2022 Volume 62 Issue 10 Pages 1981-1989
This paper aims to present new observations and relate these to other recent findings concerning the influence of local micro-stresses (Type II residual stresses) on the behaviour of martensitic steels. A major source of these stresses is the shearing that accompanies phase transformation in individual austenite grains and which is blocked by constraint from the surrounding matrix. Residual stresses are the principal reason for early plasticity and gradual yielding during tensile testing of martensite.
Diffraction techniques are commonly used to measure residual stresses, where peak profiles are influenced by the micro-strains and also by dislocations. Most publications have considered only dislocations and ignored the role of micro-strains. We demonstrate experimentally that this assumption is untenable and must lead to incorrect values of dislocation parameters. The unusual behaviour whereby diffraction peaks from martensite become narrower during plastic deformation is explained by the progressive relaxation of the micro-strains.
We hypothesise that freshly formed martensite is always tetragonal but that it decomposes spontaneously to a cubic structure by auto-tempering in most low carbon lath martensites where the Ms temperature is sufficiently high. This transformation is examined in detail in higher carbon steels which reveals another surprising effect, namely that diffraction peaks can become broader during annealing, resulting from a newly recognised source of internal micro-stresses. These arise when the contraction of crystals along the c-axis during tempering is inhibited by restraint from their surroundings, so preventing equilibrium atomic spacings from being achieved.
Quench-hardened martensitic steels have been used for centuries in tools and weapons because of their combination of hardness and toughness. In recent years there has developed new interest in these materials for weight-reduction in vehicles where high strength sheet steel is used directly with shaping by cold roll forming or alternatively processed by hot stamping and quenching. Typical steel compositions contain between 0.1% and 0.35% carbon, with very little other alloy content although a small addition of boron (~30 ppm) is often used to enhance their hardenability. The advent of these products has been accompanied by renewed research into their microstructures and mechanical behaviour.1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20) One area that has received little attention concerns internal stresses which can account for several effects such as the low micro-yield stresses and gradual yielding which are general features of martensite. In fact, this phenomenon was recognised in earlier publications21,22,23,24,25) but has been neglected recently with only a few exceptions.18,26,27) The shearing that accompanies transformation from austenite to martensite takes place within individual crystals inside a solid matrix so it would be natural to expect that the deformation will be blocked by surrounding material, leaving local residual elastic stress fields. A model proposed by Fukui et al.28) predicts that residual strains with tetragonal symmetry occur in low carbon alloy steel. However, the situation is apparently more complex. According to Morris et al.2) the formation of the hierarchical structure into packets, blocks and sub-blocks is driven by the requirement to minimise internal stress during transformation which could, in principle, be completely eliminated. In reality, perfect matching of the structure elements as described by Morris et al. would seldom be possible, especially when the prior austenite grains are small and only a few martensite variants are present in each, so some stresses will be retained. We will also show below how an additional source of stress can be introduced which has apparently not been considered previously.
Internal stresses or strains fall into three categories although more than one of these may be present simultaneously. X-ray and neutron diffraction are methods commonly employed to measure these. Type I are long range stress fields which result in macroscopic distortion and sometimes unexpected fracture. We will not be concerned with these. Type II stresses usually exist uniformly within individual crystals but their influence cancels out over many crystals at larger distances, leading to a general broadening of the peaks. These can result from plastic deformation and phase transformations, especially when the latter are of a displacive nature such as in the formation of martensite from austenite. It should be noted that neither Type I nor Type II stresses can exceed the flow stress of the metal as they would be spontaneously relaxed by plastic deformation. However, martensite is a very strong phase with a high plastic flow stress so these internal stresses may be very high indeed. The combination of tensile and compressive Type II strains results in diffraction lines becoming broader. An additional category, sometimes referred to as Type III strains, is the presence of dislocations inside the crystals. These also lead to broadening of diffraction lines so are difficult to distinguish from Type II strains. In fact, most publicationse.g.10,14,15,16,19) have ignored the possible role of Type II strains and attributed the whole diffraction peak profile to dislocations. We will show below that this simplification is not justified in the case of martensite.
