Metallurgical and Materials Transactions A

, Volume 43, Issue 8, pp 2676–2679

The Effects of Fatigue on the Atomic Structure with Cyclic Loading in Zr50Cu40Al10 and Zr60Cu30Al10 Glasses


  • Peng Tong
    • Department of PhysicsUniversity of Virginia
    • Department of PhysicsUniversity of Virginia
  • G. Wang
    • Department of Materials Science and EngineeringUniversity of Tennessee
  • P. K. Liaw
    • Department of Materials Science and EngineeringUniversity of Tennessee
  • E. Maxey
    • Argonne National Laboratory
  • Y. Yokoyama
    • Institute for Materials ResearchTohoku University
Symposium: Bulk Metallic Glasses VIII

DOI: 10.1007/s11661-011-0887-5

Cite this article as:
Tong, P., Louca, D., Wang, G. et al. Metall and Mat Trans A (2012) 43: 2676. doi:10.1007/s11661-011-0887-5


The potential damage effect from fatigue on Zr bulk metallic glass alloys of Zr50Cu40Al10 at the eutectic point and Zr60Cu30Al10 away from the eutectic point (in atomic percent) is examined via the local atomic structure, which was obtained from the pair density function analysis of the synchrotron X-ray radiation and neutron data. Samples cut from the same rods were subjected to 104, 105, and 106 compression cycles ex situ, and the evidence for fatigue damage was investigated by comparing alloys before and after cyclic loading. Bond orientation was observed particularly in Zr50Cu40Al10, suggesting that fatigue damage occurs even in the elastic range, below the yield point, and during cyclic loading. The initiation of fatigue changes is observed first within small localized atomic regions.

1 Introduction

Bulk metallic glass (BMG) alloys with good glass-forming abilities and slow cooling rates can be potentially suitable in a wide range of engineering applications.[15] BMGs have superb physical properties, such as high corrosion and wear resistance, high yield strength, soft magnetic properties, and even superconducting properties.[68] Despite their good mechanical properties, their use is limited primarily because BMGs tend to be brittle as they cannot plastically elongate during a uniaxial tensile stress. However, some BMGs can plastically deform under compression, rolling, and bending at ambient temperatures.[9] The deformation process occurs through the formation of localized shear bands.[1012] The same shear bands may become a site for further plastic flows, resulting in low ductility.[13] Improving their ductility and tolerance to damage is an important step toward allowing BMGs to be used as industrial materials.

BMGs are particularly vulnerable to fatigue damage,[1418] even under low applied stresses below the global yield limits, often with no visible effects, such as the presence of shear bands, until failure occurs. The elastic-to-plastic transition appears suddenly. Under fatigue-loading conditions, a wide range of fatigue endurance limits[19,20] is usually observed. To date, the physical mechanism that leads to catastrophic failure under fatigue-loading conditions, in which localized damage accumulates and eventually leads to failure, is not well understood.[7,1418] It is presumed that irreversible changes must be taking place under fatigue, but their nature and the mechanism leading to such localized damage have not been identified. To search for evidence of initial changes that may occur in the atomic structure under high-frequency fatigue loading, the local atomic structure of ternary Zr-based bulk metallic glasses subjected to compression-compression cyclic loading tests is investigated via neutron and X-ray diffraction. The response to cyclic fatigue loading is investigated in two compositions, Zr50Cu40Al10 and Zr60Cu30Al10, which differ only by 10 pct in the Cu content.[21]

Our results indicate that microstructural changes observed in a small sample volume are most likely the effects from cyclic fatigue during compression, where the same atomic regions may act as nucleation sites for subsequent deformation. The local atomic structures of the Zr50Cu40Al10 and Zr60Cu30Al10 were examined after subjecting both alloys to various fatigue cycles ex situ. A structural change, albeit small, is observed in both compositions regardless of the number of cycles, which may serve as evidence for damage caused by fatigue despite no visible external changes in the alloys after testing. The atomic changes are observed in the short-range pair correlations up to ~3.5 Å and occur viscoelastically, in response to the applied stress in both alloys but more so in Zr50Cu40Al10. At distances greater than 4 Å, the atomic structure shows no differences with the number of compression cycles. The results indicate that the effects caused by cyclic-fatigue loading are not elastic and bring about subtle and irreversible atomic rearrangements within small volume pockets. Zr50Cu40Al10 is close to the eutectic composition and shows significant embrittlement by structural relaxation, whereas Zr60Cu30Al10 exhibits high resistivity against the structural relaxation embrittlement. Furthermore, fracture toughness is different between them. The fracture toughness value of the former is 51 and of the latter is 110 MPa m1/2, respectively.[21]

