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Fatigue behavior of plain C–Mn steel plates with fine grained ferrite in surface layers
Materials Science and Engineering A 539 (2012) 154–162
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Materials Science and Engineering A journal homepage: www.elsevier.com/locate/msea
Fatigue behavior of plain C–Mn steel plates with fine grained ferrite in surface layers Jian-wen Fan a,∗ , Rui-ping Xie b , Yong-chun Wang b , Tian-hua Liu b a b
Central Iron & Steel Research Institute, Beijing 100081, PR China Shougang Research Institute of Technology, Beijing 100041, PR China
a r t i c l e
i n f o
Article history: Received 23 September 2011 Received in revised form 18 January 2012 Accepted 18 January 2012 Available online 25 January 2012 Keywords: Plain C–Mn steel plate Ferrite grain refinement Surface layers Fatigue strength
a b s t r a c t The effect of fine-grained surface layers on the fatigue behavior of plain C–Mn steel plates is investigated. The plain C–Mn steel plates have been manufactured by a special thermo-mechanical controlled process (TMCP). For plates rolled by the special TMCP (designated special plates), the ferrite grain size approaches 5.5 m in the surface layers and reaches 6.5 m on average in the whole thickness of the plates, while for usually rolled plates (designated usual plates), the grain size is 15 m on average in the whole thickness of the plates, without obvious difference between surface and central layers. Significant improvements of fatigue properties have been achieved by the ferrite grain refinement. Under the similar stress condition, the fatigue lifetime of the special plate is more than 10 times as long as that of the usual plate, and the first stage of fatigue crack propagation can be prolonged. With a similar lifetime of the usual plate under a load ratio R ( min / max ) approaching zero, the special plate can sustain a load 40 MPa higher than that of the usual plate. Furthermore, fatigue fractographs have been observed and analyzed by a scanning electron microscope (SEM). © 2012 Elsevier B.V. All rights reserved.
1. Introduction Since the end of the twentieth century, a lot of material research items have been focused on ultra-fine grained (UFG) steels. Some of research results in the laboratory have been put into use in metallurgical industry, such as, hot-rolled strips with the partial UFG microstructure manufactured in some steel plants in China [1]. However, owing to some confinements of the hot rolling process, the homogenous UFG microstructure in the whole thickness becomes difficult to form with an increase in product gauges, for example, strips with thickness of more than 4 mm and plates with thickness above 16 mm, and the difference in grain size between the inner and outer layers becomes great. On the other hand, much attention has been paid to the fabrication of UFG steels and the relationship between the grain size and the strength, but seldom to the effect of grain refinement on the fatigue behavior. The fatigue properties are important for structural materials in engineering applications. Plain C–Mn steel products with chemical contents of 0.12–0.18C, 0.10–0.35Si and 1.20–1.50Mn (wt%) are important structural materials in mass production and used economically and widely in the world. It is reported that the fatigue strength of plain C–Mn steel plates can be increased when ultra-fine grained ferrite forms in the
∗ Corresponding author. Tel.: +86 10 62187215; fax: +86 10 62182664. E-mail address: fanjw [email protected] (J.-w. Fan). 0921-5093/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2012.01.073
surface layers [2]. However, specimens for fatigue tests were made of sheets cut from the plates parallel to the rolling surfaces along the thickness direction in that study. The results cannot directly illustrate the fatigue properties of whole plates. In this paper, the plain C–Mn steel plates with grain refinement in the surface layers have been successfully manufactured by a special thermo-mechanical controlled process (TMCP). An attempt is made to provide information about an improvement of fatigue properties in the plain C–Mn steel plates with fine grained ferrite in surface layers. 2. Experimental procedures Plain C–Mn steel plates (Fe, 0.15–0.17C, 0.35–0.38Si, 1.30–1.36Mn, 0.020P, 0.020S, wt%) with 20 mm thickness and fine grained ferrite in surface layers (designated special plates) have been produced by means of a special TMCP using a 3300 mm four roll mill of Shougang Group in China. The continuously casting slabs with size of 220 mm thick, 1400 mm wide and 1700 mm long were reheated at 1200 ◦ C for more than 3 h. Rough rolling passes were performed in the range of 1100–1000 ◦ C from 220 mm down to 90 mm in thickness. Then finish rolling passes were performed in the range of 830–740 ◦ C from 90 mm to 20 mm. An accelerated cooling process followed immediately with the start cooling temperature of about 720 ◦ C and the final cooling temperature of 600 ◦ C. Finally, the hot rolled plates were hot-leveled. For comparison, some plates with the same thickness and similar
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Table 1 Ferrite grain size and mechanical properties of special thermomechanical controlled process (TMCP) plate and usually rolled plates.
Special TMCP plate Usual rolled plate
Surface (m)
Quarter section (m)
Center (m)
Yield strength (MPa)
Tensile strength (MPa)
Elongation (%)
5.53 15
6.19 15
6.84 15
420 365
547 515
30 25
Fig. 1. Scheme for the fatigue test specimens with thickness of 20 mm.
chemical contents (designated usual plates) were also produced by usually rolling process with finish rolling passes in 950–850 ◦ C from 50 mm to 20 mm and final cooling temperature above 650 ◦ C. The microstructures were observed using an optical microscope (MEF3 type, Leica) after the specimens had been polished and etched with 4% Nital. The ferrite grain size was measured according to ASTM standard E112-1996. Tensile tests were carried out at the ambient temperature. The fatigue tests in a constant load range were carried out using full scale thickness specimens of both the special and usual plates with an MTS 810II Material Test System.
The specimen scheme for fatigue tests is shown in Fig. 1. The corners between the machined plane and the primitive hot-rolled plane have been rounded and polished so that the initiation of fatigue cracks from the corners has an influence as little as possible on the test results. After all, the purpose of the test is to study the effect of ferrite grain size in hot rolled surface layers on the fatigue behavior of the whole plates. Specimens were sinusoidally tested under a load ratio R approaching zero ( min ≈ 0), max = 0.45–0.9 b (where min is minimum stress, max is maximum stress and b is tensile stress), at a frequency of 10 Hz with the sine-waves. Fatigue fractographs were observed with a scanning electron microscopy (SEM, Oxford S360) to study fatigue damage mechanism. 3. Results 3.1. Microstructure and mechanical properties Microstructures of the plates are shown in Fig. 2. The ferrite grain sizes of the special TMCP plate and usually rolled plate are
Fig. 2. Comparison of microstructures of special thermomechanical controlled process (TMCP) plate and usual rolled plate with 20 mm thickness. Usual rolled plate: (a) surface layer, (c) quarter section, (e) center; special TMCP plate: (b) surface layer, (d) quarter section, (f) center.
