and that glasses are a unique phase of matter. The less controversial explanation follows the kinetics argument above and defines T g as the temperature at which the material begins to flow. The glass transition is visible as a discontinuous jump in heat capacity = Δc p . In the kinetics argument, Δc p arises from changes in the slope of the volume, entropy, and enthalpy curves at the glass transition due to the kinetic freezing of the liquid [2] (see Derivation 2). Above T g , the mobility of the atoms in the undercooled liquid increases and at T x a crystalline configuration is found and the sample reaches the desired thermodynamic low energy crystalline state. As the sample transitions from a high energy liquid to a low energy crystal, heat must be released and the exothermic crystallization peak is observed. The total heat released in the crystallization process is H x . The temperatures at which melting begins and ends are T s and T L respectively. In an elemental solid, melting peaks are very sharp and theoretically T s = T L . Melting a solid is an endothermic process meaning that heat input is required to cause the phase change from crystal to liquid. The amount of heat required to melt the crystal = H f . If the sample was heated quickly enough, crystallization and melting would not have occurred and the glass could be taken back above the crystalline melting temperature with only a discontinuity in heat capacity.
and that glasses are a unique phase of matter. The less controversial explanation follows the kinetics argument above and defines T g as the temperature at which the material begins to flow. The glass transition is visible as a discontinuous jump in heat capacity = Δc p . In the kinetics argument, Δc p arises from changes in the slope of the volume, entropy, and enthalpy curves at the glass transition due to the kinetic freezing of the liquid [2] (see Derivation 2). Above T g , the mobility of the atoms in the undercooled liquid increases and at T x a crystalline configuration is found and the sample reaches the desired thermodynamic low energy crystalline state. As the sample transitions from a high energy liquid to a low energy crystal, heat must be released and the exothermic crystallization peak is observed. The total heat released in the crystallization process is H x . The temperatures at which melting begins and ends are T s and T L respectively. In an elemental solid, melting peaks are very sharp and theoretically T s = T L . Melting a solid is an endothermic process meaning that heat input is required to cause the phase change from crystal to liquid. The amount of heat required to melt the crystal = H f . If the sample was heated quickly enough, crystallization and melting would not have occurred and the glass could be taken back above the crystalline melting temperature with only a discontinuity in heat capacity.
rate in a Differential Scanning Calorimeter (DSC)
However, there is some difficulty associated with the thermodynamic/calorimetric definition of the glass transition. Different heating rates can yield different glass tran- sition temperatures for the same alloy; in the literature most DSC curves are taken at a rate of 10 or 20 K/s. However, the apparent glass transition temperature can shift due to different heating rates — typically a lower heating rate corresponds to a lower T g . This is largely related to the idea of frequency dependence of measurements, a concept that will be discussed in more detail throughout this thesis. Different heating rates correspond to different characteristic-length (in distance and time) atomic vi- brations/rearrangements in the alloy, thus the transition from solid-like to liquid-like occurs at different temperatures.
In addition to the experimental studies on the GFA fac- tors for metallicglasses, a number of theoretical studies have been carried out to evaluate the R c 3–14) and to clarify the re- lation between R c and T g / T m . 4, 6, 13) The GFA factors have been recently summarized 15, 16) for typical metallicglasses by combining the theoretical R c with the experimental results of T g / T m and ∆ T x . To our knowledge, however, the relationship among all the GFA factors have not been analyzed theoreti- cally in the framework of a general model.
The elastic constants are important for discussing the structural stability, because they provide the important physical information such as the Debye temperatures and the characteristics of the glass transitions. Several papers related with the elastic constants have appeared in various alloy systems. 8–14) On the other hand, there are several studies on the low-frequency (1 Hz) internal friction. 15–17) It is well-known that the peak magnitude of internal friction Q 1 becomes higher when the measurement frequency f is lower:
The morphologies of the samples subjected to fracture were examined by scanning electron microscopy (SEM).
