Study on three-point-bending fatigue properties of Cu45Zr45Ag7Al3 amorphous alloy

In this article, Cu45Zr45Ag7Al3 amorphous alloys were prepared by copper mold suction casting method and its three-point-bending fatigue performance were researched. The structural characteristics of the alloy were analyzed using x-ray diffraction (XRD), and the fatigue fracture morphology was analyzed using scanning electron microscopy (SEM). The results indicate that the surface morphology of the three-point-bending fatigue fracture mainly includes three regions: the fatigue crack initiation region, the steady-state crack propagation region with typical fatigue stripes and the final rapidly fracture region. The fatigue crack source is micropores ranging in size from 30 to 50 μm, where numerous shear bands formed. And the fatigue limit of amorphous alloys is 410MPa, which is higher than the four-point-bending fatigue limit.


Introduction
Amorphous alloys, due to their high strength, hardness, excellent wear and corrosion resistance, as well as excellent soft magnetism, superconductivity, and low magnetic losses, have broad application prospects in engineering materials, functional materials, and other fields [1,2]. And with the deepening of theoretical research, their application scope continues to expand. Fatigue performance, as an important indicator of material engineering applications, has been extensively studied for the fatigue behavior of amorphous alloys with different compositions under different load modes for a long time, including bending fatigue, tensile fatigue, compressive fatigue, and torsional fatigue [3][4][5][6][7][8][9].
Gilberl et al [10] researched the four-point-bending fatigue performance of Vit1 (Zr 41.2 Ti 1.8 Cu 12.5 Ni 10 Be 22.5 ) bulk amorphous alloy. It was found that the fatigue crack propagation behavior of Zr based bulk amorphous alloys is similar to that of crystalline alloys, but its stress life is lower. This phenomenon may be related to different initiation modes of fatigue cracks. Subsequently, Peter, Wang, and Qiao et al [11][12][13][14] used different testing methods to study the fatigue performance of bulk amorphous alloys, and investigated the impact of external environmental changes on the fatigue performance of bulk amorphous alloys. They found that the mechanism of fatigue crack generation in amorphous alloys in NaCl salt solution is similar to that of the alloys in air, but the way of fatigue crack propagation is different. At the same time, it was found that due to the general use of casting methods to prepare amorphous alloys, casting defects (such as inclusions and pores) that exist inside the material will become stress concentration points and expand into micro cracks. Some other researchers suggested that fatigue cracks start in the local shear band region, and the fatigue failure of amorphous alloy materials is related to the formation and propagation of shear bands [15]. Some researchers found that the plastic deformation of amorphous alloys is mainly dominated by the initiation and propagation of shear bands [16][17][18][19]. Yang et al [20] defined shear-dominated zones, dilatation-dominated zones, and rotation-dominated zones to reveal the physical mechanism of shear band formation from the perspective of the participation fraction. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
In this study, the stress versus fatigue cycle-life (S versus N) curve of Cu 45 Zr 45 Ag 7 Al 3 amorphous alloy under the three-point-bending fatigue were investigated. And the fatigue crack initiation and failure mechanism were presented based on the fracture morphology analysis.

Experimental
Cu 45 Zr 45 Ag 7 Al 3 amorphous alloys were prepared by vacuum arc melting/copper mold suction casting, and the purity of the raw materials used were not less than 99.95% (wt%). The dimension of the three-point-bending fatigue samples are 3 mm × 3 mm × 25 mm. The compressive yield strength of Cu 45 Zr 45 Ag 7 Al 3 amorphous alloy is 1.51ield GPa.
The amorphous nature of alloys were confirmed by x-ray diffractometer with Cu Kα radiation. The fatigue fracture morphology was observed by Quanta2000 environmental scanning electron microscopy (SEM) and the fracture characteristics were analyzed.
The three-point-bending fatigue test was conducted on a computer-controlled MTS 10 kN fatigue testing machine, using axial strain control. The loading waveform was a cosine wave, and the stress ratio R was 0.1 (R = σ min /σ max , σ min and σ max is the minimum and maximum load), with a frequency of 10 Hz. The schematic diagram of three-point-bending loading is shown in figure 1. Generally speaking, the relationship between load and sample size and fulcrum distance can be represented by the 'beam theory' [21]: Where P is the load, b and t are the thickness and height of the sample, S is the span of the lower support point. In this experiment, S = 20 mm.
The fatigue test starts at a higher stress amplitude and gradually decreases. Therefore, the sample can be fractured after a very limited number of cycles. Subsequently, we gradually reduce the applied stress amplitude until the sample undergoes 10 7 cycles and still does not experience fatigue fracture, then terminate the fatigue test. In addition, the stress amplitude (σ a ) in this study is defined as half of the stress range (Δσ).

