Influence of Mn Addition on Fatigue Limit and Coaxing Effect in Ferritic Steel Containing Solute Carbon

Abstract

The influence of Mn addition on fatigue properties of ferritic steel containing solute carbon was examined using rotating bending fatigue tests on water-quenched Fe–0.016C–1.9Mn ferrite–pearlite steel containing 0.0035 mass% solute carbon in comparison with water-quenched Fe–C ferritic steels containing 0.0063–0.017 mass% solute carbon. The fatigue tests were carried out at ambient temperature around 300 K and a frequency of 50 Hz with a stress ratio of −1. The Fe–C–Mn steel exhibited a comparable hardness and fatigue limit to the water-quenched Fe–0.017C steel which contains about three times the amount of solute carbon than the Fe–C–Mn steel. In addition, the Fe–C–Mn steel exhibited a significant coaxing effect in comparison to the Fe–C steels, when the test was started from a stress amplitude just below the fatigue limit. Crack initiation sites were changed by stress amplitude unlike in the Fe–C steels. Specifically, intergranular cracks were observed at the high stress amplitudes and transgranular cracks were observed at the low stress amplitudes near the fatigue limit. It was concluded that the Mn addition suppresses intergranular cracking at the low stress amplitudes.

1. Introduction

Metal fatigue is a major cause of failure accidents of steel structural components. Therefore, fatigue limit, which is the minimum stress amplitude for occurrence of fatigue failure, is treated as one of critical-strength values for safety design of the components. The fatigue limit in many steels including carbon steels is the stress amplitude below which cracks cannot propagate rather than that below which they cannot initiate. At stress amplitudes just below the fatigue limit, fatigue cracks stop to propagate after their initiation, resulting in non-propagating cracks. In other words, the fatigue limit in steels corresponds to the upper limit of crack non-propagation.^1,2,3,4) Dynamic strain aging is closely related to non-propagating cracks in steels. Dislocation pinning by carbon atoms increases hardness of the plastic zones at crack tips, which contributes to occurrence of fatigue crack non-propagation.^5,6,7) From a viewpoint of crack non-propagation, we focused on an Fe–0.017C (mass%) steel with supersaturated carbon atoms in the ferrite, which was prepared by solution treatment and subsequent quenching. The fatigue limit⁸⁾ and the crack non-propagation limit^9,10) of the steel are higher than those of conventional carbon steels because of significant hardening by strain aging due to supersaturated carbon atoms. On the other hand, carbon atoms near grain boundaries diffuse to and segregate at the grain boundaries during the quenching process after solution treatment.¹¹⁾ As a result, low-carbon regions are formed near the grain boundaries.^8,10) In these regions, effects of solution hardening and strain aging due to carbon atoms are marginal compared to the grain interiors, and hence fatigue cracks tend to form near grain boundaries. When intergranular cracks occur frequently, the main crack becomes long easily by their coalescence and can no longer be stopped. Therefore, consideration not only of crack non-propagation but also of crack initiation is important to understand the fatigue limit of Fe–C ferritic steels with supersaturated solute carbon.

In this study, we focus on effect of Mn addition in the Fe–C steels, because Mn is one of the major elements in steels and Mn atoms have an attractive interaction with carbon. Mn addition can reduce the diffusion coefficient of carbon atoms in ferrite through their attractive interaction on the assumption that the saddle point energy does not change in the potential energy curve of carbon atom(s).¹²⁾ In other words, Mn addition suppresses formation of low-carbon regions near grain boundaries due to low carbon-diffusivity, and hence crack initiation along grain boundaries is expected to be suppressed. On the other hand, it has been reported that reduction of carbon diffusivity by Mn addition delays hardening by strain aging in ultra-low carbon steels.¹³⁾ Thus, from the viewpoint of carbon-diffusivity, Mn addition has both positive and negative effects on fatigue properties, i.e., it may suppress formation of low-carbon regions and delay hardening by strain aging.

In relation to strain aging, it has been reported in ferritic steels that Mn–C couples form due to attractive interaction of Mn atoms with carbon.^14,15,16,17) It has been also discussed that Mn addition increases the hardening effect by strain aging per carbon atom in austenitic steels. For example, in Fe–high Mn–C austenitic steels,^18,19,20) it has been reported that formation of Mn–C couples increases strain age effect, resulting in appearance of non-propagating cracks and an increase in fatigue limit.^21,22) It is thus possible that the effect of strain aging per carbon atom is enhanced by Mn addition also in ferritic steels. In this study, fatigue tests were conducted on smooth specimens of a quenched Fe–C–Mn ferritic steel. Through comparison with the results previously obtained in the Fe–C steels,^8,9,10) the effects of Mn addition on the high cycle fatigue properties of ferritic steels were investigated.

