Previous Article in Journal
Editorial for Advances in 3D Printing Technologies of Metals—2nd Edition
 
 
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
Article

A Compressive Flow Prediction Model of Zr56Co28Al16 Bulk Metallic Glass in Supercooled Liquid Region

1
Fujian Provincial Key Laboratory of Featured Materials in Biochemical Industry, College of New Energy and Materials, Ningde Normal University, Ningde 352100, China
2
College of Materials Science and Engineering, Chongqing University, Chongqing 400044, China
*
Authors to whom correspondence should be addressed.
Metals 2026, 16(3), 280; https://doi.org/10.3390/met16030280
Submission received: 28 January 2026 / Revised: 19 February 2026 / Accepted: 27 February 2026 / Published: 2 March 2026
(This article belongs to the Section Metal Failure Analysis)

Abstract

Bulk metallic glasses exhibit unique viscoplastic flow behavior within their supercooled liquid region. Their high-temperature deformation mechanisms diverge markedly from the highly localized deformation at room temperature. This contrast offers a critical window for investigating their compressive flow models and assessing their forming potential. This study aims to systematically reveal the high-temperature compressive flow behavior of bulk metallic glasses within the supercooled liquid region and to establish a corresponding flow model. Through constant strain rate high-temperature compression experiments conducted on Zr56Co28Al16 bulk metallic glass within its supercooled liquid region, the variations in flow stress, crystallinity, and surface deformation characteristics with temperature were systematically investigated. The results indicate that the compressive behavior of the bulk metallic glass exhibits significant temperature dependence within this temperature range. The compressive strength decreased from 689 MPa at 487 °C to 330 MPa at 507 °C, and then increased to 435 MPa at 527 °C. The angle between the fracture/bulging direction and the loading direction increased from 45° at 487 °C to 88° at 507 °C, and then decreased to 60° at 527 °C. The shear band average spacing increased from 1.797 μm at 487 °C to 2.060 μm at 507 °C, and then decreased to 1.189 μm at 527 °C. These results consistently indicate that the plastic deformability is optimal at a compression temperature of around 510 °C. By integrating the analysis of mechanical curves and morphological characteristics, the applicability of three deformation mechanisms was evaluated: highly localized shear banding, homogeneous viscoplastic flow, and dynamic structural relaxation hardening. A constitutive relationship between compressive strength and temperature was established, which accurately describes their correlation. Simultaneously, it reveals that the dominant deformation mechanism evolves through highly localized shear banding and homogeneous viscoplastic flow, ultimately transforming into dynamic structural relaxation hardening as the temperature increases. This study provides theoretical guidance for predicting the compressive flow behavior of bulk metallic glasses in the supercooled liquid region and offers critical model support for precisely controlling their thermoplastic forming processes.

1. Introduction

Due to their unique disordered atomic structure, bulk metallic glasses (BMGs) exhibit outstanding physical and mechanical properties, such as high strength and hardness, a large elastic limit, excellent wear resistance, and superior corrosion resistance. These exceptional characteristics endow BMGs with promising application prospects in fields including aerospace, precision instruments, and sporting equipment [1,2,3,4,5,6]. However, as a promising functional and structural material, bulk metallic glasses (BMGs) suffer from extremely limited macroscopic plasticity at room temperature. Their deformation is highly localized within nanoscale shear bands, resulting in catastrophic brittle failure, which severely hinders their engineering application as structural materials [7,8,9,10,11].
It is noteworthy that when the temperature rises into the supercooled liquid region between the glass transition temperature and the crystallization onset temperature, bulk metallic glasses exhibit superplastic flow behavior with significantly reduced viscosity [12,13,14,15,16,17]. This exceptional property makes it feasible to process BMGs into complex precision components under extremely low flow stress [18,19,20,21]. Currently, the theoretical models describing the viscous flow behavior of bulk metallic glasses in the supercooled liquid region primarily include the free volume model, the shear transformation zone (STZ) model, and the cooperative shear model [22,23]. However, the universality and predictive accuracy of these models across different temperature ranges within the supercooled liquid region still require systematic verification. Particularly when approaching the crystallization onset temperature, deformation may be accompanied by structural relaxation or crystallization, which complicates the deformation mechanisms [14,16].
In this work, the Zr56Co28Al16 bulk metallic glass was selected due to its excellent glass-forming ability and wide supercooled liquid region [23]. Zr-based amorphous alloys exhibit outstanding mechanical properties and relatively low cost, making them promising for applications in aerospace, precision instruments, and other fields [24,25,26,27,28]. Within the supercooled liquid region, amorphous alloys demonstrate superplastic deformation capability, enabling the fabrication of precision components [29,30]. Therefore, investigating their high-temperature processability is of great significance for promoting their practical applications. The Zr56Co28Al16 alloy combines fundamental research value with engineering application prospects, making it an ideal model material for studying the deformation behavior of bulk metallic glasses within the supercooled liquid region.
Based on this, the present study selects the Zr56Co28Al16 bulk metallic glass and systematically conducts high-temperature compression experiments across a broad temperature spectrum within its supercooled liquid region. The objectives are to: (1) analyze the quantitative influence of compression temperature on flow stress; (2) identify the dominant deformation mechanisms in different temperature intervals by combining deformation characteristics; (3) compare mainstream constitutive models and establish a high-temperature compressive flow model system that can more accurately predict the experimental results, thereby providing solid theoretical guidance for the thermoplastic forming of BMGs.

