Pure metals in the ‘as-cast’ condition after slow cooling are generally soft, have low yield stresses and are very ductile; this is a consequence of the ease of dislocation movement or slip. They are therefore unsuitable for use as a structural material, with perhaps the most critical property for design being the low yield stress.

Clearly if we can increase the yield stress then the safe working stress can be correspondingly increased. In using the term ‘strengthening’, we are concerned with ways by which we can make the start of slip more difficult. We now consider some of these ways and their consequences.

Strengthening of Metals

Grain Size

In a single crystal of a pure metal the shear stress required to move a dislocation is small, in some cases maybe only ~1MPa. However, most materials are polycrystalline, and the grain boundaries are discontinuities in the atomic lattice, which will have differing orientations on either side of the boundary, as illustrated in Fig. 1 (but note that the numerous atomic bonds across the grain boundary are usually strong enough not to weaken the material).

A dislocation that reaches a grain boundary cannot produce a slip step there unless the neighbouring grain also deforms to accommodate the shape change. A dislocation in the second grain cannot move until the shear stress, resolved on to the new slip plane and in the new slip direction, reaches the value needed to continue movement.

Back in the first grain, the dislocation is stuck and other dislocations will pile up behind, like a traffic jam, exerting a force on it, until, ultimately, the push is too great and it is forced through the grain boundary.

The stress on the leading dislocation is a simple function of the number of dislocations in the pile-up. In a coarse-grained structure many dislocations can pile up and the critical stress is reached early, whereas in a fine-grained structure the length of the pile-up is smaller and more stress must be applied from external forces, i.e. the yield point is raised.

The outcome is summarised in the famous Hall–Petch equation:

σ_y = σ₀ + kd^−1/2  

where σ_y is the yield strength of our polycrystalline material, σ₀ is the yield strength of one crystal on its own, k is a proportionality constant and d is the grain size of the material.

Mild steel with a grain size of 250 mm has σ_y ≈100 MPa, but when d = 2.5 mm, σ_y ≈ 500 MPa. The incentive for making fine-grained steels is clear.

Control of grain size in castings is generally achieved by ‘inoculating’ the liquid metal with substances that can react with ingredients in the metal to form small solid particles that act as nucleation sites for crystal growth.

In wrought products, the thermal and mechanical history of the working process can be controlled to give fine grains, as discussed below. Rolling and forging are therefore used not only to shape materials but also, perhaps more importantly, to control their microstructures and hence their properties.

Strain Hardening 

We can increase the yield stress of a material by work or strain hardening. This involves loading into the region of plastic deformation with a positive slope of stress–strain behaviour. In a tension test, a reasonably ductile metal becomes unstable and begins to form a neck at strains of only about 30% or so.

But when we roll the same metal or form it into wire by drawing, the deformation in the local area being worked is essentially compressive. This allows us, for example, to draw a wire to many times its original length with relative ease. The work hardening is extended well beyond what can be achieved in a tension test; for example with some steels, the yield strength can be increased by 4 or 5 times by drawing it to a thin wire.

Metals, especially those with the face-centred and body-centred cubic systems, have many different planes on which dislocations can move to produce slip. But none of these are markedly different from the others and, under increasing stress, all dislocations try to move at once.

If the slip planes intersect each other, as indeed they do, the dislocations on one slip plane act as a barrier to dislocations trying to move across them. With any significant amount of plastic deformation, many millions of dislocations are on the move, the traffic pile-up is considerable and the dislocations get jammed.

Very much more stress needs to be applied to get things moving again and so strain hardening is the result. It is one of the most effective ways of raising the yield strength of a metal, though if carried too far it results in fracture, as we have seen.

Annealing

An undesirable effect of strain hardening at room temperatures (or cold working) is that it can cause local internal stresses and hence non-uniformity of the metal. Since each dislocation is a region of high strain in the lattice, they are not thermodynamically stable and comparatively little energy is required to cause a redistribution and cancellation of the trapped dislocation arrays.

The energy is most conveniently supplied in the form of heat, which gives the atoms enough energy to move spontaneously and to form small areas that are relatively free of dislocations. This is called recovery but, since the dislocation density is only slightly reduced, the yield strength and ductility remain almost unchanged. The major change involves recrystallisation.

New grains nucleate and grow, the material is restored to its original dislocation density and the yield point returns to its original value. This process is known as annealing, and the annealing temperature is normally kept fairly low (say at most to around 0.6 T_m, where T_m is the melting point in degrees K) so that the increase in strength due to cold working is not affected. Annealing is also a useful way of controlling grain size.

Alloying 

One of the most powerful ways of impeding dislocation movement, and hence of increasing the yield strength, is to add another element or elements to the metal in order to distort the atomic lattice. We know that foreign atoms can be located as either interstitial or substitutional impurities. Deliberate introduction of an appropriate type and quantity of the foreign element(s) produces alloys whose properties are significantly enhanced over that of the parent metal. Nearly all metals used in construction are alloys, the most notable being steel, an alloy of iron and carbon (and normally other elements as well).

Dispersion hardening is a particular form of alloying in which the alloying element or impurity combines with the parent metal. The impurity is added to the molten metal at high temperature and then, as the alloy cools and solidifies, the impurity– metal compound precipitates as small, hard, often brittle, particles dispersed throughout the structure.

Examples of such particles are CuAl₂ formed after adding small quantities of copper to aluminium or iron carbides formed after adding small quantities of carbon to iron.

Figure 2 illustrates how such particles obstruct the movement of a dislocation line. An increased stress is required to push the line between the particles ((a) and (b)), but eventually it is forced through ((c) and (d)); it will of course, soon encounter, more obstacles. Clearly the greatest hardening is produced by strong, closely spaced precipitates or dispersions.

Quenching and Tempering

Many of us know that if you take a piece of steel containing, say, 0.5% carbon, heat it to glowing red (~900°C) and then quench it by placing it in a bath of water, the outcome is a very hard but brittle substance. Indeed, it could be used to cut a piece of steel that had not been so treated. The quenching of steel is an example in which an unstable microstructure is generated when there is no time for diffusion to keep up with the requirements of thermodynamic equilibrium.

The procedure generates a new and unexpected structure (called martensite) in which there are large internal locked-in stresses. In the as-quenched condition this is too brittle to be useful, but if it is heated to just a few hundred degrees C a number of subtle changes come about.

The steel is softened a little, not much, but a useful degree of toughness is restored. This second heating is called tempering, and gives us tempered steel. In this state it finds many uses as components in machinery, gears, cranks, etc. A difficulty with this method of obtaining strength is that it works well only for certain types of steel.

Strengthening, Ductility and Toughness

As in most things in nature, you do not get something for nothing, and there is a cost to be paid for increasing the yield strength of metals by the above processes. This is that as yield and tensile strength increase ductility, toughness and fracture toughness are reduced. Figure 3 shows the relationship between yield strength and fracture toughness for a range of alloys. We must, however, take care that the reduction in toughness is not too excessive.

For example, continued cold working will raise the yield strength ever closer to the tensile strength but at the same time the reserve of ductility is progressively diminished and, in the limit, the material will snap under heavy cold working. This is familiar to anyone who has broken a piece of wire by continually bending and rebending it.

Thanks for reading about “strengthening of metals.”