In this study, we also focused on coaxing effect, a phenomenon known to be related to hardening by dynamic strain aging and existence of clear fatigue limit in steels. It has been found in the coaxing effect that a process of fatigue deformation at a stress amplitude just below the fatigue limit and following gradual increment in stress amplitude increases the critical stress amplitude for fatigue failure.^23,24) The marked coaxing effect appears in materials where work hardening²⁵⁾ and strain aging^26,27,28) are prominent. It has been reported that both of crack initiation and propagation behaviors are closely associated to the coaxing effect.^27,28) In this study, the effects of the Mn addition on the coaxing effect were also examined.

2. Experimental Procedure

2.1. Material

In this study, an Fe–0.016C–1.9Mn steel (mass%) was used (hereinafter referred to as the Fe–C–Mn steel). The chemical composition is shown in Table 1. Figure 2 shows the heat treatment process of the steel. A 50 kg ingot of Fe–C–Mn steel was cast with a vacuum induction melting furnace and hot-rolled at 1100°C. The hot-rolled bar was homogenized in an Ar atmosphere at 1200°C for two hours. The bar was then hot-rolled again at 1100°C and air cooled. The hot-rolled material was cut into round bars of 9 mm in diameter, held in a salt bath at 640°C for 30 minutes, and then quenched in iced water. The final heat-treatment condition was determined from the equilibrium phase diagram of the Fe–C–1.9Mn system shown in Fig. 1, which was calculated based on the para-equilibrium condition considering only carbon diffusion. Namely, 640°C is a temperature in the ferrite and cementite two phase region and was selected to maximize the solute carbon content in the ferrite as high as possible. The heat-treated bars were kept at −85°C after quenching to suppress carbon diffusion, except for sample preparation and mechanical testing at room temperature. As shown in Fig. 3, the microstructure after the heat treatment consisted of ferrite and cementite. Specifically, pearlite (Fig. 3(b)) and cementite located at ferrite grain boundaries (Fig. 3(c)) were observed. The volume fraction of cementite was 0.20% (calculated value according to the phase diagram), and the area fraction of pearlite microstructure consisting of cementite and ferrite was 0.90% (measured value) on the rolling direction (RD) surface, both of which were small amounts. The cementite, which is a hard phase, at grain boundaries prevents fatigue crack growth,²⁹⁾ and the pearlite also shows the same effect.³⁰⁾ The crack-growth inhibition effect depends on the probability that the crack tip faces the cementite and pearlite. When the volume fractions of cementite and pearlite are small, the probability is extremely small. In fact, the crack-growth prevention by cementite or pearlite was not observed in the present study. Therefore, the effects of cementite and pearlite are not considered in this paper. The average ferrite-grain size of the specimens was 38 μm, calculated by the area measurement method. The ferrite-grain size of the Fe–0.017C steel, which will be compared in the discussion, was 65 μm.^3,4) The Vickers hardness of the steel after heat treatment was 123. The Vickers hardness test was performed under a load of 4.907 N, where each indent covered several ferrite grains. The hardness values were measured twelve times, and the average value was calculated with ten values excluding the largest and smallest values.

Table 1. Chemical composition of the material used in this study (mass%).

C	Si	Mn	P	S	Al	Cr	O	N	Fe
0.016	0.03	1.87	<0.002	0.001	0.013	0.01	0.004	0.0027	Bal.

Fig. 1.

Calculated phase diagram of Fe–C–1.9 mass% Mn system. (a) wide-field view and (b) enlarged view. The phase diagram was obtained using the para-equilibrium condition by Pandat ^TM, PanFe-2013. (Online version in color.)

Fig. 2.

Heat treatment diagram for the specimen. Ar G.C.: Ar gas cooling and I.W.Q.: iced water quenching. The tensile and fatigue specimens were machined after the second hot rolling.

Fig. 3.

Secondary electron (SE) images of specimen captured on rolling-direction (RD) plane after I.W.Q. from 640°C. (a) low magnification, (b) high magnification of the pearlite region, and (c) high magnification of the cementite particles formed along a ferrite boundary.

2.2. Tensile Test

Tensile tests were performed at strain rates of 10⁻³ and 10⁻⁵ s⁻¹ at room temperature (approximately 20°C). The shape of the tensile specimens is shown in Fig. 4(a). The gauge section is 3.5 mm wide, 30 mm long, and 2 mm thick. The tensile direction was parallel to the hot rolling direction of the plate. The specimens were cut by spark erosion machining and mechanically ground with a #1000 abrasive paper to leave only parallel scratches in the tensile direction.

Fig. 4.

Specimen geometries and dimensions for (a) the tensile test and (b) the rotating bending fatigue test (mm).

2.3. Fatigue Test

Rotating bending fatigue tests were conducted in a small Ono-type rotating fatigue machine at a frequency of 50 Hz and a stress ratio of −1 at room temperature. The specimens were machined to the shape shown in Fig. 4(b) using a lathe, then polished to a mirror finish and etched with a 3% nital solution.