2 Methods

Master alloy ingots were prepared by arc melting pure Zr, Cu, and Al metals in an argon atmosphere. The master alloys were remelted several times to ensure homogeneity and then cast into rods with dimension of ~5 mm in height and ~2.5 mm in diameter. No crystalline second phases were detected by either neutron or X-ray diffraction. The compression–compression fatigue experiments were performed on the samples used for the diffraction experiments using a computer-controlled materials test system servohydraulic machine at a frequency of 10 Hz with an R ratio (the ratio of the minimum σmin and maximum σmax applied stresses) of 0.1 under a maximum stress of 1600 MPa. The response to cyclic fatigue for the two compositions studied under compression is summarized in Figure 1 for a total of 18 samples where the applied stress is 1600 to 1850 MPa. The number of cycles to failure varied from 104 to 106 and the cycles at which each sample failed is recorded as a point in the maximum stress vs cycles to failure plot of Figure 1. The 104 test takes about 0.278 hours, the 105 takes 2.78 hours, and the 106 takes 27.8 hours. A tendency was observed for Zr60Cu30Al10 to break under fewer cycles than Zr50Cu40Al10 at a similar applied stress. This finding indicates that Zr60Cu30Al10 may be more susceptible to cyclic fatigue loading than Zr50Cu40Al10.
Fig. 1

Maximum stress as a function of cycles to fatigue for Zr50Cu40Al10 and Zr60Cu30Al10

Several rods per composition were used for the neutron measurements at room temperature for a total of 15 g because of the low neutron flux. The neutron data were collected at the neutron pair density function diffractometer of the Los Alamos Neutron Science Center for a total of 8 hours per sample. Three rods used in the neutron measurement subsequently were subjected to fatigue under a stress of 1600 MPa for 104, 105, and 106 cycles, and each rod was then measured with synchrotron X-rays. The same procedure was carried out for both compositions. The X-ray diffraction data were collected at the Advanced Photon Source of the Argonne National Laboratory, at the 11-ID B beam line using a wavelength of 1.54 Å. Each data set was collected for a period of 1 hour at room temperature. The reflection mode was used in the X-ray scattering experiment. The data were analyzed using the pair density function (PDF) analysis technique. First, the structure function, S(Q) was obtained from the diffraction intensity with the instrumental background and sample container contributions subtracted. The error included in the S(Q) includes both statistical and systematic ones. The statistical error originates from the counting statistics and is propagated through the analysis to the final step in obtaining the error in PDF. The systematic error is minimized by treating all data identically during the PDF processing. The PDF, ρ(r), is a real space representation of the atomic correlations obtained through a Fourier transformation of the S(Q), where the S(Q) is an integral over a finite energy window[22]:
$$ \rho (r) = \rho_{0} + \frac{1}{{2\pi^{2} r}}\int_{0}^{Q\max } {Q\left[ {S\left( Q \right) - 1} \right]} \sin \left( {Qr} \right)dQ $$
ρ0 is the average atomic number density of the sample and Q is the momentum transfer. Theoretically, the Fourier integration should be carried out to Q = ∞, but in reality it has to be terminated at a finite value of Q determined by the wavelength of the probe. The highest Qmax used in the analysis was 27 Å−1. The PDF function represents the probability of finding pairs of atoms at a given distance.

3 Results and discussion

Shown in Figure 2(a) is the S(Q) at room temperature determined from the X-ray data of the four specimens with the Zr50Cu40Al10 composition. The data from the three specimens under fatigue are compared with the data collected on the specimen with no fatigue. Subtle structural differences are observed in the S(Q) before and after fatigue, which is evidenced by the upward shift of the S(Q) in all three specimens after cyclic loading. The first S(Q) peak is shown in the inset of Figure 2(a) up to 3 Å−1, and the rest of the function is shown in the main figure. The subtle changes in S(Q) are observed in all three samples under fatigue of the same composition; they are not localized in Q-space but rather vary slowly with Q. In contrast, in Zr60Cu30Al10, changes in the S(Q) are less obvious (Figure 2(b)). The changes indicate that the structure does not recover its initial configuration after cyclic loading and unloading, and the microstructural changes induced in the process are different between the two alloys.
Fig. 2

Changes in the structure function S(Q) with cyclic fatigue. In (a), the S(Q) is determined from the room temperature diffraction data collected on Zr50Cu40Al10 subjected to three different cyclic fatigue tests. In (b), the S(Q) is determined for Zr60Cu30Al10 under the same testing conditions. The insets are plots of the corresponding first peak in S(Q). The differences between the S(Q)fatigue and S(Q)as cast are spread out in reciprocal space

