COLD ROLLING: Tempered Martensite

Introduction
Tempering is a term historically associated with the heat treatment of martensite in steels. It describes how the microstructure and mechanical properties change as the metastable sample is held isothermally at a temperature where austenite cannot form. The changes during the tempering of martensite can be categorised into stages. During the first stage, excess carbon in solid solution segregates to defects or forms clusters within the solid solution. It then precipitates, either as cementite in low-carbon steels, or as transition iron-carbides in high-carbon alloys. The carbon concentration that remains in solid solution may be quite large if the precipitate is a transition carbide. Further annealing leads to stage 2, in which almost all of the excess carbon is precipitated, and the carbides all convert into more stable cementite. Any retained austenite may decompose during this stage. Continued tempering then leads to the coarsening of carbides, extensive recovery of the dislocation structure, and finally to the recrystallisation of the ferrite plates into equiaxed grains.

This is a useful description but it is revealing to consider first, the factors responsible for driving the process in the first place.

Deviation from Equilibrium
Tempering is a process in which the microstructure approaches equilibrium under the influence of thermal activation. It follows that the tendency to temper depends on how far the starting microstructure deviates from equilibrium. It is interesting therefore to consider how metastable a material can be, before dealing specifically with martensite. Turnbull characterised metastability in terms of the unit RTm where R is the universal gas constant and Tm is the absolute melting temperature. This coarse unit is a measure of the thermal energy in the system at the melting temperature; it represents a large amount of energy, typically in excess of 20,000 J mol-1.

Table 1: Degree of metastability Metastable structure RTm
Supersaturated solutions 1
Amorphous metal 0.5
Modulated films, nanostructures 0.1

Supersaturated solutions are prominent in this list and the extent of metastability depends both on the excess concentration and on the equilibrium solubility. It can be demonstrated that excess carbon which is forced into solution in martensite is the major contributor to the stored energy of martensite.

The calculations presented in Table 2 show the components of the stored energy of martensite in a typical low--alloy martensitic steel Fe-0.2C-1.5Mn wt%. It is necessary to define a reference state, which is here taken to be an equilibrium mixture of ferrite, graphite and cementite, with a zero stored energy. Graphite does not in fact form because it is too slow to precipitate; the effect of replacing the graphite with cementite is to increase the stored energy by some 70 J mol-1.

When transformations occur at low temperatures, it is often the case that substitutional elements like manganese and iron cannot diffuse during the time scale of the experiment, whereas carbon is still mobile. The transformation then happens in such a way that the Fe/Mn ratio is maintained constant whilst the carbon redistributes subject to this constrain, until its chemical potential becomes uniform. This is known as paraequilibrium. Unlike the equilibrium state, because the iron and manganese atoms are trapped during transformation, their chemical potentials are no longer uniform. This adds a further 315 J mol-1 to the stored energy.

When bainite forms, the transformation mechanism is displacive, there is a shape deformation, which leads to an additional 400 J mol-1 of stored energy. Since there is no diffusion during transformations, but the carbon partitions following growth, the total stored energy is that for the paraequilibrium state added to the strain energy term, giving a net value of 785 J mol-1.

Martensite is not only a diffusionless transformation, but it frequently occurs at low temperatures where its virgin microstructure is preserved. Even the carbon remains trapped in the product crystal. Furthermore, the strain energy term associated with martensite is greater at about 600 J mol-1 because the plates tend to have a larger aspect ratio (thickness/length). There may also be twin interfaces within the martensite plates, which cost about 100 J mol-1. The trapping of carbon inside the martensite adds a further 629 J mol-1, which makes the total stored energy in excess of 1700 J mol-1!

Table 2: Stored energies of a variety of microstructures

Phase Mixture in Fe-0.2C-1.5Mn wt% at 300 K Stored Energy / J mol-1
1. Ferrite, graphite and cementite 0
2. Ferrite and cementite 70
3. Paraequilibrium ferrite and paraequilibrium cementite 385
4. Bainite and paraequilibrium cementite 385+400=785
5. Martensite 385+600+100+629=1714
6. Mechanically alloyed ODS metal 55

The stored energy becomes even larger as the carbon concentration is increased (Figure 1).

Figure 1: The free energy due to the trapping of carbon in martensite, as a function of its carbon concentration. The results are for a temperature of 473 K.

