2-1 The development of metallic glasses
In 1960, Klement et al. [44] developed the first metallic glasses of Au75Si25 by the rapid quenching techniques for cooling the metallic liquids at very fast rates of 105-106 K/s.
Their works initiate broad interest quickly among the scientists and engineers because they showed the process of nucleation and growth of crystalline phase could be skipped to produce a frozen liquid configuration. A few years later, the ternary amorphous alloys of Pd-Si-X (X = Ag, Cu or Au) were prepared successfully by Chen and Turnbull [45], and the Pd-T-Si (T = Ni, Co or Fe) ternary amorphous alloys which included the magnetic atoms were also presented soon after [46]. The maximum diameter of these metallic glasses was reached to 1 mm by using the die casting and roller-quenching method. The effects of the alloy systems, compositions and the existence of a glass transition was demonstrated, it leaded to the first detailed studies in the formation, structure and property investigations of amorphous alloys.
Because of their fundamental sciences and engineering application potential, metallic glasses have attracted great attention.
The geometry of metallic glasses, however, is limited to thin foils or lines as a result of high cooling rate, which are not easy to find the wide application. How to determine the glass forming ability (GFA) of amorphous alloys and increase the diameter of specimens becomes the important topic in that period. Turnbull and Fisher [47]advanced a criterion to predict the glass forming ability of an alloy. According to his criterion, the reduced glass transition temperature Trg, equal to the glass transition temperature Tg over liquids temperature Tl, or Trg = Tg/Tl is the primary factor. If Tg is larger and Tl smaller, the value of Trg will be higher so that such a liquid can be easily undercooled into a glassy state at a lower
8
cooling rate. Although there are several new criteria proposed following them [48, 49], the Trg
has been proved to be useful in reflecting the GFA of metallic glasses including BMGs.
In 1974, the rods of Pd-Cu-Si alloy measuring 1-3 mm in diameter, the first bulk metallic glasses were prepared by Chen [46] using simple suction-casting methods. In 1982, Turnbull’s group [50, 51] pushed the diameter of critical casting thickness of the Pd-Ni-P alloys up to 10 mm by processing the Pd–Ni–P melt in a boron oxide flux, and eliminate heterogeneous nucleation. A series of solid state amophization techniques that are completely different from the mechanism of rapid quenching had been developed during this time. For example, mechanical alloying, diffusion induced amorphization in multilayers, ion beam mixing, hydrogen absorption, and inverse melting [52]. The thin films or powders of metallic glasses can be acquired as well by interdiffusion and interfacial reaction when the temperature is just below the glass transition temperature.
In the late 1980s, Inoue’s group [53, 54]in Tohoku University of Japan developed many new multicomponent metallic glass systems with lower cooling rates in Mg-, Ln-, Zr-, Fe-, Pd-, Cu-, Ti- and Ni- based systems. They found exceptional glass forming ability in La-Al-Ni and La-Al-Cu ternary alloys system [53]. By casting the alloy melt in water-cooling Cu molds, the cylindrical samples with diameters up to 5 mm or sheets with similar thicknesses were made fully glassy in the La55Al25Ni20 alloy, and the La55Al25Ni10Cu10 alloy was fabricated later with a diameter up to 9 mm by the same method.
In 1990s, the Inoue group further developed a series of multicomponent Zr-based bulk metallic glasses, such as Zr-Cu-Ni, Zr-Cu-Ni-Al, etc., along with Mg-based, e.g. Mg–Cu–Y and Mg–Ni–Y alloys, all exhibiting a high GFA and thermal stability [55-58]. For one of the Zr-based BMGs, Zr65Al7.5Ni10Cu17.5,the critical casting thickness was raised up to 15 mm,
9
and the largest critical casting thickness could reach to 72 mm in the Pd–Cu–Ni–P family[59].
The evolution of such category alloys demonstrated that bulk metallic glass composition were not a laboratory curiosity and could be quite interesting and for promising engineering applications. In fact, the Zr-based bulk metallic glasses found application in the industries just three years after it was invented. The typical bulk metallic glasses systems and the reported years are listed in Table 2-1[20]. Subsequently, a set of empirical rules in order to direct the selection of alloying elements and composition of glass forming alloys have been proposed by Inoue and Johnson as follows[19, 60]:
(1) Multicomponent alloys with three or more elements.
(2) More than 12% atomic radius difference among them.
(3) Negative heat of mixing between constituent elements.
(4) The deep eutectic rule based on the Trg criterion.