In this study, the fatigue limit was defined as the maximum stress amplitude at which the specimen did not fracture at least until 10⁷ cycles. The coaxing effect was evaluated by increasing the stress amplitude by 5 MPa every 10⁷ cycles. The crack propagation behavior was observed using a plastic replica method. An acetyl cellulose film used was immersed in methyl acetate before the replication. The film was directly attached to the specimen surface to transfer the surface relief. The replicas were observed by optical microscopy.

After the fatigue tests, fracture surfaces were observed by scanning electron microscopy (SEM). The accelerating voltage for secondary electron imaging was 15 kV and the working distance was 10 to 25 mm. The electron channeling contrast imaging (ECCI) was performed at an acceleration voltage of 30 kV with a working distance of 3–4 mm. Electron back scattering diffraction (EBSD) was performed with an acceleration voltage of 20 kV, a working distance of 15 mm, and a beam step size of 0.2 μm.

3. Results

3.1. Tensile Test

Figure 5 shows the nominal stress–nominal strain curve and the work hardening rate–true strain curve for the Fe–C–Mn steel. The stress–strain curve of the Fe–0.017C steel at a strain rate of 2.5×10⁻⁵ s⁻¹ is also shown here as a reference data.¹⁰⁾ For the clarify, enlarged curves in the nominal strain range of 2–20% are also shown in the inset.

Fig. 5.

(a) Nominal stress-strain curves and (b) true stress-strain curves and strain hardening rate curves tested at strain rates of 10⁻³ and 10⁻⁵ s⁻¹. The serrations which are the manifestation of dynamic strain aging were observed at 10⁻⁵ s⁻¹. For comparison, the nominal stress-strain curve¹⁰⁾ of Fe–0.017C steel at a strain rate of 2.5×10⁻⁵ s⁻¹ is redrawn as dotted line for the strain range of 2–20%. (Online version in color.)

In general, as the strain rate is increased, the flow stress increases because of decrease in probability of dislocations passing through short-range obstacles with a thermal activation process. However, in the Fe–C–Mn steel, the flow stress in the late stage of deformation decreases with increasing strain rate. This is a typical behavior when dynamic strain aging occurs.^18,31) In other words, as the strain rate decreases, carbon atoms tend to accumulate into dislocations and the pinning effect of dislocations increases. As a result, the work hardening rate increases, leading to an increase in flow stress. In addition, serrations are seen on the stress-strain curve at 10⁻⁵ s⁻¹. In the case of room temperature deformation of carbon steels, these serrations are evidence of occurrence of dynamic strain aging.^31,32) The two facts indicate that dynamic strain aging occurs in the Fe–C–Mn steel at room temperature. It is also noteworthy in Fig. 5(a) that the tensile strength of Fe–C–Mn steel and Fe–0.017C steel are similar, but the work hardening rate of Fe–C–Mn steel is lower than that of Fe–0.017C steel.

3.2. Fatigue Test

3.2.1. S–N Diagram

Figure 6 shows the stress amplitude–number of cycles (S–N) diagram of the Fe–C–Mn steel along with the result of the Fe–0.017C steel where all the carbon atoms are dissolved in ferrite.^3,4) The fatigue limit of the Fe–C–Mn steel is 220 MPa, which is comparable to that of the Fe–0.017C steel (210 MPa).

Fig. 6.

S–N diagram (triangles) with the result of the coaxing effect (the stepwise line) of the Fe–0.016C–1.9Mn steel. The cross indicates fracture. The S–N diagram of the Fe–0.017C steel^3,4) is also shown for comparison (diamonds).

Figure 7 shows the fatigue limits of the Fe–C–Mn steel and three quenched Fe–C ferritic steels,^27,28) as a function of Vickers hardness. Vickers hardness represents a static strength like tensile strength that includes solution strengthening by carbon and Mn atoms as well as second-phase particle strengthening by cementite. The fatigue limit of the Fe–C–Mn steel is the same as that of the Fe–C steel when compared at a constant Vickers hardness. Since the tensile-strength values of the Fe–C–Mn steel and the Fe–0.017C steel are comparable (Fig. 5(a)), the fatigue limits of the two steels are also comparable when arranged in terms of tensile strength. The carbon solubility limit at 640°C of the Fe–C–Mn steel is 0.0035 mass% (Fig. 1), which is significantly lower than that of the Fe–0.017C steel in which all the carbon atoms are in solid solution. However, the Vickers hardness, tensile strength, and fatigue limit of these two steels were similar, which is one of the important results of this study. (The exact amount of solute carbon in the Fe–C–Mn steel needs to be experimentally determined in the future using internal friction method³³⁾).

Fig. 7.

The relationship between fatigue limit and Vickers hardness. The Fe–0.016C–1.9Mn steel exhibits a comparable fatigue limit to Fe–C steel^10,27,28) for the same value of Vickers hardness.