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Table 2 Fatigue properties of special TMCP plate and usual rolled plate. Specimen no.
r = min / max
(MPa)
min (MPa)
max (MPa)
max / b
Cycle number to fracture, Nf
3C02 3F02 3F03
0 0 0
437 437 477
0 0 0
437 437 477
0.8485 0.7989 0.8720
75,313 1,184,030 69,659
Fig. 3. The fatigue test result of the special plate and usual plate. The arrow means that the specimen has not fractured.
given in Table 1. It can be seen that the ferrite grain size of the special plate is obviously finer than that of the usual plate in the whole thickness direction. For the special plate, the ferrite grains in the surface layers are obviously finer than those in both the center and quarter thickness layers. There is no notable difference in microstructure between the surface and the center layers for the usual plate. Finally, pearlite in the special plates is distributed more homogenously and is finer than that in the usual plate. Furthermore, the yield strength of the special plate is 55 MPa higher than that of usual plate, and the tensile strength of the special plate also increases by 30 MPa with little difference in elongation. 3.2. Fatigue strength Fatigue test results are given in Fig. 3. The experiments were conducted using the whole thickness and keeping the original hot rolled surface without machining. The ratio of the minimum and maximum stress, R approaches zero. The S–N curve of the special plate is obviously higher than that of the usual plate. The results show that grain refinement in the surface layers of plain C–Mn steel plates can improve fatigue properties. In Ref. [6], some sheets were cut from the plates with chemical contents of 0.13C–0.20Si–1.27Mn–0.007P–0.002S–0.027Al (wt%) along the thickness direction with which comparison fatigue tests were
carried out. The results of Ref. [6] indicated the effect tendency of ferrite grain refinement in the surface layers on the fatigue strength of the plates. but did not give fatigue property values of the plates in a direct way. Therefore, the present results obtained using whole thickness, as-rolled specimens in this paper are more convincing than those of the study in Ref. [6]. Table 2 shows the fatigue behavior comparison of the special plate with the usual plate. For the same constant stress range, the fatigue cycle number of the special plate with fine ferrite grains in the surface layers is more than that of the usual plate, and that with the same cycle number, the fatigue strength of the special plate is higher than that of the usual plate. For example, for a similar fatigue stress range, i.e. 437 MPa for the special plate (Specimen 3F02) and the usual plate (Specimen 3C02), the cycle number to fracture of the former is 1.184 million, 15 times higher than that of the latter which is 75,313. Also for a similar cycle number, 69,659 for the special plate (Specimen 3F03) and 75,313 for the usual plate (Specimen 3C02), the strength range of the former is 40 MPa higher than that of the latter. In comparison of the results of 3F02 and 3F03, the cycle number decreases drastically with the increase of strength range when the test is carried out in relatively high strength. 3.3. Fatigue fractographs To distinguish the mechanism of fatigue evolution of the special plates from that of the usual plates, the fatigue fracture of the specimens mentioned in Table 2 were observed with a S360 scanning electronic microscope (SEM). The stress range of 3F02 with the fine grained ferrite is similar to that of 3C02 with coarse grained ferrite but the lifetime (cycle number to fracture) is much longer than that of 3C02. And the lifetime of 3F03 with fine grained ferrite is similar to that of 3C02, but the stress range of 3F03 is higher than that of 3C02. Therefore, the three specimens were selected for comparison. All fatigue cracks in the three specimens initiated near the edges between the hot rolled plane and the machined plane. Fig. 4 shows a scheme of the location that were observed with the SEM. Fractographs of these specimens at various distance from the fatigue crack source are shown in Figs. 5–11 respectively.
Fig. 4. Scheme of location where the fractographs are taken. Plane xoz, hot rolled primitive surface; plane yoz, machined surface; direction oz, tension direction.
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Fig. 5. Fatigue SEM fractograph (crack initiation): (a) Specimen 3C02, = 437 MPa, Nf = 75.3 × 103 ; (b) Specimen 3F02, = 437 MPa, Nf = 1.184 × 106 ; (c) Specimen 3F03, = 477 MPa, Nf = 69.6 × 103 .
Fractographs taken near the fatigue crack source (distance < 1 mm) of the three specimens are shown in Fig. 5. The observed field is divided into several striation zones by peaked edges. As shown in Fig. 5a for Specimen 3C02 with coarse grained ferrite, there are zones of clear plastic deformation banding with 15–20 m wide in the fractograph adjacent to the outer surface of the specimen. Near the plastic deformation zone, there are some smooth facets. Then next, there appear the fatigue striations extending zones in which there are micro-cracks with 10–20 m long parallel to the hot-rolled primitive plane. In Fig. 5b, under the same cycling loading condition, the boundary between the fatigue crack zone and the outer primitive plane of Specimen 3F02 of the plate with fine grained ferrite is clearer than that of Specimen 3C02, and no obvious plastic deformation zone appears
and no smooth facet exists. Adjacent to the primitive outer surface, there are the fatigue crack extending zones. The orientation directions of the secondary cracks are random. When the stress range increases, the fractograph near the fatigue source of Specimen 3F03 with fine grained ferrite under high stress loading as shown in Fig. 5c is similar to that of Specimen 3C02 with coarse grained ferrite under low stress loading in Fig. 5a. Combined with the microstructures of the plates, as shown in Fig. 2, the banding pearlite with coarse grained ferrite is severer than that with fine grained ferrite and the micro-cracks parallel to the hot rolled primitive plane of the former are more than those of the latter. It seems that there exists some relationship between the banding pearlite and the micro-cracks. Therefore, the fractograph near the fatigue crack source has something with the grain
Fig. 6. Fatigue SEM fractograph (dis = 200 m): (a) Specimen 3C02, = 437 MPa, Nf = 75.3 × 103 ; (b) Specimen 3F02, = 437 MPa, Nf = 1.184 × 106 ; (c) Specimen 3F03, = 477 MPa, Nf = 69.6 × 103 .
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Fig. 7. Fatigue SEM fractograph (dis = 800 m): (a) Specimen 3C02, = 437 MPa, Nf = 75.3 × 103 ; (b) Specimen 3F02, = 437 MPa, Nf = 1.184 × 106 ; (c) Specimen 3F03, = 477 MPa, Nf = 69.6 × 103 .
size, banding pearlite of the steel plates and the cycling loading conditions. A little further from the fatigue crack initiation, at a distance of 200 m, as shown in Fig. 6. Under the same cycling loading condition, the fractograph of the plate with fine grained ferrite, specimen 3F02 in Fig. 6b consists of more peaked edges than that with coarse grained ferrite, specimen 3C02 in Fig. 6a. And the areas surrounded by the peaked edges in fractograph with fine grained ferrite are smaller than those with coarse grained ferrite. The phenomenon illustrates that in comparison with that in the plate with coarse grained ferrite, the development of fatigue cracks has to overcome more resistance and the extension speed is decelerated effectively in the plate with fine grained ferrite. And a few secondary microcracks appear in both Fig. 6a and b. The peaked edges near the
fatigue crack source in specimen 3F03, which sustained higher cycling stress, seen in Fig. 6c, are smaller and thinner than those in specimen 3F02. And under the same cycling loading condition, fatigue striations in specimen with coarse grained ferrite are clearer than those in specimen with fine grained ferrite, which implies that the refinement of ferrite grains prolongs the first stage of fatigue striation extension. Fig. 6 together with Fig. 5, the fatigue striations are perpendicular to the primitive hot rolled surface. In addition, during the observation period of each specimen, the specimen did not rotate but moved in parallel direction. The fatigue striations did not initiate from the machined surface as shown in Fig. 5, or the edge between the primitive hot rolled surface and the machined surface, but from the primitive surface. Therefore, the design of specimens for the study is reasonable. At a distance of 800 m in
Fig. 8. Fatigue SEM fractograph (dis = 3 mm): (a) Specimen 3C02, = 437 MPa, Nf = 75.3 × 103 ; (b) Specimen 3F02, = 437 MPa, Nf = 1.184 × 106 ; (c) Specimen 3F03, = 477 MPa, Nf = 69.6 × 103 .
