Fatigue Crack Growth at Different Frequencies and Temperatures in an Fe-based Metastable High-entropy Alloy

Abstract

In this study, the fatigue crack growth behaviors of Fe30Mn10Cr10Co (at%) metastable high-entropy alloy at different frequencies and test temperatures were evaluated by compact tension tests. The fatigue crack growth rate did not significantly change with varying frequency. However, it increased with decreasing temperature from room temperature (RT) to 103 K owing to the promotion of the hexagonal close-packed (HCP) martensite-related cracking. Increasing the test temperature from RT to 373 K decelerated the fatigue crack growth rate perhaps owing to the formation of the ductile and reversible HCP martensite.

1. Introduction

Compositional design of high-entropy alloys (HEAs) is a new strategy for achieving extraordinary strength–ductility balance^1,2,3) and fracture resistance.⁴⁾ This alloy design strategy is based on increasing the configurational entropy^5,6) and enhancing the short-range ordering,^7,8) which result in high yield strength and high work-hardening capability of the alloy. Furthermore, by controlling the austenite phase stability of the Fe-based HEAs, deformation-induced martensitic transformation from the face-centered cubic (FCC) to hexagonal close-packed (HCP) structures occurs. This transformation results in a transformation-induced plasticity (TRIP) effect, which further improves the strength–ductility balance of the FCC-based HEAs.^9,10) In particular, the dislocation motion is inhibited by the presence of HCP martensite plates, and this results in high work-hardening capacity and associated superior uniform elongation. Therefore, FCC-HCP martensitic transformation has been widely investigated in the HEAs field to harness the benefits of the TRIP effect.^{11,12,13,14,15,16,17)}

The FCC–HCP martensitic transformation generally plays a crucial role for the failure. Specifically, the HCP martensite acts as a preferential site for crack or void initiation, which deteriorates the ductility.^18,19,20) This deterioration affects the tensile properties^21,22,23) and fatigue resistance,^24,25) of which the degrees depend on the fraction and ductility of the HCP martensite. For instance, FCC–HCP martensitic transformation occurred in a Fe-30Mn-6Si alloy with brittle-like cracking at the main fatigue crack tip, which accelerated fatigue crack growth.²⁶⁾ In contrast, the formation of a “ductile” HCP martensite in an Fe-30Mn-4Si-2Al alloy improved its fatigue life²⁷⁾ and the associated fatigue crack growth was decelerated.^26,28) This is associated with a geometrical constraint of the crack tip deformation²⁹⁾ and reversible FCC↔HCP TRIP effect.^30,31,32,33) An important factor in the formation of the ductile HCP martensite is c/a ratio of the lattice constant, which enables non-basal slip or twinning. The HCP martensite in the Fe-based HEAs has an optimal c/a ratio for strength–ductility balance.^34,35) According to the compact tension (CT) tests, Fe30Mn10Cr10Co (at%) metastable HEA had a fatigue crack growth rate comparable to that of SUS316L.³⁶⁾ This indicates that the negative effects of HCP martensite did not act as a factor accelerating the fatigue crack growth in the HEA. Therefore, this opened a new venue for designing fatigue-resistant alloys in terms of configurational entropy and short-range ordering.

However, these results also indicate that the positive effects of HCP martensite did not appear, although the formation of the “ductile” HCP martensite occurred. The high fraction of the HCP martensite near the crack tip might have caused this since the intersection and impingement of the HCP martensite plates affect the smooth motion of the leading partials and deteriorate the reversibility of the deformation-induced HCP martensite. In this context, a change in the test temperature, which determines the HCP martensite fraction at identical chemical compositions, can drastically alter the fatigue crack growth behavior of the metastable HEA. In particular, it is postulated that decreasing the temperature accelerates the fatigue crack via promoting the martensite-related crack/void formation, and increasing the temperature induces the positive effects of the HCP martensite, which decelerates the fatigue crack growth. In addition, the frequency may also affect the fatigue crack growth, which is associated with the thermal activation process of the dislocation emission and other dislocation motions. Therefore, understanding the effects of frequency is helpful in understanding the effects of temperature that consist of the effects of the chemical driving force and dislocation mobility associated with the thermal activation process.

In this study, we investigated the effects of frequency and temperature on the growth behavior of mechanically long cracks through CT testing and associated microstructure characterization.

