Effect of variable amplitude on fatigue life of 17CrNi steel beyond 10 7 cycles

Abstract

To study the effect of the variable amplitude on the carburised 17CrNi high-strength steel, very high cycle fatigue tests were performed on smooth specimens under the stress ratios of 0 and −1. After the experiment, the characteristics of the fracture surfaces were investigated by means of an optical microscope and a scanning electron microscope. Circular-formed marks were found around the inclusion inside the fisheye. Finally, based on five damage models, the fatigue life of the carburised 17CrNi high-strength steel was predicted. The comparison of the calculated lives with the experimental data shows that the modified Miner's criterion is the most accurate and it can adequately characterise the fatigue life of the 17CrNi steel.

Keywords

Variable amplitude very high cycle fatigue stress ratio damage model life prediction

Introduction

Components and structures (e.g. wind turbine components, helicopter rotors, or wheelset axels) are frequently exposed to a very high number of cycles with different stress ratios and variable amplitudes (VA). As already discussed in previous studies [1,2], fatigue properties of high-strength steels under Very High Cycle Fatigue (VHCF) are strongly affected by metallurgical defects such the non-metallic inclusions, and the crack nucleus often takes place in the interior, and that fatigue failure involves the initiation and propagation of the crack. Paris et al. revealed that the time consumed in crack propagation only occupies a very small portion of total fatigue life in the VHCF regime whereas the crack initiation period is of overriding importance [3 -5]. Furthermore, several research papers have introduced experimental methods to estimate the cycles-number for crack growth from an interior inclusion under VHCF [6,7]. Nakasone et al. calculated the interior crack growth using Paris law and found that the crack growth life is about 10²–10⁵ cycles of the total life, and it can be ignored if compared to the long crack initiation life with more than 10⁷ cycles [6]. In addition, Wagner et al. used a thermo-mechanical fatigue approach to elicit that over 90% of the total fatigue life in the VHCF range is used in the crack initiation stage in the FGA [7]. Moreover, some models are proposed to predict the fatigue life in the VHCF regime such as the parameter model [8], the inclusion size model [9], material characteristics such as tensile strength [10], the accumulative damage [11], etc … For the high-strength steels that show a high crack growth rate and low fracture toughness, the fatigue life within the VHCF is expected to be primarily governed by crack initiation. Thus, the VHCF lifetime prediction approach related to crack initiation needs to be discussed in more detail.

Despite significant advances in fatigue testing equipment and techniques, there remains a need to understand how fatigue characteristics change under different loading conditions. Since it is impossible to carry out fatigue tests under real service conditions for all machine components and structural elements, it is necessary to find experimental procedures that can serve as a reference. Except for a few studies that consider VA loading and stress ratio (eg: [12 -16]), most available research does not focus on investigating these two important factors.

In the last decades, researchers attempted to find the most suitable rule to describe the behaviour of fatigue damage accumulation. Although, previous works [17 -22] concluded that damage due to fatigue increases with applied loading cycles in both VA and CA, however, the damage accumulation characteristics under VA need to be further discussed.

For the reasons mentioned above, the effect of VA loading on crack morphology was studied in this paper: The axial fatigue testing under CA and VA loading of the smooth specimens of carburised 17Cr2Ni2Mo steel at the stress ratios of 0 and −1 were performed, then the S-N curves were plotted. After that, the microscopic observation of fracture surfaces was conducted and the characteristic crack size of inclusion and fisheye were calculated. Finally, based on the Miner criterion, Modified Miner criterion, Damage Curve with maximum stress level (DCA1), Damage Curve with minimum stress level (DCA2), and Corten-Dolan theory, the fatigue life under the VA loading was predicted, and then the prediction accuracy of the five methods was compared to experimental results.

Material and methods

Material and specimen

The material used in this paper is the carburised 17Cr2Ni2Mo steel. Its chemical composition is given in Table 1. From the annealed steel bar with a diameter of 18 mm, test specimens were machined into an hourglass shape with a certain finishing margin and then polished in a direction parallel to their axis using sandpaper with grades ranging from 400 to 2000, as shown in Figure 1. The minimum diameter and the corresponding stress concentration factor of the samples are 6 mm and 1.03, respectively.

Figure 1

Shape and dimensions of specimen (units: mm).