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Fig. 9. Fatigue SEM fractograph (dis = 6 mm): (a) Specimen 3C02, = 437 MPa, Nf = 75.3 × 103 ; (b) Specimen 3F02, = 437 MPa, Nf = 1.184 × 106 ; (c) Specimen 3F03, = 477 MPa, Nf = 69.6 × 103 .
Fig. 7, the secondary micro-cracks increase in both Specimen 3C02 and 3F02. At a distance of 3 mm in Fig. 8, the fractographs show fatigue cracks extending steadily. The secondary cracks are parallel to the primitive hot-rolled surface. The fractographs are taken of the area between the surface layer and a quarter section. Considering the fractographs in Fig. 8 with the microstructure of plates in Fig. 2, it seems that the formation of the secondary cracks has something with the banding pearlite. As shown in Fig. 9, all of the three fractographs changes greatly, at a distance of 6 mm which corresponding to the area 4.2 mm far from the primitive hot rolled surface. For the specimen 3C02 with coarse grained ferrite and low cycling stress, the fatigue striation areas become wider than the formers. The ductile dimples appear in the peaked edges. The similar things take place in the specimen
3F02 with fine grained ferrite and low cycling stress, but the width of fatigue striations of Specimen 3F02 is smaller with clearer ductile dimples in peaked edges than those of 3C02. The width of striations in the specimen 3F03 with fine grained ferrite and high cycling stress, is similar to that of 3C02, but the area of ductile dimples of 3F03 is larger than those of 3C02. Even though this, the fractograph is still in the fatigue cleavage fracture period. The appearance of ductile dimples in the depth of 4 mm from the hot rolled surface implies that the development of fatigue cracks enter the end period. Therefore, the total depth of fatigue crack extension in both sides is no more than 40% of the plate thickness. Figs. 10 and 11 show the fractographs at a distance of 9 mm. The peaked edges change into the ductile dimples. The proportion of dimples increases and the proportion of fatigue striations decreases, which illustrates that the fatigue evolutions come into
Fig. 10. Fatigue SEM fractograph (dis = 9 mm): (a) Specimen 3C02, = 437 MPa, Nf = 75.3 × 103 ; (b) Specimen 3F02, = 437 MPa, Nf = 1.184 × 106 ; (c) Specimen 3F03, = 477 MPa, Nf = 69.6 × 103 .
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Fig. 11. Fatigue SEM fractograph (dis = 9 mm): (a) Specimen 3C02, = 437 MPa, Nf = 75.3 × 103 ; (b) Specimen 3F02, = 437 MPa, Nf = 1.184 × 106 ; (c) Specimen 3F03, = 477 MPa, Nf = 69.6 × 103 .
the unstable and instant fracture period. For the whole period of fatigue fracture, the place where the secondary cracks appear in the plain C–Mn steel plates is nearer from the fatigue crack source than the place in the low carbon steel plates, which may have something with the banding pearlite besides much higher cycling stress. 4. Discussion
increase. Therefore, the fatigue behavior may have something with the yield strength. Some empirical formulae have been brought out to evaluate the fatigue properties of materials. The fatigue endurance of structural steels under the symmetric cycling loading (r = −1), to say tensile and compression statue, can be estimated with the equation: −1L = 0.23 ( s + b ) [6]. Using the equation 0L = 1.42 −1L , we get the equation:
4.1. The evaluation of fatigue stress limit
0L = 0.3266 · (s + b )
The fatigue behavior of steel plate is influenced by a lot of factors. In previous research, fatigue limit mainly depends on the tensile strength, b , such as the empiric formula: −1 ≈ 0.5 b [3,4]. The fatigue limit, −1L under the condition of tensile and compress, similarly equals to 0.85 times of the −1 under the condition of rotating and bending of steel [5]. So the following equation can be obtained, −1L ≈ 0.425 b . For the impulsive cycling (R = 0) of structural steel, 0L = 1.42 −1L [6]. Therefore, we can obtain the following equation:
in which, s means yield strength. The fatigue strength amplitude for asymmetric cycling loading under the tensile and compression statue can be estimated with Goodman equation.
0L = 0.6035 · b
(1)
The study of strengthening mechanisms on fatigue properties of ferrite–pearlite hot rolled sheet steel show that the ratio of an increase in fatigue limit to an increase in tensile strength severely depended on strengthening mechanism. The ratio was higher for both solid solution and precipitation strengthening than that for bainite or grain-refinement strengthening, while lower than that for dislocation and pearlite strengthening [7]. For the plain C–Mn steel plates, the solid solution strengthening is caused by the addition of Si, Mn and P while the addition of P is detrimental to the impact toughness, and precipitate strengthening is weak because of the lack of Nb and V addition. Owing to the final rolling temperature a little higher than the Ar3, mediate cooling rate with final cooling temperature in the range of 600–700 ◦ C and also simple chemical contents without the addition of Nb, Mo and so on, the microstructure of the steel plates rolled by special TMCP consists of ferrite and pearlite without bainite appearance so that the effects of both bainite and dislocation density on fatigue behavior can be ignored. Therefore, for the C–Mn steel plate, the effect of ferrite grain size on fatigue behavior is negligible but important. In addition, the grain size also takes an important role in the yield strength
a = −1L 1 −
m b
(2)
In which, a refers to the fatigue stress amplitude and m refers to average stress, b refers to tensile strength and −1L refers to the fatigue limit under the condition of tensile and compress. The fatigue endurance of materials under r >−1, can be evaluated with the equation.