3. Results and Discussion
The DSC curves of the as-spun Ni 80x Pd x P 20 ribbon samples are shown in Fig. 1. During heating, all the samples exhibit a distinct endothermic peak due to glass transition, followed by a supercooledliquidregion, and then a sharp exothermic peak due to crystallization. With further increas- ing temperature, the alloys finally melt after several steps of endothermic events. When x increases from 10 to 35, T x
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By calculating the sum of crystallization enthalpy of the exothermic peaks (Σ ∆H), the specimens deformed at 2.5×10 -3 s -1 and 2.5×10 -4 s -1 consist of ~26 vol.% and ~24 vol.% volume fraction of crystallized phases, respectively. Combined with the structural analysis in section 5.3, α-(Ti, Zr) and CuTi phases are perhaps participated in the samples deformed at 716 K and 2.5×10 -4 s -1 . These DSC results confirm that at the highest testing temperature of 716 K, the glass partially crystallizes during the compression tests in the supercooledliquidregion. Furthermore, lower strain rates can result in the formation of large crystalline volume since the specimen was exposed to higher temperatures for much longer time until the compression test finished compared to higher strain rates. After crystallization the chemical composition of the remained glass should be different with the original composition of Ti 40 Zr 10 Cu 34 Pd 14 Sn 2 , which in turn causes the shift of peak temperatures.
To process metallicglasses thermoplastically by electromagnetic forming, it is essential that the processes of ohmic heating and magnetic forming are independently controlled. This requires that the electric current, which travels through the metallic glass dissipating electrical energy and producing volumetric heating, be controlled independently of the magnetic field, which interacts with the electric current to generate the magnetic force. This is achieved by placing the metallic glass in series with an electric current source directed transverse to an independently applied magnetic field. Such a configuration is shown in Fig. 3.1, where a metallic glass sample is connected in series to a capacitor via electrodes while situated transverse to a magnetic field generated by two permanent magnets. Application of an intense electric current pulse ohmically heats the metallic glass rapidly and uniformly to a predetermined temperature in the supercooledliquidregion, while the coupling between electric current and magnetic field generates a force pulse on the sample urging it against a permanent die tool, where it forms and subsequently cools and revitrifies. Here, we show that typical currents produced by discharge of a conventional capacitor and typical magnetic field strengths generated by conventional permanent magnets are adequate to rapidly and uniformly heat a bulk metallic glass sample to a low viscosity state and thermoplastically shape it against a die tool prior to the intervention of crystallization.
As for the conventional diffusion, for example, self- diffusion of constituent atoms in the Zr-Al-Ni-Cu-Be and Pd-Cu-Ni-P metallicglasses, 22,23) it was reported that the diffusion coefficient increases significantly just at the temperature higher than T g . Knorr et al. investigated the self-diffusion in the supercooledliquid state of the Zr-Ti-Cu- Ni-Be metallic glass and proposed the collective diffusion mechanism mediated by vacancy-like thermal defects. 24) Besides, Fielitz et al. also investigated the diffusivities of impurities in the Zr-Ti-Cu-Ni-Be metallic glass and con- cluded that the diffusion mechanism could be changed just at the temperature around T g and that the cooperative motion of atoms improves predominantly the diffusivity in the super- cooled liquid state. 25) However, hydrogen permeation starts to increase significantly at the temperature below T g as shown in this study. It is known that some physical parameters of the metallic glass start to change at the temperature much lower than T g . For example, the flow stress of the metallic glass decreases at the temperature much lower than T g . 26) Since hydrogen atoms are the smallest among the elements, hydrogen diffusion can be affected sensitively by the local atomic structure change even at the temperature below T g , resulting that hydrogen diffusion
2.2 Introduction
The previous chapter explored some of the numerous ways that environment, impu- rities, and other external factors could affect a glass former’s GFA. There are several intrinsic factors that help determine a material’s GFA, and considerable work has been done to try and identify the characteristics of good glass formers. Over time there have been several notable characteristics of good glass formers, and these characteristics became heuristics in developing new alloys. The most prominent heuristic is to identify deep eutectics in composition space. The first metallic glass developed was based around the very deep Au-Si eutectic[44] and many of the best metallicglasses are based around deep binary eutectics such as Ni-P, Fe-P, Cu-Zr, Pd-Si, among others. While binary phase diagrams exist for almost all alloys of interest, ternary and higher order phase diagrams are significantly rarer. The exper- imental efforts to create meaningful ternary or higher dimension diagrams are very substantial, so if experimental analysis is done it is usually to map out areas near compounds of interest. Computational techniques are much more able to tackle these higher dimension composition spaces, but it is still very time consuming to make generalized phase diagrams. As such, the ability to use eutectics as the only design tool is very limited.