Table 1

Chemical composition of 17CrNi steel (wt %).

Steel	C	Si	Mn	P	S	Cr	Ni	Mo	V	Nb	Al	Cu
CrNi	0.16	0.05	0.50	0.004	0.001	1.62	1.50	0.29	0.10	0.036	0.032	0.08

In order to determine the mechanical characteristics of the material, monotonic tension testing was performed on the carburised 17Cr2Ni2Mo specimens. The tested specimens were subjected to controlled tension until failure. According to the results of monotonic tension testing, values of Poisson's ratio (υ), Young's modulus (E), tensile strength (σ _b), yield strength (σ _y), and the shear modulus (µ_m) of 17Cr2Ni2Mo steel were determined: 0.3, 205 GPa, 1800MPa, 1510 MPa, and 80.4 GPa, respectively.

Surface-treatment and microstructural property

The specimens were put into a container riddled with carburisation powder which consists of charcoal, calcium carbonate, and barium carbonate solution with 12:1:5. The container was shuttered by fire clay and heated by a vacuum furnace. The temperature of the furnace first elevates up to 800–850°C, and then it was held for 2 or 4 h steeping time and finally reaches the carburising temperature of about 930°C. The carburising time is about 6 h with pack-carburising speed about 0.1–0.15 mm/h and the expected depth of carburised layer is about 0.6–0.8 mm. Upon completion of the process, direct quenching and low tempering were performed. The furnace temperature is stepped down to 860°C for 30 min prior to quenching in oil, followed by tempering at 200°C for 2 h.

After the heat treatment process, a multi-process including grinding, polishing, and etching with a 4% alcohol nitric acid solution is performed. Then, the microstructure in the cross-sectional area of the specimen was observed using the Scanning Electron Microscope (SEM) and the Optical Microscope (OM), as shown in Figure 2. Acicular high-carbon martensites and partial residual austenites are observed in the carburised layer (Figure 2(b)), while low-carbon lath martensites are observed in the matrix region (Figure 2(c)).

Figure 2

OM and SEM observation of microstructure: (a) thickness of carburised layer; (b) microstructure in carburised layer; (c) microstructure in core region; (d) inclusion.

Additionally, some non-metallic inclusions can be observed in the microstructure (Figure 2(d)). Based on energy dispersive X-ray spectrometer (EDS) analysis, the main chemical composition of the inclusion is Al₂O₃. These non-metallic inclusions are usually produced in the smelting process. Poisson's ratio and Young's modulus for the inclusion, υ _inc and E _inc, are about 0.25 and 390 GPa, respectively [23].

Fatigue testing method

The 17Cr2Ni2Mo samples were tested under CA loading and VA loading with two distinct stress ratios: R = 0 and R = −1; by an electromagnetic resonant fatigue testing machine with a frequency of 100 Hz. The experiment was carried out in normal conditions (an open environment with room temperature). The fatigue life varies approximately in the range of 10⁴–10⁹ cycles. The VA test contains two loading modes: step loading and block program loading. The step loading contains only the load-decreasing sequence. In block program testing, and by means a CPU-control unit, the values of loading sequence and stress amplitude can be controlled based on a common method. The stress level in a block varies from two levels to three levels with a load ranging from 10% to 80% of the yield strength and the number of cumulative cycles n ranges from 5 × 10³ to 2 × 10⁵ for each stress level.

After the experiment, the fracture surfaces were observed by the Optical Microscope (OM) and the SEM to examine the crack nucleation and propagation sites and then define their morphologies and characteristics.

Results and discussion

S–N diagram

The VA loading sequences for each test are presented in Table 2 (Table 2(a); R = 0 and Table 2(b); R = −1). The S-N diagram related to stress amplitude and fatigue life is given in Figure 3. Figure 3(a) shows the CA and VA tests under R = 0, the S-N data were scattered in the life region between 10⁴ and 10⁹ cycles for the values of stress varying from 400 to 700 MPa. Figure 3(b) shows the CA and VA tests under R = −1, the S-N data were scattered in the life region between 10⁴ and 10⁸ cycles for the values of stress varying from 500 to 1000 MPa. The steel represents the continuously descending S-N property without duplex characteristics, and the conventional fatigue limit cannot be observed. In this situation, the typical S-N formula proposed by Basquin was used to represent the S-N curve of the 17CrNi steel under the VA loading within 10⁴–10⁹ life cycles, as indicated by solid lines in Figure 3.

