Microstructure
The volume fractions of phases measured by metallography method are demonstrated in Fig. 4. As shown in this figure, the austenite volume fraction is ~16.5 % in the CHT sample, which is more than those in all DCT samples. With an increasing holding time of the deep cryogenic treatment, the austenite volume fraction remains unaltered while considering the error percentage. This confirmed that the transformation of austenite to martensite is naturally not time dependent. According to Fig. 5, the (200) and (311) peaks of the retained austenite in the CHT sample can be observed, but this phase completely transformed to martensite and its percentage fell down the detection limit of the XRD techniques (<1 %). This evidence validated the data in Fig. 4 that shows variation of retained austenite volume fraction. Changes in carbide volume fractions of the studied microstructures are also shown in Fig. 4. It is clear from this figure that with the increasing holding time of the deep cryogenic treatment up to 48 h in the DCT steels, the carbide volume fraction increases and carbide particles are getting finer and more spherical (Fig. 3). This can be related to the precipitates thought to result from the migration of carbon atoms towards the dislocations during long holding at low temperatures. The carbon clouds around the dislocations serve as nuclei for the η-carbide, which is consistent with the previous studies by Oila et al. (2014) who observed precipitates of η-carbide in the vicinity of dislocations in the DCT martensite of a low-alloy medium-carbon steel. The carbide nuclei can grow during the subsequent tempering. The thermodynamical driving force for the time-dependent migration of carbon atoms from supersaturated martensite towards the dislocations is originated from the transformation stresses and thermal contraction during the deep cryogenic process. The thermal contraction is due to the cooling down to liquid nitrogen temperature. The stresses of martensitic transformation originated from the difference between volumes of crystal lattices of the origin austenite and produced martensite. This evidence injects internal stresses to the DCT steels. This thermodynamical driving force will decrease gradually (relaxation of internal stresses), with increasing the holding time up to 48 h, which shows a plateau in 48 h. By holding the DCT steels for more than the 48 h at the liquid nitrogen, no more η-carbide is nucleated, because there is not enough driving force to move the carbon atoms by the mechanism of stress-assisted diffusion (Tyshchenko et al. 2010).
It is pretended that carbides in the CHT steel are cementite while those in the DCT steels are η-carbide. This pretention can be proved as follows. (i) As can be seen from Fig. 3, carbides morphology of DCT48 microstructure is consisting of uniform distribution of small spherical particles, on the contrary of carbides that belong to the CHT microstructure. In other words, the carbides of the CHT microstructure are large blocky islands with non-uniform distribution. This observation proved that carbide types are different in the DCT steels from the CHT steel. (ii) The microhardness values of carbides for the investigated steels are shown in Fig. 6, which indicates that the CHT steel has carbides with microhardness values of ~900 HV. While for the DCT steels, the microhardness values of carbides increased to ~2020 HV and remained unaltered for the different holding times of the deep cryogenic treatment. Higher order of microhardness values for the DCT steels compared to that of the CHT steel can be seen to imply change in the type of carbides. According to microhardness measurements on carbide phase and what is mentioned by Oila et al. (2014), the carbides of DCT microstructure could be η-type with a higher order of microhardness magnitude while the carbides of CHT microstructure could be cementite. (iii) The microhardness results in Fig. 6 also indicate that the CHT steel has a greater microhardness value of martensite in comparison to those of the DCT steels. According to many studies (Chi et al. 2010; Jaswin and Lal 2011; Oila et al. 2014), microhardness of martensite is directionally proportional to its carbon content; thus, lower microhardness of martensite in DCT microstructures could be attributed to its lower carbon content. The decrement in carbon content of DCT martensite corroborates the idea of formation of η-carbides which absorbed more carbon atoms of martensitic matrix during the deep cryogenic process. (iv) TEM diffraction pattern of carbides of DCT48 steel is also given in Fig. 7c. It confirms that carbides are η-type (Me2C) in the DCT48 microstructure.
