Introduction
Carbon is an essential element in most ultrahigh strength steels, playing an important role both in strengthening mechanisms and in the transformation kinetics. Ultrahigh strength steels (UHSS) are key structural materials of aircrafts, automotive/rail vehicles, and advanced civil engineering structures (Ref
1,
2). The latest development of ultrahigh strength steels has followed a new concept of microstructure design of multi-phases, meta-stable, and multi-scales (Ref
3). In the last decade, a few novel heat treatment processes have emerged to enhance the strength and toughness properties, including quenching-partitioning (Q-P) (Ref
4,
5), quenching-partitioning-tempering (Q-P-T) (Ref
6), and low-temperature bainitic isothermal treatment (Ref
7-
9). However, it is still a technically challengeable issue to measure the carbon contents of martensitic or bainitic ferrites in most medium-carbon steels.
X-ray diffraction (XRD) analysis has been applied to determine the lattice parameters of martensitic ferrites by measuring the {200} diffraction peak which, when the tetragonal ratio of the martensite is high enough, is well separated as two sub-peaks (200) and (002) (Ref
10,
11). This method, however, is not applicable to most hardened medium-carbon steels. First, the microstructure of hardened medium-carbon steel contains two types of martensite grains, namely the plate and lath martensites, having different carbon contents and thereafter different tetragonal ratios (Ref
12,
13). A successful measurement should include the two martensite types. Second, the resultant {200} diffraction exhibits always as a single peak because of severe peak overlapping. Up to now, XRD method described in Ref
10,
11 is not applied to measure the martensites of medium-carbon steels because of the peak overlapping. Interestingly, a modified XRD analytical method was reported in Ref
14-
16, which was applied to measure the carbon content of martensite in hardened medium-carbon steels. This method separately used the {200} diffraction to measure parameter
a and the {110} diffraction to measure parameter
c of the tetragonal lattice. Here the martensite was obviously treated as a single phase with homogeneous carbon content. Similar to that, dilatometric technique is able to measure the starting temperature of martensite transformation,
M
s, and thereafter to estimate martensite carbon content (Ref
17). The dilatometric method again considers the martensite as a single phase, and fails to differentiate the carbon contents between martensite and retained austenite.
The carbon contents of austenite and martensitic or bainitic ferrites can also be measured by electron energy loss spectroscopy (EELS) (Ref
18,
19) and atomic probe tomography (APT) (Ref
5,
10,
20,
21). The advantages of these latest sophisticated analyses include their extremely high spatial resolution to determine the heterogeneous distributions of carbon at the bainite-austenite and martensite-austenite interfaces. However, such analyses require complicated sample preparation and are only available in a limited number of laboratories worldwide. Moreover, EELS analysis also suffers from carbon contamination in sample surface which makes quantitative analysis of carbon less reliable. In brief, there is no analytical technique available to provide quantitative characterization of co-existing lath and plate martensites of medium-carbon steels.
In this paper, we introduce a new XRD method to determine the tetragonal ratios, and subsequently the different carbon contents, of the lath and plate martensites co-existing in hardened medium-carbon steel. The method was developed and extensively used in the recent research on novel heat treatments of ultrahigh strength steels having ultimate tensile strength 2100 MPa and yielding strength 1750 MPa. The key step of the method is the separation of overlapping diffraction peaks using a self-made numerical process of Gaussian multiple peak-fitting. Then combining the conventional XRD analysis of retained austenite as described before, it has become feasible to quantify the volume fractions and carbon contents of the martensitic ferrites and retained austenite of ultrahigh strength steels.
Sample Material, Characterization, and XRD Experiment
The sample material being employed to demonstrate the method is a hot-rolled steel bar having chemical composition (in wt.%) of C 0.55, Ni 1.69, Cr 1.05, Mo 0.50, Mn 0.76, V 0.084, and Fe in balance. The nominal
M
s point (starting temperature of austenite-to-martensite transformation) of the sample steel is 230 °C. Small rectangular samples of dimensions 20 × 15 × 8 mm were hardened by heating to an austenization temperature 850 °C and holding for 30 min, oil-quenching to room temperature (approximately 23 °C), and tempering at temperatures of 200, 250, and 300 °C for 120 min. The heat-treated samples were characterized by Vickers hardness, scanning electron microscopy (SEM), and transmission electron microscopy (TEM). A high-resolution FEG-SEM instrument, FEI NOVA 200, was employed for the SEM work using pre-polished and 2% nital pre-etched samples. A 200 kV TEM instrument, Philips CM20 STEM, was used to characterize the martensite sub-structures. The TEM samples were first ground to 120-150 μm thick, and then electro-chemically polished in an electrolyte solution of 7% perchloric acid and 93% glacial acetic acid at room temperature and a voltage of 32 V. Some results of the microstructure characterization have been published in Ref
22.
A Philips X’Pert X-ray diffractometer with Cu Kα radiation (λ = 0.154056 nm, powered at 40 kV and 40 mA) was employed to acquire the {200}M and {211}M diffraction peaks of martensite and the {200}γ, {220}γ, and {311}γ peaks of retained austenite, when the instrument was operated at the θ-2θ (Bragg-Brentano) mode. The diffraction peaks were obtained at a small step size of 0.0167° and a long acquisition time of 1000 s per step. The as-acquired diffraction curve was processed by Kα2 stripping and substrate removing.