4.2) Parameters obtained for a single La shell model for the Ga enviromnent in Lal,,Ga, glasses.. 4.3) Summary of the physical parameters found for Lal,,Ga, glasses using EXAFS [r]
P ternary glassy alloys in the case of conventional copper mold casting or water quenching is about 2 mm. 8) It has been found in 1996 that the replacement of Ni by 30 at% Cu in Pd 40 Ni 40 P 20 alloy causes a drastic increase in the maximum diameter to more than 40 mm even in a non-fluxed melting state. 11) Very recently, Pd- and Pt-based bulk glassy alloys have drawn increasing interest as biomedical materials. In their application field, it is necessary to develop a Pd-based bulk glassy alloy without Ni element. The complete elimination of Ni element in Pd-based alloys has been recognized to significantly decrease the glass-forming ability as well as the supercooledliquidregion before crystalliza- tion. 12) For instance, the maximum sample diameter and the temperature interval of supercooledliquidregion are about 100 mm and 95 K, respectively, for Pd 40 Cu 30 Ni 10 P 20 13) and less than 1 mm and 48 K, respectively, for Pd 40 Cu 40 P 20 . 12) We have found that the partial replacement of Pd by Pt in Pd 40 Cu 40 P 20 alloy is effective for the increases in maximum sample diameter and supercooledliquidregion and the resulting Pd–Pt–Cu–P bulk glassy alloy can be regarded as a new type of Pd-based bulk glassy alloy which is important for basic research and biomedical application. This paper presents the glass-forming ability, thermal stability and mechanical properties of the new Pd–Pt–Cu–P bulk glassy
Considering that the I-phase is precipitated from the glassy state as a primary phase in the Zr 70 Cu 30 glassy alloy by addition of only 0.5 at% Pd or Au, it is suggested that an icosahedral local atomic configuration exists in the glassy state. Since the coordination number around Zr in the glassy state is approximately 12, the icosahedral local atomic configuration may be formed around the Zr atom. The authors have also reported that the icosahedral atomic configuration is confirmed by the high-resolution trans- mission microscopic observations in the Zr-based glassy alloys, in which the I-phase is formed as a primary phase. 27,28) These results also suggest the investigation of stability of supercooledliquid state in correlation with the local structure. It is well known that high GFA is attributed to a high stability of the supercooledliquid state. 29) From the distinct glass transition prior to crystallization in the melt- spun Zr 70 Cu 30 alloy, we suggest that the icosahedral local structure stabilizes the supercooledliquid state. We demon- strated that the melt-spun Zr 70 Ni 30 alloy which exhibits no distinct glass transition, has the tetragonal Zr 2 Ni-like local structure by the RDF analysis. However, it was reported that the glass transition is observed in the rapidly quenched Zr-Ni alloys in a wide compositional range by addition of a small amount of Al. 23) Considering the I-phase formation by addition of a small amount of Pd and the total coordination number around Zr of 12.5 in the as-quenched state in the Zr 60 Ni 25 Al 15 glassy alloy, which is different from those in the crystallized state (13.1) as well as in the melt-spun Zr 70 Ni 30 alloy (10.7), we can realize the formation of the icosahedral local structure in Zr-Al-Ni ternary glassy alloy. Therefore, it is concluded that the icosahedral local structure stabilizes the supercooledliquid state and the elemental combinations of Zr + Cu and Zr + Al + Ni are necessary for the icosahedral local structure formation. We also suggest that bulk glass- forming ability is attributed to the difference of stability of the icosahedral local structure with the combination of constitutional elements. The satisfaction of three component rules for high GFA leads to the high stability of icosahedral local structure by retarding the atomic rearrangements for the formation of stable crystalline phase.