2. Materials and Methods

Ingots with nominal composite Zr56Co28Al16 were prepared by arc melting pure (≥99.99%) metals in a Ti-gettered high-purity argon atmosphere. Cylindrical bulk amorphous samples with a diameter of 2 mm and a length of approximately 50 mm were prepared by the copper mold suction casting technique. The structures of the as-cast and deformed samples were examined by X-ray diffraction (XRD) using a Rigaku MiniFlex-600 diffractometer (Rigaku Corporation, Tokyo, Japan) with Cu Kα characteristic X-ray, λ = 1.5406 Å. The thermodynamic properties of the as-cast BMG were analyzed by differential scanning calorimetry (DSC, STA449F3). Compressive specimens with a height-to-diameter ratio of 2:1 were fabricated from the as-cast cylindrical rods by a diamond saw blade. They were carefully polished to ensure flat and parallel surfaces. High-temperature compression tests were performed on a Gleeble 3500 simulator (Dynamic Systems Inc., New York, NY, USA). The samples were heated at a rate of 5 °C/s and deformed to a strain of 30% at a constant strain rate of 0.01 s−1. Based on the glass transition temperature (476 °C), crystallization onset temperature (518 °C), and supercooled liquid region width (42 °C) determined from Figure 1b, the temperatures for high-temperature compression tests in this work were selected as 487, 497, 507, 517, and 527 °C. The deformed specimens were ultrasonically cleaned in ethanol. Subsequently, the surface deformation characteristics and fracture morphologies of the bulk metallic glass compressed at different temperatures were observed using a scanning electron microscope (SEM, EVO 18) (Carl Zeiss, Oberkochen, Germany).