These rules provide an important role for the synthesizing of BMGs in the last decade.
However, in the subsequent experiments finding some binary alloys such as Ni-Nb[61], Ca-Al [62] Zr-Ni[63, 64], and Cu-Zr [65-67] etc., BMGs can also be obtained with several millimeters and the best glass formers are not fixed on the eutectics of them, indicating that the above mentioned rules are not the necessary concern in all cases for designing BMGs.
Formation mechanism and criteria for the binary BMGs may be distinct from the multicomponent systems. These results suggest that there are many potential forming systems of the metallic glasses to be discovered. On the other hand, these kinds of simple binary systems of BMGs are the very ideal model for studying their characteristics of the deformation mechanism and structure by computer simulation and theorizing.
Recently, many scholars attempt to detect the regulations on the glass forming ability from thermodynamic modeling or statistical mechanics that can help to design the larger size
10
of amorphous alloys in general [49, 53]; others focus on the studies of their mechanical properties and structural topology that can build the structural modeling of BMGs as well as improve their strength and ductility. In future, the trends of investigations of BMGs are not only kept on the experimental competition but also extended into complete modeling of fundamental theory.
2-2 Microstructures in metallic glasses
In 1959, a structural model of dense random packing of hard spheres is first suggested by Bernal [68] to be a simple model for metal liquids, and subsequently indicated by Cohen and Turnbull [69] that this simple model can be also applied to describe the metallic glasses.
In 1979, Wang [70] supposed that the amorphous metal alloys may be a special class of the glassy state whose short-range structure is random Kasper polyhedral close packing of soft atoms similar to those in the crystalline counterparts. This short-range structure is described based on a new type of glassy structure with a high degree of dense randomly packed atomic configurations. The density measurements show that the density difference is in the range 0.3~1.0% between bulk metallic glasses and fully crystallized state [71, 72]. There is neither splitting of the second peak nor pre-peak at the lower wave vector as seen in the reduced density function curve of the BMGs [71, 73, 74]. These results confirm that the multicomponent BMGs has a homogeneously mixed atomic configuration corresponding to a high dense randomly packing.
One of the most important topological short range structures developed among glasses and supercooled liquids is the local icosahedral clusters, which are revealed by many simulation studies [75-79]. Figure 2-1 (a) shows a typical fragment of an icosahedron, the central atom forms a fivefold symmetry arrangements with each of its 12 neighbors. In
11
contrast as shown in Fig. 2-1 (b) is a regular fragment of an FCC order, and the same pair will become an HCP order if the bottom close-packed plane is shifted as the same as the top plane.
This fivefold symmetry and icosahedral clusters is also detected from the experiments of liquids and metallic glasses [80, 81], even though in an immiscible binary system with positive heat of mixing [77-79]. The binding energy of an icosahedral cluster of 13 Lennard-Jones (LJ) atoms is 8.4% lower than an FCC or HCP arrangement [82]. The critical size for a transition from icosahedral cluster to icosahedral phase is about 8 nm [54].
Icosahedral packing is a basic structural unit in extended amorphous systems, and the existence of icosahedral clusters offer seeds for the precipitation of the icosahedral phase.
The icosahedral quasicrystalline phase will precipitate in the primary crystallization process and then transforms to stable crystalline phases when the amorphous alloys is annealing at higher temperatures [83-85].
In recent years, an order effect, called the medium range order, existing over length scale larger than the short range order but not extends to the long range order as crystalline state, has been detected in the some amorphous alloys [86-88]. Figure 2-2 shows a typical high-resolution electron microscopy image of the BCC-Fe medium range order with the sizes around 1-3 nm existing in the Fe-Nb-B amorphous matrix [89]. Although the icosahedral type model gives a sound description on the structure in the short range order of metallic glasses but fails beyond the nearest-neighbor shell. For instance, how can the medium range order be defined with the local structural unit, and how would the local structural units be connected to full three-dimensional space?