Evidence for Type II strains is supported also by high resolution EBSD measurements.29,30) For example, direct measurements were made by Archie et al.30) using FIB sectioning of micro-pillars in a quenched steel containing 0.27%C. From the dimensional changes accompanying stress relaxation it was deduced that residual stresses up to 380 MPa had existed. However, this figure must be considered as a lower limit since many stress components would already have been relaxed prior to FIB when preparing the initial free surface. The true local stresses in 3-dimensions should be significantly higher.
A further complication when analysing polycrystalline diffraction patterns from martensite is the question as to whether the crystals have cubic or tetragonal structures. Elastically strained cubic crystals may closely resemble tetragonality in this regard, which probably accounts for varying conclusions that different researchers have reached from x-ray diffraction4,17,29,31,32,33,34) even in quite recent times. Kurdjumov35) summarised his extensive experience on structures in iron-carbon alloys which can be expressed as follows. Below about 0.2%C the structures are cubic. Between 0.2%C and 0.6%C they consist of mixtures of cubic and tetragonal crystals with the proportion of tetragonal increasing with carbon content. Above about 0.6%C the steels are completely tetragonal (today’s most widely used steels with around 0.2%C should accordingly be almost completely cubic). Also, the c/a ratio is well known to increase linearly with carbon content. A logical rationale for this interpretation is that the initially formed martensite is always tetragonal but it may decompose spontaneously to cubic by auto-tempering at sufficiently high temperatures, even with fast quenching. This is particularly relevant when the Ms temperature is high as with low carbon steels. However, the transformation to martensite is spread over a wide range of temperatures. Thus, in the intermediate carbon range of mixed structures, the first martensite crystals formed at higher temperatures become cubic during cooling while the later ones that form at lower temperatures retain their tetragonality. Diffraction peaks then correspond to a combination of the two structures. This viewpoint is supported by the fact that Ni-alloyed steels with reduced Ms temperatures are fully tetragonal even with low carbon levels (~0.1%C)e.g.36) and also that fully tetragonal structure could be observed in plain steel containing as little as 0.21%C when cooled extremely quickly by ‘splat cooling’.34)
The crystal structure has important implications for interpretation of XRD patterns since the unique lines from cubics become split into two or three closely spaced overlapping lines in the case of tetragonals, resulting in different shapes and breadths of the peaks. An exception to this behaviour exists, however, in the case of the 222 reflection which has a single d-spacing, irrespective of the c/a ratio.37) These 222 reflections have, therefore, been applied in the present work when such clarity was demanded. Rather surprisingly, this simplification does not seem to have been recognised in previous publications on martensite.
The understanding that Type II stresses are significant in quenched steel accounts not only for the initial yielding behaviour of the steel but also several other phenomena that are peculiar to martensite. Unlike almost every other metal, plastic deformation causes the diffraction lines to become narrower in martensite. Equally remarkable is that diffraction lines from martensite become broader during annealing in some circumstances. These behaviours will be demonstrated and explained further below. As well as presenting new results, we review some earlier results in the light of current thinking, including an additional source of residual stress that has not previously been recognised.
We report here on various experiments carried out on steels of different compositions as summarised in Table 1. Excepting 0.71%C, these were initially in sheet form. Heat treatments involved austenitisation by holding for 5 minutes or longer at temperatures that were about 70 degrees above their Ae3 temperatures according to the iron-carbon phase diagram, followed by quenching into saturated brine. Subsequently, the specimens were first chemically polished by 0.1 mm to remove any decarburised surface layers and then electropolished for microscopy and XRD.