Figure 3

S–N curves of carburised 17CrNi steel under axial loading. (a) CA vs. VA under R = 0. (b) CA vs. VA under R = −1

Table 2

Results of axial loading tests (VA).

σ_a (MPa)	n (cycles)	N _f (cycles)
(a) R = 0
600→500	5 × 10³	30,200
600→500	5 × 10³	14,600
500→400	10⁵	188,200
700→600	10⁴	94,000
600→500	10⁴	544,200
600→500	5 × 10⁴	143,700
500→400	10⁵	90,403,200
(b) R = −1
1000→800→600	10⁴	56,900
900→800→ 700	10⁴	222,200
800→700→ 600	10⁴	492,500
700→600	5 × 10³	1,902,500
600→500	5 × 10³	18,009,500
1000→900→ 800	5 × 10³	37,400
900→800→ 700	10⁴	64,600
800→700→ 600	5 × 10³	315,000
700→600	5 × 10³	1,424,200
600→500	3 × 10⁴	3,436,600
550→450	2 × 10⁵	42,935,100

Compared to the S-N curves of the same steel under the CA loading (denoted by interrupted lines in Figure 3 [23 -25]), the fatigue strength of the carburised 17Cr2Ni2Mo steel under the VA loading is a bit higher. The main reason is related to the existence of only one stress level in the CA loading however there are several stress levels in VA loading with a medium stress that is generally lower than that of CA loading (Table 2(a) and (b)). As a consequence, the total life is inevitably longer in VA loading due to the effect of low stresses. This is similar to the results of some other studies [26].

Observation of fracture surfaces

Typical fracture surfaces for the VA loading under two stress ratios (R = 0 and R = −1) are presented in Figure 4(a,c) and Figure 5(a,c,d,e,g,i). The enlarged images of the inclusions and the adjacent zones inside the fisheye are given in Figure 5(b,d) and Figure 5(b,f,h,j).

Figure 4

Observation of typical fracture surfaces of carburised 17CrNi under VA loading, R = 0: (a) entire fracture surface, two stress levels (σ_a = 700 MPa, N _f= 94,000); (b) inclusion; (c) entire fracture surface, two stress levels (σ_a = 600 MPa, N _f= 544,200); (d) Inclusion.

Figure 5

Observation of typical fracture surfaces of smooth specimens under VA loading, R = −1: (a) entire fracture surface, three stress levels (σ_a = 1000 MPa, N _f= 56,900); (b) inclusion; (c) entire fracture surface, three stress levels (R = –1, σ_a = 900 MPa, N _f= 222,200); (d) entire fracture surface, three stress levels (R = –1, σ_a = 800 MPa, N _f= 315,000); (e) entire fracture surface, three stress levels (σ_a = 800 MPa, N _f= 492,500); (f) inclusion; (g) entire fracture surface, two stress levels (σ_a = 600 MPa, N _f= 3,436,600); (h) inclusion; (i) entire fracture surface, two stress levels (σ_a = 550 MPa, N _f= 42,935,000); (j) inclusio

For the VA loading, it can be observed that the interior failure is the only failure mode and the fisheye region can be seen on the fracture surface for the two stress ratios, with an interior inclusion that can be found in the centre of the fisheye. The inclusions are playing a key role in crack nucleation as they serve as stress concentrators on a micro-level during repeated loading. Similar results were obtained for the CA loading.

Moreover, under relatively high-stress levels, multiple crack initiation sites were observed on the fracture surface. Figure 5(c) gives the case of three cracks interfering with each other: the crack initiated from inclusion (1) is predominant compared to the other cracks initiated from inclusions (2) and (3). The fact that inclusion (1) has a larger size makes the stress concentration at the interface with the ambient matrix greater than that of inclusions (2) and (3). Thus, we can say that the crack initiated from inclusion (1) is responsible for the final failure.