The typical TEM microstructures of the CHT and DCT48 steels are shown in Fig. 7. Before preparing TEM foils, the samples were not plastically deformed and just cryo-treated; thus, martensite as well as austenite phase have low density of dislocations. The dislocation density in the martensite phase adjacent to the η-carbide particles is low (Fig. 7b). Fig. 7a shows cementite particles which are located in the martensitic matrix. It is observed from this micrograph that the martensitic areas adjacent to the cementite involve high density of dislocations, unlike the martensite which is located close to the particles of η-carbides. Furthermore, the size of cementite (~320 nm) in CHT steel becomes much larger in comparison to η-carbides (~210 nm) in DCT48 microstructure.
Strain hardening behavior
Figure 8 shows the true stress–true strain curves on a double natural logarithmic scale, which were plotted for CHT and DCT steels with different holding times. As observed in Fig. 8, variation of ln σ with ln ε for the CHT steel is non-linear and obeys the two-stage strain hardening mechanism. The presence of different deformation micromechanisms makes distinct stages of strain hardening in the CHT steel. Lian et al. (1991), who said that hard phases deform elastically at the first stage and then deform partly elastically and partly plastically, proposed a model for multi-phase steels with hard and tough phases. It seems that the model of Lian et al. is applicable to the CHT steel since both hard and soft phases exist together. According to the model of Lian et al. on CHT steel with microstructure consisting of martensite and austenite, the first stage can be related to the plastic deformation of austenite, and the second stage can be related to the co-deformation of both austenite and martensite. Martensite is naturally stronger than austenite (Fig. 6), so its plastic deformation begins during the second stage of strain hardening. At the second stage of strain hardening of CHT steel, martensite flow depends on its location. If it is located adjacent to austenite phase, when austenite strength reaches the yield strength of martensite due to strain hardening, martensite yields as a result of load transfer phenomenon in austenite–martensite interface (Zare and Ekrami 2011).
According to Fig. 8, the DCT steels show typical linear behavior of strain hardening. Linear variation of ln σ with ln ε indicates that the investigated DCT steels, with low volume fractions of retained austenite (<1 %), obey the one-stage strain hardening mechanism. At this stage, martensite deforms plastically and η-carbide particles could not deform because of their complex crystalline structure (orthorhombic). It should be mentioned that volume fractions of austenite are low enough (<1 %) (Figs. 4 and 5); this evidence has no significant effect on the plastic deformation of the DCT steels (Sakaki et al. 1990).
The variation of strain hardening exponent
As can also be seen from Fig. 8 for the CHT sample, the first stage has a high strain hardening exponent (n
1) (~0.54) and the second stage (n
2) has a low one (~0.21). The n
1 is a criterion for strain hardening of austenite, while n
2 is related to the co-strain hardening of austenite and martensite. According to more ductile nature of austenite in comparison with that of martensite, it is expected that the first stage has a greater strain hardening exponent compared to that of the second stage.
A comparison of strain hardening exponent of the CHT and DCT steels is shown in Fig. 9. Whereas martensite deforms plastically at the second stage of strain hardening of the CHT sample, it is able to compare n
2 with the strain hardening exponent of the DCT steels. This is because the deformation micromechanism is strain hardening of martensite in both the CHT (at the second stage) and DCT steels. According to Fig. 9, n
2 for CHT steel is lower than strain hardening exponents of all DCT steels. This is due to the higher carbon content of the CHT steel compared to those of the DCT samples. The higher the carbon content of martensite, the lower its strain hardening ability (n) (Krauss 2005). In the DCT steels, carbon atoms of martensitic matrix are absorbed by the formation of η-carbides and the low-carbon DCT martensite has a higher strain hardening ability compared to the high-carbon CHT martensite.