| Name | %C | %Si | %Mn | %P | %S | %N | %Cr | %Ni | %Mo | %Al | %B | %Ti |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0.06%C | 0.056 | 0.21 | 1.79 | 0.009 | 0.003 | 0.0040 | 0.03 | 0.06 | 0.01 | 0.039 | 0.0002 | 0.004 |
| 0.10%C | 0.103 | 0.21 | 1.60 | 0.012 | 0.002 | 0.0053 | 0.03 | 0.04 | 0.04 | 0.043 | 0.0003 | 0.04 |
| 0.198%C | 0.198 | 0.19 | 0.98 | 0.009 | 0.004 | – | – | – | – | 0.035 | 0.0024 | 0.032 |
| 0,20%C | 0.202 | 0.19 | 1.06 | 0.009 | 0.002 | 0.0054 | 0.04 | 0.03 | 0.00 | 0.044 | 0.0022 | 0.034 |
| 0.26%C | 0.263 | 0.19 | 0.50 | 0.008 | 0.003 | 0.0029 | 0.02 | 0.03 | 0.01 | 0.047 | 0.0023 | 0.036 |
| 0.35%C | 0.348 | 0.01 | 0.38 | 0.011 | – | 0.0023 | 0.14 | – | – | 0.034 | 0.0047 | 0.032 |
| 0.49%C | 0.489 | 0.25 | 0.78 | 0.016 | 0.027 | – | 0.09 | 0.13 | 0.02 | 0.00 | 0.0001 | 0.001 |
| 0.71%C | 0.710 | 0.21 | 0.49 | 0.011 | 0.005 | 0.0023 | 0.09 | 0.13 | 0.02 | 0.005 | – | 0.001 |
| 0.76%C | 0.756 | 0.24 | 0.70 | 0.018 | 0.003 | – | 0.21 | 0.05 | 0.02 | 0.007 | – | 0–002 |
| 1.02%C | 1.020 | 0.23 | 0.39 | 0.009 | 0.002 | 0.006 | 0.21 | 0.06 | – | 0.014 | – | 0.001 |
| 1.04%C | 1.040 | 0.26 | 0.44 | 0.008 | 0.001 | 0.0054 | 0.02 | 0.09 | 0.03 | 0.006 | – | – |
In the 1950’s, Arbusov38,39) reported that the Type II short range stresses in martensite could be relaxed by potentiostatic etching. This method was found to be applicable for high carbon martensites that contain a significant content of residual austenite which acts as a ‘cement’ between packets of martensite crystals and which could be removed by selective dissolution under suitable circumstances. Unfortunately, Arbusov gave few details of how this was done but a similar result was obtained in the present work after some experimentation. Details about this are given in the appendix. The 1.04%C steel was used here. Figure 1(a) is a SEM micrograph showing the specimen surface after the potentiostatic treatment where it is evident that a network of troughs has been created by a selective etching process. Figure 2(b) compares the 220 XRD diffraction peaks for the austenite phase in the polished and etched conditions. Virtually all the austenite signal has disappeared after etching so the removal of austenite in the surface layer was successfully achieved as described in the earlier work of Arbusov.
(a) SEM image of the specimen surface after selective potentiostatic etching, (b) austenite 220 reflections from the surfaces after polishing and selective etching. (Online version in color.)
222 peaks for 1.04%C steel after surface preparation by electropolishing and by selective etching of the austenite phase. (Online version in color.)
Figure 2 shows the martensite 222 peaks for the same two surface conditions. It is evident that etching has significantly changed the martensite diffraction peak, making it narrower and higher as a result of the relaxation of residual strains. The individual crystals become freely separated from one another by the etching so stresses cannot be sustained within them. It is inconceivable that the dislocations inside the martensite crystals would be affected by the etching and their contribution to the diffracted intensity will remain unchanged. This demonstrates the inherent error that must result if the peak profiles in martensite are assumed to derive only from dislocations. In fact, the length scale of the retained austenite distribution is greater than the finer block structures of the martensite so it is probable that only some of the residual stresses can be relaxed by the etching treatment. The discrepancy between measured peak shape and that due to dislocations may be even larger than seen here. Furthermore, since dislocations exist inside the grain volumes that constitute Type II strains, the two contributions to peak shape are not independently additive. The effect from dislocations is convoluted by the Type II strains so these local strains contribute to the whole of the diffraction peak and their influence extends to the furthest tails, even if they themselves are not large. An important conclusion from this argument is that many publications where dislocation densities in martensite have been deduced from XRD or neutron diffraction patterns may be in significant error.
It can also be noticed in Fig. 2 that the peak position is somewhat shifted to a higher Bragg angle after selective etching. We believe that this originates from the relaxation of hydrostatic stresses induced by the phase transformation. The effective penetration of CuKα radiation in iron is extremely shallow, of the order of only a few micrometres, so these strains perpendicular to the surface result from the biaxial stress condition and are not affected by gradients.