AUSTRALIA
E-mail: nima.akhavan@anu.edu.au
Abstract: This paper investigates forming and failure behaviours of a consolidated woven self- reinforced polypropylene (SRPP) composite through combined stamp forming experiment and finite element analysis. Mechanical properties of a woven SRPP composite were characterised using a universal testing machine and a non-contact photogrammetry system. Constitutive equations were derived as functions of strains using a homogenised orthotropic material model. Consolidated SRPP specimens with novel geometries, different aspect ratios and fibre orientations, were stretch formed in a custom built press until catastrophic failure. Evolution of principal strains was captured using a real time Digital Image Correlation (DIC) system. A path dependant failure criterion was developed as a function of deformation modes and invariants of strain tensor at the vicinity of fractured region. Material and failure models were implemented into a finite element analysis using Abaqus/implicit. Strain path at the pole of specimens, evolution of surface strains, and onset of failure were predicted using a homogenised numerical scheme. Comparison with experimental outcomes demonstrated high accuracy of the developed numerical model in predicting deformation and failure behaviours of a thermoplastic composite under a wide range of deformation modes. The model demonstrated its potential to predict formability and failure behaviour of woven thermoplastic composites during manufacturing by eliminating the need to conduct expensive, time consuming trial and error procedures.
However, if nanocrystal/amorphous composite is formed during solidificatin, it can lead to enhancement of the plastic strain as reported in Cu-Zr-Ti BMG. 19) Melt temperature is also very much important as shown in Fig. 8. There are reports that the same BMG studied by different research groups gives different plasticity values. For example, Cu 50 Zr 50 shows more than 50% plasticity in one case 12) where injection casting has been employed. The same composition gives only 8% strain in another case 13) where suction casting has been used. Recent report 20) also has suggested that even if the same injection casting is used, still there would be wide difference in the plasticity values of the Cu 50 Zr 50 metallic glass due to inherent change in the structure. This could be either due to difference in cooling rate or difference in melt temperature which definitely change the structure of the glassy phase which, in turn, leads to such a wide difference in plasticity in Cu 50 Zr 50 system.
Based on binary phase diagrams, 24) Zr forms deep eutectics with Fe, Cu and Al and heating of mixing of the Zr-Fe, Zr-Cu and Zr-Al atomic pair is 25, 23 and 44 kJ/mol, respec- tively. 25,26) Meantime, Cu, Fe and Al have large mutual solu- bility with each other 24) and the heat of mixing of Cu-Fe, Cu- Al and Fe-Al is +13, 1 and 11 kJ/mol, 25,26) respectively, all of which are much smaller than that of the three strong atomic pairs. As such, the Zr-Fe-Cu-Al alloys can be simpli- fied to an A-B i type ideal liquid. Next, we will use the Zr- (Fe,Cu,Al) system as an example to further elucidate the pro- posed strategy and also to demonstrate how new BMGs with superior GFA can be quickly explored with this strategy.
At a first look the mechanical properties of metallicglasses do not appear to reflect the disordered nature of the atomic structure, because they seem to be superficially similar to those of crystalline metals. Upon a closer look, however, we recognize that the structure has profound and intricate effects on the mechanical properties. This is because at the atomic level the local response of a metallic glass to the external stress field is strongly heterogeneous. Even in the case of elastic response to a uniform stress the local compliance is not uniform. And yet each local portion of the system cannot independently respond to the stress, because they are connected to each other, and thus have to satisfy the elastic compatibility condition. Similarly in plastic deformation local structural changes create long-range stress fields and affect each other, as a consequence of satisfying the elastic compatibility condition. In addition local structural changes alter the effective, or fictive, temperature. Here we reviewed recent advances in our understanding of such unique features of elastic, anelastic and plastic deformation of metallicglasses, focusing on the atomic-level phenomena. A large amount of researches on the mesoscopic behavior, such as the effect of shear bands, are not included in this review, even though they are important in understanding the actual behavior of a macroscopic sample.
