1. Introduction
In recent years, bulk metal glasses (BMG) have been intensively investigated [
1,
2,
3]. The compositions of the BMG alloys are selected in such a way that an amorphous structure can be obtained even at a cooling rate of about 10
2 K/s, which makes it possible to obtain bulk amorphous samples up to several centimetres in diameter. Today these materials have been used in certain types of technology [
4].
Deformation of amorphous alloys and BMG is carried out mainly due to the formation and propagation of shear bands (SBs)—narrow, 10–50 nm thick, deformation zones [
5,
6]. This feature leads to the fact that amorphous alloys demonstrate extremely low plasticity under tension—the very first formed SB becomes a stress concentrator and deformation occurs until the sample is fractured. At the same time, during compression or bending, when compressive stresses appear in addition to tensile stresses, amorphous alloys can show some plasticity [
1,
4]. In this regard, numerous studies have been undertaken to improve the plasticity of amorphous alloys [
6,
7,
8,
9,
10].
An increase in plasticity and an improvement in mechanical properties is possible through modifying the chemical composition, as well as through various additional treatments [
1,
2,
9,
11,
12,
13]. One way to increase plasticity is the preliminary formation of a high density of SBs in the amorphous phase or the formation of inhomogeneous nanocluster amorphous structures [
6,
7,
8,
9]. For example, preliminary deformation by cold rolling, compression, etc., enables an increase in the ductility of BMG due to the nucleation of secondary SBs and branching of primary SBs under consequent loading [
6,
7]. As a result, the overall plasticity increases [
6,
7,
8,
9]. However, conventional deformation methods do not make it possible to achieve large deformations in the case of brittle amorphous materials.
A promising method for introducing high deformation and, consequently, a high density of structural defects into an amorphous solid is the use of high-pressure torsion (HPT) [
14,
15]. The HPT process is one of the most powerful techniques to prepare ultrafine-grained materials due to severe deformation [
14,
15]. Numerous publications have been devoted to the study of the effect of HPT on the structure and properties of amorphous alloys [
16,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27]. Recently, there have been few reviews on this topic, in particular [
28,
29].
It was shown that HPT led to partial nanocrystallization in amorphous alloys of some compositions [
17,
18,
21,
22,
25]. In amorphous alloys of other compositions, nanocrystallization is not observed during HPT; however, HPT leads to changes in the amorphous phase, the formation of inhomogeneities in the amorphous structure occurs, and free volume increases, which in some cases causes a change in alloy properties [
19,
23,
26].
The study of the deformation behaviour in BMG previously exposed to HPT is not an easy task. Specimens after HPT usually have the form of discs 10 mm in diameter and 0.5 mm thick [
27,
28,
29], and it is difficult to perform compression or three-point bending tests on specimens of this geometry. Upon tensile stress, BMG samples usually experience a brittle fracture. Indentation and nanoindentation methods, owing to their ability to induce permanent deformation in a controlled manner even in highly brittle materials, are widely used for studying the mechanical behaviour of amorphous materials [
30,
31,
32]. Thus, measurements by nanoindentation demonstrate that HPT leads to a decrease in the elastic modulus of BMG, a decrease in hardness, and an increase in strain rate sensitivity relative to the initial condition [
27]. Note that the tensile ductility of Zr
65Al
7.5Ni
10Cu
12.5Pd
5 BMG after HPT was reported in [
26]. The authors assumed that the work-hardening behaviour with a tensile ductility of Zr-BMG resulted from the multiple SBs caused by the distribution of heterogeneities in BMG after HPT [
26].
It is of interest to study the pattern of deformation of BMG pre-processed HPT—the formation and propagation of SBs under loading and other deformation features. An effective method proposed for assessing the formation and propagation of SBs on amorphous materials is the bonded-interface indentation technique [
33]. In the bonded-interface indentation technique, two samples of amorphous alloy with polished top and side faces are fixed together in the clamp, after which indentation is carried out into the joint of the two samples (
Figure 1a). Previously, a similar method was used to observe the steps on the surface due to the formation of SBs in BMG Vitreloy 106 Zr
57Nb
5Ni
12.6Cu
15.4Al
10, where authors performed Vickers indentations along the joint of the samples and investigated the deformation pattern and the formation of shear bands in the indentation region under different applied loads [
33]. Studies have shown that at small indentation loads (10 g), semi-circular primary SBs primarily accommodated the plastic deformation around the indenter. At higher loads (100–1000 g), secondary and tertiary SBs were formed inside this plastic zone. To assess the plastic zone size, and characterize and identify the stress forming under the indenter, the authors used “a modified expanding cavity model” [
33]. The role of free volume in the inhomogeneous plastic flow of the BMG was systematically analysed by performing the bonded-interface indentation technique to the as-cast BMG and BMG after relaxation annealing, with a minimum free volume [
34]. However, in the latter two mentioned articles, bonded-interface indentation was used to analyse the pattern of deformation only in the as-cast and relaxed state of the BMG. In the present work, indentation was carried out into the joint of the Vit105 BMG alloy in various structured states—before and after HPT, as well as after relaxing annealing.
