ABSTRACT. amorphous metals, and utilized the correlation between elastic properties and fragility as a

Transcription

1 ABSTRACT In the present thesis study, we combined molecular dynamics (MD) simulations and experiments to systematically investigate the Debye-Grüneisen thermal expansion effect and configurational potential energy dependence of elastic properties for glassy states of amorphous metals, and utilized the correlation between elastic properties and fragility as a guiding tool to design and to develop novel bulk metallic glasses. It is extremely important to create appropriate interatomic potentials, generate glassy configurations, and study the local structures of the system before moving to the next step. An effective tight-bonding, RGL-type, n-body force field for the binary Cu-Zr alloy system was constructed and employed in MD simulations. Partial radial distribution functions, coordination numbers, and Honeycutt Andersen (HA) indices have been calculated to analyze the local structures of Cu 46 Zr 54 metallic glass. We report the strong dependence of elastic properties on configurational changes in a Cu-Zr binary metallic glass assessed by molecular dynamics simulations. By directly evaluating the temperature dependence and configurational potential energy dependence of elastic constants, we show that the shear modulus dependence on the specific configurational inherent state of metallic glasses is much stronger than the dependence on Debye-Grüneisen thermal expansion. We present the isothermal equation of state (EOS) in a wide range of temperatures and pressures by carrying out molecular dynamics simulations on a simple binary model metallic glass. A universal form of EOS proposed by Vinet et al. is utilized to fit the data, vii

2 assuming no phase transitions. Pressure-induced cavitation was observed in glassy states and liquids from our simulations. The thermodynamic limit of instability and kinetic limit of instability of the cavitation behavior were analyzed. Negative pressure is critical to trigger the cavitation. The cavitation barrier height was estimated using the classical nucleation theory. The intrinsic origin of why and how Poisson s ratio or the ratio of G/B is involved in the deformation and fracture behavior of glasses is discussed. The compositional dependence of thermal and elastic properties of Cu-Zr-Be ternary bulk-metallic-glass-forming alloys was systematically studied. There exists a linear relationship between the glass transition temperature, T g, and the total Zr concentration. Shear modulus G decreases linearly with increasing Zr concentration as well. The results also show that T g, G, and Poisson s ratio, ν, are very sensitive to changes in compositions. Low T g, low G, and relatively high ν can be achieved with high Zr and Ti concentration. Lightweight Ti-based bulk amorphous structural metals with more than double the specific strength of conventional titanium alloys have been discovered. Thermal, elastic, and mechanical properties of these metallic glasses were studied and are presented. These amorphous alloys exhibit good glass-forming ability, exceptional thermal stability, and high strength. The research results have important implications for designing and developing low-density bulk metallic glasses. The technological potential of this class of lightweight Ti-based glassy alloys as structural metals is very promising. The exceptional processability and large supercooled liquid region of bulk amorphous metals makes them highly promising candidates for thermoplastic processing. We report a viii

3 lightweight (ρ = 5.4 g/cc) quaternary glass-forming alloy, Zr 35 Ti 30 Cu 8.25 Be 26.75, having the largest supercooled liquid region, (ΔT = 159 K at 20 K/min heating rate) of any known bulk-glass-forming alloy. The alloy can be cast into fully amorphous rods of diameter ~ 1.5 cm. The undercooled liquid exhibits an unexpectedly high Angell Fragility of m = Based on these features, it is demonstrated that this alloy exhibits benchmark characteristics for thermoplastic processing. We report results of mechanical, thermal, rheological, and crystallization (TTT-diagrams) studies on this new material. The alloy exhibits high yield strength and excellent fracture toughness, and a relatively high Poisson ratio compared with other Zr- or Ti-based glasses. Simple micro-replication experiments carried out in open air using relatively low applied pressures demonstrate superior thermoplastic processability for engineering applications. Starting from the two binary bulk-glass formers in the Cu-Zr system, we systematically investigated the compositional dependence of glass formation, and thermal, elastic and mechanical properties in the Cu-Zr-Ag ternary alloys. Both the Cu (50-x) Zr 50 Ag x and Cu (64- x)zr 36 Ag x series alloys show a good combination of high glass-forming ability and high Poisson s ratio. ix

4 TABLE OF CONTENTS Acknowledgements...iv Abstract...vii Table of Contents... x List of Tables...xiii List of Figures... xv Chapter 1: Overview, Motivations, and Key Contributions Historical Background Mechanical and Rheological Aspects of BMGs Potential Energy Landscape Theory and Cooperative Shear Model Motivations and Key Contributions References Chapter 2: Molecular Dynamics Study of a Binary Cu-Zr Metallic Glass: Glass Formation and Atomic-level Structure Introduction MD Simulation Details Force Field Parameters Molecular Dynamics Results and Discussions Glass Transition Radial Distribution Function Coordination Numbers Honeycut-Anderson Analysis Chapter Concluding Remarks References Chapter 3: Strong Configurational Dependence of Elastic Properties of a Cu-Zr Binary Model Metallic Glass Introduction x

