III. RESULTS AND DISCUSSION

Typical annealing microstructures that evolved in HNSS during annealing treatment at a temperature of 1050 °C are shown in Fig. 1. Figures 1(a) and 1(b) shows the recrystallization distribution of Type-A and Type-B samples after annealing, respectively. The disappearance of the deformed grains in both the samples indicates the full recrystallization. The completion of the recrystallization means that the 2-min annealing time is sufficient. With the further increase of the annealing time, the grains in Fig. 1(d) are significantly larger than those in Fig. 1(c). Figure 1 also shows the equiaxed, random orientation, and heavily twinned microstructure. The microstructure evolutions of Type-A and Type-B samples after isothermal treatment for 1 h at 100–900 °C are shown in Fig. 2. Apparently, compared with Fig. 1, finer grains of the two samples are obtained during isothermal treatment.

FIG. 1.

EBSD maps about recrystallization distribution of HNSS wire after annealing treatment at 1050 °C for (a) 2 min and (b) 60 min. The grains are color coded as follows: recrystallization grains = green; substructured grains = yellow; deformed grains = red. EBSD maps with all Euler angles of HNSS wire after annealing treatment at 1050 °C for (c) 2 min and (d) 60 min.

FIG. 2.

EBSD maps with all Euler angles of HNSS wire after isothermal treatment for 1 h under different temperatures: (a) Type-A, 200 °C; (b) Type-A, 900 °C; (c) Type-B, 200 °C; (d) Type-B, 900 °C.

The effect of isothermal temperatures on mean grain size and microhardness of Type-A and Type-B samples is depicted in Figs. 3(a) and 3(b), respectively. With the isothermal temperature increase, the grain size of Type-A and Type-B samples first decreases and reaches a minimum at 200 °C, and then the grains begin to coarse. However, the grain coarsening is inhibited when isothermal temperature reaches a certain value (Type-A = 300 °C and Type-B = 500 °C). Grain refining is commonly known to increase the strength and hardness of polycrystalline materials.^{Reference Schino and Kenny26} The microhardness of Type-A samples is significantly higher than those of Type-B. With the increase of isothermal temperatures, the microhardness increases to an intermediate maximum at 200 °C. The microhardness of Type-A and Type-B samples reaches to the valley at the temperature of 300 °C and 500 °C, respectively. Further increase of isothermal temperature, the microhardness of Type-A and Type-B samples begins to increase again gradually. This might be related to the changes in grain size and the number of precipitates during the isothermal treatment process.

FIG. 3.

Effects of isothermal temperatures on mean grain size (a) and microhardness (b) of HNSS wire after annealing treatment at 1050 °C.

It can be seen from Fig. 3, the microhardness, mean grain size with temperature trends showed a significant inverse relationship. As is commonly known, the H–P equation can express the relation of strength and hardness dependence on grain size. The variation of microhardness with mean grain size is linearly regressed, as shown in Fig. 4. Two linear fittings were obtained by analyzing the data of microhardness and grain size, namely: the linear fitting of Type-A samples (black line), which can be described by H = 135.9 + 9.0D ^−0.5; the linear fitting of Type-B samples (red line), which can be described by H = 122.1 + 8.1D ^−0.5. It can be seen that the actual points of Type-A and Type-B samples are distributed in the form of trace deviations near the linear fittings. The parameters of H ₀ and k for this alloy are different from the results obtained by Hong et al.^{Reference Hong, Shi, Sheng, Cao, Hui and Dong24} with H ₀ of 247.93 and k of 6.50, as their composition is different. However, the slope k, which is a material-dependent constant, of the two linear fittings is different even if they are the same steel.

FIG. 4.

Relations between grain size and microhardness of HNSS wire after annealing treatment at 1050 °C.

There are some models, which have been proposed to account for the grain size dependence of hardness, assuming that the GB primarily hinders the motion of lattice dislocation and acts as an obstacle for their slip.^{Reference Malyar, Micha, Dehm and Kirchlechner27} In one type of models, GB acts as obstacle to pile up dislocations, causing stress concentration and activation of the dislocation source in adjacent grains, thereby initiating slip from grain to grain.^{Reference Li, Wei, Lu, Lu and Gao28,Reference Kacher, Eftink, Cui and Robertson29} In the other type of models, the GB is regarded as dislocation barriers that limit the mean free path of dislocations, thus increasing strain hardening and resulting in the H–P relation.^{Reference Lu, Lu and Suresh30} The dislocations cannot simply transmit through a GB, as the Burger’s vector of one grain is generally not a lattice vector in the adjacent grain.^{Reference Malyar, Micha, Dehm and Kirchlechner31}