2. Materials and Methods
The Vit105 BMG ingots with a standard composition of Zr52.5Cu17.9Al10Ni14.6Ti5 (at %) were prepared by arc melting using pure (>99.9%) components under a Ti-gettered pure argon atmosphere. The ingots were remelted four times for chemical homogeneity. The melt was subsequently cast into a water-cooled suction casting machine with a copper mould at a cooling rate of 102 K/s. The ingots were obtained in the form of 10 × 65 × 2 mm plates.
The X-ray diffraction (XRD) analysis of the BMG samples was conducted using the Bruker D2 Phaser (Bruker AXS GmbH, Karlsruhe, Germany) diffractometer with CuKα radiation in the reflected beam; the LynxEye XE-T detector was used. The obtained data were processed using the DIFFRAC.EVA v.5.2 software (Bruker AXS GmbH, Karlsruhe, Germany), including the determination of the centre of gravity position and the full-width at half maximum (FWHM) of the amorphous halo.
According to [
35,
36], the radius of the first coordination sphere (
R1) can be found from the position of the main amorphous halo using the equation:
where
θ is the gravity centre angle, and
λ is the radiation wavelength [
35].
The change in free volume Δ
V could be estimated according to:
where
R0 and
RHPT are the radii of the first coordination sphere of as-cast and HPT-processed BMG, respectively [
37].
Vit105 10 mm in diameter and 1 mm thick disk samples were cut out of plates using wire electrical discharge machining and then deformed using HPT anvils with a groove 0.3 mm deep and 10 mm in diameter. One revolution of the anvils was made at the speed of 1 rpm under an applied pressure of 6 GPa at room temperature. Some of the initial samples were subjected to relaxing annealing in a vacuum furnace VacETO D-4,5.3.E-16UU-IV (NPP VacETO LLC, Moscow, Russia), the residual air pressure at the beginning of the cycle was 10−5 Pa. The annealing temperature was 430 °C, the dwell time at the temperature was 10 min, and the heating rate of 20 K/min was used.
The Vickers microhardness (HV) was measured at a grid array of points using the spacing of 0.7 mm with loads of 100 g at each point for 10 s, at least 42 points per sample. Then sets of two samples in the form of flat plates 10 × 2 × 0.7 mm in dimensions were cut from the initial BMG, from the HPT-processed disks, and from BMG subjected to relaxing annealing (
Figure 1b). The wide faces of the obtained plates were polished to mirror finish, next they were fixed together tightly with a clamp (
Figure 1c), and then the top surfaces of the clamped samples were polished to mirror finish. Indentation with load of 200 g was conducted into the joint and as a result, a pattern of SBs was formed under the indenter on the polished surfaces of the samples. Both microindentation and bonded-interface indentation tests were carried out using an Emco-Test Durascan 50 (EMCO-TEST Prüfmaschinen GmbH, Kuchl, Austria) automatic microhardness tester. A set of test bricks MTV-MET (Centre “MET”, Moscow, Russia) was used for the verification of the tester. A scanning electron microscope (SEM) JEOL JSM-6490LV (JEOL Co. Ltd., Tokyo, Japan) was used to study the relief after indentation.
To obtain a stress-strain state diagram during indentation, finite element computer modelling was carried out using the DEFORM-3D (Scientific Forming Technologies Corporation, Columbus, OH, USA) software package. The sample and tool models were created in the KOMPAS-3D (ASCON LLC, Saint Petersburg, Russia) three-dimensional modelling system, saved and imported into DEFORM-3D in the “.stl” format. The volumetric model of the indenter was made in the form of a tetrahedral pyramid with a square base and an apex angle of 136°. For modelling purposes, it was assumed that the initial workpiece was a homogeneous and isotropic plastic body, and the tool was a rigid body. The mechanical behaviour of Vit105 for modelling was determined as follows: the elastic modulus of 90 GPa and Poisson’s ratio of 0.36 were set, and hardening curves were introduced using a tabular form. Until the conventional yield strength (1550 MPa) is reached, the material is deformed elastically and then deformed without hardening, as is typical for BMG. The generated finite element mesh for the workpiece consisted of 150,000 tetrahedrons. Volume compensation option for the model has been used, and the indenter was not meshed. The indentation speed during the simulation was chosen constant and equal to 0.1 mm/sec, at constant room temperature (20 °C). To set the contact behaviour between the indenter and the workpiece, the Siebel friction factor f = 0.12 was used. The impermeability condition was set on the contact surfaces of the rig. The number of simulation steps was 300.