3. Results and Discussion

As shown in Figure 1a, the XRD pattern of the as-cast Zr56Co28Al16 BMG exhibits a broad diffuse scattering halo at around ≈ 44° with no sharp Bragg diffraction peaks corresponding to any crystalline phases, indicating that the as-cast BMG is fully amorphous. Figure 1b presents the DSC curve of the as-cast Zr56Co28Al16 BMG. The results reveal distinct glass transition and crystallization exotherms, with the glass transition temperature Tg = 476 °C, the crystallization onset temperature Tx = 518 °C, and the supercooled liquid region width ΔT = 42 °C. These thermal characteristics not only further confirm the amorphous nature of the as-cast samples but also provide a direct basis for selecting the deformation temperatures within the supercooled liquid region.
Figure 2a shows the stress–strain curves of the Zr56Co28Al16 bulk metallic glass compressed at a strain rate of 0.01 s−1 within the temperature range of 487 to 527 °C. It can be seen that the compressive flow behavior of BMGs within the supercooled liquid region is highly sensitive to the deformation temperature. The compressive strength is taken as the maximum stress on the upper envelope of the stress–strain curve. At a compression temperature of 487 °C, the bulk metallic glass reached a peak stress of 689 MPa at an elastic strain of approximately 0.10, followed by strain softening. Similarly, at 497 °C, the stress–strain curve was characterized by a maximum stress of 472 MPa corresponding to an elastic strain of 0.13, after which strain softening was observed. Strain softening is caused by the work conducted up to the peak stress, which squeezes atoms into a smaller volume, thereby generating new free volume. This facilitates atomic participation in flow, leading to a decrease in stress. At compression temperatures of 507 and 517 °C, the bulk metallic glass exhibited homogeneous plastic deformation following elastic deformation, with compressive strengths of 330 MPa and 352 MPa, respectively. Compared with the compressive strengths of the bulk metallic glass at 507 and 517 °C, when the compression temperature was increased to 527 °C, which is above the onset crystallization temperature (Tx) of 518 °C, the compressive strength increased to 435 MPa. All samples exhibited serrated flow behavior in their stress–strain curves, which is attributed to the plastic deformation model of metallic glasses [31].
To provide a more intuitive analysis of the effect of compression temperature on the high-temperature deformation behavior of the bulk metallic glass, the compressive strength values at different temperatures are summarized in Table 1 and presented graphically in Figure 2b. It was found that the compressive strength first decreased and then increased with rising compression temperature. This non-monotonic trend is likely related to changes in the dominant plastic deformation mechanism of the BMGs at different temperatures. Specifically, the compressive strength reached its minimum value of 330 MPa at 507 °C. When the compression temperature was below 507 °C, the compressive strength decreased monotonically. This can be attributed to thermal activation just above Tg, which increases atomic mobility and thus makes the evolution of free volume the dominant factor. This promotes the transition of the glass from a “rigid glassy structure” to a “viscoplastic supercooled liquid structure”. When the compression temperature exceeded 507 °C, the compressive strength of the bulk metallic glass increased monotonically. This may be attributed to the increased crystallization of the amorphous matrix within the bulk metallic glass, which facilitates the rapid annihilation of free volume generated during deformation. This process is accompanied by dynamic atomic rearrangement and crystallization phenomena. Consequently, both the interatomic bonding strength and the structural rigidity recover, leading to a notable increase in deformation resistance. Macroscopically, the deformation mode transitions from strain softening to homogeneous plastic flow.
To further analyze the relationship between compressive strength and compression temperature for the bulk metallic glass within the supercooled liquid region, the data were fitted with a binomial function, as shown in Equation (1):
σ = 148662 578.657 × T + 0.56433 × T 2
where σ is the compressive strength, and T is the compression temperature.
The binomial fitting curve for the compressive strength versus temperature of the bulk metallic glass is shown in Figure 2b. From this fitting, it was found that with increasing compression temperature, the compressive strength first decreases and then increases, exhibiting a parabolic trend. The minimum peak stress occurs at around 510 °C, which is not the midpoint temperature of the supercooled liquid region. This deviation may be attributed to stress inhomogeneity within the bulk metallic glass during compression. This binomial relationship provides theoretical guidance for processing the bulk metallic glass within its supercooled liquid region.
Even when deformed within the supercooled liquid region, the bulk metallic glass can still undergo partial crystallization with prolonged deformation time. To analyze the degree of crystallization in the bulk metallic glass during high-temperature compression within the supercooled liquid region, XRD measurements were performed on samples compressed at different temperatures. Figure 3a shows the XRD patterns of the bulk metallic glass after compression at different temperatures. All specimens exhibited varying levels of crystallization. The crystalline phases corresponding to the bulk metallic glass compressed at various temperatures are presented in Figure 3a. It was found that within the compression temperature range of 487–517 °C (below the onset crystallization temperature), the crystalline phases in the Zr56Co28Al16 bulk metallic glass remained essentially consistent, consisting of AlCo, AlCoZr, and AlZr phases, and possibly containing B2 phases such as ZrCo and Al5Co2. The intensity of the crystallization peaks increased with higher compression temperatures. When the compression temperature reached 527 °C (above the onset crystallization temperature), an additional Al3Zr4 phase appeared in the crystalline phases of the bulk metallic glass. This may be related to the atomic radii of Zr, Co, and Al, with Zr having a significantly larger atomic radius than the other two elements. With increasing compression temperature and deformation, AlCo-rich regions formed first. Subsequently, stress release and the resulting adiabatic heating effect promoted the diffusion of Zr, leading to the formation of AlCoZr and AlZr phases. When the temperature is further increased to 527 °C, the metallic glass forms an Al3Zr4 phase with sharp diffraction peaks.
To further analyze the degree of crystallization in the bulk metallic glass at different compression temperatures, the crystallinity of each sample was estimated using Formula (2):
I c = ω c ω c + ω A
