# Tensile Creep Characterization and Prediction of Zr-Based Metallic Glass at High Temperatures

^{1}

^{2}

^{3}

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## Abstract

**:**

## 1. Introduction

_{41}Co

_{7}Cr

_{15}Mo

_{14}C

_{15}B

_{6}Y

_{2}BMG using the nanoindentation technique and found that the creep exponent varied with the peak load or loading rate, which has been interpreted based on the shear transformation zone theory [6]. Yu et al. suggested that the nanoindentation creep behaviors of Co

_{56}Ta

_{9}B

_{35}metallic glass could be described by a Kelvin model [7]. However, it should be noted that the nanoindentation creep is sensitive to the ambient environment, and the different holding times used in creep tests in previous literature have caused paradoxical results. The compressive creep and stress relaxation experiments of Zr-based BMGs at high temperatures were also performed [15].

_{50.7}Cu

_{28}Ni

_{9}Al

_{12.3}(at %) alloy, which has a critical diameter of 14 mm for glass formation [24], was selected as the model material. Its creep behavior was studied through tensile tests. The microstructures of the alloy samples after the creep tests were studied in detail. Furthermore, constitutive models for predicting the high temperature creep behaviors of the Zr-based BMG were established based on the θ projection method, and the validity of the established creep models was confirmed. This work aims to investigate the creep behaviors and further predict the creep lifetime of the ZrCuNiAl glassy alloy below the T

_{g}, which ensures that the Zr-based alloy remains in the amorphous state. The present work also provides the experimental and theoretical cornerstones for extending the applications of BMGs as structural materials.

## 2. Materials and Methods

_{g}, and applied stresses of 50–180 MPa were selected for 24 h creep tests in a high temperature creep fatigue testing apparatus (CRIMS RPL, Changchun, China). Tensile tests were carried out at different temperatures on an Instron type tensile machine (Instron Corp., Norwood, MA, USA) at an initial strain rate of 5 × 10

^{−2}s

^{−1}. The microstructures of the samples after creep tests were examined by scanning electron microscopy (SEM, Quanta 200FEG, FEI, Hillsboro, OR, USA) and transmission electron microscopy (TEM, TECNAI G2, FEI, Hillsboro, OR, USA). The TEM samples were prepared by mechanical polishing, followed by twin-jet electropolishing.

## 3. Results and Discussion

_{g}and crystallization temperature, T

_{x}, were determined to be 715 K and 790 K, respectively. The inset of Figure 2a shows the XRD patterns of the as-cast Zr-based BMG alloy samples. A broad halo diffraction peak was observed, denoting a fully glassy phase. Figure 2b demonstrates the tensile stress-strain curves at different temperatures. The values of fracture stress were determined to be 1743 MPa, 1074 MPa, 887 MPa, and 788 MPa for 293 K, 660 K, 680 K, and 700 K, respectively. It is interesting to notice that the strength decreases remarkably from 1743 MPa to 788 MPa, following the temperature increases from 293 K to 700 K. It has been reported that the concept of shear transformation zones (STZs) can be introduced into the deformation mechanism of amorphous metals by argon [25]. In STZ theory, STZ is considered to be a basic shear unit in an amorphous metallic alloy. The cooperative rearrangement of atomic-scale STZs under applied stress results in the macroscopic shear deformation. Johnson and Samwer [26] suggested that the yield strength of a metallic glass can be determined by the cooperative shear motion of STZs, as follows:

_{0}is the attempt frequency, and $\stackrel{\u2022}{\mathsf{\gamma}}$ is the shear strain rate. The ratio of G

_{0T}/G

_{0Tg}is a factor that incorporates the weak dependence of G on the thermal expansion of a fixed glass configuration, and t = T/T

_{g}. The shear strength, τ, can be converted into the fracture strength, σ, according to the following equation [27]:

_{0}is the strength at T = 0 K, and $A={[(k/\mathsf{\beta})\mathrm{ln}({\mathsf{\omega}}_{0}/C\stackrel{\u2022}{\mathsf{\gamma}})({G}_{0T}/{G}_{0T\mathrm{g}})]}^{2/3}$, which can be considered to have a constant value. It is apparent, following the above relationship, that the strength of the bulk metallic glass decreases with an increasing testing temperature, which is consistent with previous reports [28,29,30].

^{−7}s

^{−1}and 3.9 × 10

^{−7}s

^{−1}at 660 K and 680 K, respectively. The secondary stage was greatly shortened, and the creep rate reached up to 6.83 × 10

^{−6}s

^{−1}when the creep temperature was 700 K. The tertiary stage at 700 K started after 5 h, and the fracture happened at 6.3 h with a creep strain of 0.34%. Figure 2d demonstrates the creep behaviors of the BMG at 680 K under different applied stresses. No tertiary stage appeared below 100 MPa, and the steady state creep rates at the secondary stages were 5.1 × 10

^{−7}s

^{−1}and 3.9 × 10

^{−7}s

^{−1}for 50 MPa and 100 MPa, respectively. For the case of the 180 MPa applied stress, after 1 h creep, the creep curve entered the secondary stage with a steady creep rate of 1.96 × 10

^{−6}s

^{−1}and lasted for 20 h. The tertiary stage began after 20 h. The total creep strain was ~0.7% for 24 h. The corresponding strain rate curves are shown in Figure 2e,f. For the case of 100 MPa applied stress, higher temperatures caused higher strain rates for the studied BMG sample. For the 680 K testing temperature, a higher applied stress resulted in a higher strain rate.

