3.1 General strengthening mechanisms: the effect of processing
3.1.3 Alloy hardening
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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.
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Precipitation hardening
Thermal treatment can be used to control the size and distribution of second- phase particles in any alloy which undergoes a phase transformation in the solid state. In many alloy systems, the solid solubility changes with temperature in the way illustrated in Fig. 1.20. Above temperature T1, a single phase (α) solid solution exists and, if the material is quenched rapidly from this temperature range, a supersaturated α solid solution is formed, the degree of supersaturation increasing with increasing supercooling below the solvus line, ab. If the temperature is then raised again in order to allow solid state diffusion to proceed, the supersaturation will be relieved by the nucleation and growth of a precipitated second phase.
In alloys of relatively low melting-point (in aluminium alloys, for example), there will be an appreciable diffusion rate of solute atoms at room temperature, so that over a period of time a second phase will precipitate out in a very finely divided form. This effect is known as ‘ageing’, but, in most alloys, the temperature has to be raised in order to cause precipitation to occur and the material is said to be ‘artificially aged’. The ageing temperature affects the precipitate size in the manner illustrated schematically in Fig. 3.4. Low
Temperature
α
α + β
Composition
3.4 Variation of precipitate size with ageing temperature.
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ageing temperatures correspond to high supersaturation and prolific nucleation of precipitates occurs, whereas at higher ageing temperatures (lower supersaturation) fewer, coarser particles are formed. The kinetics of precipitation can be represented by a temperature–time–transformation (TTT) diagram, Fig. 3.5. At small undercoolings, there is a long incubation period, due to the low probability of formation of the (large) critical nucleus (equation [1.6]).
As the supercooling increases, the nucleation rate will increase, since the critical nucleus size is smaller. The lower the transformation temperature, therefore, the more prolific the nucleation and the finer the dispersion of particles. However, the lower the temperature the more sluggish the solid state diffusion becomes and the TTT curve has a ‘C’ shape indicating a more sluggish transformation at low temperature.
Quenching and ageing therefore constitute a very powerful means of controlling the distribution of a precipitate of second phase in an alloy. After quenching the alloy from the single-phase region of the phase diagram, a high ageing temperature is selected if a coarse, widely spaced dispersion of particles is required and a lower ageing temperature is used to produce the second phase in a more finely divided form.
These precipitates can have a profound effect upon the mobility of dislocations and it is possible to produce large changes in the yield strength of such alloys by suitable heat-treatment. A great advantage is that the required strength can be induced in a product at the most convenient stage in its manufacture. For example, the alloy may be retained in a soft form throughout the period when it is being shaped by forging and it is finally hardened by precipitation in order to give it good strength in service.
Nucleation time (log scale)
Temperature
TI
3.5 A TTT diagram
Metals and alloys 79 On being held up by a precipitate, a dislocation can continue in its path across the crystal in two possible ways. If the particles are very close together, the dislocation may cut through each particle, but if the particles are further apart, the dislocation may loop between the particles. During the ageing process, as the particles grow, the stress increment required to make the dislocations cut them also rises (Fig. 3.6, curve C). The increase in shear stress due to precipitate cutting, ∆τc, is given by an equation of the form:
∆τc = Af1/2r1/2 [3.4]
where r is the particle radius, f the volume fraction of precipitate, and A a material constant.
As ageing proceeds, the particles gradually increase in size and, because they are fewer in number, the average spacing between the particles also increases. The stress increment to cause dislocation looping ( ∆τl) decreases as the inter-particle spacing increases (curve L, Fig. 3.6), depending on the precipitate size and volume fraction according to:
∆τ1 = BGbf1/2r–1 [3.5]
where B is a constant dependent upon precipitate particle shape.
As ageing continues, the measured yield stress would therefore be expected to follow the form of the dotted curve in Fig. 3.6 and this general pattern of
Ageing time
C
L
∆τ
3.6 Showing change in yield stress (∆τ) with ageing time for a precipitation-hardened alloy. Curve C is followed if the precipitates are cut by dislocations, and curve L is followed if the dislocations loop between the particles. The response is given by the dashed curve.
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behaviour, with an optimum ageing time to give a maximum hardness, is commonly observed in many commercial alloys. The time to peak hardness depends on the solute diffusion rate and, thus, on the ageing temperature.
Combinations of strengthening mechanisms
Most commercial alloys owe their strength to a combination of several of the strengthening mechanisms we have reviewed. We will return to this later and Figs 3.22 and 3.26 illustrate how the strength of certain steels may be understood in terms of the additive contributions of grain size strengthening, solute strengthening and the presence of second phases.
Perhaps the most dramatic example of strengthening from several mechanisms is the formation of martensite when steel is rapidly quenched from a high temperature (see Chapter 1). An extremely hard (and brittle) phase is formed in this diffusionless transformation. Martensite owes its strength to the combination of a high dislocation density, a very fine grain size and a high supersaturation of solute atoms (carbon).