where Ic is the crystallinity of the sample, ωc is the mass fraction of the crystalline phase, and ωA is the mass fraction of the amorphous phase. The crystallinity ωc was determined by the integrated intensity method using the crystalline peaks in the XRD pattern. The crystallinity of the bulk metallic glass at different compression temperatures is summarized in Table 2 and plotted in Figure 3b. It was found that the crystallinity of the bulk metallic glass increased with increasing compression temperature. Despite the high-temperature compression tests being conducted within the supercooled liquid region, the crystallinity of all samples was nevertheless high, exceeding 80%. This is likely due to the activation of atomic diffusion in this temperature range, where the applied compressive stress can provide the driving force for nucleation and growth of crystals.
To further analyze the high-temperature compression model of the bulk metallic glass within the supercooled liquid region, SEM observations were performed on the fracture surfaces or deformed surfaces of samples compressed at different temperatures. Among all deformed bulk metallic glass samples, only the one compressed at 487 °C exhibited fracture. The corresponding surface deformation features and fracture morphology of this sample are shown in Figure 4. Two distinct types of surface deformation features were observed, one consisting of large-area, intersecting shear bands forming a network (Figure 4a), and the other is characterized by dense, parallel, and uniformly distributed fine shear bands (Figure 4b). This can be attributed to the fact that at 487 °C, a temperature only slightly above the glass transition temperature (Tg), part of the BMG retains the rigid structure of the glassy state, while another part transforms into the viscoplastic structure of the supercooled liquid.
Figure 4a corresponds to the deformation characteristics of the rigid glassy structure, featuring intersecting shear bands that form a network, where localized sliding along these shear bands is observed. The rigid amorphous structure undergoes highly localized deformation, leading to stress concentration and the initiation of a primary shear band. When the propagation of this primary band is impeded, a large number of secondary shear bands are triggered, forming an interconnected network to dissipate stress. Ultimately, a brittle fracture occurs along the primary shear band. Figure 4b corresponds to the deformation characteristics of the partially viscoplastic supercooled liquid structure. It is characterized by dense, parallel, and uniformly distributed fine shear bands, which are regularly aligned without noticeable intersection or branching. In these regions, deformation is no longer confined to a single primary shear band. Stress is released through the nucleation of numerous fine shear bands, forming a dense, parallel array. The continuous nucleation and sliding of these bands indicate more homogeneous plastic deformation. At 487 °C, the bulk metallic glass fractured during high-temperature compression. The corresponding fracture surface morphologies are shown in Figure 4c,d. The occurrence of brittle fracture in this sample indicates that deformation was dominated by highly localized shear banding characteristic of the rigid glassy structure, rather than by the homogeneous plastic flow of the viscoplastic supercooled liquid structure. The fracture surface is predominantly characterized by a vein-like pattern, which is consistent with previously reported vein patterns on deformed BMG fracture surfaces [32]. Additionally, fine molten droplets are observed on these veins, resulting from adiabatic heating caused by the catastrophic propagation of highly localized shear bands.
Figure 5 shows the macroscopic deformation morphologies of the Zr56Co28Al16 bulk metallic glass compressed at temperatures ranging from 497 °C to 527 °C. This indicates that the bulk metallic glass did not undergo catastrophic fracture under these compressive conditions. With increasing compression temperature, the macroscopic deformation morphology of the bulk metallic glass transitioned from an N-shape to a single-drum shape and finally to a double N-shape. Figure 5a shows the macroscopic deformation morphology of the bulk metallic glass compressed at 497 °C. The deformed sample exhibits N-type barreling, with the bulging direction approximately 59° to the loading axis, and localized cracking at the edges. This suggests the absence of homogeneous viscoplastic flow. The likely reason is the high viscosity and limited atomic mobility at this temperature, causing deformation to remain dominated by the propagation of localized shear bands rather than transitioning to uniform viscous flow. Figure 5b shows the macroscopic deformation morphology of the bulk metallic glass compressed at 507 °C. It displays pronounced single-barrel homogeneous necking, with the bulging direction perpendicular (88°) to the loading axis and a smooth, crack-free surface. This indicates homogeneous plastic flow, demonstrating excellent thermoplasticity. This behavior is likely due to the substantial decrease in viscosity and significant increase in atomic mobility at this elevated temperature, allowing deformation to proceed via uniform viscoplastic flow. Stress is thus dissipated through homogeneous viscoplastic flow without highly localized deformation, resulting in uniform necking. Consequently, this temperature represents the optimal temperature for the thermoplastic forming of this BMG. As shown in Figure 5c and Figure 5d, the macroscopic deformation morphologies of the BMG compressed at 517 °C and 527 °C, respectively, are presented. Both samples exhibit double N-type barreling with pronounced torsional slip, manifested as helical shear striations on the surface, accompanied by localized fracture. For the BMGs compressed at 517 °C and 527 °C, the bulging direction forms angles of 70° and 60° with the loading direction, respectively. This indicates that deformation in these samples is dominated by viscous torsional shear. This can be attributed to a further decrease in the viscosity of the BMG, where the compressive stress induces torsional slip, forming helical shear bands. Concurrently, the higher temperatures promote partial crystallization, leading to stress concentration and some cracking.
When compressed at 487 °C, the BMG fractured along a direction oriented at 45° to the loading axis. The angles between the fracture/bulging direction and the loading direction at different compression temperatures are summarized in Table 3. It is observed that with increasing compression temperature, the angle first increases and then decreases, reaching a maximum value of 88° at 507 °C. This trend is exactly opposite to the variation in compressive strength with temperature. The lower the compressive strength, the higher the plastic deformability of the bulk metallic glass.
