Effects of inclusion size and stress ratio on fatigue strength for high-strength steels with fish-eye mode failure
Highlights
► Fatigue life reduces by about two orders of magnitude when inclusion size doubles. ► A model is proposed for predicting fatigue strength of high-strength steels. ► The model is based on experiments for the effect of inclusion size and stress ratio. ► Predicted results are in agreement with our experimental data and those in literature.
Introduction
Since the work by Naito et al. [1], a number of researches have shown that fatigue failures of high-strength steels may occur at the stress lower than the conventional fatigue limit defined at failure cycles of 107 [2], [3], [4], [5], [6], [7]. Different from low cycle fatigue, the crack initiation site for the fatigue life larger than 107 (very-high-cycle fatigue, VHCF) for high-strength steels usually changes from the surface to the interior of specimen and the failure is mostly caused by interior non-metallic inclusions. Further, a fish-eye fracture mode often presented with the morphology of fine granular area (FGA) [8], also called optical dark area (ODA) [9] or granular-bright-facet (GBF) [10] observed around the inclusion at fracture origin. The term of FGA is used in this paper.
Many researches have shown that inclusion size has great influence on VHCF properties of high strength steels [11]. The studies by Murakami et al. [12] indicated that the relative size of FGA to that of the inclusion at the fracture origin increased with the increase of the fatigue life and that the formation of FGA played a crucial role in VHCF failure. Zhao et al. [13] investigated the formation mechanism of FGA in high-strength steels and proposed a model to predict the threshold value of its formation based on the plastic zone at crack tip. It was shown that the stress intensity factor range at the front of FGA kept constant and was close to the threshold value of the crack propagation ΔKth. The similar results were reported by Shiozawa et al. [10], [14] and Sakai [15], which showed that the stress intensity factor range at the front of FGA kept constant value corresponding to the threshold value of the crack propagation for a kind of high carbon chromium steel.
Some methods are also proposed to predict the fatigue life or fatigue strength containing VHCF regime [16], [17], [18], [19]. Murakami et al. [9], [20] combined the parameters of fatigue strength σ (MPa), Vickers hardness Hv (kgf/mm2) and the square root of inclusion or defect projection area (μm) to give an equation for predicting the fatigue strength of high-strength steels:where R is the stress ratio, α = 0.226 + Hv × 10−4, C = 1.43 for surface inclusions or defects and C = 1.56 for interior inclusions or defects.
Wang et al. [21] incorporated the number of cycles to failure into Murakami’s model and proposed:where β = 3.09–0.12 log Nf for interior inclusions or defects and β = 2.79–0.108 log Nf for surface inclusions or defects for four low-alloy high-strength steels (42Cr–Mo4, Cr–Si (54SC6), Cr–Si (55SC7) and Cr–V (60CV2)).
Akiniwa et al. [22] assumed that Paris relation was still valid for the fatigue crack propagation in FGA, and derived an approximate relation for the fatigue strength and the number of cycles to failure:where the subscript “Inc” denotes inclusion. Tanaka and Akiniwa [23] gave the parameters mA = 14.2 and CA = 3.44 × 10−21 for bearing steel JIS SUJ2 with the tensile strength of 2316 MPa. Then, the model by Akiniwa et al. [22] was modified as
Chapetti et al. [24] showed a relation between FGA size, inclusion size and the number of cycles to failure in the form of by fitting the experimental data of quenched and tempered JIS SUJ2, SCM435 and SNCM439 steels, and then proposed an expression to correlate the total fatigue life with the threshold stress σth aswhere Δσth in MPa, in μm, and Hv in kgf/mm2.
Here, we omit the subscript “th” and note Δσth = 2σa, Eq. (5) is rewritten as
Mayer et al. [25] pointed out that the fatigue life is approximated by the stress amplitude and the inclusion size by the formulawhere n = 28.82 and C = 6.47 × 1098 by fitting the fatigue data of specimens failed from interior inclusions for bainitic bearing 100Cr6 steel with tensile strength of 2387 MPa, and the dimension of stress amplitude is MPa and areaInc is μm2.
This relation is rearranged as
Liu et al. [26] proposed an expression in form of Basquin equation for predicting the S–N curves based on the prediction of fatigue strengths at 106 cycles and at 109 cycles, i.e.where and , with σa in MPa, in μm and Hv in kgf/mm2.