However, due to the low stacking fault energy,^{Reference Gavriljuk, Petrov and Shanina32,Reference Yonezawa, Suzuki, Ooki and Hashimoto33} a large number of annealing twins exist in the HNSS. The interfaces of annealing twins can also play a similar role as GBs. TBs can be a weak/strong barrier for the dislocation transmission which depends on the type of incoming dislocation.^{Reference Polcarová, Gemperlová, Jacques, Brádler and George34–Reference Jin, Gumbsch, Albe, Ma, Lu, Gleiter and Hahn36} Therefore, the TB should also be included in calculating the H–P type relation, which is an important reason for the difference of the slope k of the two linear fittings in Fig. 4. The EBSD map of relative spatial distribution of random and special GBs is shown in Fig. 5(a). It is obvious that a large number of CSL boundaries exist in HNSS. Annealing twins are a subset of Σ3 interfaces. The TEM map of the morphologies of coherent twin boundaries (CTBs) and incoherent twin boundaries (ITBs) are shown in Fig. 5(b). Traditionally, the “coherent twin”, a 〈111〉 symmetrical tilt boundary, and the “incoherent twin”, a 〈112〉 symmetrical tilt boundary, were recognized although it should be realized that the Σ3 classification also encompasses a range of asymmetrical tilts, twists, and irrational boundary planes. A high proportion of Σ3 is present in the crystal and Σ9 appears at the intersection of two Σ3, as shown by the black arrows in Fig. 5(a). The interactions are governed by the following rule concerning the joining or dissociation of CSL:

(3a)$$\Sigma A + \Sigma B \mathbin{\lower.3ex\hbox{$\buildrel\textstyle\leftarrow\over{\smash{\rightarrow}\vphantom{_{\vbox to.5ex{\vss}}}}$}} \Sigma \left( {A \times B} \right)\quad ,$$

or

(3b)$$\Sigma A + \Sigma B \mathbin{\lower.3ex\hbox{$\buildrel\textstyle\leftarrow\over{\smash{\rightarrow}\vphantom{_{\vbox to.5ex{\vss}}}}$}} \Sigma \left( {{A / B}} \right)\quad .$$

FIG. 5.

EBSD map shows the relative spatial distribution of random and special GBs of Type-A, 300 °C (a). The lines are color coded as follows: random boundaries = black; Σ3 = red; Σ5 = green; Σ7 = purple; Σ9 = lime green; Σ27 = blue. TEM map shows the morphologies of coherent twin boundaries and incoherent twin boundaries (b).

[Eq. (3b) applies only if A/B is an integer and A > B.] Hence the meeting of two Σ3 leads to a Σ9.^{Reference Randle37} One of the characteristics of Fig. 5 also confirms the theory reported by Watanabe^{Reference Watanabe38} that the frequency of CSL boundaries generally increased with the mean grain size decreased.

Taking into account the presence of TBs, the mean grain size D in Eq. (1) should be changed to an effective grain size “D _eff”, which contains the barrier effects of GBs and TBs. Since the ratio of TBs, F, and the mean grain size D can be measured by EBSD, the effective grain size D _eff can be expressed as

(4)$${D_{{\rm{eff}}}} = {D / {\left( {1 + pF} \right)}}\quad ,$$

where p is a correction factor and is used to correct the difference in the role of the barrier effect in TBs with GBs. If p < 1, it signifies that the twin interface is less effective as barrier than GB, as is likely to be the case.^{Reference Imrich, Kirchlechner, Motz and Dehm39} Then the modified H–P relation, Eq. (1), can be expressed as

(5)$${H_{{\rm{eff}}}} = {H_0} + k{D^{{{ - 1} / 2}}}{\left[ {1 + pF} \right]^{{1 / 2}}}\quad .$$

Equation (5) is similar to the modified H–P relation that reported by Pande et al.^{Reference Pande, Rath and Imam23} In his study, the ratio of TBs, F, was represented as $2{K_{\rm{t}}}\ln \hbox( {{D \over {{D_0}}}} \hbox)$, where K _t is a constant and D ₀ is the grain size at which there were no twins. Since ${K_{\rm{t}}}\ln \hbox( {{D \over {{D_0}}}} \hbox)$ is an approximate value of the number of twins per grain, it is more appropriate to utilize a carefully measured F. The ratio of TBs, F, in this study is listed in Table I.

TABLE I.

The ratio of TBs measured by EBSD in the HNSS after different isothermal temperatures.