To further investigate the plastic deformation model of the bulk metallic glass within the supercooled liquid region, SEM observations were conducted on the surface deformation features of samples compressed at different temperatures. As shown in Figure 6a, the surface deformation features of the bulk metallic glass compressed at 497 °C are presented. The shear bands appear rough, broad, and intricately interwoven, with irregular edges showing distinct undulations and tear marks. This can be attributed to the high viscosity and limited atomic mobility at this temperature, which leads to highly localized deformation. Additionally, the high rigidity of the amorphous matrix impedes smooth shear band propagation, resulting in tearing and interweaving. As shown in Figure 6b, the surface deformation features of the bulk metallic glass compressed at 507 °C are presented. The shear bands have become finer, more densely spaced, parallel, and more regularly aligned. This is attributed to the decreased viscosity and enhanced atomic mobility at this higher temperature, which facilitates a transition in deformation mode from highly localized to more homogeneous. Consequently, the shear bands are narrower and greater in number. As shown in Figure 6c, the surface deformation features of the bulk metallic glass compressed at 517 °C are presented. The shear bands appear as uniform, parallel fine striations with a smooth surface, showing minimal undulation or interweaving. This is because the viscosity is moderate and atomic mobility is favorable at this temperature, allowing deformation to proceed via homogeneous viscoplastic flow. A multitude of fine shear bands nucleate uniformly and slide stably, leading to homogeneous stress dissipation and ultimately resulting in the formation of regular, smooth, parallel shear bands. Figure 6d reveals the surface deformation features of the bulk metallic glass compressed at 527 °C. The shear bands appear blurred, with their edges displaying a molten or wavy appearance, and show evidence of adhesion in some regions. This complex morphology can be attributed to a combination of factors. First, when the temperature exceeds the onset crystallization temperature (Tx), the viscosity becomes extremely low and atomic mobility becomes extremely high, leading to a transition of the deformation mechanism from sliding to viscoplastic flow. Second, the rapid stress release generates significant adiabatic heating, leading to localized melting and consequent adhesion at shear band edges. Furthermore, concurrent partial crystallization introduces hardened phases that impede shear band sliding. The interplay of these processes ultimately yields the observed blurred and adherent shear bands.
Given that the plastic deformation of metallic glasses is primarily governed by shear band propagation, this study aims to clarify the evolution of the deformation model within the supercooled liquid region. To investigate the deformation mechanism of the bulk metallic glass in the supercooled liquid region at elevated temperatures, a quantitative analysis of the shear bands formed at different compression temperatures was conducted based on Figure 5 and Figure 6. The analysis included measurements of shear band density, spacing, and spacing variance. Shear band density is defined as the number of shear bands per unit length along a direction perpendicular to the shear bands in SEM images. This parameter reflects the degree of deformation homogenization. The higher the shear band density, the more uniform the deformation. The formula for calculating the shear band density, ρ, is given by Equation (3):
ρ = N i n L
where L is the length of the measurement line drawn perpendicular to the shear bands, n is the number of such measurement lines, and Ni is the number of intersections between the i-th measurement line and the shear bands.
The average shear band spacing is inversely proportional to the shear band density. The smaller the spacing, the more uniform the deformation. The formula for calculating the average shear band spacing, d ¯ , is given by Equation (4):
d ¯ = Σ i = 1 N 1 ( x i + 1 x i ) N 1
where x1, x2, …, xN are the positional coordinates of all marked shear bands along the measurement line, and N is the total number of shear bands.
The variance in shear band spacing reflects the uniformity of their distribution; the smaller the variance, the more regular the band arrangement. The formula for calculating this variance, σ d 2 , is given by Equation (5):
σ d 2 = Σ i = 1 N 1 ( x i + 1 x i d ¯ ) N 2
The shear band density, average spacing, and spacing variance of the bulk metallic glass at different compression temperatures are summarized in Table 4 and plotted in Figure 7. As can be seen from Figure 7, with increasing compression temperature, the shear band density first decreases and then increases, while the average shear band spacing is inversely proportional to the density. With the exception of the 487 °C sample, which fractured, the higher the compression temperature, the lower the variance in shear band spacing. At a compression temperature of 507 °C, the variance is relatively low at 0.501, indicating that deformation is relatively uniform and dominated by homogeneous viscoplastic flow at this temperature. Concurrently, the shear band spacing is relatively large at 2.060 μm, suggesting that the sample retains potential for further plastic deformation. At a compression temperature of 527 °C, the shear bands become blurred and adherent. This is accompanied by a molten appearance due to adiabatic heating, and concurrent crystallization induces the phenomenon of dynamic structural relaxation hardening. Therefore, within the compression temperature range of 507–517 °C, the surface deformation features indicate uniform viscoplastic flow, making this range more suitable for processing the bulk metallic glass within its supercooled liquid region.
Based on the integration of macroscopic and microscopic deformation characteristics, a plastic deformation model for the BMG at different compression temperatures in the supercooled liquid region is proposed, as illustrated in Figure 8. Based on the macroscopic deformation morphologies shown in Figure 5, schematic illustrations of the BMG’s macroscopic deformation at different compression temperatures are provided in Figure 8a–e. Combined with the surface deformation features, the deformation mechanisms corresponding to each temperature are derived and illustrated in Figure 8f–h. As shown in Figure 8f, which illustrates the deformation mechanism of the BMG at 487 °C and 497 °C, stress concentration induces free-volume clusters, which eventually lead to the formation of shear bands. The deformation in these BMGs is dominated by highly localized shear banding. As shown in Figure 8g, the deformation mechanism schematic for the BMGs at 507–517 °C indicates that the shear band spacing decreases and deformation becomes more uniform. This leads to uniform deformation dominated by viscoplastic flow, driven by free-volume diffusion in response to temperature and stress. At compression temperatures of 517–527 °C (above the onset crystallization temperature, Tx), the shear band spacing remains relatively small, and deformation appears uniform, as shown in Figure 8h. However, compared to the 507–517 °C range, this BMG features larger crystalline particles. These particles impede shear-band motion, causing stress concentration. The rapid release of this concentrated stress generates adiabatic heating, leading to local melting within shear bands, which consequently become blurred and adherent. The dominant deformation mechanism in this temperature range is therefore dynamic structural relaxation hardening.