rL = m + a = m + −1L 1 −
m b
In which, rL refers to fatigue strength under r > −1. In this study, the fatigue tests are carried out under the impulsive tension status (r = 0, m = 0.5 0L ). So the following equation can be obtained. 0L =
0.46 · (s + b ) 1 + 0.23 · (s + b )/b
(3)
The ratio of the yield strength versus the tensile strength for most of plain C–Mn steel plates is 0.7–0.9. By simplifying formula (3), formula (4) is obtained in which k is 0.32–0.33. The k value in formula (2) is 0.3266. However, the effect of grain size on fatigue limit is not considered in all the three formulae. 0L = k(s + b )
(4)
A lot of research work has been carried out on the effect of grain size on fatigue behavior. Grain refinement can increase yield strength effectively and tensile strength to some extent. So, grain
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Table 3 The mechanical properties and the evaluated fatigue limit of the C–Mn steel plates. Grain sizea (m)
Yield strength (MPa)
Tensile strength (MPa)
Elongation (%)
The calculated values (r = 0) Eq. (1)
Special TMCP Usual rolled a
6.19 15
420 365
547 515
30 25
330 311
Eq. (2)
Eq. (3)
Eq. (5)
Eq. (7)
316 287
316 291
355 284
300 264
Grain size refers to the value in the quarter thickness section.
refinement can increase the fatigue limit. On the one hand, fatigue limit is inversely related to grain size as shown in mild steels [8]. And an empiric formula was obtained as: −1 = 110 + 11d−1/2 , in which d means grain size in m. Using the equation 0L = 1.42 −1L again, we get the equation: −1L = 1.42 · (110 + 11d−1/2 )
(5)
On the other hand, yield strength is considered in both formulae (2) and (3). In Hall–Petch relationship, k, the factor of grain refinement is in 14–23. Here, another formula is introduced as follows [9]: s = 70 + 84Si + 32Mn + 680P − 30Cr + 38Cu + 33Ni + 11Mo + 5000(C + N) + kd−1/2 + p + D + t
(6)
In the above equation, k is 18.1, p refers to the precipitation strengthening increment, D refers to the dislocation strengthening increment and t refers to the texture strengthening increment. Here, p , D and t are ignored. The yield strength H–P equation can be put into formula (4). And formula (7) can be obtained for the C–Mn steel and micro-alloying steels, in which the effect of grain size on fatigue limit is considered. Here, k1 = k2 = 0.3266 for simplifying. The predicted fatigue limit values with formula (7) are similar to but less than those by formulae (2) and (3). This is attributed to relatively lower yield strength predicted by the H–P relationship than the practical values. 0L = k1 · (70 + 84Si + 32Mn + 680P + ky · d−1/2 ) + k2 · b
(7)
Using Eqs. (1)–(3), (5) and (7), the fatigue limit 0L is calculated and the results are shown in Table 3. The fatigue limit difference of the special TMCP plate and the usual one evaluated with formula (1), is 19 MPa, which is the lest among the difference values with the 5 formulae, because the yield strength is not considered in formula (1). The difference values calculated with formulae (2) and (3) are similar and lie in the mediate position. The fatigue limit difference of the two plates calculated with formula (5), 71 MPa, is the largest, for the effect of grain size in formula (5) may be considered most. The calculated difference with formula (7), 36 MPa, is less than that with formula (5). Owing to the calculated yield strength less than the practical ones, the calculated fatigue limit of both the special TMCP plate and usual plate calculated with formula (7) are the lest respectively. Therefore, owing to the effect of ferrite grain, the fatigue limit may be increased by 25–70 MPa. The tendency of the experimental curves in Fig. 3 may agree with the evaluated values using formulae (2), (3), (5) and (7). Furthermore, Kage and Miller also drew the similar conclusion. In low carbon steel, fatigue resistance, in terms of the relative positions of the S–N curves, increases with decreasing grain size. This phenomenon is related to the number of cycles to propagate a crack to failure and the condition for the non-propagation of a fatigue crack. The size of a non-propagating crack, which initiates below the fatigue limit, tends to become larger as grain size increases [10]. Liu reviews the fatigue behavior experimental observations and synthesizes the diverse observations into an integral and self-consistent analysis in terms of dislocation glide force and the resistance of dislocation barriers [11]. In Liu’s
dislocation barrier model, the strong dislocation barriers in a surface layer are more likely overcome by a dislocation array than those in the interior. Pre-cracking fatigue damage is confined to a surface layer, and a nucleated Stage-I crack is a surface shear crack. The critical grain size dominates the fatigue limit determined by crack non-propagation or non-initiation. For low carbon steel, the value is 76 m [11]. It is obvious that the fatigue limit is controlled by the crack non-propagation for both the special TMCP plate and usual rolled plate. Once a fatigue crack nucleates, the crack growth process of crack-tip shear decohesion may be stopped by a strong dislocation barrier. The nucleated crack becomes dormant. As the grain size becomes smaller, the grain boundary resistance to fatigue crack growth becomes stronger. Therefore, the ferrite grain refinement in the surface layers of the steel plates can hold back or postpone the formation of surface fatigue cracks. The fractographs in Fig. 6a and b agree well with the viewpoint. And the ferrite grain size in the quarter section of the special TMCP plate has been refined so that the resistance to the fatigue crack propagation can also be enhanced effectively. Both of them contribute the improvement of fatigue properties of the special TMCP plates. 4.2. The secondary cracks of fatigue fractograph of C–Mn steel plates The banding pearlite of C–Mn steel is severer than that of plain carbon steel as shown in Ref. [12]. The pearlite is a kind of brittle phase. Therefore, the secondary cracks have something with the banding pearlite. Decreasing the banding pearlite may increase the fatigue properties of steel plates. The formation of fine and ultrafine grained ferrite can lessen the banding pearlite and make them small and scatter homogenously [13]. From this, the grain refinement is also beneficial to improvement of fatigue properties. 5. Conclusion • Grain refinement can improve effectively the fatigue properties of C–Mn steel plates. • Under the same cycling loading condition, the fatigue striations appear in plate with fine grained ferrite later than in plate with coarse grained ferrite. • The area of fatigue striations in plate with fine grained ferrite is less than that with coarse grained ferrite. • The ferrite grain refinement in the surface layers of the steel plates can hold back or postpone the formation of surface fatigue cracks. • The banding pearlite can promote the formation and extension of the secondary cracks. Acknowledgment The Beijing Science and Technology Committee sponsored this study as a Beijing Science and Technology Nova Research Item (Serial no. H013610320111). References [1] Guodong Wang, Proceedings of the Workshop on New Generation Steels (NG STEEL ‘2001), November 13–16, Beijing China, 2001, pp. 299–306.
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[2] Hidesato Mabuchi, ISIJ International 39 (5) (1999) 477–485. [3] R.B. Heywood, Designing Against Fatigue, Chapman & Hall, London, 1962. [4] H.O. Fuchs, Metal Fatigue and Engineering, John Wiley & Sons, New York, 1980. [5] Weizhi Jiang, Shixi Zhao, Mechanical Properties of Engineering Materials, Beijing Aeronautical and Astronomical University Publisher, Beijing, 1991, pp. 180–182. [6] Hao Xu, Design of Fatigue Strength, Machinery Industry Publisher, Beijing, 1981, pp. 39–46. [7] Masato Kurita, ISIJ International 36 (4) (1996) 481–486.