Miracle [90] suggested a compelling structural model for metallic glasses based on the dense packing of atomic clusters. An FCC packing of overlapping clusters is taken as the building scheme for medium range order in metallic glasses. Figure 2-3 illustrate his
12
promoted model of medium range order. A reality check for these previous structural concepts was proposed by Sheng et al. [23] with experiments and simulations. They indicate the icosahedral ordering of single-solute-centered quasi-equivalent clusters is an efficient packing scheme, but is not the only type of medium range order. The atomic packing configurations of different binary amorphous alloys are shown in Fig. 2-4. For each one of the metallic glasses, the several types of local coordination polyhedra units are geometrically different, and not identical in their topology and coordination number. They can be considered quasi-equivalent, or cluster-like units for a given glass, supporting the framework of cluster packing. The cluster connection diagrams for the several metallic glasses are shown in Fig. 2-5 to illustrate the specific packing and connection schemes of the quasi-equivalent clusters, through the sharing of edges, faces and vertices. This maybe represents the important question of how the clusters are connected and packed to fill the three-dimensional space, giving rise to the medium range order. It is short range for the packing of clusters, but already medium range from the standpoint of atomic correlation beyond one cluster.
A new insight, imperfect ordered packing, which is closely related to the cooling rate, is exposed on the medium range order embedded in the disordered atomic matrix by selected simulation of high-resolution electron microscopy image [91]. It points out that the packing character of medium range ordering structures can be of two types, i.e. icosahedron-like and lattice-like, and indicates that the solidification from melts or crystallization of metallic glasses is controlled by preferential growth of the most stable imperfect ordered packing. On the other hand, Fan et al. [92-94] proposed a structural model for bulk amorphous alloys based on the pair distribution functions measured using neutron scattering and reverse Monte Carlo simulations. Figure 2-6 shows a refined model of bulk amorphous alloys due to the reverse Monte Carlo method that has a good agreement with the experimental measurement.
There are many clusters of imperfect icosahedral and cubic forms extracted from Fig. 2-6.
13
These clusters are randomly distributed, strongly connected, and result in the space between the clusters. The space between the clusters forms free volume, which provides a degree of freedom for the rotation of the clusters under applied load. This cooperative rotation of clusters forms a layer motion (i.e. shear bands), and plastically deforms the amorphous alloys.
This model implies that the mechanical properties, e.g. strength and ductility, are dominated by the combination of the bonding characteristics inside and between these clusters.
2-3 Mechanical properties
Unlike the dislocation mechanisms for plastic deformation in crystalline alloys, the amorphous alloys only allow limited atomic displacements to resist deformation as a result of the glassy structure with a high degree of dense randomly packed atomic configurations, when the applied stress is on the amorphous alloys. Figure 2-7 summarizes the relationship between tensile strength, Vickers hardness and Young’s modulus for bulk glassy alloys, and the data on crystalline metallic alloys are also included for comparison [54, 95]. As the figure indicates, the BMGs have higher tensile fracture strength σf of 0.8-2.5 GPa, Vickers hardness Hv of 200-600, and lower Young’s modulus E of 47-102 GPa, than ordinary metallic crystals [54]. It is considered that the significant difference in the mechanical properties is due to the discrepancy in the deformation and fracture mechanisms between bulk metallic glasses and crystalline alloys.
It has been widely accepted that shear-band propagation is the major cause affecting the ductility and toughness of the amorphous alloys. Plastic deformation in metallic glasses is generally associated with inhomogeneous flow in highly localized shear bands. When the shear band went through in the metallic glasses, it is often accompanied with locally rising high temperature to influence the shear flow. Figure 2-8 (a) is good evidence from tensile
14
experiments to show that local melting occurs under high strain rate situations through unstable fracture [96]. Even under slower loading rates, a veined fracture surface indicates a decrease in the glass viscosity, as shown in Fig. 2-8 (b). Due to the highly localized nature of flow and the lack of microstructural features in the metallic glass to distract the flow, shear band formation typically leads to catastrophic failure. The strain softening and thermal softening mechanisms are tightly associated with the localization of shear band [97].
Generally speaking, the metallic glasses have high fracture toughness but brittle as well as negligible plasticity. For instance, the Zr-based bulk metallic glasses present high Charpy impact fracture energies ranging from 110-140 kJ/m2 and high fracture toughness limit [98].
Their fatigue limit is close to those of the crystalline alloys. However, standard stress–strain fatigue tests show that the Vitreloy alloy (commercial Zr-based BMG) has an extremely low resistance to crack initiation and a crack propagates rapidly once it has formed. If this alloy does start to yield or fracture, it fails quickly. Geometrical confinement of shear bands can dramatically enhance overall plasticity.
Furthermore, the plastic yield point of most bulk metallic glasses is located within a small range around εy = 2% at room temperature [99]. Composite approach is used to enhance the ductility and toughness of metallic glasses in recent fabricating efforts[100].