To evaluate the coaxing effect, a fatigue test was conducted with the initial stress amplitude was 210 MPa, which was 10 MPa lower than the fatigue limit and at which a non-propagating crack was observed, as will be shown in Fig. 9 later. Note that the initial stress amplitude of the coaxing effect test, 210 MPa, is the same as that used in the Fe–0.017C steel. No failure occurred even when the stress amplitude was increased to 245 MPa, which is more than 10% above the initial stress amplitude (210 MPa). In the quenched ferritic Fe–C steels^27,28) with super-saturated solute carbon, the specimens fractured after the stress amplitude increased by 15 MPa from the fatigue limit (150 MPa) in the Fe-0.0063C steel and by 45 MPa from the fatigue limit (210 MPa) in the Fe–0.017C steel. Compared with these results of the Fe–C steels, the Fe–C–Mn steel showed a marked coaxing effect, even though the estimated value of solute carbon content was as low as 0.0035 mass%.

Fig. 9.

Replica images of the specimen tested for the coaxing effect. The initial stress amplitude was 210 MPa. (a) before the test, and (b) upon crack formation observed at 4.0×10⁶ cycles. After 10⁷ cycles, the stress amplitude was increased by 5 MPa every 10⁷ cycles. The fatigue crack did not propagate from (b) 4.0×10⁶ cycles at 210 MPa to (d) 1.0×10⁷ cycles at 210 MPa. The crack propagated slightly from (d) to (e) 5.0×10⁷ cycles at 230 MPa, but it did not propagate during the following stress amplitude increases, as shown from (e) to (f) 8.5×10⁷ cycles at 250 MPa. (Online version in color.)

In addition to the coaxing effect test with the same initial stress-amplitude as the Fe-0.017C steel, another coaxing effect test of the Fe–C–Mn steel was conducted with the initial stress-amplitude of 220 MPa (the fatigue limit), matching the initial stress-amplitude conditions of conventional carbon steels.^34,35) In this case, after 1.0 × 10⁷ cycles at 220 MPa, the specimen fractured during testing at 225 MPa and at 1.7 × 10⁷ cycles in total. In other words, no significant coaxing effect was observed in this case. In this test, it was confirmed that a fatigue crack already initiated in a grain at 1.0 × 10⁷ cycles. However, because the specimen fractured soon after that, it was not possible to observe the growth behavior of the crack in detail. Therefore, detailed discussion for the additional test is difficult at present.

3.2.2. Fatigue Crack Initiation and Propagation Behavior

As shown in Fig. 8, fatigue cracks were observed to initiate along grain boundaries at a stress amplitude of 230 MPa which was 10 MPa higher than the fatigue limit (220 MPa). On the other hand, several fatigue cracks were observed within grain interiors at 210 MPa just below the fatigue limit, as showing one of the examples in Fig. 9. The crack observed in a grain interior at 4.0×10⁶ cycles did not grow in the subsequent fatigue cycles until 10⁷ cycles (Figs. 9(b)–9(d)). The non-propagating cracks observed at 210 MPa did not grow even after the stress amplitude was increased to 250 MPa in the coaxing effect test (Figs. 9(d)–9(f)). The crack initiation sites within grain interiors observed just below the fatigue limit in the Fe–C–Mn steel were different from those of the Fe–C steels: the fatigue cracks were initiated along grain boundaries in the Fe-0.0063C and Fe–0.017C steels.^27,28)

Fig. 8.

Replica images of the specimen tested at a high stress amplitude of 230 MPa showing two different cracks. (a) and (d) before the test, (b) and (e) at N_t = 1.0×10⁶ cycles, and (c) and (f) at N_t = 2.0×10⁶ cycles. (Online version in color.)

Figure 10 shows the initiation and propagation behavior of the crack that became the main cause for fracture in the coaxing effect test with the initial stress amplitude of 210 MPa. The fatigue crack appeared within a grain interior at 245 MPa just before the fracture step of 250 MPa. This crack was not observed at 7.0 × 10⁷ cycles (Fig. 10(b); 240 MPa) but was first observed as a crack of about 100 μm in length at 7.5 × 10⁷ cycles (Fig. 10(c); 245 MPa). The crack propagated at 8.0 × 10⁷ cycles (Fig. 10(d); 245 MPa), and when the stress amplitude was increased to 250 MPa, the crack propagated through the grain interiors without surface relief and with bright contrast (Fig. 10(e)), leading to the final fracture.

Fig. 10.

Replica images showing the propagation of a new crack formed in the later stage of the coaxing effect test. The new crack was first recognized in (c) 7.5×10⁷ cycles at 245 MPa, and further propagated with increasing stress amplitude, as shown in (d) and (e). The crack is attributed to the final failure. Note that three additional, similar cracks were observed in the later stage. (Online version in color.)