2.3. Early Stages of Tempering in High Carbon Martensite – A New Source of Residual StressIn low carbon martensites, auto-tempering takes place already during conventional quenching so it is not feasible to investigate these early structural changes. With higher carbon contents the tetragonal state is retained to room temperature and it is then possible to examine its decomposition under controlled conditions. The 0.71%C steel was first adopted for this purpose and was examined during and after heating in the dilatometer at a rate of 25°C/s. Samples quenched at various temperatures were sectioned and measured by XRD on the 002/200,020 diffraction peaks as shown in Fig. 3. There is a small increase in length at around 190°C under these conditions which correspond to the transformation from tetragonal to cubic structures as confirmed by the elimination of the 002 sub-peak at the lower Bragg angles.
Change in length during heating the quenched 0.71%C steel at 25°C/s, together with 002/200,020 XRD peaks from samples quenched at the indicated temperatures. The complete abscissa scales are from 60° to 70° in 2θ and the peak intensities are in arbitrary units. (Online version in color.)
A more thorough investigation of these changes was then made for the nearly identical 0.76%C steel using isothermal anneals at 150°C. Two similar specimens were used for measurements following progressively longer annealing times. In the second run, great care was taken to replace the specimen on the instrument table in exactly the same position so that the total integrated intensities could be compared after the successive heat treatments. The low angle hump from the 002 reflection, which is the signature of tetragonality after quenching, decreased with time at 150°C up to 100 s and was not at all evident after the longer annealing times. Data acquired from these scans are summarised in Table 2.
| Condition | Peak position (2θ) degrees | 020,200 lattice spacing (Å) | Skewness (fraction I002/I020,200) | FWHM for 020,200 peak (degrees) | Integrated intensity × 10−3 counts |
|---|---|---|---|---|---|
| As quenched | 65.40 | 2.854 | 0.22±0.02* | 1.225±0.01* | 225.1 |
| 150°C/10 s | 65.32 | 2.857 | 0.23±0.02* | 1.30±0.01* | 236.4 |
| 150°C/30 s | 65.37 | 2.855 | 0.18±0.02* | 1.27±0.01* | 236.6 |
| 150°C/100 s | 65.31 | 2.858 | 0.18±0.02 | 1.32±0.01 | – |
| 150°C/300 s | 65.32 | 2.857 | 0.11±0.01* | 1.47±0.01* | 255.3 |
| 150°C/1000 s | 65.24 | 2.860 | 0.10±0.01* | 1.51±0.01* | 261.4 |
| 300°C/300 s | 65.13 | 2.865 | 0.05±0.005* | 1.02±0.005 | 267.9 |
Relative intensities for the a and c reflections were obtained by mirroring the high angle side of the peaks and subtracting this symmetrical area from the complete spectrum, as done previously by Moss.40) The ratio of the residual area to the mirrored peak is used as a measure of peak asymmetry or skewness which for a tetragonal crystal structure gives the intensity fraction I002/I200,020. It would normally be expected that this ratio should be 0.5 based on multiplicity but it is known since the work of Lipson et al.41) that interstitial carbon atoms in tetragonal martensite displace the iron atoms, most notably in the c-direction, which reduces the intensity ratio. The increase in integrated intensity on annealing is, therefore, further evidence for the destruction of the tetragonal phase and its replacement by cubic ferrite. The present results show that, although the 002 hump disappears during annealing, the associated intensity persists to a significant degree. These peaks are smooth but somewhat asymmetrical, being less steep on the low angle side, and they also become broader as tempering proceeds. Increasing peak breadth during annealing is a most unusual phenomenon but it is confirmed by similar observations in the low temperature tempering results of van Genderen et al.42) Such an Increase in peak breadth during annealing is contrary to almost all other experience in x-ray diffraction and indicates that there is an increase in the local elastic strains since any increase in dislocation density on annealing is highly improbable. At the same time, the peak position shifts slightly to lower angles as the a-spacing relaxes towards the value for pure iron (0.1433 nm) with increasing annealing time or temperature.