This paper is focused on the quantification of the lath and plate martensites by proposing a new method to separate the {200}
M diffraction peak. For the retained austenite, its volume fraction (γ%) was calculated using equation γ% =
I
γ/(
I
γ ±
G ·
I
M), where
I
γ and
I
M stand for the integrated intensities of the austenite and martensite diffraction peaks, respectively, and
G is a constant depending on the combination of the austenite and martensite planes. The values of the
G constants were adopted from selected literature (Ref
10,
11).
Discussion
This paper has introduced an XRD method to analyze the martensite structure of hardened medium-carbon steels. The method is based on two principal considerations. First, based on the tetragonal crystalline structure of martensite, it proposes a multiple Gaussian peak-fitting technique to retrieve the overall {200}
M diffraction peak as four individual sub-peaks of the (200) and (002) peaks of lath and plate martensites. Consequently, the tetragonal ratio and relative fraction of the two martensites can be calculated, Fig.
4. Second, this approach has considered both carbon atoms contributing to the tetragoneity, owing to their preferential distribution, and those not contributing to the tetragoneity. Based on that, a modified equation has been proposed to calculate the carbon concentration of martensite from its tetragonal ratio, Eq
5. Thus, combining with the existing XRD method of retained austenite measurement, it is possible to provide quantitative measurement of the volume fraction and carbon concentration of the three structural constituents of hardened medium-carbon steels, namely the lath and plate martensites and retained austenite.
It is believed that the new method would help improve characterization of hardened steels and contribute to the development of new strengthening and toughening heat treatments. The research on martensitic structures have been enormous, which however concerned mostly the morphology and crystallographic characteristics but little on their carbon contents (Ref
13,
23-
25,
31,
32). On the other hand, it is appreciated that comprehensive fundamental research on the carbon partitioning behavior in the martensitic and bainitic transformation of under-cooled austenite gave birth to several novel strengthening processes, including quenching-partitioning (Ref
4,
5), quenching-partitioning-tempering (Ref
6), and superbainitic isothermal treatments (Ref
7-
9). The new XRD method would provide further opportunity to characterize the co-existing lath and plate martensites for their different carbon enrichment, as well as to investigate the structural evolution of hardened steels in subsequent tempering. In fact, it has played an important role in recent research of ultrahigh strength steels, whereas some example analyses have been given in this paper, see section
3.5, as well as in other recent papers (Ref
22,
33). In particular, the newly developed quantitative analysis of co-existing lath and plate martensites provide a complementary tool to the existing analytical techniques, such as field emission SEM and TEM (Fig.
1 and
5), electron back-scattered diffraction (known as EBSD) (Ref
34,
35), APT (Ref
20,
21), and TEM-EELS (Ref
18,
19).
The relationship between the lattice parameters
a and
c of tetragonal martensite and its carbon content was derived from XRD experiment results of quenched high-carbon steels (Ref
23), and has been widely adopted as the basis in the estimation of martensite carbon contents (Ref
10,
11,
14-
16). XRD and Gaussian peak-fitting techniques have been employed in quantitative analysis of high-carbon martensites for many years (Ref
10,
11,
14-
16). This paper differs from those that, for the first time, it extends the quantitative analysis to hardened medium-carbon steels. Meanwhile, the author has adopted the opinion of Liu and co-workers (Ref
15,
16) that in a tetragonal martensite structure there are always some carbon atoms which do not contribute to the lattice tetragoneity through either randomly occupying some octagonal vacancies or agglomerating along dislocations. The linear relations (Eq
2 and
3) could only determine the concentration of carbon which preferentially occupies the [½, ½, 1] vacancies, Fig.
3. Therefore, unlike the approximation proposed in literature (Ref
14-
16), we assume that there is a minimum amount of carbon atoms which exhibits randomly in the tetragonal lattice making no contribution to the tetragonal ratio. The actual carbon content should include both the randomly and preferentially distributed parts of carbon, Eq
5. This assumption is consistent to the experimental and theoretical results of literature (Ref
15,
16,
25).
It should be pointed out that, uncertainty may exist when the carbon content is calculated from the tetragonal ratio of a martensite using Eq
5, where the maximum concentration of randomly distributing carbon has been estimated to be 0.18%. In fact, the distribution of carbon atoms in a ferrite lattice depends strongly on the type and quantity of alloying elements. For example, it is known that, the out shell electrons of different alloying elements have different repulsive or attractive interactions with the out shell electrons of carbon atoms (Ref
36). These interactions determine the chemical bonds between carbon and the different metal elements and consequently influence the carbon distribution. Obviously, it is not the aim of this paper to make further discussion on this issue, whereas there is still lack of theoretical understanding on the occupation statue of carbon in a martensite structure (Ref
23-
25,
31,
32). Nevertheless, by assuming 0.18% of randomly distributed carbon, the estimated carbon contents of the martensites agree well to the actual composition of the sample steel.
The limitation of this method is that it cannot be applied to measure the carbon content of a martensitic ferrite if their carbon content is less than 0.18% and therefore exhibits no measurable tetragoneity. Such low-carbon ferrites do exist, e.g., in some isothermal treated bainitic steels and quenched low-carbon steels (Ref
7,
14,
16,
32).