2. Experimental Procedure

2.1. Material

In this study, we prepared Fe30Mn10Cr10Co (at%) HEA. A 50 kg ingot of Fe30Mn10Cr10Co HEA was prepared by vacuum induction melting. The ingot was hot-rolled to 52% thickness at 1273 K, followed by homogenization at 1473 K for 2 h in an Ar atmosphere and furnace cooling. The homogenized bar was further hot-rolled to obtain a thickness reduction of 77% (from 60 to 20 mm) at 1273 K. The rolled bar was solution-treated at 1073 K in air for 1 h, followed by water quenching. The as-solution-treated HEA consisted of a metastable austenite matrix and HCP martensite second phase, as shown in Fig. 1. A 32% fraction of the thermally induced HCP martensite was measured by electron backscatter diffraction (EBSD) for the CT specimens. The details of the chemical compositions in wt.% are listed in Table 1. Meanwhile, the transformation temperatures were measured by differential scanning calorimetry. The start and finish temperatures for the martensitic transformation (M_s and M_f) and those for the reverse transformation (A_s and A_f) were 328, 315, 406, and 425 K, respectively. The equilibrium temperature of the FCC and HCP phases, T₀ was calculated using Eq. (1) as 377 K.   

$$T_0=\frac{M_s+A_s}{2}.$$(1)

Fig. 1.

(a) Rolling direction-inverse pole figure (RD-IPF) and (b) phase maps of the initial microstructure. (Online version in color.)

Table 1. Chemical composition of the HEA in wt.%.

C	Mn	P	S	N	O	Al	Cr	Co	Ni	Fe
0.009	29.80	0.004	0.007	0.0087	0.015	0.028	9.29	10.46	0.01	50.37

2.2. CT Test

CT specimens were produced in conformity with the ASTM standard E647. Their gauge dimensions were 50.8 mm wide, 10 mm thick, and 10 mm machined-notch-length (Figs. 2(a) and 2(b)). The CT specimens were machined using a shaper and grinder, and the notch was shaped by electric discharge machining. Then, the surfaces of the specimens were mechanically polished to a mirror finish. The loading axis was parallel to the rolling direction (RD). Fatigue crack growth tests were carried out in a constant test load range (ΔP) at room temperature (RT), at constant test frequencies of f = 1 and 25 Hz and constant stress ratio R = 0.1. The stress intensity factor range (ΔK) in the experiment was from approximately 15 to 30 MPa·m^1/2 The test load was varied sinusoidally. A small scale-yielding condition was satisfied under these conditions. In addition, the test temperature was varied from 103 to 373 K at a constant frequency of 10 Hz, with the other test conditions remaining the same as those for the RT tests.

Fig. 2.

(a) CT specimen geometry and (b) detail of the notch (in mm).

2.3. Microstructure Characterization

After the fatigue crack growth tests, the CT specimens were cut through the middle of their thickness and mechanically polished with colloidal silica to remove damaged layers (Fig. 3). Then, microstructure observations were performed by EBSD analysis and electron channeling contrast imaging (ECCI). The EBSD analysis was performed at 20 kV, with a beam step size of 170 nm. Meanwhile, the ECCI was performed at 30 kV. The other half of the specimen was used for fractographic analysis using a scanning electron microscope.

Fig. 3.

Specimen preparation for EBSD and ECCI.

3. Results and Discussion

3.1. Effect of Frequency on Fatigue Crack Growth

Figure 4 shows the fatigue crack growth rates plotted against the ΔK. The fatigue crack growth rate at RT did not show a remarkable change when frequency was varied from 1 to 25 Hz, although there exists a slight difference in the low ΔK region. The slightly higher fatigue crack growth rate with the frequency of 25 Hz in the low ΔK region is probably owing to the degree of crack surface roughness. As shown in Fig. 5(a), there was a significant crack roughness in the specimen tested at 1 Hz, and some portions of the fracture surface were chipped as indicated by the white arrow. The presence of the chipped parts indicates the occurrence of crack surface contact during the cyclic loading, which decelerates fatigue crack growth. The degree of crack roughness became smaller when the frequency was increased to 25 Hz (Fig. 5(b)) and when ΔK was increased to 30 MPa·m^1/2 (Figs. 5(c), 5(d)). However, the size, frequency, and sharpness of the crack surface roughness observed in the low ΔK region at 1 Hz were lower than laminated microstructure steels such as pearlitic steels in which the effect of crack roughness appears markedly.^37,38) Therefore, the crack surface roughness can cause the slight deceleration of crack growth in the present alloy, but the crack propagation path was macroscopically smooth.

Fig. 4.

Fatigue crack growth rate plotted against the ΔK at different frequencies and test temperatures. Some data of the test at RT and frequency of 1 Hz were extracted from a previous study.³⁶⁾ The stress ratio R was 0.1 for all conditions. (Online version in color.)

Fig. 5.

Cross-sectional ECC images of the fracture surfaces obtained at (a, b) ΔK = 18 and (c, d) 30 MPa·m^1/2 with the frequencies of 1 and 25 Hz. The black arrows indicate portions that have remarkable crack roughness.