By Fourier transforming the S(Q) into real space, the PDF of Eq. [1] corresponding to the local atomic structure is obtained.[2325] Although a long-range order is absent in glasses, they do exhibit a short-to-medium range order with well-defined peaks as shown in Figure 3, which is a plot of the neutron PDFs corresponding to the local atomic structure of the two compositions obtained by Fourier transforming the neutron diffraction data. The two metallic glass systems show substantial differences in the shape of the PDF peaks originating from the differences in composition. Zr is nominally a larger ion than Cu, and one would expect the peaks involving Zr to shift to the right as the concentration of Zr increases, which is what is observed in the figure for Zr60Cu30Al10. By increasing the Zr concentration, the center of mass of the peak shifts to the right. In the case of the Zr50Cu40Al10, the peak is clearly asymmetric and is shifted to the left, to lower r values. Increasing the concentration of Cu increases the number of Cu-Cu and Cu-Al correlations that nominally have shorter bonds than the other bonds in the structure.
Fig. 3

The PDFs corresponding to the local atomic structure of as-cast samples for the two compositions determined at room temperature from the neutron diffraction data. Also shown in the figure is the difference between the two compositions

In Figure 4, the X-ray PDFs corresponding to the local atomic structure of the four Zr50Cu40Al10 as a function of fatigue cycles are shown. As these PDFs were determined from the X-ray data, the peak shapes are different from Figure 3 because of the differences in the scattering factors between neutrons and X-rays. Focusing closely on the first PDF peak in Zr50Cu40Al10 (Figure 4(a)), it is evident that the atomic structure is different before and after cyclic fatigue loading. These differences are outside the statistical error. Note that because the differences in the S(Q)fatigueS(Q)as cast varied slowly with Q, when Fourier transformed, these differences, resulting from small structural rearrangements, are localized in real space within a sphere of radius ~3.5 Å. Thus, it is clear that in comparison with the as-cast sample, all three samples under fatigue exhibit similar behavior, namely an increase in the peak intensity. Thus, although the local volume change under fatigue is small, it is consistently occurring in all specimens, indicating that this may serve as the initiation of nucleation sites leading to plastic behavior. The structural differences among specimens subjected to different fatigue cycles are small, and we cannot quantify the changes occurring between 104 to 106 cycles, for instance. Future experiments in which cyclic loading is prolonged over longer times are planned. The increase in peak intensity with fatigue is analogous to the increase in peak intensity with cooling. In a cooling process, the atomic vibrations are reduced and the width of the peak narrows while the intensity increases corresponding to a reduction in the bond distribution. This is similar to what we observe with fatigue as well; namely, the effects of fatigue are observed as hardening where the peak intensity increases while the area is conserved. In contrast, in the local structure of Zr60Cu30Al10 shown in Figure 4(b), the response to cyclic fatigue loading is smaller. Thus, it is suggested that in Zr60Cu30Al10, less work hardening is occurring.
Fig. 4

The dependence of the local atomic structure to cyclic fatigue determined from X-ray data. In (a), the local atomic structure corresponding to Zr50Cu40Al10 is shown. In (b), the results are shown for Zr60Cu30Al10. The inset in (b) is a plot of the PDF over a longer r range

4 Conclusions

The increase in the intensity of the pair correlation peaks at room temperature must be a consequence of the progressive and localized structural hardening that occurs in the material, when subjected to cyclic loading. With fatigue, the atomic bonds are changed permanently as clearly the atomic structure undergoes irreversible changes. At the same time, the damage is cumulative with increased fatigue cycles for specimens that do not break. The observed changes in the atomic structure may reflect the onset of an elastic to plastic transformation. They must have an impact on the macroscopic yield point and the formation of the first shear band. Note that at longer distances, beyond 3.5 Å, the local structure shows no visible changes under the cyclic loading conditions of this experiment, and neither alloy exhibited any observed changes within the resolution of this experiment. It may be that extending the cyclic loading tests on the same samples, the structural changes may expand to longer distances leading to failure. Such experiments are planned.

What is the origin of the difference in the response observed in the two alloys? The answer must be in the nature of the Zr-Cu correlations. The difference in the atomic percent of Zr and Cu in the two alloys is reflected in the shape of the first PDF peak.[25,26] A higher Cu content shifts the peak’s center of mass to lower r values, whereas a higher Zr content shifts the peak’s center of mass to higher r values, in response to the size of their nominal ionic radii. In Zr50Cu40Al10, one can expect a higher number of Cu-Cu and Zr-Cu bond pair correlations and a lower number of Zr-Zr bond pair correlations in comparison with Zr60Cu30Al10. The reverse is true for Zr60Cu30Al10. To understand the difference in the response to the fatigue damage of the first PDF peak shift in the two alloys requires detailed modeling. To summarize, these results provide evidence for irreversible structural changes with cyclic fatigue similar to the nanoindentation measurements reported in Reference 18.


The authors would like to acknowledge valuable discussions with S.J. Poon and M. Widom. Support for this work was provided by the National Science Foundation, Nos: 130398GA10715 and DMR 0231320. The use of the Advanced Photon Source was supported by the U. S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02-06CH11357.

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© The Minerals, Metals & Materials Society and ASM International 2011