[8] S. Taira, K. Tanaka, M. Hoshina, in: J.T. Fong (Ed.), Fatigue Mechanisms. ASTM STP675, American Society for Testing and Materials, 1979, pp. 135–173. [9] Zexiong, Yao, Micro-alloying HSLA Steels (Translated in Chinese) (Low Carbon Structural Steels for the Eighties, English edition), Metallurgy Industry Publisher, Beijing, 1982, pp. 51–57. [10] M. Kage, K.J. Miller, R.A. Smith, Fatigue Fracture Engineering Structure 15 (8) (1992) 763–774. [11] H.W. Liu, International Journal of Fracture 96 (4) (1999) 331–344. [12] Jianwen Fan, Materials Science and Technology 21 (5) (2005) 583–589. [13] J.-w. Fan, Iron and Steel (China) 39 (8) (2004) 100–104.
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Fatigue behavior of plain C–Mn steel plates with fine grained ferrite in surface layers Jian-wen Fan a,∗ , Rui-ping Xie b , Yong-chun Wang b , Tian-hua Liu b a b
Central Iron & Steel Research Institute, Beijing 100081, PR China Shougang Research Institute of Technology, Beijing 100041, PR China
a r t i c l e
i n f o
Article history: Received 23 September 2011 Received in revised form 18 January 2012 Accepted 18 January 2012 Available online 25 January 2012 Keywords: Plain C–Mn steel plate Ferrite grain refinement Surface layers Fatigue strength
a b s t r a c t The effect of fine-grained surface layers on the fatigue behavior of plain C–Mn steel plates is investigated. The plain C–Mn steel plates have been manufactured by a special thermo-mechanical controlled process (TMCP). For plates rolled by the special TMCP (designated special plates), the ferrite grain size approaches 5.5 m in the surface layers and reaches 6.5 m on average in the whole thickness of the plates, while for usually rolled plates (designated usual plates), the grain size is 15 m on average in the whole thickness of the plates, without obvious difference between surface and central layers. Significant improvements of fatigue properties have been achieved by the ferrite grain refinement. Under the similar stress condition, the fatigue lifetime of the special plate is more than 10 times as long as that of the usual plate, and the first stage of fatigue crack propagation can be prolonged. With a similar lifetime of the usual plate under a load ratio R ( min / max ) approaching zero, the special plate can sustain a load 40 MPa higher than that of the usual plate. Furthermore, fatigue fractographs have been observed and analyzed by a scanning electron microscope (SEM). © 2012 Elsevier B.V. All rights reserved.
1. Introduction Since the end of the twentieth century, a lot of material research items have been focused on ultra-fine grained (UFG) steels. Some of research results in the laboratory have been put into use in metallurgical industry, such as, hot-rolled strips with the partial UFG microstructure manufactured in some steel plants in China [1]. However, owing to some confinements of the hot rolling process, the homogenous UFG microstructure in the whole thickness becomes difficult to form with an increase in product gauges, for example, strips with thickness of more than 4 mm and plates with thickness above 16 mm, and the difference in grain size between the inner and outer layers becomes great. On the other hand, much attention has been paid to the fabrication of UFG steels and the relationship between the grain size and the strength, but seldom to the effect of grain refinement on the fatigue behavior. The fatigue properties are important for structural materials in engineering applications. Plain C–Mn steel products with chemical contents of 0.12–0.18C, 0.10–0.35Si and 1.20–1.50Mn (wt%) are important structural materials in mass production and used economically and widely in the world. It is reported that the fatigue strength of plain C–Mn steel plates can be increased when ultra-fine grained ferrite forms in the
∗ Corresponding author. Tel.: +86 10 62187215; fax: +86 10 62182664. E-mail address: fanjw [email protected] (J.-w. Fan). 0921-5093/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2012.01.073
surface layers [2]. However, specimens for fatigue tests were made of sheets cut from the plates parallel to the rolling surfaces along the thickness direction in that study. The results cannot directly illustrate the fatigue properties of whole plates. In this paper, the plain C–Mn steel plates with grain refinement in the surface layers have been successfully manufactured by a special thermo-mechanical controlled process (TMCP). An attempt is made to provide information about an improvement of fatigue properties in the plain C–Mn steel plates with fine grained ferrite in surface layers. 2. Experimental procedures Plain C–Mn steel plates (Fe, 0.15–0.17C, 0.35–0.38Si, 1.30–1.36Mn, 0.020P, 0.020S, wt%) with 20 mm thickness and fine grained ferrite in surface layers (designated special plates) have been produced by means of a special TMCP using a 3300 mm four roll mill of Shougang Group in China. The continuously casting slabs with size of 220 mm thick, 1400 mm wide and 1700 mm long were reheated at 1200 ◦ C for more than 3 h. Rough rolling passes were performed in the range of 1100–1000 ◦ C from 220 mm down to 90 mm in thickness. Then finish rolling passes were performed in the range of 830–740 ◦ C from 90 mm to 20 mm. An accelerated cooling process followed immediately with the start cooling temperature of about 720 ◦ C and the final cooling temperature of 600 ◦ C. Finally, the hot rolled plates were hot-leveled. For comparison, some plates with the same thickness and similar
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Table 1 Ferrite grain size and mechanical properties of special thermomechanical controlled process (TMCP) plate and usually rolled plates.
Special TMCP plate Usual rolled plate
Surface (m)
Quarter section (m)
Center (m)
Yield strength (MPa)
Tensile strength (MPa)
Elongation (%)
5.53 15
6.19 15
6.84 15
420 365
547 515
30 25
Fig. 1. Scheme for the fatigue test specimens with thickness of 20 mm.
chemical contents (designated usual plates) were also produced by usually rolling process with finish rolling passes in 950–850 ◦ C from 50 mm to 20 mm and final cooling temperature above 650 ◦ C. The microstructures were observed using an optical microscope (MEF3 type, Leica) after the specimens had been polished and etched with 4% Nital. The ferrite grain size was measured according to ASTM standard E112-1996. Tensile tests were carried out at the ambient temperature. The fatigue tests in a constant load range were carried out using full scale thickness specimens of both the special and usual plates with an MTS 810II Material Test System.
The specimen scheme for fatigue tests is shown in Fig. 1. The corners between the machined plane and the primitive hot-rolled plane have been rounded and polished so that the initiation of fatigue cracks from the corners has an influence as little as possible on the test results. After all, the purpose of the test is to study the effect of ferrite grain size in hot rolled surface layers on the fatigue behavior of the whole plates. Specimens were sinusoidally tested under a load ratio R approaching zero ( min ≈ 0), max = 0.45–0.9 b (where min is minimum stress, max is maximum stress and b is tensile stress), at a frequency of 10 Hz with the sine-waves. Fatigue fractographs were observed with a scanning electron microscopy (SEM, Oxford S360) to study fatigue damage mechanism. 3. Results 3.1. Microstructure and mechanical properties Microstructures of the plates are shown in Fig. 2. The ferrite grain sizes of the special TMCP plate and usually rolled plate are
Fig. 2. Comparison of microstructures of special thermomechanical controlled process (TMCP) plate and usual rolled plate with 20 mm thickness. Usual rolled plate: (a) surface layer, (c) quarter section, (e) center; special TMCP plate: (b) surface layer, (d) quarter section, (f) center.