In consideration of the FGA occurrence under VA loading, the interior failure with FGA mainly occurs in the VHCF region beyond 10⁷ cycles in both cases (R = 0 as shown in Figure 4(d) and R = −1 as shown in Figure 5(j)). However, it should be noted that the FGA can occur even under the limit of 10⁷ in a few cases especially under R = −1 as shown in Figure 5(h). Moreover, the FGA is not obvious at R = 0 compared to the same stress at R = −1. This is due to the crack closure effect [27] which is more effective under R = −1. Therefore, we can say that even under VA loading, FGA is more prominent under compressive stress.

The analyses of fracture surfaces show circular-shaped marks around the inclusion within the fisheye (Figure 4(b,d) and Figure 5(b,f,h)). This phenomenon is mainly due to the interference between the two crack surfaces: crack's starting and growing at different rates during the VA loading. In addition, the intervals between the circular marks are distinct for different VA tests. This is mainly due to the difference in crack growth rate [6,7] from one test to another.

Evaluation of characteristic crack size

For further discussion on crack size characteristics, the parameters r _inc, r _fisheye and d _inc were defined as: the radius of inclusion, the radius of fisheye, and the inclusion depth; respectively. The inclusion depth was measured from the inclusion's centre to the nearest starting edge of the fracture surface. Figure 6 shows the relationships between d _inc and N _f for both CA and VA tests under the stress ratio −1. As can be seen in the figure, there is no difference between the values of d _inc under both: CA and VA. In addition, all the inclusions were found inside the matrix region, and the range of d _inc is 1663.5–2179.3 µm.

Figure 6

Relationship between d _inc and N _f, R = −1.

Comparisons between the values of r _inc under CA and VA are given in Figure 7. It can be said that r _inc is independent of both the fatigue life and the loading mode. The slight difference in the r _inc values between CA and VA is mainly caused by the difference in the overall stress applied for each level in the two cases. The range of r _inc under VA loading is 16.1–41.5 µm and the range of r _inc under CA loading is 14.6 and 33.7 μm.

Figure 7

Relationships between r _inc and r _fisheye, and N _f, R = −1.

Moreover, the value of r _fisheye under the CA loading and the VA loading tends to be constant with the increase of fatigue life N _f as shown in Figure 7. The range of r _fisheye under VA loading is 1350.6–1546.3 µm and under CA loading is 343.7–1880.7 µm. The difference between r _fisheye values from CA to VA is mainly due to the difference in the overall stress applied in the two cases. Thus, the value of r _fisheye is independent of the loading mode. Thus, it can be said that the ‘crack size’ value is independent of the loading mode and it is mainly related to the applied stress [27].

Life prediction

Under fully reversed loading condition and based on five damage models, the fatigue life of the carburised 17CrNi high-strength steel was predicted.

Linear damage rule (LDR) or Miner's criterion

The linear cumulative damage method of Miner's criterion is the earliest cumulative damage calculation method. It was first proposed by Palmgren in 1924. This method is well-known as the name of ‘Palmgren-Miner's criterion’. The mathematical expression of this criterion is given as follows [28]: (1) with D is defined as cumulative damage. The fatigue failure is supposed to occur until D = 1. n _i is the number of cycles of the i^th level of applied stress in VA loading. N _i,f is the fatigue life under CA loading corresponding to the i^th level of stress in VA loading.

Modified linear damage rule (MLDR) or modified miner's criterion

Many previous researchers have found that the value of cumulative damage D doesn't equal to 1 when fatigue failure occurs. Thus, it can be said that the fatigue life based on Miner's rule is inadequate. For this reason, the Miner's criterion has been revised then a new formula ‘the Modified Miner's criterion’ was proposed [29]: (2) where α _D is defined as the modified damage value. In this modified Miner's rule, it's assumed that the specimens will fail when damage accumulates a specified value α _D, which is confirmed by two-level loading tests.

Based on Miner's criterion (Eq. (1)) and according to the experimental data of the VA tests, the accumulated damage (D) was calculated and presented in Table 3(a). The average value of D was substituted into the modified Miner's criterion (Eq. (2)), then the value of α _D was determined; α _D = 1.96. The results of the predicted life under R = −1 according to Miner's criterion and the modified Miner's criterion are given in Table 3(a).

Table 3

Prediction results (VA).