Three types of termination of the coaxing effect tests have been reported for carbon steels from the viewpoint of crack initiation and propagation. The first is the case of annealed carbon steel (ferrite–pearlite steel),³⁵⁾ where one of few non-propagating cracks formed at the fatigue limit stops and propagates repeatedly as the stress amplitude increases, leading to fracture. The second type is observed in the Fe–0.0063C steel,^27,28) where many intergranular cracks formed at the fatigue limit coalesce and cause an increase in crack length, leading to fracture. The third type is the Fe–0.017C steel.^27,28) In this steel, the cracks formed at the fatigue limit stop to propagate once and never propagate again even when the stress amplitude is increased to the final stage of the coaxing effect test. In addition, no new crack forms in the early stages of the test. Instead, a new crack appears just before the fracture, and propagates for the final fracture. In comparison with the previous findings described above, the termination type of the coaxing effect test in the present Fe–C–Mn steel is similar to the Fe–0.017C steel (the third type), indicating a significant suppression effect on crack growth in the Fe–C–Mn steel.

3.2.3. Fractography

The fracture surface after the coaxing effect test with the initial stress amplitude of 210 MPa is shown in Fig. 11. The crack propagation direction is from top to bottom as shown by the arrow in Fig. 11(a). The fracture surface is rather flat and there is no evidence of coalescence of multiple cracks after initiation and propagation, suggesting that a single crack continued to propagate to fracture. Striations were observed near the center of the fracture surface (Fig. 11(b)), indicating the crack propagation by the blunting and resharpening mechanism.³⁶⁾ As shown in Fig. 11(c), the specimen was finally fractured in a ductile manner with dimples.

Fig. 11.

SE images of the fracture surface after the coaxing effect test was commenced at a stress amplitude of 210 MPa. The specimen was fractured at 8.6×10⁷ cycles at 250 MPa. (a) low magnification view of the fracture surface, (b) high magnification in the central area of the fracture surface showing striations and (c) high magnification in the lower area of the fracture surface showing dimples. The white arrow indicates the propagating direction of the dominant crack at failure. (Online version in color.)

3.2.4. Deformation Microstructure

Figure 12 shows a Kernel Average Misorientation (KAM) map of the specimen surface near the fracture surface for the specimen of the coaxing effect test with the initial stress amplitude of 220 MPa (the fatigue limit) and failed at 225 MPa and at 1.7 × 10⁷ cycles in total. This specimen was selected for observation from the following two reasons. (1) The observation of the deformation structure of the Fe–0.017C steel for comparison was performed on the specimen at the fatigue limit.⁸⁾ Therefore, it is desirable to observe the deformation microstructure of the Fe–C–Mn steel after the fatigue test at the fatigue limit. (2) The other specimen of Fe–C–Mn steel that was subjected to the coaxing effect test with the initial stress amplitude of 210 MPa, had the stress amplitude increased to 250 MPa by 40 MPa afterwards. Its deformation history is complicated so that the specimen is not suitable for the present purpose.

Fig. 12.

Kernel average misorientation (KAM) map coupled with grain boundary maps near the fracture surface after the coaxing test was commenced at a stress amplitude of 220 MPa. The specimen was fractured at 1.7×10⁷ cycles at 225 MPa. The fracture surface is located just beneath of Fig. 12(a). (a) is an overall view. (b) and (c) are high magnifications of the regions indicated in (a). (b) is 115 μm from the fracture surface and (c) is 330 μm from the fracture surface. (Online version in color.)

Figure 12 was taken after removing from outermost surface by 80 μm at the crack initiation region, which was identified by detail surface observation using SEM. The crack initiation region corresponds to the top portion of the fracture surface shown in Fig. 11. The fatigue fracture surface is located downward just beneath of Fig. 12(a). Figures 12(b) and 12(c) are high magnifications of the regions indicated in (a): (b) is 115 μm and (c) is 330 μm away from the fracture surface. The data with confidence-index values of less than 0.3 are excluded and shown in black in the images. The KAM values correspond to the geometrically necessary (GN) dislocation density and thus to the local plastic strain given by dislocation motion.³⁷⁾ As a general trend in Fig. 12, the KAM values are uniform within each grain. However, high KAM values are observed in some regions near the grain boundaries, which correspond to pearlite microstructure, because dislocations tend to accumulate at hard cementite.

Figure 13 shows the ECC images of the regions shown in Figs. 12(b) and 12(c). Figures 13(a) and 13(b) show a set of the dislocation structures of the grain center regions, while Figs. 13(c) and 13(d) a set of the regions near grain boundaries. As can be seen from the comparison, the dislocation structure is similar, irrespective of the regions. Note that the Fe–0.017C steel showed different dislocation microstructures between the regions within grain interiors and near grain boundaries.⁸⁾ It is thus concluded that there was no peculiarity of deformation near grain boundaries in the Fe–C–Mn steel unlike in the Fe–0.017C steel.