According to a previous study,³⁶⁾ the fatigue crack growth at 1 Hz and RT in the CT test had the following characteristics.

1) The fatigue crack was covered with a large amount of HCP martensite.

2) The crack growth path was smooth like stable austenitic steels, which indicates that the crack propagation mode was mainly of mode I type.

3) Mode I type fatigue crack growth occurred via plastic deformation of both the FCC and HCP phases.

4) Secondary cracks were observed, but they did not accelerate the fatigue crack growth.

As shown in Fig. 6(a), the fatigue crack of the specimen tested at 25 Hz and RT was also covered with a large amount of HCP martensite. In addition, the crack growth path was smooth even when it propagated through multiple grains with different orientations (Fig. 6(b)). Secondary cracks were observed on the fracture surface (Fig. 6(c)) and cross-sectional image (Fig. 6(d)). As shown in Fig. 6(c) inset, the fracture surface had a slip-mark-like pattern that is a trace of plasticity, which indicates that the fatigue crack growth occurred via plastic deformation. Finally, note the ECC image shown in Fig. 6(e). In the ECC image, HCP martensite appears to be bright with the plate-like morphology, and the other region is FCC austenite. Both of the FCC and HCP regions showed contrast gradients, and the HCP plates near the crack was highly distorted. These facts also indicate that occurrence of plastic deformation in the FCC and HCP phases. Therefore, both the macroscopic fatigue crack growth rate and associated microscopic crack growth behavior were insensitive to frequency in the range of 1 to 25 Hz at RT.

Fig. 6.

A set of images obtained in the region that had fatigue crack growth at the ΔK = 18 MPa·m^1/2. The test was performed at 25 Hz and RT. (a) Phase and (b) RD-IPF maps near the fracture surface. (c) Fracture surface in which the white arrows indicate secondary cracks. The inset indicates its magnification. (d) Cross-sectional ECC image and (e) its magnification. The white arrows in (e) indicates distorted HCP plates. (Online version in color.)

3.2. Effect of the Test Temperature on the Fatigue Crack Growth

As shown in Fig. 4, the fatigue crack growth rate increased with decreasing test temperature from RT to 103 K, except for the region around ΔK = 30 MPa·m^1/2. In contrast, increasing the test temperature from RT to 373 K decelerated the fatigue crack growth rate, particularly in the relatively low ΔK region. The fracture surfaces of the specimens tested at 103 and 373 K showed features of transgranular crack growth (Figs. 7(a) and 7(b)). In addition, slip lines or striation-like patterns were also observed in both specimens tested at 103 and 373 K (Figs. 7(aʹ) and 7(bʹ)). These were similar to the fracture surface obtained at RT. Namely, a remarkable change in the fractographic features as a result of changing the test temperature was not observed, which indicates that plastic deformation contributed to the fatigue crack growth, irrespective of the test temperature.

Fig. 7.

Fractographs of the regions with ΔK = 18 MPa·m^1/2 in the specimens tested at (a) 103 K, and (b) 373 K. The test frequency was 10 Hz. (aʹ and bʹ) Magnifications of the regions highlighted in (a) and (b). The small arrows in (a) indicate secondary cracks.

Compared to the fracture surface obtained at RT, more secondary cracks were observed at 103 K at ΔK = 18 MPa·m^1/2 (Fig. 7(a)). In contrast, no large secondary cracks were observed at 373 K at ΔK = 18 MPa·m^1/2 (Fig. 7(b)). Correspondingly, the cross-sectional image of the specimen tested at 103 K had a secondary crack (Fig. 8(a)), but the crack did not appear at 373 K (Fig. 8(b)) at ΔK = 18 MPa·m^1/2. The increased secondary crack density indicates that decreasing the temperature deteriorates the ductility of the HCP martensite since the HCP-martensite-related cracking is attributed to the plasticity-driven stress concentration along or in the HCP martensite.²⁰⁾ Therefore, the plastic strain distribution and HCP martensite fraction are key in interpreting the test temperature dependence of the fatigue crack growth.

Fig. 8.

(a) Cross-sectional ECC images of the regions with ΔK = 18 MPa·m^1/2 in the specimens tested at (a) 103 K and (b) 373 K. The test frequency was 10 Hz.