Virgin Microstructure
The virgin microstructure obtained immediately after quenching from austenite consists of plates or laths of martensite which is supersaturated with carbon. In the vast majority of steels, the martensite contains a substantial density of dislocations which are generated during the imperfect accommodation of the shape change accompanying the transformation. The plates may be separated by thin films of retained austenite, the amount of untransformed austenite becoming larger as the martensite-start temperature MS is reduced.

a) Transmission electron micrograph of as-quenched martensite in a Fe-4Mo-0.2C wt% steel. The mottled contrast within the plates is due to a high density of dislocations. (b) Corresponding dark-field image showing the distribution of retained austenite.

Carbon Atoms
Carbon is an interstitial atom in ferritic iron, primarily occupying the octahedral interstices. There are three such interstices per iron atom. At a typical concentration of 0.4 wt% or about 2 at%, less than 1% of these interstices are occupied by carbon. Furthermore, there is a strong repulsion between carbon atoms in nearest neighbour sites. This means that carbon atoms almost always have an adjacent interstitial site vacant, leading to a very high diffusion coefficient when compared with the diffusion of substitutional solutes. In the latter case, the substitutional vacancy concentration is only 10-6 at temperatures close to melting, and many orders of magnitude less at the sort of temperatures where martensite is tempered. It follows that carbon diffuses much faster than substitutional atoms (including iron), as illustrated below.

a) A carbon atom in an octahedral interstice in body-centered cubic iron

b) The ratio of the diffusivity of a substitutional atom to that of carbon in body-centered cubic iron.

Given that carbon is able to migrate in martensite even at ambient temperature, it is likely that some of it redistributes, for example by migrating to defects, or by rearranging in the lattice such that the overall free energy is minimised.

Precipitation of Iron Carbides
In high-carbon steels, the precipitation of excess carbon begins with the formation of a transition carbide, such as ε (Fe2.4C). ε-carbide can grow at temperatures as low as 50oC. Indeed, most of the iron carbides can precipitate at low temperatures, well below those associated with the motion of substitutional solutes. This is because they grow by a displacive mechanism which does not require the redistribution of substitutional atoms (including iron); carbon naturally has to partition. This corresponds to a process known as paraequilibrium transformation in which the iron to substitutional solute ratio is maintained constant but subject to that constraint, the carbon achieves a uniform chemical potential.

Martensite is said to be supersaturated with carbon when the concentration exceeds its equilibrium solubility with respect to another phase. However, the equilibrium solubility depends on the phase. The solubility will be larger when the martensite is in equilibrium with a metastable phase such as ε carbide. Some 0.25 wt% of carbon is said to remain in solution after the precipitation of ε-carbide is completed.

Although most textbooks will begin a discussion of tempering with this first stage of tempering, involving the redistribution of carbon and precipitation of transition carbides, cementite can precipitate directly. This is particularly the case when the defect density is large. Trapped carbon atoms will not precipitate as transition carbides but cementite is more stable than trapped carbon

a) Transmission electron micrograph of martensite in a Fe-4Mo-0.2C wt% steel after tempering at 190oC for 1 hour. The carbon has in this case precipitated as fine particles of cementite. (b) Corresponding dark-field image showing the distribution of retained austenite, which has not been affected by the temperin

Decomposition of Retained Austenite

Tempering at higher temperatures, in the range 200-300oC for 1 h induces the retained austenite to decompose into a mixture of cementite and ferrite. When the austenite is present as a film, the cementite also precipitates as a continuous array of particles which have the appearance of a film.

Dark field transmission electron micrograph of martensite in a Fe-4Mo-0.2C wt% steel after tempering at 295oC for 1 hour. Only the cementite is illuminated. The film of cementite at the martensite plate boundaries is due to the decomposition of retained austenite.

Further Tempering
Tempering at even higher temperatures leads to a coarsening of the cementite particles, with those located at the plate boundaries growing at the expense of the intra-plate particles. The dislocation structure tends to recover, the extent depending on the chemical composition. The recovery is less marked in steels containing alloying elements such as molybdenum and chromium.

Bright field transmission electron micrograph of martensite in a Fe-4Mo-0.2C wt% steel after tempering at 420oC for 1 hour.