Fig. 13.

Electron channeling contrast images showing the dislocation structures. The observation regions are indicated in Fig. 12. (a) and (c) are images for the grain center; (b) and (d) are images near grain boundaries. A significant difference in dislocation structure was not observed. (Online version in color.)

4. Discussion

4.1. Effect of Mn Addition on Coaxing Effect

The Fe–C–Mn steel in this study showed a significant coaxing effect when the initial stress amplitude was 210 MPa, even though the solute carbon content was low (0.0035 mass%). The distinct coaxing effects have been observed in alloys where significant work hardening²⁵⁾ and strain age hardening^26,27,28) are exhibited. The Fe–0.017C steel showed a work hardening rate higher than that of the Fe–C–Mn steel, even though the strain rate was higher (Fig. 5(a)). Thus, the significant coaxing effect of the Fe–C–Mn steel like the Fe–0.017C steel cannot be explained solely in terms of work hardening. As shown in Section 3.2.2, the fracture in the coaxing effect test was caused by propagation of a new crack initiated just before the fracture. This fracture behavior is similar to that in the Fe–0.017C steel. In the case of Fe–C steels,^27,28) as judged from the termination types described in 3.2.2, the marked coaxing effect is related not only to non-propagating cracks but also to crack initiation frequency. Therefore, the marked coaxing effect of the Fe–C–Mn steel (Fig. 6) is discussed by focusing on the crack initiation frequency.

In the Fe–C–Mn steel, the main cause of fracture was the crack that newly initiated just before fracture, as shown in Fig. 10. In addition, the cracks formed at the fatigue limit were not observed to grow and coalesce during the subsequent steps of the coaxing effect test. This fact indicates that suppression of crack initiation during stepwise-increasing of stress amplitude is related to the significant coaxing effect of the Fe–C–Mn steel. Furthermore, in the Fe–0.0063C steel with a marginal coaxing effect, the crack initiation sites at the fatigue limit were near grain boundaries, while they were grain interiors in the Fe–C–Mn steel. Therefore, the difference in the crack initiation sites may be associated with the reasons for the suppression of crack initiation. In the next section, the effect of Mn addition on the difference in the crack initiation sites is discussed.

4.2. Effect of Mn Addition on Intergranular Crack Initiation

As described in the previous section, the crack initiation sites at low stress amplitudes near the fatigue limit were different between the Fe–C–Mn steel and the Fe–C steels. In the case of Fe–C steels, low-carbon regions formed near grain boundaries act as crack initiation sites. In the Fe–C steel, the specimens were quenched from 700°C, at which they were in the single ferritic region. During the quenching process, carbon atoms near grain boundaries tend to diffuse and segregate to the grain boundaries to reduce the free energy.¹¹⁾ This carbon diffusion and segregation will be discussed using an Fe–C steel as an example. When a thermal equilibrium condition is assumed, the carbon concentration at a grain boundary (equilibrium segregation concentration) is low at high temperatures and high at low temperatures due to contribution of the entropy term of atom configuration in the free energy. Thus, carbon diffusion from ferrite grain interiors to grain boundaries occurs during quenching from 700°C. If carbon diffusion occurs significantly, the carbon concentration in the ferrite grains near the grain boundaries becomes lower than that in the ferrite grain interiors. As a result, the near-grain boundary region acts as the weakest region where cracks are preferentially formed. In fact, TEM observations of the Fe–0.017C steel after fatigue tests conducted at the fatigue limit confirmed that the near-grain boundary region (with a width of about 2 μm from the grain boundary) has a dislocation structure significantly different from that in the grain interiors.⁸⁾

On the other hand, the Fe–C–Mn steel showed a uniform dislocation structure within the ferrite grains, and there was no peculiarity of deformation near the grain boundaries (Fig. 13). This fact indicates that the vicinity of the grain boundaries no longer functions as the weakest region in the Fe–C–Mn steel. Following two reasons for the Mn addition effect can be considered: (1) the thickness of low-carbon regions becomes small, and (2) the strength ratio between near-grain boundary regions and grain interiors is not significantly low.

First, we evaluate the thickness of low-carbon regions formed by carbon diffusion during quenching and the Mn addition effect on it. The diffusion coefficient of carbon, D₁, can be expressed by Eq. (1).   

