STRENGTH, PLASTICITY, AND FRACTURE OF BULK METALLIC GLASSES HAN ZHENG (B. Eng, Beihang Univ.) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF MATERIALS SCIENCE & ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2009 Acknowledgements First and foremost, I would like to express my sincerest gratitude to my supervisor, Professor Li Yi, whose exceptional enthusiasm, dedication and integrity for scientific discovery have been a major influence on my development during my candidature. Due to his insightful intuition and quickness of thought, discussing with him has always brought about refreshing ideas. It was extremely pleasant to be working with him. Over the years, I have benefited tremendously from his emphasis on critical thinking and encouragements to innovate, transforming me from a class-taking student to a real researcher. I am grateful to Professor Gao Huajian at Brown University for his great efforts in the collaborative work presented in Chapter 4. His erudition and patience have left a deep impression on me. I would also like to thank Professor Evan Ma at University of Johns Hopkins for fruitful discussions that led to the current understanding of the plastic serrated flow (Chapter 5). In addition, I also profited from collaborations with Professor Tang Loon Ching at NUS, for his detailed instructions on statistics; and Professor Xu Jian at Chinese Academy of Sciences, for his valuable suggestions and assistance in paper writing. I will always appreciate the friendship and support of my group members. Special thanks go to Zhang Jie and Wu Wenfei. Zhang Jie taught me how to operate i most of the lab equipment and generously shared tips on the design and conduction of experiments. Wenfei is both an advisor as well as a role model for me. He offered fruitful discussions and inspirations for my research in the mechanical properties of bulk metallic glasses. On my first day at the lab, he was also the first person to introduce me the basic knowledge in this field and the ongoing research of our group, making me feel welcomed ever since. I would like to extend my thanks to Yang Hai. Although we have only been working together for two years, his great personality and helpfulness are especially appreciated. And to Grace Lim, whose cheerful and optimistic nature has brightened up my days. My work would not be possible without the support from many individuals. Our department staffs have always been helpful, providing trainings and guidance for utilizing the technical facilities. I wish to express my sincere gratitude to Mr Chan, Agnes, Chen Qun, and Roger. I was lucky to meet the staffs and students in the Impact Lab under Department of Mechanical Engineering in 2008, especially Joe, Zhang Bao and Alvin. They have been extremely supportive and friendly, making their facilities and equipment available without hesitation. The joyful conversations and outings with my friends Ran Min, Yuan Du, Yong Zhihua and Li Zhipeng . in the past a few years have also enriched my life in Singapore. Finally, I am deeply indebted to my parents for their unconditional love and to my boyfriend Liu Bing for his endless support and loving care. July 2009 in Singapore Han Zheng ii Table of Contents Acknowledgements i Table of Contents iii Summary . vi List of Tables . ix List of Figures . xi List of Publications xviii Chapter Introduction 1.1 Historical background and development of MGs . 1.2 Formation of MGs . 1.3 Macroscopic mechanical behaviors of MGs . 1.3.1 Deformation map 1.3.2 Mechanical behaviors at room temperature 1.4 Deformation mechanisms of MGs 1.4.1 Free-volume model . 1.4.2 Shear transformation zone (STZ) model . 1.4.3 Heat evolution . 1.5 Yield strength of MGs 1.5.1 Mohr-Coulomb yield criterion 1.5.2 Microscopic origin of yield strength . 1.6 Objectives and outline of this thesis . 1 11 11 13 20 21 23 26 27 27 29 30 Chapter A three-parameter Weibull statistical analysis of the strength variation of BMGs 2.1 Introduction . 2.2 Experimental procedure 2.3 Results and discussion 2.3.1 Compressive stress-strain behaviors . 2.3.2 Estimation of the 3-parameter Weibull parameters . 2.3.3 Indication of the Weibull modulus m 32 32 35 38 38 41 42 iii 2.3.4 Indication of the failure-free stress σu . 2.3.5 Advantage of the 3-parameter Weibull model over the 2-parameter one . 2.4 Conclusions . 45 46 48 Chapter Invariant critical stress for continuous shear banding in an intrinsically plastic BMG 3.1 Introduction . 3.2 Experimental procedure 3.3 Results . 3.3.1 Case 3.3.2 Case 3.3.3 Case 3.4 Discussion . 3.4.1 Consistent yield strength of samples under three deformation modes . 3.4.2 Randomness in the location of initial shear bands 3.4.3 Invariant critical stress in an individual sample 3.5 Conclusions . 63 64 65 67 Chapter An instability index of shear band for plasticity in MGs . 4.1 Introduction . 4.2 Experimental procedure 4.3 Shear-band instability index (SBI) 4.4 Results . 4.4.1 Samples with an aspect ratio (ρ) of 2:1 . 4.4.2 Samples with an aspect ratio (ρ) of 1:1 . 4.5 Discussion . 4.5.1 Effect of machine stiffness 4.5.2 Upper size limit for stability and intrinsic size effect . 4.5.3 Effect of the sample aspect ratio . 4.5.4 Numerical studies of shear band behaviors at low SBI 4.6 Conclusions . 68 68 70 73 76 76 85 88 88 91 94 95 98 Chapter Cooperative shear and catastrophic fracture of BMGs from a shear-band instability perspective 5.1 Introduction . 5.2 Experimental procedure 5.3 Results . 5.3.1 Identification of two morphologically distinct zones . 5.3.2 Length scale of a single shear event . 5.4 Discussion . 5.4.1 Interpretation of the increasing length scale of a single shear (∆uc) for increasing sized samples . 50 50 53 55 56 59 61 63 99 99 102 104 104 105 108 108 iv 5.4.2 Interpretation of the serrated flow and catastrophic fracture in terms of temperature rises 5.4.3 Indication from a simulation work 5.5 Conclusions . 111 117 119 Chapter Concluding remarks 6.1 Summary of results . 6.2 Future work . 121 121 124 Bibliography . 126 Appendix . 