Figure 6(a) shows the bright field images and the corresponding selected area electron diffraction (SAED) of the precipitates at TBs in the HNSS. In Fig. 6(a), the diffraction pattern corresponds to the cubic structure of M₂₃C₆, with a lattice parameter of 1.066 nm, which is approximately three times larger than that of the austenite matrix (0.362 nm).^{Reference Weiss and Stickler40} The cube-on-cube orientation relationship between M₂₃C₆ carbides and the matrix is ${\left[ {001} \right]_\gamma }{\rm{//}}{\left[ {001} \right]_{{{\rm{M}}_{23}}{{\rm{C}}_6}}}$ and ${\left( {100} \right)_\gamma }{\rm{//}}{\left( {100} \right)_{{{\rm{M}}_{23}}{{\rm{C}}_6}}}$, which agrees with the report presented by Lewis and Kenji et al.^{Reference Lewis and Hattersley41,Reference Kaneko, Fukunaga, Yamada, Nakada, Kikuchi, Saghi, Barnard and Midgley42} M₂₃C₆ mainly refers to (Cr, Fe)₂₃C₆ and the ratio of Cr and Fe depends upon the degree of Fe substitution in the basic carbide Cr₂₃C₆. The thin lamellar M₂₃C₆ carbides [Fig. 6(a)] precipitate on TBs discontinuously. The size of the discontinuous thin lamellar M₂₃C₆ carbides is about 100 nm. The presence of M₂₃C₆ carbides on TBs confirms previous TEM observations by Sasmal.^{Reference Sasmal43} EBSD investigations were carried out to further characterize the precipitation behavior of M₂₃C₆ carbides on TBs. The Kikuchi patterns highly match the M₂₃C₆ carbides in the EBSD database. In Fig. 6(b), the distributions of TBs and M₂₃C₆ carbides on TBs were shown. According to Fig. 6(a), the carbides size was around 100 nm and in the discontinuous thin lamellar structure. Therefore, the carbides appeared as dots on TBs in EBSD maps. The precipitation behavior of M₂₃C₆ carbides occurs in part of the TBs, and some of the TBs do not show any carbide precipitation.

FIG. 6.

TEM images with the precipitation behavior of M₂₃C₆ carbides on TBs (a). The inset in (a) shows the corresponding SAED pattern. The EBSD map shows the distributions of TBs and precipitates of M₂₃C₆ carbides on TBs (b). The black lines, lime green lines, and red dots represent GB, TB, and M₂₃C₆ carbides, respectively.

The precipitation of M₂₃C₆ carbides on TBs was associated with the gliding of Shockley partial dislocation and the interactions of dislocations and TBs. As discussed by Mahajan,^{Reference Mahajan, Pande, Imam and Rath44} annealing twins form by either growth accidents or by nucleation of stacking faults. TBs can be described by the glide of one (111) plane over another to the position defined by the Shockley partial dislocation, 1/6〈211〉 type. These partial dislocations provided favorable sites for the precipitation of M₂₃C₆ carbides, while the nucleation driving force of M₂₃C₆ carbides varies with the nucleation sites. According to Trillo et al.,^{Reference Trillo and Murr45} the average GB (γ_gb), ITB (γ_IT), and CTB (γ_CT) free energy at 600 °C are estimated to be 1034 mJ/m², 259 mJ/m², and 16 mJ/m² in 304 stainless steels, respectively. The authors know that the GB/TB free energy is strongly depend on the local chemistry and structure and might be subjected to tremendous variations. However, the GB/TB free energy of the HNSS is difficult to be measured for the authors and only the comparative trends are of interest here which can be well represented by 304 stainless steels. The ITB has nominal energies about four times less than GB over a wide temperature range and the CTB possesses an interfacial free energy that is roughly a factor 60 below that of GB. This energy difference has a definite effect on precipitation behavior, namely, a critical nucleation energy value exists between γ_CT and γ_IT. The M₂₃C₆ carbides can be nucleated smoothly on ITB, while an extra energy is required to be nucleated on CTB.

For polycrystalline materials, TBs act as obstacles for dislocation motion, although the influence of TBs varies with the sample size, orientation, and dislocation density.^{Reference Lu, Shen, Chen, Qian and Lu8,Reference Lu, Lu and Suresh30,Reference Imrich, Kirchlechner, Motz and Dehm39,Reference Li, Wang, Misra, Zhang, Huang and Hirth46} An example about dislocation–twin interaction is schematically depicted in Fig. 7. A source (single arm or Frank–Read type) in one grain is activated and then the dislocations appear and pile-up alone TBs. The pile-up can produce high stresses (τ), which is n times that of the global shear stress and n is the number of dislocations in the pile-up.^{Reference Hull and Bacon47} This stress can be served as a driving force for carbide precipitation. Similar to the barrier effect of TBs, the stress value varies with orientation and dislocation density. However, there is a threshold stress for the driving force. That is the reason why M₂₃C₆ carbides only precipitate on part of TBs [Fig. 6(b)]. In addition, there is a critical length (L) corresponding to the threshold stress:

(6)$$L = {{nGb} \over {\pi \tau }}\quad ,$$

where G = shear modulus; b = Burgers vector. A pile-up length of 0.7 μm can be calculated assuming a pile-up of 10 dislocations, according to Imrich et al.^{Reference Imrich, Kirchlechner, Motz and Dehm39} If the size of the precipitates on TBs is much smaller than the critical dimension L, the morphology of the precipitates is discontinuous.