Figure 4 summarises these results as fractional changes in the parameters for easier comparison. A consistent explanation of these effects is that the destruction of ordering of the carbon atoms necessitates changes in the crystal dimensions with contraction along c and a small expansion along a. However, the crystals are not free to change in size and shape, being constrained by the surrounding metal. The tetragonal crystallinity is therefore replaced by degrees of elastic strain that preserve some extensions along the prior c directions and some contraction along the a directions and which broaden the diffraction peaks. In the present context it should be noted that this change occurring during tempering cannot be regarded as relaxation. There is actually an increase in the magnitude of the Type II residual stresses. The same can be expected to apply to low carbon steels but in those materials, the change happens already before quenching is complete and, for this reason, has not been previously recognised. The skewed peak shape of the high carbon steel after this tempering is, in fact, also found in quenched low carbon martensites and probably explains why these have sometimes been interpreted as being crystallographically tetragonal, for example in Rietveld analyses.31,33)
Fractional changes in various parameters from XRD measurements on the 0.76%C steel after successive isothermal anneals at 150°C. (Online version in color.)
Further analysis of the diffraction peaks from the 0.76%C steel were carried out to better understand the structural changes by fitting pseudo-Voigt model peaks to them. Figure 5(a) shows the results for the as-quenched steel. The expected double peak for the tetragonal structure is clearly resolved with d-spacings as expected from the literature.35) The integrated intensities of the 002:200/020 peaks are in the ratio 53:234 or in other words the c-peak contains 18% of the total diffracted intensity. As explained above, this is less than the 33% that would be expected due solely to multiplicity because of the displacement in the iron atom positions. The profile after tempering for 30 seconds at 150°C is shown in Fig. 5(b). No change in the diffracted intensity of the 200/020 planes can be expected when the tetragonal symmetry is lost so the same a-peak profile is retained as before but with a small shift to lower angles to account for the expansion in the d200/020 plane spacings. The c-peak parameters are unchanged except for its height so that this peak accounts now for only 8% of the total diffracted intensity. Subtracting this from the total measured intensity leaves a broad residual intermediate peak which is named as a* here. Further tempering to a total time of 1000 s seconds led to the peaks shown in Fig. 5(c). The original c-peak has now completely disappeared and the profile is composed of the original cubic a-peak together with a second broad overlapping cubic a*-peak at slightly lower Bragg angles and which can be identified as the intensity resulting from the decomposed c-peak. The fact that this does not correspond entirely in position with the residual a-peak is a result of the systematic elastic restraint placed on the shrinking c-axis material directions by the surrounding material. The broadening of the measured profile that was noted earlier can now be understood as the overlapping of these distinct a and a* peaks after tempering.
Modelled and measured diffraction peaks for the 0.76%C steel, (a) as quenched, (b) tempered 30 s at 150°C and (c) tempered 1000 s at 150°C. (Online version in color.)
We can also make an estimate of the residual stress level along the prior c-direction of the decomposed tetragonal structure after annealing for 1000 s. The new a*-peak is centred at 64.60° in 2θ which corresponds to a d200 plane spacing of 0.14416 nm. The d200 spacing in strain-free iron is 0.14332 nm, so the elastic strains have an average value of +5.900×10−3. Young’s modulus of iron in the <100> direction is 132 GPa which means that the residual tensile stress is evaluated as approximately 778 MPa. An uncertainty in this estimate arises from the possible contribution to lattice spacing from dissolved carbon atoms. That is difficult to evaluate but if the a- and a*-peaks are compared (assuming both crystal types contain similar levels of dissolved carbon) the strain appears to be somewhat larger at about 1.1×10−2 and the stresses also correspondingly greater. Despite the considerable uncertainty in these estimates, it appears to be necessary for very high local tensile stress to exist in the martensite when the tetragonality disappears on tempering or auto-tempering. The plastic flow stress of quenched 0.7%C steel is more than 2000 MPa so the values of stress deduced here can exist without spontaneous plastic relaxation.
High carbon martensites in plain and Ni-alloyed steels have been studied by XRD in considerable detail previously.e.g.42,43,44,45,46,47) A third, intermediate, peak similar to the one shown here has frequently been reported and different explanations have been suggested. These include an incomplete decomposition to a more dilute tetragonal crystallinity,35) local redistributions of carbon atoms among the three orientations of octahedral sites47) or an orthorhombic martensite structure.48) It seems that no authors have previously suggested that the extra peak actually belongs to cubic iron that is systematically strained following the decomposition of the initial tetragonal martensite. A possible exception is Chen et al.47) who noted that that the intermediate peak was much weaker in tempered martensite from single crystals of austenite than fine grained austenite. They commented that the massive martensite plates in single crystal samples, which were comparable to the specimen dimensions, should be less constrained than the much smaller plates in the polycrystal. Although their description is not explicit, it is in good accord with our present viewpoint.