N _f (cycles) (VA, R = −1)	D		N _p (cycles)		e _p
(a) Miner's criterion and the modified Miner's criterion
			Miner	Modified Miner	Miner	Modified Miner
56,900	1.48		40,369	79,528.07	48.62%	24.55%
222,200	1.90		116,523	229,550.8	90.69%	3.20%
492,500	2.91		169,019	332,968.9	191.38%	47.91%
1,902,500	11.53		665,000	825,000	65.04%	130.60%
18,009,500	90.49		882,8186	12251,360	79.66%	47.91%
37,400	1.02		36,447	71,801.8	2.61%	47.91%
64,600	0.55		116,523	229,550.8	44.56%	71.85%
345,000	2.04		169,019	332,968.9	104.11%	3.61%
1,424,200	8.63		664,990	825,030.4	53.30%	72.62%
3,436,600	17.26		699,003	892,037	79.66%	285.25%
42,935,100	215.75		210,4661	29,207,551	79.66%	47.91%
Mean e _p					79.66%	47.91%
(b) Damage Curve Approach (DCA)
	DCA₁	DCA₂	DCA₁	DCA₂	DCA₁	DCA₂
56,900	1.15	2.12	139,275	84,372	56.91%	28.88%
222,200	1.37	4.30	402,005	243,533	44.72%	8.76%
492,500	3.45	2.06	583,118	353,251	15.54%	39.41%
1,902,500	32.42	9.12	1,069,000	845,000	77.97%	125.14%
18,009,500	84.87	647.35	1,059,3823	1,193,4724	70.25%	50.90%
37,400	0.74	1.22	125,744	76,175	70.25%	50.90%
64,600	0.39	1.25	402,005	243,533	83.93%	73.47%
345,000	2.63	1.38	583,118	353,251	40.83%	2.33%
1,424,200	24.27	6.82	1069,215	844,829	33.20%	68.57%
3,436,600	16.19	38.45	1,186,562	915,917	189.62%	275.20%
42,935,100	202.56	146.38	2,521,8854	2,845,2683	70.25%	50.90%
Mean e _p					70.25%	50.90%
(c) Corten-Dolan's theory
56,900	0.98		74,683		19.66%
222,200	1.85		215,567		3.07%
492,500	1.25		312,686		57.50%
1902500	3.18		805,000		136.33%
18,009,500	100.64		11,434,603		57.50%
37,400	0.81		67,428		44.53%
64,600	0.53		215,567		70.03%
345,000	0.88		312,686		10.33%
1,424,200	2.38		805,231		76.86%
3,436,600	19.20		868,156		295.85%
42,935,100	234.07		27,260,380		57.50%
Mean e _p					57.50%

Damage curve approach (DCA)

Both, Miner's and modified Miner's rules ignore the impact of loading sequence on fatigue life. To improve the accuracy of fatigue life prediction, Manson [30] proposed the Damage Curve Approach. For multiple-level loading, the Damage Curve Approach is given as follows: (3) (4) where a ₁ is the initial crack length and a _f is the crack length when the specimen fails. In this model, D will be defined as 1 in order to predict the fatigue life for the VA test. Therefore, for the two-stage VA loading, the following relationships can be written: (5) where n ₁ and n ₂ are the number of cycles of the first stress level and second stress level, respectively. N _1,f, and N _2,f are fatigue lives of the corresponding level under the CA loading, respectively.

For multi-stage loading, the fatigue life at the highest stress level can be regarded as the reference fatigue life, and the corresponding relationship can be constructed. Therefore, the amount of damage caused by the second stress level can be calculated as follows: (6) After extending Eq. (6) to multi-stage loading, the accumulated damage can be calculated as follows: (7) where D _i is the damage caused by the applied stress at the range i^th and n _i is the number of cycles for the i^th stress stage. N _i and N _r are the fatigue lives under the CA test of the i^th stress level and of the reference stress level (maximum stress), respectively.

Based on the Damage Curve Approach (DCA) (Eq. (3)), D and the predicted fatigue life (Np) were calculated under R = −1 as given in Table 3(b). DCA1 represents the case of the Damage Curve Approach with the maximum stress as a reference and DCA2 represents the case of the Damage Curve Approach with the minimum stress as a reference.