FIG. 7.

Schematic image showing the interaction between dislocations and TBs, resulting in the precipitation of M₂₃C₆ carbides on TBs.

In addition, the presence of a residual specific stress field around TB in the quenched samples is also responsible for the formation of M₂₃C₆ precipitates on TBs.^{Reference Sasmal43} The maximum value of residual stress is

(7)$${\sigma _{\max }} = {{E\alpha \Delta T} \over {1 - \nu }} \cdot {{{S^2}} \over {3a{t_0}}}\quad ,$$

where E = Young’s modulus; α = coefficient of thermal expansion; ΔT = temperature range (T _q − T _room); ν = Poisson’s ratio (=0.3); 2S = thickness of the plate; a = thermal diffusivity in cm²/s; t ₀ = total transient time. For air-cooled samples in this study, t ₀ is very high. Therefore, compared with the effect of interaction between dislocations and TBs, the effect of residual stress plays a supporting role in the driving force for carbide precipitation.

There is a good fit between M₂₃C₆ carbides and matrix atoms. The atomic volume of M₂₃C₆ exceeds that of austenite so stress will be set up by the precipitates at TBs. In general, TBs can be a weak/strong barrier for dislocation transmission or a dislocation sink for absorption.^{Reference Malyar, Micha, Dehm and Kirchlechner27,Reference Malyar, Micha, Dehm and Kirchlechner31} The appearance of M₂₃C₆ precipitates on TBs may in turn affect the interaction between TBs and dislocations, which could eventually have some influence on mechanical properties of HNSS. The TB can be regarded as an array of Shockley partial dislocations and those dislocations may glide out of the boundary under the action of the stresses generated by M₂₃C₆ carbides. However, since the Burgers vectors of the boundary dislocations are zero, the glide of additional partials on adjacent planes will restore rather than relieve the stresses set up by the M₂₃C₆ carbides. Thus the stresses should be relieved by a flow of vacancies to the precipitates’ interface. The strain energy of the precipitates could therefore acts as the driving force for the migration of the TB if this boundary is able (ITB), as it moves into the grain, to collect the vacancies required to relieve the strain and transfer them to the boundary precipitates. As for the immobile CTB, a stress field could be set up due to the irrelievable stress. This stress field may interact with the stress field generated by the pile-up dislocations in front of TBs, thus affecting the barrier effect of TB on dislocation motion.

Taking into account the presence of M₂₃C₆ carbides at TBs, the ratio of the TB F should be modified according to the proportion (M) of M₂₃C₆ carbides at TBs. Thus, the modified ratio of TBs, F _eff is given by

(8)$${F_{{\rm{eff}}}} = F\left( {1 + qM} \right)\quad ,$$

where q is a correction factor. If q > 0, it indicates that the M₂₃C₆ carbides at TBs play a role in strengthening the barrier effect. If q < 0, it indicates that the M₂₃C₆ carbides at TBs play a role in weakening the barrier effect. Substituting F _eff into the modified H–P relation, Eq. (5), a more accurate expression should be

(9)$${H_{{\rm{fin}}}} = {H_0} + k{D^{ - 1{\rm{/}}2}}{\left[ {1 + pF\left( {1 + qM} \right)} \right]^{{1 / 2}}}\quad .$$

Compared with Eq. (1), D is replaced by D _fin, which is given by

(10)$${D_{{\rm{fin}}}} = {D \over {1 + pF\left( {1 + qM} \right)}}\quad ,$$

D _fin depends on mean grain size, twin density, and the precipitates at TBs. According to Eq. (9), the variation of microhardness with D _fin is linearly regressed, as shown in Fig. 8. Two linear fittings were obtained, namely: the linear fitting of Type-A samples (black line), which can be described by H = 148.6 + 6.6D ^−0.5; the linear fitting of Type-B samples (red line), which can be described by H = 127.5 + 6.6D ^−0.5. Obviously, the slope k of the two linear fittings has the same value. In addition, the standard error of the intercept and the slope of the two linear fittings is decreased after the correction. The relevant parameters in Figs. 4 and 8 are shown in Table II.

FIG. 8.

Relations between microhardness and the effective grain size show the effect of TBs and precipitates at TBs in HNSS wire after annealing treatment at 1050 °C.

TABLE II.

The values and standard error of the intercept and slope of the two linear fittings before and after correction.