$${\mathrm{D}}_1={\mathrm{D}}_0\mathrm{\hspace{0.17em} }\mathrm{e}\mathrm{x}\mathrm{p}\left(–{\mathrm{Q}}_{\mathrm{m}}/\mathrm{R}\mathrm{T}\right)$$(1)

where D₀ is the pre-exponential factor, Q_m is the activation energy of carbon diffusion in ferrite, R is the gas constant, and T is the absolute temperature. When Mn atoms are added, the diffusion coefficient of carbon atoms, D₂, can be expressed by Eq. (2).¹²⁾ Note that Mn atoms have an attractive interaction with carbon, and we assume in Eq. (2) that the saddle point energy does not change in the potential energy curve of carbon atom(s).¹²⁾   

$${\mathrm{D}}_2={\mathrm{D}}_1/\left(1-2{\mathrm{C}}_{\mathrm{S}}+2{\mathrm{C}}_{\mathrm{S}}\mathrm{\hspace{0.17em} }\mathrm{e}\mathrm{x}\mathrm{p}\left({\mathrm{Q}}_{\mathrm{b}}/\mathrm{R}\mathrm{T}\right)\right)$$(2)

where C_S is the concentration of the alloying element (Mn) and Q_b is the Mn–C binding energy. To evaluate the carbon diffusion in ferrite during quenching, we set that the pre-exponential factor is 3.94×10⁻⁷ m²/s³⁸⁾ and the activation energy of carbon diffusion in ferrite is 80.22 kJ/mol.³⁸⁾ Among several reports on the Mn–C binding energy,^12,39,40,41) we used the energy of 0.1 eV (9.65 kJ/mol),⁴¹⁾ because the examined steel contains the similar Mn content to that of the present Fe–C–Mn steel. Since the sample temperature during quenching cannot be clearly specified, we calculated the diffusion coefficients from 0°C (273 K: sample temperature) to 640°C (913 K: quenching start temperature) and obtained D₁ = 1.76×10⁻²² to 1.01×10⁻¹¹ m²/s and D₂ = 4.86×10⁻²³ to 9.23×10⁻¹² m²/s, respectively. The calculated diffusion coefficients were used to estimate the carbon distribution near a grain boundary using the error-function solution, Eq. (3), of the diffusion equation.   

$$\mathrm{C}\left(\mathrm{x},\mathrm{t}\right)={\mathrm{C}}_0\mathrm{\hspace{0.17em} }\mathrm{e}\mathrm{r}\mathrm{f}\left(\mathrm{x}/2\sqrt{\mathrm{D}\mathrm{t}}\right)$$(3)

where x is the distance from the grain boundary, t is the diffusion time at a given temperature, C₀ is the initial concentration of solute carbon, and D is the diffusion coefficient at a given temperature. In calculation, we assumed the following conditions: (1) the carbon concentration within a ferrite grain is uniform before quenching, and (2) the carbon concentration in the ferrite matrix contacted with the grain boundary becomes zero soon after quenching. Figure 14 shows the distribution of carbon concentration for two Fe–C steels and the Fe–C–Mn steel. In Figs. 14(a) and 14(b), the diffusion time was set to 5 s for convenience to simulate the heat treatment (quenching process). In Figs. 14(c) and 14(d), the diffusion time was set to 8.0×10⁴ s, which corresponds to a time for 4.0×10⁶ cycles, the number of cycles for which fatigue crack initiation was observed at 210 MPa in the Fe–C–Mn steel. In Fig. 14, we focus on the distance where the carbon concentration becomes almost the same as the initial concentration of solute carbon after increasing from zero in the ferrite matrix contacted with the grain boundary. At each temperature and diffusion time, this specific distance is slightly shorter in the Fe–C–Mn steel because the diffusion coefficient of carbon atoms is smaller, but the difference is not significant when we consider for deformation. Therefore, we should exclude the factor (1) the thickness of the low-carbon regions as the main factor for the difference in crack initiation sites at the fatigue limit.

Fig. 14.

Comparisons of solute carbon concentration distribution among Fe–C–Mn ternary steel and Fe–C binary steels for four calculation conditions. (a) T = 400°C and t = 5 s, (b) T = 200°C and t = 5 s, (c) T = 40°C and t = 8.0×10⁴ s and (d) T = 25°C and t = 8.0×10⁴ s. Note that T is the holding temperature and t is the time for diffusion at T.

Next, we examine the factor (2) the strength ratio between near-grain boundary regions and grain interiors. To evaluate the strength, the Vickers hardness values of Fe–0.0063C steel and Fe–0.017C steel were obtained from literature.¹⁰⁾ The width of low-carbon regions near grain boundaries is about 2 μm, and its volume is negligibly small compared to the total. Therefore, the effect of the Vickers hardness of the low-carbon regions on the average value must be small, and hence the average Vickers hardness can be used for the hardness of grain interiors. For the hardness of near-grain boundary regions of the two Fe–C steels, the average hardness of the IF steel is used instead, because it is assumed that there are almost no solute carbon atoms in the near-grain boundary regions. For the hardness of grain interiors of the Fe–C–Mn steel, we used the Vickers hardness measured under a load of 98.07 mN such that each indent does not extend over a single grain. For the hardness in the near-grain boundary region of the Fe–C–Mn steel, we measured the Vickers hardness within a grain in the specimen after furnace-cooling from 640°C, where the solute carbon content can be ignored. Table 2 shows the Vickers hardness of the Fe–C steels and the Fe–C–Mn steel. The ratio of the hardness near grain boundaries to the hardness in grain interiors for the Fe–C–Mn steel is 0.86, which is larger than the values of 0.73 and 0.49 for the Fe–C steels. The amount of solute carbon in the Fe–C–Mn steel is 0.0035 mass%, which is lower than that in the Fe–C steels, and hence it is reasonable that the strength difference between near-grain boundary regions and grain interiors is small. As a result, the deformation is not localized near the grain boundaries as shown in Fig. 12, and intergranular crack initiation was suppressed in the Fe–C–Mn steel.