Characteristics of amorphous structure
The XRD diffraction curve of Cu 45 Zr 45 Ag 7 Al 3 amorphous alloy is shown in figure 2. It can be seen that there are no sharp crystal diffraction peaks in the sample, only relatively flat dispersion diffraction peaks appear between 35°and 45°, indicating its amorphous characteristics.
The stress-life (S-N) curve of amorphous alloys under three-point-bending fatigue load is plotted in figure 3. It can be seen that the fatigue life values of Cu 45 Zr 45 Ag 7 Al 3 amorphous alloys are mostly between 10 3 and 10 5 . As the stress amplitude decreases, the fatigue life gradually increases. When the applied stress amplitude drops to a certain critical value, the slope of the S-N curve will undergo a sudden change, commonly referred to as the 'inflection point'. After the fatigue life is 10 6 , the stress amplitude changes very little. When the stress amplitude is 410 MPa, the sample failed or shows no damaged above 10 7 cycles. Therefore, the fatigue limit of amorphous alloys is 410 MPa.
At the same time, in order to facilitate the application in engineering practice, the stress life test data is fitted to obtain: Where σ a is the stress amplitude, and N f is the fatigue life. Figure 4 shows the fatigue fracture morphology of amorphous alloys under a stress amplitude of 650 MPa. As shown in figure 4(a), the overall fatigue fracture surface consists of three different regions, which are the fatigue crack initiation region; the steady-state crack propagation region with typical fatigue stripes and the final rapidly fracture region. Figure 4(b) is an enlarged view of the crack initiation zone in figure 4(a), where some micropores with diameters ranging from 30-50 μm can be observed. This indicates that the fatigue crack of the sample originated from external defects. In addition, it can be observed that initial small cracks propagate along different paths from these small pores to the interior of the sample. These small pores may originate from the mechanical polishing process of the sample or from the pores generated during the casting process of the sample. After crack initiation and initial small crack propagation, 'Ridge-valley' shape of crack growth can be observed as shown in figure 4(c). Where the inclined surface between the ridge and valley is caused by type III shear deformation, the multiple undulating crack growth morphologies converge at the interface of the rapidly  destabilizing fracture zone. In addition, high-power observations reveal thin stripes (about 2 μm) on these coarse stripes (about 4-6 μm), as shown in figure 4(d). As the crack continues to propagate, rough fatigue stripes perpendicular to the direction of crack growth are clearly observed on the fracture surface, as shown in figure 4(e). For amorphous alloys, the fatigue crack propagates along the shear band network at the crack tip. The mechanism of fatigue crack growth is still the alternating process of passivation and sharpening at the crack tip. As a result, typical fatigue stripe morphology is formed on the surface of the fracture. The thinner fatigue stripe is the result of one step crack growth in a single loading cycle, while the thicker fatigue stripe is the result of periodic deflection of the main crack [22,23].

S-N curves
From figure 3, it can be seen that the S-N curve of amorphous alloys tends to be horizontal under a certain stress amplitude, which is similar to steel, but different from non-ferrous metals such as aluminum, magnesium, copper, and their alloys [24]. In addition, the fatigue ratio of amorphous alloys is also comparable to most crystalline materials (the fatigue ratio of crystalline materials are usually between 0.3 and 0.5) [25].
At the same time, it was found that the three-point-bending fatigue life and fatigue limit of the amorphous alloy are higher than those of the four-point bending fatigue through comparison [9]. This is because the surface area exposed by the material under the four-point-bending fatigue test is higher than that of the three-pointbending fatigue, and a larger surface area means more defects and stress concentration, which will increase the probability of fatigue crack initiation [26,27].