Author Contributions
Conceptualization, V.A. and D.G.; methodology, V.A.; software, R.A.; validation, D.G.; formal analysis, V.T. and R.A.; investigation, V.T. and R.A.; resources, D.G.; data curation, V.A.; writing—original draft preparation, V.A. and D.G.; writing—review and editing, V.A.; visualization, V.T.; supervision, D.G.; project administration, D.G.; funding acquisition, D.G. All authors have read and agreed to the published version of the manuscript.
Funding
This research was funded by the Russian Science Foundation project № 22-19-00347 (HPT processing) and Russian Foundation for Basic Research, grant number 20-08-00497 (SEM investigation).
Institutional Review Board Statement
Not applicable.
Informed Consent Statement
Not applicable.
Data Availability Statement
All data generated or analysed during this study are included in the published article, and are available from the corresponding authors upon reasonable request.
Acknowledgments
The work was carried out using the equipment of the Research Equipment Sharing Center “Nanotech” (
http://nanotech.ugatu.su (accessed on 18 June 2022)).
Conflicts of Interest
The authors declare no conflict of interest.
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Figure 1.
Joint indentation scheme: (a) samples are clamped in vice polished surfaces to each other; (b) a sample cut from HPT n = 1 BMG; (c) samples are clamped in a vice.
Figure 2.
XRD results for the Vit105 BMG: as-cast; after HPT n = 2, BMG after relaxation annealing.
Figure 3.
Microhardness distribution: (a) in the initial sample; (b) after HPT n = 1; (c) after relaxing annealing at 430 °C, 10 min.
Figure 4.
Bonded indentation of the tightly fixed samples of BMG Vit105 in the initial state: (a) top view; (b) deformation area on the side surface area near the indent (SEM); (c) same, enlarged.
Figure 5.
Bonded indentation of BMG Vit105 in the initial state fixed with a gasket: (a) top view; (b) deformation area on the side surface area near the indent (SEM); (c) same, enlarged.
Figure 6.
Bonded indentation of BMG Vit105 after relaxed annealing: (a) deformation area on the side surface area near the indent (SEM); (b) same, enlarged.
Figure 7.
Bonded indentation of BMG Vit105 after HPT n = 1: (a) deformation area on the side surface area near the indent (SEM); (b) same, enlarged.
Figure 8.
Diagrams of the stress-strain state under the indenter: (a) stress intensity, general view; (b) the accumulated strain; (c) stress intensity, detailed; (d) mean stress (hydrostatic pressure) values are negative, according to the theory of metal forming for compressive stress).
Table 1.
Amorphous structure parameters in Vit105 BMG in various states: first amorphous halo gravity centre position 2θ, radius of the first coordination sphere R1, full-width at half maximum (FWHM), change in free volume ΔV, and microhardness HV0.1.
Condition | Gravity Centre Position, 2θ, ° | R1, Ǻ | FWHM, ° | ΔV 1, % | HV0.1 |
---|
As-cast | 37.713 | 2.931508 | 5.577 | | 514 ± 13 |
HPT n = 1 | 37.647 | 2.936514 | 6.364 | 0.51 | 499 ± 43 |
Annealing 430 °C, 10 min | 37.784 | 2.926232 | 5.084 | −0.54 | 575 ± 25 |
Table 2.
Pattern parameters of band formation at bonded-interface indentation tests on BMG Vit105 samples in various states—Distances from the indenter tip imprint to the farthest band, number of observed bands, average distance between bands, [µm]. Where indicated, without parentheses refers to all bands, in parentheses—only to intense shear bands.
Condition | Distance to the Far-End Band, µm | Number of Bands | The Average Distance between the Bands, µm |
---|
As-cast | 10 | 19 | 0.5 |
HPT n = 1 | 12 (8) | 24 | 0.5 (3) |
Annealing 430/10 | 14 | 16 | 0.75 |
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