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Table 2 Fatigue properties of special TMCP plate and usual rolled plate. Specimen no.
r = min / max
(MPa)
min (MPa)
max (MPa)
max / b
Cycle number to fracture, Nf
3C02 3F02 3F03
0 0 0
437 437 477
0 0 0
437 437 477
0.8485 0.7989 0.8720
75,313 1,184,030 69,659
Fig. 3. The fatigue test result of the special plate and usual plate. The arrow means that the specimen has not fractured.
given in Table 1. It can be seen that the ferrite grain size of the special plate is obviously finer than that of the usual plate in the whole thickness direction. For the special plate, the ferrite grains in the surface layers are obviously finer than those in both the center and quarter thickness layers. There is no notable difference in microstructure between the surface and the center layers for the usual plate. Finally, pearlite in the special plates is distributed more homogenously and is finer than that in the usual plate. Furthermore, the yield strength of the special plate is 55 MPa higher than that of usual plate, and the tensile strength of the special plate also increases by 30 MPa with little difference in elongation. 3.2. Fatigue strength Fatigue test results are given in Fig. 3. The experiments were conducted using the whole thickness and keeping the original hot rolled surface without machining. The ratio of the minimum and maximum stress, R approaches zero. The S–N curve of the special plate is obviously higher than that of the usual plate. The results show that grain refinement in the surface layers of plain C–Mn steel plates can improve fatigue properties. In Ref. [6], some sheets were cut from the plates with chemical contents of 0.13C–0.20Si–1.27Mn–0.007P–0.002S–0.027Al (wt%) along the thickness direction with which comparison fatigue tests were
carried out. The results of Ref. [6] indicated the effect tendency of ferrite grain refinement in the surface layers on the fatigue strength of the plates. but did not give fatigue property values of the plates in a direct way. Therefore, the present results obtained using whole thickness, as-rolled specimens in this paper are more convincing than those of the study in Ref. [6]. Table 2 shows the fatigue behavior comparison of the special plate with the usual plate. For the same constant stress range, the fatigue cycle number of the special plate with fine ferrite grains in the surface layers is more than that of the usual plate, and that with the same cycle number, the fatigue strength of the special plate is higher than that of the usual plate. For example, for a similar fatigue stress range, i.e. 437 MPa for the special plate (Specimen 3F02) and the usual plate (Specimen 3C02), the cycle number to fracture of the former is 1.184 million, 15 times higher than that of the latter which is 75,313. Also for a similar cycle number, 69,659 for the special plate (Specimen 3F03) and 75,313 for the usual plate (Specimen 3C02), the strength range of the former is 40 MPa higher than that of the latter. In comparison of the results of 3F02 and 3F03, the cycle number decreases drastically with the increase of strength range when the test is carried out in relatively high strength. 3.3. Fatigue fractographs To distinguish the mechanism of fatigue evolution of the special plates from that of the usual plates, the fatigue fracture of the specimens mentioned in Table 2 were observed with a S360 scanning electronic microscope (SEM). The stress range of 3F02 with the fine grained ferrite is similar to that of 3C02 with coarse grained ferrite but the lifetime (cycle number to fracture) is much longer than that of 3C02. And the lifetime of 3F03 with fine grained ferrite is similar to that of 3C02, but the stress range of 3F03 is higher than that of 3C02. Therefore, the three specimens were selected for comparison. All fatigue cracks in the three specimens initiated near the edges between the hot rolled plane and the machined plane. Fig. 4 shows a scheme of the location that were observed with the SEM. Fractographs of these specimens at various distance from the fatigue crack source are shown in Figs. 5–11 respectively.
Fig. 4. Scheme of location where the fractographs are taken. Plane xoz, hot rolled primitive surface; plane yoz, machined surface; direction oz, tension direction.
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Fig. 5. Fatigue SEM fractograph (crack initiation): (a) Specimen 3C02, = 437 MPa, Nf = 75.3 × 103 ; (b) Specimen 3F02, = 437 MPa, Nf = 1.184 × 106 ; (c) Specimen 3F03, = 477 MPa, Nf = 69.6 × 103 .
Fractographs taken near the fatigue crack source (distance < 1 mm) of the three specimens are shown in Fig. 5. The observed field is divided into several striation zones by peaked edges. As shown in Fig. 5a for Specimen 3C02 with coarse grained ferrite, there are zones of clear plastic deformation banding with 15–20 m wide in the fractograph adjacent to the outer surface of the specimen. Near the plastic deformation zone, there are some smooth facets. Then next, there appear the fatigue striations extending zones in which there are micro-cracks with 10–20 m long parallel to the hot-rolled primitive plane. In Fig. 5b, under the same cycling loading condition, the boundary between the fatigue crack zone and the outer primitive plane of Specimen 3F02 of the plate with fine grained ferrite is clearer than that of Specimen 3C02, and no obvious plastic deformation zone appears
and no smooth facet exists. Adjacent to the primitive outer surface, there are the fatigue crack extending zones. The orientation directions of the secondary cracks are random. When the stress range increases, the fractograph near the fatigue source of Specimen 3F03 with fine grained ferrite under high stress loading as shown in Fig. 5c is similar to that of Specimen 3C02 with coarse grained ferrite under low stress loading in Fig. 5a. Combined with the microstructures of the plates, as shown in Fig. 2, the banding pearlite with coarse grained ferrite is severer than that with fine grained ferrite and the micro-cracks parallel to the hot rolled primitive plane of the former are more than those of the latter. It seems that there exists some relationship between the banding pearlite and the micro-cracks. Therefore, the fractograph near the fatigue crack source has something with the grain
Fig. 6. Fatigue SEM fractograph (dis = 200 m): (a) Specimen 3C02, = 437 MPa, Nf = 75.3 × 103 ; (b) Specimen 3F02, = 437 MPa, Nf = 1.184 × 106 ; (c) Specimen 3F03, = 477 MPa, Nf = 69.6 × 103 .