Crack initiation mechanism
The fatigue crack initiation mechanism of polycrystalline materials has been widely studied. Usually, fatigue cracks in polycrystalline alloys will initiate at weak locations such as slip bands, grain boundaries, twinning, and deformation bands [24,25]. However, due to the amorphous nature of metallic glass, they do not have the crystal defects mentioned above, so their fatigue crack initiation mechanism may be different from traditional polycrystalline materials.
Some researchers reported that fracture accidents are caused by fatigue failure [24]. In addition, almost 100% of fractures begin at stress concentration locations where structural discontinuities such as holes, notches, shoulders, cracks, defects, and scratches occur [25,27,28]. In all practical macroscopic materials, defects are always inevitable, and metallic glass is no exception. According to reports, fatigue cracks in metallic glass originate from casting defects such as pores, inclusions, quasicrystals or surface defects originating from specimens such as scratches and grooves produced by polishing. Some researchers have also pointed out that fatigue cracks initiate near the shear band and are related to the free volume of the alloy [29][30][31]. According to molecular dynamics calculations of amorphous alloys, compared to a single load, only a very low load is required under cyclic loading, which can lead to the accumulation of free volume inside the alloy. Some other researchs [32,33] found that nano/micro-scale voids and cracks at the intersecting sites of shear bands and preferential etching of shear bands. These observations demonstrated that the formation of shear bands in amorphous alloy is resulted mainly from local free volume coalescence. In this three-point-bending fatigue test, the number of free volumes generated in some narrow regions under local stress is greater than the number that disappears through diffusion. Therefore, under stress, shear bands are formed locally due to the accumulation of excessive free volume. Jiang et al [34] showed through high-resolution transmission electron microscopy that a large number of nano voids were accumulated at the shear band. Under the action of tensile stress, it promotes the growth of these voids; under compressive stress, the growth of voids is hindered, leading to the propagation of shear bands. This is the result of excessive accumulation of free volume in the shear bands. The fatigue crack source in this article comes from micropores of size 30-50 μm. Figure 5 shows shear bands around the crack initiation regions during three-point-bending fatigue. It can be observed that a large number of shear bands initiate in this area, which also proves the theory that fatigue crack initiation is due to the initiation of a large number of shear bands at alloy defects. And at the same time, some microcracks are observed along shear-off steps on the surface, which are similar to the results under the tensiontension fatigue tests [35,36].

Failure mechanism
Under three-point-bending cyclic loading, shear bands will form at defects such as micropores in amorphous alloys. In these shear bands, the accumulation of free volume leads to the formation of some voids. Under the action of tensile stress, it promotes the growth of voids, leading to the formation of stress concentration in these void areas, thereby promoting the initiation of fatigue cracks in this area. As the cyclic load continues to load, fatigue cracks will propagate. A small plastic region will form at the crack tip, which serves to passivate the crack tip. However, a large number of shear bands and support cracks will propagate around the crack tip. This type of crack bifurcation exhibits a similar phenomenon in Flores et al [37] study of the crack propagation behavior of Zr based amorphous materials. In this case, the crack will propagate along these forks. Therefore, under bending cyclic loading, amorphous alloy samples will form strip like crack propagation regions due to passivation and re-sharpening phenomena.

Conclusions
(1) The surface morphology of three-point-bending fatigue fracture mainly includes three main regions: the fatigue crack initiation region, the steady-state crack propagation region with typical fatigue stripes and the final rapidly fracture region; (2) Under the conditions of three-point-bending fatigue test with a stress ratio R of 0.1 and a frequency of 10Hz, the fatigue limit is 410 MPa, which is higher than four-point bending fatigue.
(3) During the three-point-bending fatigue process, a large number of voids will accumulate at the shear band in the amorphous alloy which is caused by defects such as micropores. Under the action of tensile stress, the growth of these voids is promoted, thereby promoting the initiation of crack sources in this area. At the same time, the phenomenon of passivation and re sharpening will lead to crack propagation.