Figure 2-9 (a) shows the scanning electron microscopy (SEM) backscattered electon image of in situ Zr-Ti-Nb-Cu-Ni-Be composite microstructure, and Fig. 2-9 (b) is the compressive stress strain curve for a cylindrical in situ composite specimen. From Fig. 2-9 (a), a variety of reinforcing crystalline phase consisting of a ductile crystalline Ti-Zr-Nb β-phase, with body-centered cubic (BCC) structure, has been formed in the bulk metallic glass matrix. This bulk metallic glass matrix composite successfully increases the plastic strain to over 8% prior to failure, as shown in Fig. 2-9 (b). Later, a plastic strain of 20% is measured in the
15
Pt-Cu-Ni-P bulk metallic glasses before failure, as seen in Fig. 2-10 (a). Its behavior is like a typical bulk metallic glasses initially but performs as a perfectly plastic deformation after passing the yielding point of 2%. This Pt-Cu-Ni-P bulk metallic glass has a high Poisson ratio of 0.42, which causes the tip of a shear band to extend rather than to initiate a crack. This results in the formation of multiple shear bands in Fig. 2-10 (b), and is the origin of the large ductility [101].
2-4 Deformation mechanisms
Due to the absence of dislocation and grain boundary structures, the plastic deformation mechanism of metallic glasses is well known as shear-band evolution that deeply associates with the mechanical properties and failure behavior in bulk metallic glasses. A SEM observation showing the shear bands is given in Fig. 2-11. Nevertheless, the shear band is not the basic defect unit in the deformation mechanisms in the metallic glasses under microscopic scale. In the 1960s, Cohen and Turnbull [102] as well as Spaepen [103] suggested a concept of free volume which is considered as vacancy-like defect (Fig. 2-12) in the metallic glasses, and Argon [104] proposed a theoretical model of plastic flow in metallic glasses, termed shear transformation zone (STZ), which is the fundamental shear unit consisting of a free volume site and its close adjacent atoms in amorphous metals.
The concept of free volume
In the conceptual framework of free volume, the mechanical coupling is weak to the surrounding of free volumes, and hence the inelastic relaxation becomes possible by local atom rearrangement, without affecting the surroundings significantly [105]. Thus, free volume regions could be the preferred sites where easy caused the glass structure
16
destabilization by either temperature or applied stresses. The concept of free volume is most frequently used in explaining the deformation behaviors and atomic relaxations in the MGs due to its convenient for measurement (density or enthalpy change), and easy understanding, that is, a necessary open space allowed for shear process to operate. For instance, a simple relationship νf/νm = β．ΔH assumes that enthalpy ΔH is proportional to the variation of the average free volume per atom, νf/νm [106]. Thus, based on the enthalpy recovery measurements, the reduction of free volume difference via structural relaxation, νf/νm, was determined.
Also, a free volume exhaustion mechanism was proposed by Yang et al. [107] to explain the interesting fact that propagation of shear bands in metallic glasses can be retarded, with decreasing temperature and shear strains, in the lack of work hardening mechanisms. It is generally thought that the shear bands could form as a result of the movement and accumulation of free volumes (dilatation expansion). Atomic simulations also show that the local free volumes increase in the BMG provides an open space for the movements of atoms and is associated with the localization of shear band, and the shear softening results from the production of excessive free volume in the shear band [108-110].
Despite the successful description on the strain softening, heterogeneous deformation of MGs, and various mechanical properties of experimental observations, the validity of the free volume theory is questionable, and its atomic basis is still being challenged by atomic simulations. One can easy find the ambiguous characteristics that the free-volume sites may initiate plastic deformation and also can be the result of plastic deformation simultaneously, but not the deformation process itself [111]. Besides, the free-volume model has not made clear motion and rearrangement of constitute atoms within shear bands during plastic flow.
To clearly identify the “free volumes” is almost impossible either in experiments or
17
simulations that results in the barrier on the building complete physic model so far. Generally, the concept of free volume is successful as a phenomenology but not as a microscopic theory [105].
The model of shear transformation zones
Another well-use defect model extended from free-volume assumption used to explaining the plastic deformation of metallic glasses is STZ model proposed by A. Argon.
According to their model, shear deformation takes place by spontaneous and cooperative reorganization of a small cluster of randomly close-packed atoms [112]. An STZ can supply a small increment of shear strain under the action of an applied shear stress [113], and thus creates a localized distortion of the surroundings to accomplish the shear-band formation. A simplified picture of STZ deformation is shown in Fig. 2-13. The size of STZ is predicted among the order of 100 atoms from energetic considerations [114, 115] and is consistent with the model of molecular dynamics simulation in the investigation of Cu-Ti system [116].