Change in strain hardening exponent with holding time of the deep cryogenic treatment is also shown in Fig. 9. The peaks/plateaus trend (~0.47) is observed in the variation of this parameter as a function of holding time at the deep cryogenic temperature. The variation of strain hardening exponent can be interpreted as well as explained for changes of UTS/YS and UTS-YS in the “Result and discussion” section to the “The variations of UTS/YS and UTS-YS” section.
The variation of strength coefficient
The change in the strength coefficient (as defined in Eq. 1) for the studied steels is illustrated in Fig. 10. According to this figure, the strength coefficient of the second stage of the CHT steel (~5900 MPa) is higher than those of the DCT steels. This evidence shows that the strength level for martensite plastic deformation of the CHT steel is higher than the strength level of the DCT steels. Results of microhardness on martensitic matrixes of the CHT and DCT steels (Fig. 6) confirm the higher strength level of the martensite within the CHT steels. The reason that the K
2 of the CHT steel is compared to the K values of the DCT steels is that in the strain hardening stage 2 of the CHT steel, yielding of the martensite has activated micromechanism as well as the DCT steels.
It can also be seen in Fig. 10 that the strength coefficient of strain hardening stage 2 for the CHT steel is higher than that of stage 1. This shows that at the second stage, a phase with a higher level of yield strength (martensite) is strain hardening in comparison to austenite phase which is deforming at the first stage of strain hardening. It should be mentioned that K
1 of the CHT steel is only affected by the flow behavior of austenite while K
2 is affected by two parameters which are as follows: (i) austenite deformation can be ongoing at strain hardening stage 2, which leads to decrement in K
2 of CHT steel; and (ii) besides, as well as listed in Fig. 6, the existence of high-strength martensite in CHT steel and its deformation at the second stage of strain hardening, it compensates the decrement of the K
2 as a result of austenite plastic flow. Thus, this evidence is leading to a greater strength coefficient of stage 2 when compared to that of stage 1.
As can be observed in Fig. 10, with the increasing holding time of the cryogenic process up to 48 h, strength coefficient decreases and shows a plateau (~5100 MPa). During deep cryogenic process, η-carbides precipitate with the mechanism of stress-assisted diffusion, so carbon content of martensite decreases and as a consequence its strength decreases (Totten and Howes 1997). So, with the increasing holding time up to 48 h, more η-carbide nucleus forms and more carbon atoms are absorbed from martensitic matrix, and this evidence leads to decrement in strength coefficient. In holding times more than the optimum (72 h), the driving force for subzero diffusion (transformation and thermal stresses) decreases, and this leads to the invariable state of strength coefficient (Amini et al. 2012).
The variations of UTS/YS and UTS-YS
The variation of strain hardening exponent (Fig. 9) is also confirmed by the data in Fig. 11, which shows peaks/plateaus in changes of UTS/YS and UTS-YS with the holding time of cryogenic treatment. The larger UTS/YS ratio and UTS-YS of the DCT steels compared to those of the CHT steel mean the greater capability of energy absorption before failure. In addition, larger deformations are experienced in which could serve as visible warning to structural occupants prior to final collapse. This evidence is highly important in airplane components.
Increasing trend of the UTS/YS and UTS-YS with the holding time of the deep cryogenic treatment up to 48 h is also shown in Fig. 11. The peaks/plateaus trend of these parameters has been identified as one of the manifestation of η-carbide formation. With increasing holding time up to the peak value (48 h), more carbon atoms diffuse to form η-carbides. So with the formation of η-carbides in martensitic matrix, carbon content of martensite decreases and its stretch formability increases, which means enhancement in UTS/YS and UTS-YS as well as the strain hardening exponent (n) (Totten and Howes 1997). Also, with an increasing holding time more than 48 h, the UTS/YS and UTS-YS remained unaltered. It revealed that after 48 h, the internal stresses decrease to diffuse carbon atoms and unaltered trend in the UTS/YS and UTS-YS parameters (Amini et al. 2012).