4. Conclusions

In this study, high-temperature compression tests were conducted on Zr56Co28Al16 bulk metallic glass within its supercooled liquid region. The mechanical properties and phase composition of the compressed samples were examined, and their macro- and micro-scale deformation morphologies were characterized. The plastic deformation models at different compression temperatures were investigated, aiming to provide a theoretical basis for predicting the compressive flow behavior of BMGs in the supercooled liquid region. The main conclusions are as follows:
  • The stress–strain curves of the BMGs at different compression temperatures reveal that at 507 °C, the compressive strength reaches its lowest value of 330 MPa. Furthermore, the compressive-strength-versus-temperature curve shows a parabolic minimum in the 507–517 °C range.
  • The XRD results for the BMGs at different compression temperatures show that the crystallinity increases with increasing temperature.
  • The deformation characteristics of the BMG across different compression temperatures reveal three distinct regimes: (a) within 487–497 °C, deformation is dominated by highly localized shear banding; (b) in the 507–517 °C range, homogeneous viscoplastic flow prevails; and (c) from 517 to 527 °C, dynamic structural relaxation hardening becomes dominant.

Author Contributions

Conceptualization, J.T.; Methodology, M.L.; Formal analysis, M.L., X.Z. and J.T.; Investigation, M.L., Z.Y. and J.T.; Resources, M.L.; Data curation, M.L., X.Z. and Z.Y.; Writing—original draft, M.L.; Writing—review & editing, M.L., X.Z. and Z.Y.; Visualization, M.L.; Project administration, M.L. and J.T.; Funding acquisition, J.T. All authors have read and agreed to the published version of the manuscript.

Funding

This work was funded by the Natural Science Foundation of Fujian Province of China (Grant Nos. 2024J08223, 2024J08224), the Young and Middle-aged Teacher Education Research Project of Fujian Province of China (No. JAT231130), and the Project of Scientific Research of Ningde Normal University (No. 2022Y21).

Data Availability Statement

The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding authors.

Conflicts of Interest

The authors declare no conflicts of interest.