Compared with abstract image of free-volume concept, the STZ mechanism is easy to be studied in the atomic models. A number of MD simulation studies by Falk and Langer summarized the crucial features of STZ mechanisms as follows [111, 117]: (a) once a STZ has transformed and relieved a certain amount of shear stress, it cannot transform again in the same direction. Thus, the system saturates and becomes jammed. (b) STZs can be created and destroyed at rates proportional to the rate of irreversible plastic deformation, and plastic flow can take place only when new zones are being created as fast as existing zones are being transformed. (c) The attempt frequency of the transition is tied to the noise in the system, which is driven by the strain rate. The stochastic nature of these fluctuations is assumed to arise from random motions associated with the disorder in the system. (d) The transition rates
18
between jammed and flowing are strongly sensitive to the applied stress. Recently, they also proposed a criterion (effective temperature) that determines which materials exhibit shear bands based on the initial conditions alone, based on their STZ theory [118-120].
Figure 2-14 shows the behavior of the effective temperature as a function of time for a system that localizes and a system that does not localize, Figs. 2-14 (a) and (b) illustrating the two different initial stages, respectively [118]. Their numerical works show that perturbations to the effective temperature grow due to an instability in the transient dynamics, but unstable systems do not always develop shear bands. Nonlinear energy dissipation processes interact with perturbation growth to determine whether a material exhibits strain localization [118].
Other simulation studies in the nature of STZ model are keeping on publish [121] and become worthy of investigating this crucial issue in depth.
Theory of shear banding and shear band model
According to the experimental observations, the width of a shear band is 101-102 nm the same as its offset shear displacement [122, 123], and propagation time of shear bands is about 10-5 s [124]. Because shear bands are thin, move fast, and are short-lived, to observe the dynamic evolution of the shear bands in the metallic glasses is highly difficult. Building the atomic scale model of shear band such as the development of a shear band inside a binary bulk metallic glass model, in Fig. 2-15, is very beneficial for studying the shear band mechanism [110]. A simple conceptual quantity excess volume, νexcess = νvoro – νatom (Fig.
2-16) is used to investigate the relation between the free volume changes and shear localization. They suggested that shear banding results from the volume-expansion-induced mechanical softening [109, 110, 125, 126]. A loop of “local volume increase→local shear softening→large local strain→local volume increase” may be the basic mechanism for
19
deformation and shear banding in MGs. Similar results are observed in the shear-band simulation works of the Mg-Cu systems by Bailey et al. [127], the interactions of the shear bands with the free surfaces as well as with each other result in an initial temperature rise, but the rise of temperature are delayed somewhat with respect to the localization of plastic flow itself.
Shimizu et al proposed an aged-rejuvenation-glue-liquid (ARGL) model, Fig. 2-17, of shear band in BMGs [128]. That is a more complete theoretical model of shear band than that of others so far. They proposed that the critical condition of initiating a mature shear band (MSB) is not the nucleation of embryonic shear band (ESB), but its propagation. The ESB is easy forming in the MGs. However, to propagate an ESB, the far-field shear stress must exceed the quasi-steady-state glue traction stress of shear-alienated glass until the glass transition temperature is approached internally due to frictional heating, at which point ESB matures as a runway shear crack [128], as shown in Fig. 2-18. In contrast, when applied stress is below the glue traction, the ESB does not propagate, become diffuse, and eventually die.
At the same time, an incubation length scale linc is necessary for this maturation for the BMGs, below which sample size-sale shear localization does not happen. The incubation length linc ~ αcv2(Tg-Tenv)2 /τglue2cs, where α is the thermal diffusivity, cv is its volumetric specific heat, Tenv is initial temperature, is the cs shear wave speed. Through the calculation of this form, the linc is about 10 nm for Zr-based BMGs [128, 129].
Furthermore, it is often questioned whether the shear band mechanisms with regard to metallic glasses is similar to the dislocation mechanisms for crystalline structure, although they are of different definitions. Schuh and Lund [113] found that the plasticity in metallic glasses is consistent with the Mohr-Coulomb criterion by the STZ theory as well as molecular simulation works, and predicted a transition from dislocation-dominated yield processes
20
(following the von Mises criterion) to STZ-dominated yield (following the Mohr–Coulomb criterion) as grain size decreases toward zero for nanocrystalline materials. Ogata et al. [130]
simulated the nucleation of local shear transformation zone (STZ) and shear band, under volume-conserving simple shear deformation in molecular dynamics. A significant shear–normal stress coupling which suggests the modified Mohr-Coulomb yield criterion has also been demonstrated. They suggested that the dislocation concept may be applicable to bulk metallic glasses with modifications such as taking into account the structural features of bulk metallic glasses instead of the Burgers vector concept in crystals.