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Fig. 7. Fatigue SEM fractograph (dis = 800 m): (a) Specimen 3C02, = 437 MPa, Nf = 75.3 × 103 ; (b) Specimen 3F02, = 437 MPa, Nf = 1.184 × 106 ; (c) Specimen 3F03, = 477 MPa, Nf = 69.6 × 103 .
size, banding pearlite of the steel plates and the cycling loading conditions. A little further from the fatigue crack initiation, at a distance of 200 m, as shown in Fig. 6. Under the same cycling loading condition, the fractograph of the plate with fine grained ferrite, specimen 3F02 in Fig. 6b consists of more peaked edges than that with coarse grained ferrite, specimen 3C02 in Fig. 6a. And the areas surrounded by the peaked edges in fractograph with fine grained ferrite are smaller than those with coarse grained ferrite. The phenomenon illustrates that in comparison with that in the plate with coarse grained ferrite, the development of fatigue cracks has to overcome more resistance and the extension speed is decelerated effectively in the plate with fine grained ferrite. And a few secondary microcracks appear in both Fig. 6a and b. The peaked edges near the
fatigue crack source in specimen 3F03, which sustained higher cycling stress, seen in Fig. 6c, are smaller and thinner than those in specimen 3F02. And under the same cycling loading condition, fatigue striations in specimen with coarse grained ferrite are clearer than those in specimen with fine grained ferrite, which implies that the refinement of ferrite grains prolongs the first stage of fatigue striation extension. Fig. 6 together with Fig. 5, the fatigue striations are perpendicular to the primitive hot rolled surface. In addition, during the observation period of each specimen, the specimen did not rotate but moved in parallel direction. The fatigue striations did not initiate from the machined surface as shown in Fig. 5, or the edge between the primitive hot rolled surface and the machined surface, but from the primitive surface. Therefore, the design of specimens for the study is reasonable. At a distance of 800 m in
Fig. 8. Fatigue SEM fractograph (dis = 3 mm): (a) Specimen 3C02, = 437 MPa, Nf = 75.3 × 103 ; (b) Specimen 3F02, = 437 MPa, Nf = 1.184 × 106 ; (c) Specimen 3F03, = 477 MPa, Nf = 69.6 × 103 .
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Fig. 9. Fatigue SEM fractograph (dis = 6 mm): (a) Specimen 3C02, = 437 MPa, Nf = 75.3 × 103 ; (b) Specimen 3F02, = 437 MPa, Nf = 1.184 × 106 ; (c) Specimen 3F03, = 477 MPa, Nf = 69.6 × 103 .
Fig. 7, the secondary micro-cracks increase in both Specimen 3C02 and 3F02. At a distance of 3 mm in Fig. 8, the fractographs show fatigue cracks extending steadily. The secondary cracks are parallel to the primitive hot-rolled surface. The fractographs are taken of the area between the surface layer and a quarter section. Considering the fractographs in Fig. 8 with the microstructure of plates in Fig. 2, it seems that the formation of the secondary cracks has something with the banding pearlite. As shown in Fig. 9, all of the three fractographs changes greatly, at a distance of 6 mm which corresponding to the area 4.2 mm far from the primitive hot rolled surface. For the specimen 3C02 with coarse grained ferrite and low cycling stress, the fatigue striation areas become wider than the formers. The ductile dimples appear in the peaked edges. The similar things take place in the specimen
3F02 with fine grained ferrite and low cycling stress, but the width of fatigue striations of Specimen 3F02 is smaller with clearer ductile dimples in peaked edges than those of 3C02. The width of striations in the specimen 3F03 with fine grained ferrite and high cycling stress, is similar to that of 3C02, but the area of ductile dimples of 3F03 is larger than those of 3C02. Even though this, the fractograph is still in the fatigue cleavage fracture period. The appearance of ductile dimples in the depth of 4 mm from the hot rolled surface implies that the development of fatigue cracks enter the end period. Therefore, the total depth of fatigue crack extension in both sides is no more than 40% of the plate thickness. Figs. 10 and 11 show the fractographs at a distance of 9 mm. The peaked edges change into the ductile dimples. The proportion of dimples increases and the proportion of fatigue striations decreases, which illustrates that the fatigue evolutions come into
Fig. 10. Fatigue SEM fractograph (dis = 9 mm): (a) Specimen 3C02, = 437 MPa, Nf = 75.3 × 103 ; (b) Specimen 3F02, = 437 MPa, Nf = 1.184 × 106 ; (c) Specimen 3F03, = 477 MPa, Nf = 69.6 × 103 .
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Fig. 11. Fatigue SEM fractograph (dis = 9 mm): (a) Specimen 3C02, = 437 MPa, Nf = 75.3 × 103 ; (b) Specimen 3F02, = 437 MPa, Nf = 1.184 × 106 ; (c) Specimen 3F03, = 477 MPa, Nf = 69.6 × 103 .
the unstable and instant fracture period. For the whole period of fatigue fracture, the place where the secondary cracks appear in the plain C–Mn steel plates is nearer from the fatigue crack source than the place in the low carbon steel plates, which may have something with the banding pearlite besides much higher cycling stress. 4. Discussion
increase. Therefore, the fatigue behavior may have something with the yield strength. Some empirical formulae have been brought out to evaluate the fatigue properties of materials. The fatigue endurance of structural steels under the symmetric cycling loading (r = −1), to say tensile and compression statue, can be estimated with the equation: −1L = 0.23 ( s + b ) [6]. Using the equation 0L = 1.42 −1L , we get the equation:
4.1. The evaluation of fatigue stress limit
0L = 0.3266 · (s + b )
The fatigue behavior of steel plate is influenced by a lot of factors. In previous research, fatigue limit mainly depends on the tensile strength, b , such as the empiric formula: −1 ≈ 0.5 b [3,4]. The fatigue limit, −1L under the condition of tensile and compress, similarly equals to 0.85 times of the −1 under the condition of rotating and bending of steel [5]. So the following equation can be obtained, −1L ≈ 0.425 b . For the impulsive cycling (R = 0) of structural steel, 0L = 1.42 −1L [6]. Therefore, we can obtain the following equation:
in which, s means yield strength. The fatigue strength amplitude for asymmetric cycling loading under the tensile and compression statue can be estimated with Goodman equation.
0L = 0.6035 · b
(1)
The study of strengthening mechanisms on fatigue properties of ferrite–pearlite hot rolled sheet steel show that the ratio of an increase in fatigue limit to an increase in tensile strength severely depended on strengthening mechanism. The ratio was higher for both solid solution and precipitation strengthening than that for bainite or grain-refinement strengthening, while lower than that for dislocation and pearlite strengthening [7]. For the plain C–Mn steel plates, the solid solution strengthening is caused by the addition of Si, Mn and P while the addition of P is detrimental to the impact toughness, and precipitate strengthening is weak because of the lack of Nb and V addition. Owing to the final rolling temperature a little higher than the Ar3, mediate cooling rate with final cooling temperature in the range of 600–700 ◦ C and also simple chemical contents without the addition of Nb, Mo and so on, the microstructure of the steel plates rolled by special TMCP consists of ferrite and pearlite without bainite appearance so that the effects of both bainite and dislocation density on fatigue behavior can be ignored. Therefore, for the C–Mn steel plate, the effect of ferrite grain size on fatigue behavior is negligible but important. In addition, the grain size also takes an important role in the yield strength
a = −1L 1 −
m b
(2)
In which, a refers to the fatigue stress amplitude and m refers to average stress, b refers to tensile strength and −1L refers to the fatigue limit under the condition of tensile and compress. The fatigue endurance of materials under r >−1, can be evaluated with the equation.