(Received November 30, 2006; Accepted April 11, 2007; Published June 25, 2007) Keywords: Atomic dynamics, metallicglasses, glass transition
1. Introduction
It is a challenging task to describe the atomic structure of liquids and glasses with sufficient clarity and accuracy, since the usual diffraction techniques provide only one-dimen- sional information on the structure in terms of the pair- density function. But it is more daunting a task to relate the structure to the properties of metallicglasses, even if the structure were to be known. In the absence of a reliable framework to describe the structure-property relationship a century old concept of free-volume 1) is still widely used in this field. Indeed the free-volume theory by Cohen and Turnbull 2–4) has successfully described why small changes in the volume can result in diffusivity changes which are very large, by more than ten orders of magnitude. However, from the onset they noted that the theory is less successful for metals. 2) The critical free-volume, v , is only about 10% of the atomic volume, while it has to be almost as large as the atomic volume for the theory to be successful. Recent experiments and simulations further corroborate on this point. The pressure effect on diffusivity of metallicglasses 5) shows that the space between atoms involved in diffusion is much smaller than expected for the free-volume model; the activation volume for diffusion is much smaller than the atomic volume. Also the isotope effects on diffusion 6) fairly convincingly show that the picture of single atom diffusion is incorrect, and diffusion in liquids and glasses is a more collective phenomenon. Computer simulations 7,8) have cap- tured the shape of the collective process, and showed that it is a chain-like process involving more than ten atoms, with each atom moving only slightly. These new results challenge us to rethink the mechanism of atomic transport in metallicglasses.
3.2 Magnetic yoke for linear actuator
It is well known that conventional Fe- and Co-based amorphous alloys exhibit good soft magnetic properties, in particular, high saturated magnetic flux density for the former alloys and high permeability with zero saturated magneto- striction for the latter alloys. 9) Although these amorphous alloys have been formed in Fe-Si-B, Fe-P-C and Co-Fe-Si-B systems, the production of their amorphous alloys requires high cooling rates exceeding 10 5 K/s and the resulting material thickness is usually limited to less than 50 mm. 9) Since 1995, Inoue and his colleagues have succeeded in finding a number of Fe-based glass-forming systems. 10–14) By use of these findings, we slightly modified the composition of Fe-Si-B-Nb 15) system in order to enhance glass-forming ability and ductility. Figure 3 shows I-H loop of glassy ribbons for (Fe 0:6 Co 0:4 ) 72 Si 4 B 20 Nb 4 . Saturation magnetiza- tion (I s ) and maximum permeability ( max ) for the (Fe 0:6 - Co 0:4 ) 72 Si 4 B 20 Nb 4 glassy ribbon are 1.15 T and 73000, respectively. These values indicate that the alloy has relatively good soft magnetic properties. Using prepared BMG plate as a set of yokes, the trial product of linear actuator was constructed. Figure 4 shows the outer appear- ance of linear actuator system including power source, AC wave generation circuit, power amplifier and actuator. The actuator is assembled by two pieces of SmCo permanent
dynamic mode I fracture surfaces, which indicated that the fracture is a void dominated process. Particularly, fine 100 nm size dimples and nanoscale periodic corrugations were found as well. Based on the fracture patterns, a new atomic motion unit called as tension transformation zone (TTZ), which may be interpreted as nucleation of nanoscale voids ahead of crack tip, was proposed. Similar phenomenon has been observed in spallation experiments studied the spallation behaviour of Zr-based metallic glass (Vit. 1) via plate-impact experiments. Equiaxed cellular patterns were found on the spall surface of recovered samples, which indicated that the spallation in the materials is induced by nucleation, growth and coalescence of micro-voids. Moreover, this micro-voids dominated fracture process has also been observed in atomic scale during molecular dynamics simulations.