The plastic deformation always accompanies the localized heating within shear band that is an important key-point to result in the strain-softening mechanisms and thermal softening on the fracture surface [131]. Understanding the temperature rise in shear bands can also help to improve the ductility and toughness of the metallic glasses. A substantial increase in temperature will correspond with a drop in viscosity governed by the presence of free volume within the metallic glasses [132]. From the calculation of heat conduction theory and STZ modeling, Yang et al. [133] demonstrated that the temperature of shear bands at the fracture strength is strikingly similar to their glass transition temperature for a number of BMG systems. This offered a new guidline for the expansion of ultra-high strength bulk metallic glasses from their glass transition temperature, density, and heat capacity values. The calculated shear-band temperatures at the fracture strength for nine bulk metallic glasses with six different alloy systems is shown in Fig. 2-19.
2-5 Fatigue properties in BMGs
It is well known that the process of accumulated damage and failure due to cyclic loading is called fatigue. Fatigue is a result of a progressive, localized, and permanent
21
structural-damage behavior when the applied cyclic stresses are under the ultimate tensile strength of the materials. Two categories of fatigue testing are frequently the performed, one is high-cycle fatigue test that the initial deformation is primarily elastic, and the other is low-cycle fatigue test that results in the elastoplastic deformation. The main factors affected fatigue failures are generally the number of loading cycles, stress range, mean stress, and local stress concentrations [105]. The stress-life (S-N) curve shows the amplitude of stress, stress range, or maximum stress versus the number of cycles to failure, N. This curve can present the fatigue life (or fatigue-endurance limit) and fatigue strength of materials. Table 2-2 is a summary of fatigue properties of the Zr-based BMGs and various crystalline alloys from the literatures [134, 135]. An increasing trend of the fatigue-endurance limit with increasing material tensile strength generally occurs in the crystalline materials but not clear in BMGs.
The behavior of fatigue crack growth in BMGs is similar to that of some high-strength alloys, but the behavior of fatigue life is significantly different between them [105]. On the other hand, the fatigue properties of BMGs often reveal discrepancies in the results from different research groups. For instance, the fatigue resistance for BMGs was rated as poor relative to traditional crystalline materials [136, 137], but not all studies are in agreement on this point [42, 43]. The complicating issues in BMGs fatigue properties may be due to the differences in specimen geometry and preparation. The suitably large specimens for testing are always lack in BMGs.
Free volumes and shear bands are also relevant to the fatigue damage mechanism of BMGs. The shear band formation and propagation usually go along with the local increase of free volumes and crack sites within BMGs due to the weakness in the shear bands or shear-off steps (Fig. 2-20) [42, 43], subsequently leading a fracture and fatigue damage, as
22
demonstrated in Fig. 2-21. A simple four component Lennard-Jones simulation model was used to study the fatigue-damage behaviors in metallic glasses and proposed that the free volume level would increase and would be localized with each deformation cycle during the cyclic loading in both the shear and tension tests [138]. They believed that this occurrence would induce the initiation of fatigue damage and/or shear-band formation in BMGs. It follows that, if we can reduce the free volumes in BMGs, the plastic deformation and fatigue damage might be retarded and the fatigue life might be extended.
Through using positron annihilation spectroscopy (PAS) measurements on the effects of free volume changes, it was found that the crack growth and fatigue lifetime will increase with decreasing free volumes in the glass matrix, but the fatigue-crack-growth rates are insensitive to free-volume variations [139]. In contrast, as the crack propagates, the stress or strain concentration induces an increase in free volume within a transformation zone at the crack tip. That controls the local flow properties and makes the fatigue crack growth insensitive to the initial free volume state. The effects of reduction in free volume are often coupled with the states of residual stresses. Specifically, residual compression stresses on the specimen surfaces reduce the crack propagation rate in the threshold region and improve its fracture toughness. Their relationships with fatigue threshold, fracture toughness, and fatigue limit are shown in Fig. 2-22 [139]. In addition, the temperature does not have large influence on the propagation of fatigue crack of BMGs [105]. With the above limited information, the further exploration on the critical theoretical model and basic fatigue-damage mechanism in fatigue behavior of BMGs is still needed.