5 3.2 MD Simulations Debye-Gruneisen Thermal Expansion Effect Configurational Dependence Chapter Concluding Remarks References Chapter 4: Equation of State and Pressure-Induced Cavitation of a Cu-Zr Binary Model Metallic Glass and Liquid Introduction MD Simulations Results and Discussions Chapter Concluding Remarks References Chapter 5: Thermal and Elastic Properties of Cu-Zr-Be Bulk-Metallic- Glass-Forming Alloys Introduction Experimental Results and Discussions Chapter Concluding Remarks References Chapter 6: Lightweight Ti-based Bulk Glassy Alloys Excluding Late Transition Metals Introduction Experimental Results and Discussions Chapter Concluding Remarks References Chapter 7: Bulk Metallic Glasses with Benchmark Thermoplastic Processability Introduction Experimental xi

6 7.3 Results and Discussions Chapter Concluding Remarks References Chapter 8: Formation and Properties of Cu-Zr-Ag Bulk Metallic Glasses Introduction Experimental Results and Discussions Chapter Concluding Remarks References xii

7 LIST OF TABLES Number Page Table 1.1 Summaries of bulk metallic glass alloys with critical size 10 mm... 4 Table 1.2 Expected qualitative correlations of values of selected properties with the kinetically strong or fragile behavior of the supercooled liquid in bulk-metallic-glass forming systems Table 2.1 Rosato-Guillope-Legrand (RGL)-type force field parameters.. 37 Table 2.2 A comparison between RGL-type force field and QM results for Zr Table 2.3 A comparison between RGL-type force field and QM results for Cu Table 2.4 A comparison between RGL-type force field and QM results for Cu-Zr system Table 2.5 First peak positions from different techniques for amorphous Cu-Zr alloys Table 2.6 The numbers of near-neighbour correlations obtained from different techniques Table 5.1 Thermal and elastic properties of representative Cu-Zr-Be and Vitreloy-type glassy alloys Table 6.1 Density, thermal, and elastic properties of representative lightweight Ti-Zr-Be and Vitreloy-type glassy alloys xiii

8 Table 7.1 Thermal, mechanical, and rheological properties of various BMG-forming alloys Table 8.1 Thermal and elastic properties of representative Cu (50-x) Zr 50 Ag x bulk glassy alloys Table 8.2 Thermal and elastic properties of representative Cu (64-x) Zr 36 Ag x bulk glassy alloys xiv

9 LIST OF FIGURES Number Page Figure 1.1 Record-size bulk metallic glasses developed in various alloy systems and the year of their discovery... 5 Figure 1.2 Elastic limit plotted against Young s modulus for bulk metallic glasses and over 1500 conventional materials... 8 Figure 1.3 Experimental shear stress at yielding vs. shear modulus at room temperature for 30 bulk metallic glasses Figure 1.4 Angell plot comparing the viscosities of different types of glass-forming liquids Figure 1.5 Correlation between fragility of liquids and the ratio of instantaneous bulk to shear modulus of respective glasses Figure 1.6 The correlation between m and B/G for metallic glasses Figure 1.7 The correlation of fracture energy with Poisson s ratio for all the collected data on metallic glasses Figure 1.8 Potential energy density function in the vicinity of an inherent state Figure 2.1 Volume as a function of temperature of Cu 46 Zr 54 during heating and cooling at a rate of 5 K/ps Figure 2.2 Volume vs. temperature curves for Cu 46 Zr 54 obtained from three different quenching rates Figure 2.3 Partial radial distribution function of Cu 46 Zr 54 for different bond pairs at 400 K during the heating process (5 K/ps) Figure 2.4 Partial radial distribution function of Cu 46 Zr 54 for different bond pairs at 2000 K during heating and cooling cycles Figure 2.5 Partial radial distribution function of Cu 46 Zr 54 for different xv

10 bond pairs at 400 K during the cooling process (5 K/ps) Figure 2.6 PRDF of Cu 46 Zr 54 for different bond pairs during the cooling cycle (5 K/ps), Cu-Cu pair Figure 2.7 PRDF of Cu 46 Zr 54 for different bond pairs during the cooling cycle (5 K/ps), Zr-Zr pair Figure 2.8 PRDF of Cu 46 Zr 54 for different bond pairs during the cooling cycle (5 K/ps), Cu-Zr pair Figure 2.9 Partial, total, and average coordination numbers of Cu 46 Zr 54 calculated for the cooling cycle (5 K/ps) Figure 2.10 Variation of the fractions of Honeycutt-Andersen indices Figure 3.1 Temperature dependence of shear modulus G for the Cu 46 Zr 54 metallic glass prepared at two different cooling rates Figure 3.2 Temperature dependence of bulk modulus B for the Cu 46 Zr 54 metallic glass prepared at two different cooling rates Figure 3.3 Volume dependence of B and G for the Cu 46 Zr 54 metallic glass prepared at a cooling rate of 2.5 K/ps Figure 3.4 Strong configurational potential energy dependence of shear modulus G for the Cu 46 Zr 54 metallic glass when varying the cooling rates to obtain different configurations Figure 3.5 The shear and bulk Modulii of Vit-4 as measured in-situ from -78 to 298 K and measured from samples quenched from the equilibrium liquid around T g Figure 4.1 Pressure change with atomic volume at different temperatures of the Cu 46 Zr 54 binary model metallic glass and liquid Figure 4.2 Pressure evolution vs. time at 300 K during the whole simulation process Figure 4.3 Cavitation pressure and spinodal pressure as a function xvi