Figure 9 shows sets of the EBSD data obtained near the fracture surfaces of the specimens tested at RT, 103, and 373 K. As shown in the phase map (Figs. 9(a)–9(c)), the HCP martensite fraction near the fracture surface decreased as the temperature decreased from RT to 103 K. The HCP martensite fraction at 103 K was even lower than that at 373 K. Since decreasing the temperature generally promotes the FCC-HCP martensitic transformation, the temperature dependence of the HCP martensite fraction was unconventional. To understand this peculiar trend, we observed the local deformability near the fracture surface. Figures 9(d)–9(f) show the grain orientation spread (GOS) maps that show the plastic strain distribution at a grain-size scale.^39,40,41) The area of the high GOS value region at 103 K was smaller than the areas at RT and 373 K. Even when the GOS values near the fracture surface were only compared, the average GOS values in both the FCC and HCP phases at 103 K were lower than those at RT and 373 K (Figs. 9(g)–9(i)). In addition, the HCP martensite at 103 K was observed as sharper plates than the HCP-martensite at RT and 373 K, as shown in Figs. 8 and 9(a)–9(c). The presence of the sharp HCP martensite plates indicates that the grains of the specimen tested at 103 K contained higher internal stress that stemmed from the stress concentration at the tip of the HCP martensite plates, compared with the internal stresses at RT and 373 K at an identical martensite fraction. From these observations, it was concluded that decreasing the test temperature deteriorated the stress accommodation capability of the HCP martensite, which remained the sharpness of the HCP martensite. As a result, the accumulation of HCP-martensite-related stress induced cracking at a relatively low crack tip opening displacement and plastic strain. Therefore, the HCP martensite fraction at 103 K was lower than the fractions at RT and 373 K. In this context, the acceleration of the fatigue crack growth by decreasing temperature from RT to 103 K is attributed to the promotion of HCP martensite cracking owing to the deterioration of the ductility of the HCP martensite.

Fig. 9.

(a–c) Phase map, (d–f) GOS map, and (g–i) cross-sectional profile of the GOS values of the regions with ΔK = 18 MPa·m^1/2 in the specimens tested at (a, d, and g) RT (1 Hz), (b, e, and h) 103 K (10 Hz), and (c, f, and i) 373 K (10 Hz). (Online version in color.)

At 373 K, the deceleration of the fatigue crack growth by increasing the temperature cannot be explained only by enhancement of the HCP martensite ductility because the GOS values at 373 K were lower than those at RT (Figs. 9(d), 9(f)). Therefore, we further examined the gradient of the HCP martensite fraction and reversibility of the FCC-HCP martensitic transformation as important factors to understand the crack growth deceleration. As shown in Fig. 10, the HCP martensite fraction at 373 K was higher than that at 103 K at which fraction of thermally induced HCP martensite would be higher than that at 373 K. This fact indicates that deformation-induced FCC-HCP martensitic transformation occurred. However, the gradient of the HCP martensite fraction from the fracture surface at 373 K was lower than that at RT. More specifically, the HCP martensite fraction at the nearest region (25 μm) at 373 K was lower than that at a distance of 75 μm. This indicates that the reverse transformation of the HCP martensite to the FCC matrix occurred by crack surface contact. Although the reverse transformation can occur at RT as well, increasing the temperature to 373 K, which is near the T₀ temperature, assists in the reverse transformation from HCP martensite to the austenite matrix.⁴²⁾ Therefore, enhanced reversibility of the HCP martensite decelerates the fatigue crack growth at 373 K. Since an introduction of high plastic strain stabilizes HCP martensite,⁴³⁾ the effect of enhanced reversibility gradually degrades with increasing ΔK as shown in Fig. 4.

Fig. 10.

HCP martensite fraction at different distances from the fracture surface obtained from the regions with ΔK = 18 MPa·m^1/2. (Online version in color.)

4. Conclusions

In this study, the frequency and temperature dependency of the fatigue crack growth behavior of Fe30Mn10Cr10Co (at%) metastable HEA was characterized by CT testing and subsequent microstructure observations. The following new findings were obtained:

(1) The fatigue crack growth rate at RT was insensitive to the frequency in the range of 1 to 25 Hz. In addition, the microstructure evolution and secondary cracking behaviors were also insensitive to the frequency.

(2) The fatigue crack growth accelerated with decreasing test temperature from RT to 103 K. The acceleration is attributed to promotion of HCP-martensite-related cracking. This cracking occurred because of the deterioration of the ductility of the HCP martensite.

(3) Increasing the test temperature to 373 K decelerated the fatigue crack growth. Deformation-induced FCC-HCP martensitic transformation occurred at 373 K, particularly near the crack tip. In addition, since 373 K is just below the equilibrium temperature of the FCC and HCP phases, it can enhance the reversibility of the HCP martensite. These factors contributed to the deceleration of the fatigue crack growth.

Acknowledgements

This work was financially supported by JSPS KAKENHI (JP16H06365 and JP20H02457) and the Japan Science and Technology Agency (JST) (Grant no. 20100113) under the Industry-Academia Collaborative R&D Program.

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