_{3}Zr phase.

_{3}Ni and Al

_{4}Zr

_{5}intermetallics. Previous experiments [34] on the crystallization of the studied BMG above T

_{g}under thermal annealing have shown the same crystalline phases precipitated from the glassy matrix as those formed in the present creep experiments. It has been reported that nanocrystalline phases, identical to those formed during annealing, can be induced by nanoindentation at room temperature. The observed rapid formation of crystalline phases is a direct consequence of dramatic enhancement of atomic diffusional mobility [35]. In the present work, though 680 K and 700 K were below the T

_{g}, the external load with a duration of 24 h induced the occurrence of nanocrystallization. The different crystalline phases could be attributed to the different levels of atomic diffusional mobility at different temperatures and applied loads.

^{−1}, A is the material constant, n is the stress exponent, Q is the creep activation energy in kJ/mol, R is the gas constant (8.31 J·mol

^{−1}·K

^{−1}), and T is the absolute temperature in K.

_{1}and θ

_{3}are the primary and tertiary strains, respectively, and θ

_{2}and θ

_{4}are rate parameters governing the curvatures of the primary and tertiary components, respectively. This expression can be divided down into two parts, as shown in Figure 5a. The expression, ${\mathsf{\theta}}_{1}(1-{\mathrm{e}}^{-{\mathsf{\theta}}_{2}t})$, represents the primary creep, where θ

_{1}is the total primary strain while θ

_{2}determines the shape of the primary creep component. Likewise, ${\mathsf{\theta}}_{3}({\mathrm{e}}^{{\mathsf{\theta}}_{4}t}-1)$ represents the tertiary creep with θ

_{3}scaling tertiary creep strain, and θ

_{4}determines the curvature of tertiary creep. Therefore, θ

_{1}and θ

_{3}are termed ‘scale’ parameters, while θ

_{2}and θ

_{4}are termed ‘rate’ parameters. The relationships between the θ parameters, temperature, and applied stress can be expressed with the following [40]:

_{i}and H

_{i}are material constants, R is the universal gas constant, T is the absolute temperature, Q is the activation energy of creep deformation, and σ

_{y}represents the initial yield stress under different creep temperatures, as shown in Figure 2b.

^{the}and ε

^{exp}are the theoretical and experimental strains, respectively, and m represents the number of data points on each creep curve. Using the non-linear least-squares fitting method and a computer program based on “MATLAB”, the values of θ

_{1}and θ

_{2}under all the testing conditions were obtained based on the experiment results, as shown in Table 1.

_{1}and θ

_{2}at different testing conditions, as shown in Table 1, the values of lnθ

_{1}and lnθ

_{2}can be easily evaluated. Meanwhile, the activation energy of this alloy can be obtained from the above results. Therefore, the values of lnθ

_{2}+ Q/RT under different applied stresses can be also calculated. The relationship between θ parameters (θ

_{1}and θ

_{2}), creep temperatures and applied stresses is plotted in Figure 5. Obviously, it can be seen that there are excellent linear relationships between the θ

_{1}, θ

_{2}parameters and the applied stresses. Then, the values of H

_{1}and H

_{2}were calculated to be 18.05 and −24.13, respectively, from the slopes of the lnθ

_{1}− σ/σ

_{y}and (lnθ

_{2}+ Q/RT) − σ plots, respectively. The values of G

_{1}and G

_{2}were calculated to be e

^{−6.32}and e

^{65.11}, respectively. Thus, the constitutive model of Zr-based alloys during the primary creep stage can be expressed as follows:

_{3}and θ

_{4}under different testing conditions, the relationship, lnθ

_{3}− σ/σ

_{y}and (lnθ

_{4}+ Q/RT) − σ, is also be shown in Figure 5. The values of G

_{3}, H

_{3}, G

_{4}and H

_{4}were calculated to be e

^{−1.18}, −15.42, e

^{58.87}and −169.3 by an identical method, respectively. Therefore, the creep constitutive models during the secondary and tertiary creep stages for the studied Zr-based BMG can be expressed as

## 4. Conclusions

_{3}Zr, Al

_{3}Ni and Al

_{4}Zr

_{5}phases exist in a glassy matrix at high temperatures and high applied stresses. The creep activation energy and stress exponent were calculated to be 377 kJ/mol and 4.21, respectively. The parameters of the established models based on the θ projection method, θ