Some further evidence is seen when peak breadths are compared for quenched steels with varying carbon contents. Figure 6 shows results of integral peak breadths for the present steels made on the martensite 222 peaks in transmission XRD measurements. These were acquired using the same beam-line instrument on the Australian Synchrotron as previously.26) The almost linear increase up to about 0.4%C probably arises from a combination of higher dislocation densities and larger Type II strains because of the higher hardness. In the range where tetragonal structures are maintained, above about 0.6%C, the broadening becomes less. This behaviour may reflect changes in the martensite structure as twinning complements slip accommodation during the transformation and possibly some influence from the higher contents of retained austenite but it is certainly compatible with the view that additional residual stress is created when the tetragonal structure decomposes into cubic.
Integral breadths for 222 reflections from quenched steels having different carbon contents. (Online version in color.)
Although a very hard material, martensite actually commences to deform in tensile tests at low stress levels that may be as little as 10% of the conventional 0.2% proof stress.21) Increasing straining causes the stress level to rise rapidly up to the point of diffuse yielding followed by a low rate of hardening up to the ultimate tensile stress. Modern viewpoints hold that the rapid hardening is not due to rapid dislocation multiplication but corresponds to an extended elasto-plastic transition. A number of explanations have been put forward for the soft yielding behaviour. One of these is that fresh (unpinned) dislocations are created in the austenite to martensite transformation which can move readily on loading.20) This, however, neglects the high resistance that the dense substructure applies to all dislocation movement and also the fact that even in fresh as-quenched steel the dislocations are heavily loaded with carbon atoms as shown by atom probe tomography.17) Another view is that the local substructures in martensite vary considerably in hardness so plasticity occurs progressively at different stress levels in different volumes.9) Although this seems physically reasonable, the existing models require a much greater range in hardness than can be justified by the actual microstructural variation. The viewpoint that we put forward, which is essentially similar to earlier suggestions,24,25) is that yielding is controlled by the residual stress pattern. In a tensile test, the microstructure volumes that are already stretched will yield first during loading, followed by less favourable regions and finally by deformation in those volumes where the residual stress is opposed to the applied loading. This has been outlined in some detail previously26) so we will here simply present one figure of experimental compared with computed stress-strain curves derived from the crystal plasticity FEM modelling. Two types of transformation strain (tetragonal and shear) that created the internal stress pattern are compared but the results for these are very similar, Fig. 7. Only one single free parameter is used in this modelling which is the critical resolved shear stress for slip and which applies to both generation of the residual strains and to their relaxation during deformation. No conventional work hardening is assumed as can be seen for the modelled stress-strain curve for an isolated crystal (in-set). Comparison of the model with an experimentally measured result shows very good agreement, especially when considering that so few assumptions are included. We also want to emphasize here that significant plastic deformation, of 1% or more, is necessary to relax the internal stresses. That cannot be achieved by only very small amounts of dislocation motion as is sometimes suggested.
Experimental and modelled tensile stress-strain curves for martensite. Two assumptions for transformation strain are included, i.e. shear and tetragonal distortions that generate residual stresses. The red curves show the predicted behaviour for polycrystal and single crystal (in-set) structures in the absence of any residual stress. (Online version in color.)
A most unusual and possibly unique aspect of plastic flow in martensite is that diffraction peaks become narrower with straining. This is, of course, contrary to all normal experience where the opposite behaviour occurs with the peaks becoming broader. Several workers have reported this phenomenon previously. Proposed explanations for this involved the destruction of tetragonal structure50) or the coordinated glide and annihilation of dislocations into special arrangements.15,20) In terms of the effects of residual stresses, however, peak narrowing is the expected behaviour. Plasticity brings the (flow) stress in different regions towards a common level so that the spread in elastic strain levels is reduced. Accordingly, the diffraction peaks must become narrower. When this phenomenon is examined in more detail, it becomes evident that only the residual strain model can provide a credible explanation.