Table 2. Vickers hardness of Fe–C steels¹⁰⁾ and the Fe–C–Mn steel. *H_V1 of the Fe–C–Mn steel was measured within ferrite grains in the specimen that had been furnace-cooled from 640°C to decrease solute carbon atoms. The load 98.07 mN was used.

	Hardness near grain boundaries, Hv1	Hardness in grain interiors, Hv2	Hv1/Hv2
Fe-0.0063C	≒6110)	≒83.610)	0.73
Fe-0.017C	≒6110)	≒125.710)	0.49
Fe–C–Mn	100.3*	117.2	0.86

4.3. Effect of Mn Addition on Hardening by Strain Aging

The fatigue limit of the Fe–C–Mn steel was comparable to that of the Fe–0.017C steel (Fig. 6), even though the amount of solute carbon was much lower. The fatigue limit was the same as that of the Fe–C steels when it was compared by the Vickers hardness (Fig. 7). Note that the Vickers hardness of the Fe–C–Mn steel includes the strengthening effects of solute Mn atoms and cementite particles. This suggests that the hardening effect by strain aging per carbon atom is enhanced by Mn addition. The enhancement of the strain aging effect by Mn addition is also suggested by the feature of crack propagation behavior observed in the coaxing effect tests. In the Fe–0.017C steel, the non-propagating cracks that had formed before 10⁷ cycles did not restart to propagate even when the stress amplitude was increased, indicating a strong contribution of strain aging to crack growth resistance. A similar tendency of the non-propagating cracks was observed in the Fe–C–Mn steel (Fig. 9). This fact suggests a significant contribution of strain aging to suppress intragranular crack growth in the Fe–C–Mn steel like the case of the Fe–0.017C steel. However, the results obtained in the present study with the smooth specimens are not sufficient for detailed discussion of the effect of Mn addition on hardening by strain aging and resulting resistance to crack propagation. For clarifying the Mn addition effect, it is necessary to exclude crack initiation problems and to investigate the crack propagation resistance in detail. We now plan to measure the crack propagation resistance in a notched specimen where a sharp notch is introduced into a grain interior by focused ion beam (FIB) machining and its crack propagation path is limited to grain interiors.

5. Conclusions

Fatigue properties were investigated in the Fe–0.016C–1.9Mn steel (mass%) obtained by iced water quenching from 640°C, a ferrite and cementite two phase condition. The effects of Mn addition on the fatigue properties of ferritic steels were examined by comparing the results with those of the previously reported Fe–C steels. The main results are as follows.

(1) The Fe–C–Mn steel with an estimated solute-carbon content of 0.0035 mass% has a Vickers hardness of 123 and a fatigue limit of 220 MPa, which is comparable to 210 MPa in the Fe–0.017C steel with a large amount of solute-carbon content of 0.017 mass%.

(2) The fatigue crack initiation and propagation behavior of the Fe–C–Mn steel differed between the high stress amplitudes and the low stress amplitudes near the fatigue limit. Specifically, intergranular cracks were observed at the high stress amplitudes, and intragranular cracks were observed at the stress amplitudes near the fatigue limit. On the other hand, intergranular cracks were observed in the Fe–C steels even at the fatigue limit, indicating that the Mn addition suppresses intergranular crack initiation.

(3) The Fe–C–Mn steel showed a significant coaxing effect when it was started from the stress amplitude of 210 MPa, which was lower than the fatigue limit by 10 MPa. The final fracture in the coaxing effect test was caused by the intragranular crack that newly initiated just before fracture at 250 MPa. The marked coaxing effect in the Fe–C–Mn steel is associated with high resistance to both crack initiation and propagation.

(4) The suppression of intergranular crack initiation observed at the fatigue limit in the Fe–C–Mn steel was discussed in terms of carbon diffusion and strength distribution. In Fe–C–Mn steel, low-carbon regions are formed near grain boundaries, as in the case of Fe–C steels. However, in the Fe–C–Mn steel, the strength difference between the low-carbon regions and the grain interiors is small, so that the low-carbon regions near grain boundaries do not act as crack initiation sites.

Acknowledgements

This work was supported financially by JSPS KAKENHI (JP16H06365; JP17H04956).

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