11 of temperature Figure 4.4 Cavitation time vs. pressure at T=1200 K and the fitting curve obtained from classical nucleation theory Figure 5.1 Bulk metallic glass formation map in the Cu-Zr-Be ternary alloy system Figure 5.2 Glass transition temperature as a function of the total Zr and Ti content in Cu-Zr-Be ternary and Vitreloy-type bulk metallic glasses Figure 5.3 Shear modulus G vs. the total concentration of Zr and Ti in Cu-Zr-Be ternary and Vitreloy-type bulk metallic glasses.102 Figure 5.4 Poisson s ratio vs. the total Zr and Ti concentration in Cu-Zr-Be ternary glassy alloys and Vitreloy-type glasses Figure 6.1 Pictures of bulk amorphous samples of lightweight Ti-based bulk metallic glasses Figure 6.2 XRD patterns verifying the amorphous nature of the corresponding samples: amorphous 6 mm diameter rod of Ti 45 Zr 20 Be 35 (S1), 7 mm diameter rod of Ti 45 Zr 20 Be 30 Cr 5 (S2), and 8 mm diameter rod of Ti 40 Zr 25 Be 30 Cr 5 (S3) Figure 6.3 DSC scans of the amorphous Ti 45 Zr 20 Be 35 (S1), Ti 45 Zr 20 Be 30 Cr 5 (S2), and Ti 40 Zr 25 Be 30 Cr 5 (S3) alloys at a constant heating rate of 0.33 K/s Figure 7.1 DSC scans of three typical metallic glasses with excellent glass-forming ability and extremely high thermal stability Figure 7.2 A closer view of the glass transition temperatures of the three bulk metallic glasses from DSC curves xvii

12 Figure 7.3 Temperature dependence of equilibrium viscosity of several metallic-glass-forming liquids Figure 7.4 Angell fragility plot of several bulk-metallic-glass-forming liquids Figure 7.5 TTT diagrams for several amorphous alloys Figure 7.6 Demonstration of the strong thermoplastic processability of the Zr 35 Ti 30 Cu Be metallic glass Figure 7.7 Demonstration of the strong thermoplastic processability of the Zr 35 Ti 30 Cu Be metallic glass Figure 8.1 X-ray patterns of amorphous 4 mm rod of Cu 45 Zr 50 Ag 5, 4 mm rod of Cu 43 Zr 50 Ag 7, 5 mm rod of Cu 40 Zr 50 Ag 10, and 7 mm rod of Cu 43 Zr 40 Ag 7 Ti 10 prepared by the copper-mold casting method Figure 8.2 DSC scans of the amorphous Cu 45 Zr 50 Ag 5, Cu 43 Zr 50 Ag 7, Cu 40 Zr 50 Ag 10, and Cu 43 Zr 40 Ag 7- Ti 10 alloys at a constant heating rate of 0.33 K/s Figure 8.3 X-ray patterns of 3 mm cast rod of Cu 60 Zr 36 Ag 4, 4 mm glassy rod of Cu 57 Zr 36 Ag 7, 6 mm glassy rod of Cu 54 Zr 36 Ag 10, 7 mm cast rod of Cu 52 Zr 36 Ag 12, and 8 mm rod of Cu 49 Zr 36 Ag 10 Ti Figure 8.4 DSC scans of the amorphous Cu 57 Zr 36 Ag 7, Cu 54 Zr 36 Ag 10, and Cu 49 Zr 36 Ag 10 Ti 5 alloys at a constant heating rate of 0.33 K/s Figure 8.5 Poisson s ratio, ν, as a function of the Ag concentration for both Cu (50-x) Zr 50 Ag x and Cu (64-x) Zr 36 Ag x series Figure 8.6 Compressive stress-strain curves of 2 mm amorphous rods for Cu (50-x) Zr 50 Ag x series alloys. (a), Cu 46 Zr 54 ; (b), Cu 48 Zr 50 Ag 2 ; (c), Cu 43 Zr 50 Ag 7 ; (d), Cu 40 Zr 50 Ag 10 ; (e), Cu 38 Zr 50 Ag 12 ; and (f), Cu 43 Zr 43 Ag 7 Ti xviii

13 Figure 8.7 Compressive stress-strain curves of 2 mm amorphousrods for Cu (64-x) Zr 36 Ag x series alloys. (a), Cu 64 Zr 36 ; (b), Cu 57 Zr 36 Ag 7 ; (c), Cu 54 Zr 36 Ag 10 ; and (d), Cu 40 Zr 45 Ag 10 Ti xix