_{i}, G

_{i}and H

_{i}(i = 1, 2, 3 and 4), at different testing conditions were calculated by non-linear least-squares and linear fitting methods. It was found that the established models were closely associated with the applied stress and temperature. The creep curves of Zr-based BMGs predicted by the proposed models were consistent with the experimental curves, verifying the validity of the established models to predict the creep behaviors of BMGs. The concentration gradient region resulted from the density variation of free volume acts as a driving force for atomic motion and free volume movement. A schematic model was proposed to describe the high temperature creep deformation of BMGs based on the diffusional motion of free volume within a glassy matrix surrounded by shear bands. Higher testing temperatures cause easier atomic movement, favoring creep deformation. Meanwhile, larger applied stresses increase the deformation rate of the BMG. The atomic diffusion perpendicular to the loading force constantly facilitates the formation of a new free volume, resulting in higher creep strain and a higher steady state creep rate.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**(

**a**) Differential scanning calorimetry (DSC) curve; (

**b**) tensile stress-strain curves at different temperatures; (

**c**,

**d**) tensile creep curves; and (

**e**,

**f**) the corresponding strain rate-time curves of the Zr-based BMG alloy with different creep parameters.

**Figure 3.**SEM and TEM images, together with the selected area electron diffraction (SAED) patterns of the samples after creep tests at 680 K with different applied stresses: (

**a**) 50 MPa; (

**b**) 100 MPa; and (

**c**) 180 MPa.

**Figure 4.**SEM and TEM images, together with the SAED patterns of the samples after creep tests at 100 MPa with different temperatures: (

**a**) 660 K, (

**b**) 680 K, and (

**c**) 700 K.

**Figure 5.**(

**a**) Schematic creep curve based on the θ projection concept. Relationships of (

**b**) lnθ

_{1}− σ/σ

_{y}; (

**c**) (lnθ

_{2}+ Q/RT) − σ; (

**d**) lnθ

_{3}− σ/σ

_{y}and (

**e**) (lnθ

_{4}+ Q/RT) − σ.

**Figure 6.**Comparisons between the experimental curves and predicted curves: (

**a**) 100 MPa for different temperatures and (

**b**) 680 K for different applied stresses.

**Figure 7.**Schematic diagram of (

**a**) Nabarro-Herring creep model (black arrows: atom diffusion; green arrows: vacancy diffusion) [38], and (

**b**) creep model for bulk metallic glass (BMGs) (black arrows: atom diffusion; green arrows: free volume movement).

**Table 1.**Values of the total primary strain θ

_{1}, tertiary strain θ

_{3}, and rate parameters governing curvatures of the primary (θ

_{2}) and tertiary (θ

_{4}) components at different creep parameters.

660 K 100 MPa σ/σ_{y} = 0.0931 | 680 K 100 MPa σ/σ_{y} = 0.1127 | 700 K 100 MPa σ/σ_{y} = 0.1269 | |||||||||

θ_{1} | θ_{2} | θ_{3} | θ_{4} | θ_{1} | θ_{2} | θ_{3} | θ_{4} | θ_{1} | θ_{2} | θ_{3} | θ_{4} |

0.00954 | 0.2551 | 0.0714 | 0.007342 | 0.01382 | 0.3183 | 0.0595 | 0.015 | 0.01753 | 0.3667 | 0.04207 | 0.3271 |

680 K 50 MPa σ/σ_{y} = 0.0564 | 680 K 100 MPa σ/σ_{y} = 0.1127 | 680 K 180 MPa σ/σ_{y} = 0.2029 | |||||||||

θ_{1} | θ_{2} | θ_{3} | θ_{4} | θ_{1} | θ_{2} | θ_{3} | θ_{4} | θ_{1} | θ_{2} | θ_{3} | θ_{4} |

0.01467 | 0.2491 | 0.0459 | 0.001464 | 0.01682 | 0.3183 | 0.0565 | 0.015 | 0.07778 | 0.4358 | 0.05218 | 0.09878 |

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**MDPI and ACS Style**

Wang, G.; Pan, D.; Shi, X.; Huttula, M.; Cao, W.; Huang, Y. Tensile Creep Characterization and Prediction of Zr-Based Metallic Glass at High Temperatures. *Metals* **2018**, *8*, 457.
https://doi.org/10.3390/met8060457

**AMA Style**

Wang G, Pan D, Shi X, Huttula M, Cao W, Huang Y. Tensile Creep Characterization and Prediction of Zr-Based Metallic Glass at High Temperatures. *Metals*. 2018; 8(6):457.
https://doi.org/10.3390/met8060457

**Chicago/Turabian Style**

Wang, Gang, Daoyuan Pan, Xinying Shi, Marko Huttula, Wei Cao, and Yongjiang Huang. 2018. "Tensile Creep Characterization and Prediction of Zr-Based Metallic Glass at High Temperatures" *Metals* 8, no. 6: 457.
https://doi.org/10.3390/met8060457