Tensile tests were carried out together with synchrotron diffraction measurements on the 0.198%C sheet steel to follow the 110 peaks when the diffracting vector was aligned with the stress axis. Figure 8(a) shows the reduction of FWHM peak breadth as a function of the nominal strain in the machine which is in general agreement with results in the literature.15,18,20,49) However, the new finding from these results is that the peak does not shrink symmetrically. Both sides of the peak shift towards lower Bragg angles with increasing applied load but the displacement is greater for the high angle side so the spacing between these becomes smaller and the peak becomes narrower. If the cause of narrowing had been destruction of tetragonality as suggested by Vylezhnev et al.49) then the change in peak profile would have occurred in the opposite sense. Explanations requiring coordinated dislocation are difficult to justify on physical principles and may be regarded as speculative.
(a) variation of the FWHM peak breadth with tensile strain, (b) strain levels at the high and low angle sides of the diffraction peak at different stress levels during tensile straining. Sizes of symbols used for data points correspond to the uncertainty in measurements. (Online version in color.)
This behaviour can be understood by recognising that regions with tensile residual strains are represented predominantly by intensity in the low angle side of the peak while compressed regions are represented by the high angle side. These are indicated by the letters T and C inset in Fig. 8(b). There is, thus, a correlation between the internal stresses and the position within the profile of the peak. As loading progresses, the regions which were strongly pre-loaded in tension are the first to reach their critical flow stress so these yield and the elastic strain in them then ceases to rise. This is demonstrated by the left-hand red curve in Fig. 8(b). Regions that were pre-loaded in compression require much larger applied loads before they reach their yielding condition so these continue to deform purely elastically, as shown by the linear blue line on the right hand side in Fig. 8(b).
The results presented here necessitate re-evaluation of several aspects of martensite structures and their characteristics which can now be rationalised within a coherent narrative.
Firstly, the existence of local residual (Type II) stresses is confirmed and these are shown to contribute significantly to the diffraction peak profiles. The peak shapes cannot be understood solely in terms of scattering by dislocations.
The existence of local stresses is a natural corollary of the local shear deformations that occur during the austenite to martensite transformation that cannot be perfectly compensated within the hierarchical structure. However, additional stresses arise also after the initial transformation during quenching of lower carbon steels when the initially tetragonal crystals decompose into cubic symmetry. Constraint from the surrounding matrix prevents complete contraction of the elongated c-axes so that systematic elastic tensile strains persist. It is these strains that account for the unusual increased broadening of diffraction peaks during low temperature tempering of higher carbon steels.
The tensile stress-strain behaviour of martensite can be well rationalised by the progressive yielding in different volumes depending on their pre-existing states of residual stress. At the same time, the relaxation of those stresses during straining provides a convincing explanation for the unusual phenomenon whereby diffraction peaks actually become narrower as the plastic strain increases.
The authors thank Johan Eliasson who carried out the dilatometer measurements and Johannes Brask who measured the x-ray diffraction on these. They thank also Rachel Pettersson for advice concerning the electrochemistry for selective etching. Laboratory facilities at Deakin University were made available at the Institute for Frontier Materials by Prof. Matthew Barnett. Results shown in Figs. 6 and 8 were obtained using the Powder Diffraction beamline at the Australian Synchrotron, Victoria, Australia.
Surfaces for XRD in reflection geometry were prepared by electropolishing in a solution of 10% perchloric acid in acetic acid with a stainless steel cathode at 15 volts potential. For selective etching of the residual austenite, the specimens were subsequently treated in a solution of 10% hydrochloric acid in ethanol. A simplified potentiostatic method was employed where the cathode was fixed at earth potential and a constant current source was applied between this and the specimen. Selective etching was obtained at current densities of about 0.5–0.6 mA/mm2 and potentials in the range 4 and 5 volts.
The laboratory x-ray diffraction was carried out in Brukers D8 Discover instrument using CuKα radiation (λ=0.15406 nm) with a parallel beam geometry. The instrumental peak broadening measured on corundum powder at similar Bragg angles to those used in the present work was 0.254° degrees FWHM for the 200 reflections and 0.302 degrees for 222. Since the martensite peaks had typically FWHM values of around 1.6 degrees, the influence of the instrumental broadening could be considered as negligible assuming Gaussian distributions.