Corten-Dolan's theory

Corten-Dolan's theory is a nonlinear damage theory proposed by Corten and Dolan in 1956. According to Corten-Dolan's theory, the amount of damage caused by a single crack can be expressed as follows [31]: (8) where D is the accumulated damage, N is fatigue life, r is the damage growth factor, and α is a constant. α and r are related to the applied stress. When a two-level stress spectrum is applied and suppose that the total fatigue life is N _f, with the number of cycles N _a corresponds to the first level of stress and the number of cycles N _b corresponds to the second level of stress with (N _a+ N _b = N _f) it is assumed that the damage at the second stress level continues as D = r ₂ N ₂ α ₂. The accumulated damage is given as follows: (9) Eq. (7) can be transformed: (10) When the two stress levels are repetitive, α ₁ and α ₂ are equal, therefore the relationship between the fatigue life N _f and the initial number of cycles n ₁ can be obtained: (11) Eq. (11) can be generalised to obtain a relation of a multi-stage stress loading, as shown below: (12) with N _r is the fatigue life corresponding to the reference stress level, σ _r is the reference stress level which is the maximum stress level in the load spectrum, σ _i is the applied stress for the i^th level, N _f is the total fatigue life, Z is the total number of the series of applied stress and d is constant related to the material.

Based on Eq. (12), the amount of damage is defined as: (13) The cumulative damage corresponding to the i^th stress level D _i, can be calculated according to the following formula: (14) Based on the numerical fitting of Corten-Dolan's theory (Eq. (12)) with the use of the experimental fatigue lives with two and three stress levels, the value of the material constant, d; corresponding to the carburised 17CrNi steel is obtained, d = 9.23. Further, D and N _p were calculated for R = −1. The results are given in Table 3(c).

It can be observed from Table 3(a), (b), and (c) that by using the modified Miner's criterion and the DCA₂ the predicted lives are generally lower than the experimental life. In addition, these predicted lives are relatively stable and they are closest to the experimental life. The average value of the prediction error for the modified Miner's criterion is 47.91% and for the DCA₂ is 50.90%. Therefore, it will be safer to make a fatigue design based on these two methods.

Based on DCA1, the predicted results are slightly greater than the experimental life, with a range of prediction errors of about 15.54%–189.62%. It can be said that the prediction error is relatively high.

The predicted life based on Miner's criterion is the largest among the five methods with a range of prediction error is about 2.61%–104.11% and an average prediction error of about 79.66%.

The predicted lives using the above-studied methods were compared with the experimental data as shown in Figure 8. Both calculated lives using modified Miner's rule and Corten-Dolan's theory have no significant difference from experimental life when N _f< 10⁶ cycles. Most of the data are located near the central line, very close to the experimental data. When N _f> 10⁶ cycles, except for Miner's criterion; the other four approaches tend to be in good agreement with the experimental data.

Figure 8

Comparison between predicted and experimental fatigue lives (VA, R = −1).

Comparing the five discussed approaches, one can say that the modified Miner's criterion has the highest prediction accuracy for the carburised 17CrNi high-strength steel. It was noted that the prediction error varies in relatively wide ranges. However, there are more significant factors that can play a key factor in fatigue design such as the position of the predicted data relative to the experimental curve. Thus, in such analytical models, the best formula should be made by taking into consideration all the details but according to the importance level. Further improvements have to be made in future works in terms of minimising the prediction error.

Conclusions

Under VA loading, the FGA is more prominent in the presence of compressive stress, which is similar to the results for steels under CA loading.

The analyses of the fracture surfaces show circular marks formed around the inclusion inside the fisheye. This is mainly due to the interior cracks starting, stopping, and growing at different rates during the VA loading.

The value of the ‘crack size’ is independent of the loading mode (CA or VA) and it is mainly related to the applied stress.

Based on five damage models: Miner's criterion, Modified Miner's criterion, the Damage Curve Approach with maximum stress as a reference stress (DCA₁), the Damage Curve Approach with minimum stress as a reference stress (DCA₂), and the Corten-Dolan's theory, the fatigue life for the smooth specimens of the carburised 17CrNi high-strength steel was predicted under fully reversed loading condition. The comparison of the calculated lives with the experimental data reveals that the modified Miner's criterion is the most accurate and can adequately characterise the fatigue life of the carburised 17CrNi high-strength steel under VA loading.

Footnotes

Disclosure statement

No potential conflict of interest was reported by the authors.

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