will recrystallize and the minimum temperature for recrystallization (TR) is dependent on several factors:
(i) It is inversely proportional to the time of anneal and to the degree of prior cold work.
(ii) It is directly proportional to the initial grain-size and to the temperature of prior cold work.
The effect of the degree of prior strain and the temperature of anneal upon the final grain size produced after recrystallization is indicated in Fig. 3.3, where is it seen that, in general, coarse grain sizes result after small strains and high annealing temperatures, whereas fine-grained structures form after high strains and low annealing temperatures.
If the degree of prior strain or the annealing temperature is too low to cause recrystallization, the material may still undergo softening by a process known as recovery. Here, no microstructural change is apparent, but some lattice defects are removed by the thermal treatment.
Thermo-mechanical treatment
When materials are hot-worked, dynamic recrystallization may take place during the deformation process itself. Depending on the degree of strain and
Temperature, T(°C) 800 700 600 500 400
0 10 20 30 40 50 60 75
Deformation (%) Grain size (mm2)
0.4
0.3
0.2
0.1
0
3.3 Showing the recrystallized grain size as a function of prior deformation and recrystallisation temperature.
Materials for engineering 76
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.