rL = m + a = m + −1L 1 −
m b
In which, rL refers to fatigue strength under r > −1. In this study, the fatigue tests are carried out under the impulsive tension status (r = 0, m = 0.5 0L ). So the following equation can be obtained. 0L =
0.46 · (s + b ) 1 + 0.23 · (s + b )/b
(3)
The ratio of the yield strength versus the tensile strength for most of plain C–Mn steel plates is 0.7–0.9. By simplifying formula (3), formula (4) is obtained in which k is 0.32–0.33. The k value in formula (2) is 0.3266. However, the effect of grain size on fatigue limit is not considered in all the three formulae. 0L = k(s + b )
(4)
A lot of research work has been carried out on the effect of grain size on fatigue behavior. Grain refinement can increase yield strength effectively and tensile strength to some extent. So, grain
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Table 3 The mechanical properties and the evaluated fatigue limit of the C–Mn steel plates. Grain sizea (m)
Yield strength (MPa)
Tensile strength (MPa)
Elongation (%)
The calculated values (r = 0) Eq. (1)
Special TMCP Usual rolled a
6.19 15
420 365
547 515
30 25
330 311
Eq. (2)
Eq. (3)
Eq. (5)
Eq. (7)
316 287
316 291
355 284
300 264
Grain size refers to the value in the quarter thickness section.
refinement can increase the fatigue limit. On the one hand, fatigue limit is inversely related to grain size as shown in mild steels [8]. And an empiric formula was obtained as: −1 = 110 + 11d−1/2 , in which d means grain size in m. Using the equation 0L = 1.42 −1L again, we get the equation: −1L = 1.42 · (110 + 11d−1/2 )
(5)
On the other hand, yield strength is considered in both formulae (2) and (3). In Hall–Petch relationship, k, the factor of grain refinement is in 14–23. Here, another formula is introduced as follows [9]: s = 70 + 84Si + 32Mn + 680P − 30Cr + 38Cu + 33Ni + 11Mo + 5000(C + N) + kd−1/2 + p + D + t
(6)
In the above equation, k is 18.1, p refers to the precipitation strengthening increment, D refers to the dislocation strengthening increment and t refers to the texture strengthening increment. Here, p , D and t are ignored. The yield strength H–P equation can be put into formula (4). And formula (7) can be obtained for the C–Mn steel and micro-alloying steels, in which the effect of grain size on fatigue limit is considered. Here, k1 = k2 = 0.3266 for simplifying. The predicted fatigue limit values with formula (7) are similar to but less than those by formulae (2) and (3). This is attributed to relatively lower yield strength predicted by the H–P relationship than the practical values. 0L = k1 · (70 + 84Si + 32Mn + 680P + ky · d−1/2 ) + k2 · b
(7)
Using Eqs. (1)–(3), (5) and (7), the fatigue limit 0L is calculated and the results are shown in Table 3. The fatigue limit difference of the special TMCP plate and the usual one evaluated with formula (1), is 19 MPa, which is the lest among the difference values with the 5 formulae, because the yield strength is not considered in formula (1). The difference values calculated with formulae (2) and (3) are similar and lie in the mediate position. The fatigue limit difference of the two plates calculated with formula (5), 71 MPa, is the largest, for the effect of grain size in formula (5) may be considered most. The calculated difference with formula (7), 36 MPa, is less than that with formula (5). Owing to the calculated yield strength less than the practical ones, the calculated fatigue limit of both the special TMCP plate and usual plate calculated with formula (7) are the lest respectively. Therefore, owing to the effect of ferrite grain, the fatigue limit may be increased by 25–70 MPa. The tendency of the experimental curves in Fig. 3 may agree with the evaluated values using formulae (2), (3), (5) and (7). Furthermore, Kage and Miller also drew the similar conclusion. In low carbon steel, fatigue resistance, in terms of the relative positions of the S–N curves, increases with decreasing grain size. This phenomenon is related to the number of cycles to propagate a crack to failure and the condition for the non-propagation of a fatigue crack. The size of a non-propagating crack, which initiates below the fatigue limit, tends to become larger as grain size increases [10]. Liu reviews the fatigue behavior experimental observations and synthesizes the diverse observations into an integral and self-consistent analysis in terms of dislocation glide force and the resistance of dislocation barriers [11]. In Liu’s
dislocation barrier model, the strong dislocation barriers in a surface layer are more likely overcome by a dislocation array than those in the interior. Pre-cracking fatigue damage is confined to a surface layer, and a nucleated Stage-I crack is a surface shear crack. The critical grain size dominates the fatigue limit determined by crack non-propagation or non-initiation. For low carbon steel, the value is 76 m [11]. It is obvious that the fatigue limit is controlled by the crack non-propagation for both the special TMCP plate and usual rolled plate. Once a fatigue crack nucleates, the crack growth process of crack-tip shear decohesion may be stopped by a strong dislocation barrier. The nucleated crack becomes dormant. As the grain size becomes smaller, the grain boundary resistance to fatigue crack growth becomes stronger. Therefore, the ferrite grain refinement in the surface layers of the steel plates can hold back or postpone the formation of surface fatigue cracks. The fractographs in Fig. 6a and b agree well with the viewpoint. And the ferrite grain size in the quarter section of the special TMCP plate has been refined so that the resistance to the fatigue crack propagation can also be enhanced effectively. Both of them contribute the improvement of fatigue properties of the special TMCP plates. 4.2. The secondary cracks of fatigue fractograph of C–Mn steel plates The banding pearlite of C–Mn steel is severer than that of plain carbon steel as shown in Ref. [12]. The pearlite is a kind of brittle phase. Therefore, the secondary cracks have something with the banding pearlite. Decreasing the banding pearlite may increase the fatigue properties of steel plates. The formation of fine and ultrafine grained ferrite can lessen the banding pearlite and make them small and scatter homogenously [13]. From this, the grain refinement is also beneficial to improvement of fatigue properties. 5. Conclusion • Grain refinement can improve effectively the fatigue properties of C–Mn steel plates. • Under the same cycling loading condition, the fatigue striations appear in plate with fine grained ferrite later than in plate with coarse grained ferrite. • The area of fatigue striations in plate with fine grained ferrite is less than that with coarse grained ferrite. • The ferrite grain refinement in the surface layers of the steel plates can hold back or postpone the formation of surface fatigue cracks. • The banding pearlite can promote the formation and extension of the secondary cracks. Acknowledgment The Beijing Science and Technology Committee sponsored this study as a Beijing Science and Technology Nova Research Item (Serial no. H013610320111). References [1] Guodong Wang, Proceedings of the Workshop on New Generation Steels (NG STEEL ‘2001), November 13–16, Beijing China, 2001, pp. 299–306.
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