References

  1. Qiao, J.C.; Pelletier, J.M. Dynamic Mechanical Relaxation in Bulk Metallic Glasses: A Review. J. Mater. Sci. Technol. 2014, 30, 523–545. [Google Scholar] [CrossRef]
  2. Wang, W.H.; Dong, C.; Shek, C.H. Bulk metallic glasses. Mater. Sci. Eng. R 2008, 44, 45–89. [Google Scholar] [CrossRef]
  3. Schuh, C.A.; Hufnagel, T.C.; Ramamurty, U. Overview No.144—Mechanical behavior of amorphous alloys. Acta Mater. 2007, 55, 4067–4109. [Google Scholar] [CrossRef]
  4. Trexler, M.M.; Thadhani, N.N. Mechanical properties of bulk metallic glasses. Prog. Mater. Sci. 2010, 55, 759–839. [Google Scholar] [CrossRef]
  5. Zhu, P.; Li, X.; Zhang, Q. Effects of melt temperatures on the structure relaxation and compressive plasticity of La62Al14(Cu5/6Ag1/6)14(Ni1/2Co1/2)10 bulk metallic glass. J. Non Cryst. Solids 2017, 417, 175–178. [Google Scholar] [CrossRef]
  6. Minouei, H.; Rizi, M.S.; Kheradmandfard, M.; Shim, S.H.; Hong, S.I.; Park, N. NiNbTi(Al/Si) medium-entropy amorphous alloys with enhanced mechanical and thermal properties. Intermetallics 2025, 178, 108609. [Google Scholar] [CrossRef]
  7. Zhang, Z.F.; Eckert, J.; Schultz, L. Difference in compressive and tensile fracture mechanisms of Zr59Cu20Al10Ni8Ti3 bulk metallic glass. Acta Mater. 2003, 51, 1167–1179. [Google Scholar] [CrossRef]
  8. Xing, L.Q.; Li, Y.; Ramesh, K.T.; Li, J.; Hufnagel, T.C. Enhanced plastic strain in Zr-based bulk amorphous alloys. Phys. Rev. B 2001, 64, 607–611. [Google Scholar] [CrossRef]
  9. Zhang, C.; Qiao, J.; Pelletier, J.; Yao, Y. Arrhenius activation of Zr65Cu18Ni7Al10 bulk metallic glass in the supercooled liquid region. Intermetallics 2017, 86, 88–93. [Google Scholar] [CrossRef]
  10. Zhang, C.; Qiao, J.; Pelletier, J.; Yao, Y. Bulk metallic glasses: “Defects” determines performance. Mater. Sci. Eng. A 2016, 675, 379–385. [Google Scholar] [CrossRef]
  11. Qiao, J.; Yao, Y.; Pelletier, J.; Keer, L. Understanding of micro-alloying on plasticity in Cu46Zr47−xAl7Dyx (0 ≤ x ≤ 8) bulk metallic glasses under compression: Based on mechanical relaxations and theoretical analysis. Int. J. Plast. 2016, 82, 62–75. [Google Scholar] [CrossRef]
  12. Wang, R.; Yao, H.; Wang, E.; Shen, Y.; Jia, P. The rheological behavior of brittle BMGs of Cu44.25Ag14.75Zr36Ti5 and Ti32.8Zr30.2Cu9Ni5.3Be22.7 in the supercooled liquid region. J. Non Cryst. Solids 2024, 646, 123210. [Google Scholar] [CrossRef]
  13. Yao, D.; Deng, L.; Zhang, M.; Gong, P.; Wang, X. A size-dependent free volume prediction model of Zr55Cu30Al10Ni5 bulk metallic glass in the supercooled liquid region. Intermetallics 2017, 84, 1–10. [Google Scholar] [CrossRef]
  14. Shin, H.-S.; Jeong, Y.-J.; Choi, H.-Y.; Inoue, A. Influence of crystallization on the deformation behavior of Zr55Al10Ni5Cu30 bulk metallic glass in the supercooled liquid region. Mater. Sci. Eng. A 2007, 449, 243–247. [Google Scholar] [CrossRef]
  15. Cui, J.; Li, J.; Wang, J.; Li, L.; Kou, H. Deformation behavior of a Ti-based bulk metallic glass composite in the supercooled liquid region. Mater. Design 2016, 90, 595–600. [Google Scholar] [CrossRef]
  16. Lv, J.; Wang, F.; Zhang, S.; Ma, M.; Wang, Y.; Zhang, X.; Liu, R. Deformation behaviours of TiZrCuNiBe bulk metallic glass in supercooled liquid region. J. Alloys Compd. 2020, 844, 156101. [Google Scholar] [CrossRef]
  17. Minouei, H.; Akbari, G.; Enayati, M.; Hong, S. Non-isothermal nano-crystallization kinetics in amorphous Ni55Nb35Si10 alloy. T. Nonferr. Metal. Soc. 2019, 29, 358–364. [Google Scholar] [CrossRef]
  18. Schroers, J.; Nguyen, T.; O’kEeffe, S.; Desai, A. Thermoplastic forming of bulk metallic glass-Applications for MEMS and microstructure fabrication. J. Microelectromech. S. 2007, 16, 240–247. [Google Scholar] [CrossRef]
  19. Gravier, S.; Blandin, J.J. Forming of bulk metallic glasses: Ideal superplasticity? Materialwiss. Werkst. 2012, 43, 763–767. [Google Scholar] [CrossRef]
  20. Schroers, J. Processing of bulk metallic glass. Adv. Mater. 2010, 22, 1566–1597. [Google Scholar] [CrossRef]
  21. Lee, K.S.; Kim, S.; Lim, K.R.; Hong, S.H.; Kim, K.B.; Na, Y.S. Crystallization, high temperature deformation behavior and solid-to-solid formability of a Ti-based bulk metallic glass within supercooled liquid region. J. Alloys Compd. 2016, 663, 270–278. [Google Scholar] [CrossRef]
  22. Yang, K.; Fan, X.; Li, B.; Li, Y.; Wang, X. Optimisation of superplastic processing parameters for a TiZrHfBeCuNi high entropy bulk metallic glass in the supercooled liquid region. J. Mater. Res. Technol. 2022, 17, 1911–1921. [Google Scholar] [CrossRef]
  23. Tan, J.; Zhang, Y.; Stoica, M.; Kühn, U.; Mattern, N.; Pan, F.; Eckert, J. Study of mechanical property and crystallization of a ZrCoAl bulk metallic glass. Intermetallics 2011, 19, 567–571. [Google Scholar] [CrossRef]
  24. Yan, S.; Song, C.; Huang, L.; Han, L.; Wang, C. Crystallization of Zr-Based Amorphous Alloys in Laser Welding. Metals 2023, 13, 16. [Google Scholar] [CrossRef]
  25. Sergueeva, A.V.; Mara, N.; Mukherjee, A.K. Mechanical response of Zr-based metallic glass. J. Non Cryst. Solids 2003, 317, 169–175. [Google Scholar] [CrossRef]
  26. Sohrabi, N.; Panikar, R.S.; Jhabvala, J.; Buch, A.R.; Mischler, S.; Logé, R.E. Laser coating of a Zr-based metallic glass on an aluminum substrate. Surf. Coat. Tech. 2020, 400, 126223. [Google Scholar] [CrossRef]
  27. Rashidi, R.; Riechers, B.; Rosalie, J.; Maaß, R. Annealing-dependent elastic microstructure in a Zr-based metallic glass. Scripta Mater. 2025, 255, 116380. [Google Scholar] [CrossRef]
  28. Ramachandramoorthy, R.; Schwiedrzik, J.; Michler, J.; Stolpe, M.; Yang, F.; Jain, M.; Best, J.P.; Casari, D.; Kruzic, J.J. High strain rate in situ micropillar compression of a Zr-based metallic glass. J. Mater. Res. 2021, 36, 2325–2336. [Google Scholar] [CrossRef]
  29. Tao, P.; Zhu, K.; Long, Z.; Zhang, C.; Zhang, W.; Yang, Y. Strain rate response and rheological characteristics of ZrCuNiAl bulk metallic glass in supercooled liquid region. J. Non Cryst. Solids 2023, 607, 6. [Google Scholar] [CrossRef]