It can be expressed as
Recently, Sun et al. [27] developed a model for estimating the fatigue life of high-strength steels in high cycle and VHCF regimes with fish-eye mode failure based on the cumulative fatigue damage, which takes into account the inclusion size , FGA size and tensile strength σb of materialsorwhere α is the parameter by fitting the experimental data.
It is seen that, for several models (Eqs. (1), (2), (6), (8)) mentioned above, the effect of inclusion size on fatigue strength (i.e. the power exponent of ) is regarded as a constant, while for the other models (Eqs. (4), (10), (12)), the effect of inclusion size on fatigue strength is related to the material. Thus, the model to describe the effect of inclusion size on fatigue strength still needs to be further developed.
In this paper, ultrasonic (20 kHz) fatigue tests are performed on specimens of a high carbon chromium steel in order to further investigate the effect of inclusion size on the fatigue life. Then, a model is developed for the effect of inclusion size and stress ratio on fatigue strength of high-strength steels with fish-eye mode failure. The predicted results are in good agreement with our experimental data and the ones reported in literature. The model is also compared with some previous ones, with the comparison showing the superior of the present one.
Section snippets
Experimental procedure
The material used in the present paper is a high carbon chromium steel, with the main chemical compositions of 1.06C, 1.04Cr, 0.88Mn, 0.34Si, 0.027P and 0.005S in mass percentage (Fe balance). Specimens were heated at 845 °C for 2 h in vacuum, then oil-quenched and tempered for 2.5 h at 150 °C in vacuum with furnace-cooling. The hardness measurement was performed on two specimens by a Vickers hardness tester at a load of 50 g with the load holding time of 15 s. Fifteen points were tested on each
Experimental results
It is observed that the fish-eye mode fracture of tested specimens is originated from a single crack origin, i.e. an inclusion. The fatigue test data and the related inclusion size a0 and FGA size aFGA observed for the specimens induced by interior inclusions are listed in Table 1, in which a0 is the positive square root of inclusion projection area and aFGA is positive square root of FGA area including the inclusion projection area as used by Murakami et al. [12]. It is noted that two
Fatigue strength model and analysis
Based on the results that the fatigue life is correlated to inclusion size under the same stress level, we may write
As known, the stress amplitude is one of the uppermost factors influencing fatigue life. Thus, the parameter A should be at least a function related to the stress amplitude, i.e. . The shape of S–N curve for high-strength steels often presents a duplex pattern corresponding to surface-initiated fracture mode and interior-initiated fracture mode [8], [10], [15],
Effect of stress ratio on fatigue strength
In a previous paper [36], the effect of stress ratio on fatigue strength under the same fatigue life is expressed aswhere σ−1 denotes stress amplitude at R = −1 and α is a parameter.
Thus, the fatigue strength (Eq. (14)) involving the effect of stress ratio is expressed as
It is seen that, any of the models by Murakami et al. [9], [20] (Eq. (1)), Akiniwa et al. [22] (Eq. (4)), Chapetti et al. [24] (Eq. (6)), or Mayer et al. [25] (Eq. (8)) is a special case of the present
Maximum inclusion size estimation
Meanwhile, it is shown that the fatigue strength obtained by the present model Eq. (14) or Eq. (16) with the maximum inclusion size at fracture origin is regarded as the lower bound of fatigue strength. As known, the inclusion size at fracture origin cannot be determined before fatigue fracture occurs. So, when the model Eq. (14) or Eq. (16) is used to predict the fatigue strength, the maximum inclusion size is an important parameter to be determined first.
The estimation of the maximum
Conclusions
This paper investigates the effect of inclusion size and stress ratio on the fatigue properties of high-strength steels with fish-eye mode failure. The experimental results indicate that the fatigue life reduces by about two orders of magnitude when inclusion size doubles. Then, a model is proposed for predicting the fatigue strength of high-strength steels with fish-eye mode failure, which takes into account the effect of inclusion size and stress ratio. It is shown that the fatigue strength,
Acknowledgements
Financial support of the National Natural Science Foundations of China (11172304, 11021262 and 11202210) and the National Basic Research Program of China (2012CB937500) are very much appreciated.
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