  30. Si, M.; Gong, P.; Huang, H.; Mo, J.; Wang, X. The rheological behavior and constitutive model of Zr35Ti30Be27.5Cu7.5 metallic glass under high strain rate tensile conditions within the supercooled liquid region. Intermetallics 2024, 167, 13. [Google Scholar] [CrossRef]
  31. Torre, F.H.D.; Klaumünzer, D.; Maaß, R.; Löffler, J.F. Stick–slip behavior of serrated flow during inhomogeneous deformation of bulk metallic glasses. Acta Mater. 2010, 58, 3742–3750. [Google Scholar] [CrossRef]
  32. Scudino, S.; Surreddi, K. Shear band morphology and fracture behavior of cold-rolled Zr52.5Ti5Cu18Ni14.5Al10 bulk metallic glass under tensile loading. J. Alloys Compd. 2017, 708, 722–727. [Google Scholar] [CrossRef]
Figure 1. XRD pattern (a) and DSC curve (b) of the as-cast Zr56Co28Al16 BMG.
Figure 1. XRD pattern (a) and DSC curve (b) of the as-cast Zr56Co28Al16 BMG.
Metals 16 00280 g001
Figure 2. (a) Compressive stress–strain curves of the Zr56Co28Al16 bulk metallic glass at different temperatures; (b) Variation in compressive strength with compression temperature for the bulk metallic glass.
Figure 2. (a) Compressive stress–strain curves of the Zr56Co28Al16 bulk metallic glass at different temperatures; (b) Variation in compressive strength with compression temperature for the bulk metallic glass.
Metals 16 00280 g002
Figure 3. (a) XRD patterns of the Zr56Co28Al16 bulk metallic glass after compression at different temperatures; (b) Variation in crystallinity with compression temperature for the bulk metallic glass.
Figure 3. (a) XRD patterns of the Zr56Co28Al16 bulk metallic glass after compression at different temperatures; (b) Variation in crystallinity with compression temperature for the bulk metallic glass.
Metals 16 00280 g003
Figure 4. Surface deformation features (a,b) and fracture morphology (c,d) of the Zr56Co28Al16 bulk metallic glass compressed at 487 °C.
Figure 4. Surface deformation features (a,b) and fracture morphology (c,d) of the Zr56Co28Al16 bulk metallic glass compressed at 487 °C.
Metals 16 00280 g004
Figure 5. Macroscopic deformation morphologies of the Zr56Co28Al16 bulk metallic glass after compression at 497 °C (a), 507 °C (b), 517 °C (c), and 527 °C (d).
Figure 5. Macroscopic deformation morphologies of the Zr56Co28Al16 bulk metallic glass after compression at 497 °C (a), 507 °C (b), 517 °C (c), and 527 °C (d).
Metals 16 00280 g005
Figure 6. The surface deformation features (SEM images) of Zr56Co28Al16 bulk metallic glass at different compression temperatures, (a) 497 °C, (b) 507 °C, (c) 517 °C, (d) 527 °C.
Figure 6. The surface deformation features (SEM images) of Zr56Co28Al16 bulk metallic glass at different compression temperatures, (a) 497 °C, (b) 507 °C, (c) 517 °C, (d) 527 °C.
Metals 16 00280 g006
Figure 7. The shear band density ρ, average spacing d ¯ , and spacing variance σ d 2 of the bulk metallic glass at different compression temperatures.
Figure 7. The shear band density ρ, average spacing d ¯ , and spacing variance σ d 2 of the bulk metallic glass at different compression temperatures.
Metals 16 00280 g007
Figure 8. Schematic illustrations of macroscopic deformation (ae) and compressive flow models (fh) for the Zr56Co28Al16 BMGs at different temperatures.
Figure 8. Schematic illustrations of macroscopic deformation (ae) and compressive flow models (fh) for the Zr56Co28Al16 BMGs at different temperatures.
Metals 16 00280 g008
Table 1. Compressive strength of the bulk metallic glass at different compression temperatures.
Table 1. Compressive strength of the bulk metallic glass at different compression temperatures.
Compression temperature (°C)487497507517527
Compressive strength (MPa)689472330352435
Table 2. Crystallinity of the bulk metallic glass at different compression temperatures.
Table 2. Crystallinity of the bulk metallic glass at different compression temperatures.
Compression temperature (°C)487497507517527
Crystallinity (%)82.6391.2894.6995.4996.25
Table 3. The angles between the fracture/bulging direction and the loading direction at different compression temperatures.
Table 3. The angles between the fracture/bulging direction and the loading direction at different compression temperatures.
Compression temperature (°C)487497507517527
Angle (°)4559887060
Table 4. The shear band density ρ, average spacing d ¯ , and spacing variance σ d 2 of the bulk metallic glass at different compression temperatures.
Table 4. The shear band density ρ, average spacing d ¯ , and spacing variance σ d 2 of the bulk metallic glass at different compression temperatures.
Compression temperature (°C)487497507517527
Ρ (μm−1)0.5570.5480.4850.7350.841
d ¯ (μm)1.7971.8242.0601.3611.189
σ d 2 1.2271.5090.5010.1170.064
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Share and Cite

MDPI and ACS Style

Li, M.; Zhang, X.; Yu, Z.; Tan, J. A Compressive Flow Prediction Model of Zr56Co28Al16 Bulk Metallic Glass in Supercooled Liquid Region. Metals 2026, 16, 280. https://doi.org/10.3390/met16030280

AMA Style

Li M, Zhang X, Yu Z, Tan J. A Compressive Flow Prediction Model of Zr56Co28Al16 Bulk Metallic Glass in Supercooled Liquid Region. Metals. 2026; 16(3):280. https://doi.org/10.3390/met16030280

Chicago/Turabian Style

Li, Min, Xuefei Zhang, Zhongfen Yu, and Jun Tan. 2026. "A Compressive Flow Prediction Model of Zr56Co28Al16 Bulk Metallic Glass in Supercooled Liquid Region" Metals 16, no. 3: 280. https://doi.org/10.3390/met16030280

APA Style

Li, M., Zhang, X., Yu, Z., & Tan, J. (2026). A Compressive Flow Prediction Model of Zr56Co28Al16 Bulk Metallic Glass in Supercooled Liquid Region. Metals, 16(3), 280. https://doi.org/10.3390/met16030280

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Metrics

Article metric data becomes available approximately 24 hours after publication online.
Back to TopTop