137 v Summary One of the enduring attractions of metallic glasses (MGs) is their impressive suite of mechanical properties, such as high strength, high hardness and high elastic strain limit. However, the widely recognized shortcoming of MGs is their highly localized plastic deformation mode, usually leading to limited plasticity/ductility under room temperature and uniaxial-stress states. For crystalline materials, the intrinsic relationship between their mechanical properties and crystal structures has been well established with the development of dislocation theory, which can explain, in general, the atomic origins of their strength and plasticity/ductility. In contrast, for amorphous materials, theories on the controlling factors of their strength and plasticity/ductility at temperatures well below their glass transition points (Tg) are far from complete. This work employs uniaxial compression tests and materials characterization methods to study mainly the shear band behaviors of monolithic bulk metallic glasses (BMGs) at room temperature. Through combining experimental results with the mechanics and thermodynamics analyses, this work aims to reveal, essentially, the plastic deformation and fracture mechanism of MGs. The ultimate goal of this work is to provide insights for improving the mechanical performance of MGs. vi The MGs, usually termed as (quasi-) brittle materials, are expected to be flaw sensitive and should in principle exhibit scattering in their fracture strength. Through investigating the strength variation of BMG samples in the framework of 3-parameter Weibull statistics, the first contribution of this work is to provide a complete reliability assessment of BMGs. The BMGs were identified to exhibit high strength uniformity, manifested by high Weibull moduli. Moreover, the presence of a critical failure-free stress (FFS) was identified for BMGs, and a method for estimating the FFS was for the first time introduced to the BMG committee. In view of the conflicting reports of either “strain-softening” or “strain-hardening” for BMGs, the second goal of this work is to study their true stress for continuous shear banding. By properly taking the instant load-bearing area into consideration, our analyses reveal that the critical stress for continuous shear banding maintains invariant on and after yielding, suggesting neither “strain-softening” nor “strain-hardening”. This finding is significant in that it points out that the atomic cohesive energy constantly serves to be the controlling factor of the critical stress for shear banding. The third, which is also the major contribution of this thesis, is to establish a shear-band instability index (SBI) that quantitatively sets the condition where high plasticity in MGs can be obtained, i.e., small samples on stiff machines in general. The theory of SBI has also led us to a more comprehensive understanding of the mechanism of the plastic deformation in MGs via simultaneous operation of multiple shear bands versus a single dominant one. This concept provides a theoretical basis vii for designing systems which promote plasticity/ductility in MGs by suppressing or delaying shear-band instability. On the other hand, since most of the previously reported results on the mechanical behaviors of MGs are perhaps entirely interpreted without incorporating the influence of the testing machine, the concept of SBI is of fundamental importance for a shift of paradigm in the future study of MGs. The fourth contribution of this work is to uncover the mechanisms of the plastic serrated flow and fracture of MGs. It has been identified that the catastrophic fracture of MGs always follows a cooperative shear event, the length scale of which is correlated with both the sample size and the machine stiffness. An estimation of the temperature rises in the shear band due to the work done during the shear reveals that: the temperature rises in small samples are insignificant, leading to the serrated flow without catastrophic fracture, while those in large samples are sufficiently high so that the temperatures in the shear band are over their glass transition or even melting temperature, leading to the catastrophic fracture. viii List of Tables Table 1.1 Representative BMGs with the largest critical casting diameter in corresponding alloy systems Table 1.2 Possible application fields of BMGs . Table 1.3 Recently-developed BMGs with large plasticity under compression 17 Table 2.1 Summary of the compressive strength and Weibull parameters of the (Zr0.48Cu0.45Al0.07)100-xYx (x=0, 0.5, 1, 2) BMGs estimated based on the 3-parameter Weibull statistics . 39 Table 2.2 List of the 3-parameter Weibull modulus (m) and the location parameter (σu) of some typical engineering materials together with the currently-investigated ZrCuAl(Y) BMGs 44 Table 2.3 Summary of the Weibull parameters of the (Zr0.48Cu0.45Al0.07)100-xYx (x=0, 0.5, 1, 2) BMGs estimated based on the 2-parameter Weibull statistics . 47 Table 4.1 List of the values of the machine stiffness for various sized Zr64.13Cu15.75Ni10.12Al10 BMG samples and three machines. The yield points of corresponding sized samples are also indicated 71 Table 4.2 “Stable” or “unstable” identification of each sized 2:1 Zr64.13Cu15.75Ni10.12Al10 BMG samples tested at a specific machine stiffness . 82 Table 4.3 “Stable” or “unstable” identification of each sized 1:1 ix 6. Concluding remarks (1) The SBI theory presented in Chapter quantitatively illustrated the effects of sample size and machine stiffness on the stability/plasticity of BMGs under compression. It is plausible that this theory should be applicable to the tensile loading condition as well. It will be meaningful if a stability/instability map for a certain BMG under tensile loading could be established. Moreover, after realizing that the elastic energy released from the machine promotes the instability of shear band, designing a BMG/polycrystalline metal coupled component to alleviate the elastic energy released from the machine to the BMG sample should be promising to suppress the instability of shear band. The BMG/polycrystalline metal coupled component is expected to have reasonably high strength and high plasticity, which has practical importance. (2) The theoretical modeling result presented in Chapter indicates that (σys-σyk), E, Tg, ρ, cp and α are the materials properties that control the stability of a shear band. Specifically, BMGs with smaller EY (or equivalently Tg) and (σys-σyk), and larger ρ, cp and α should principally be more plastic. This opens the door for the search of the plastic BMGs in various alloy systems. 125 Bibliography [1] Luborsky FE. Amorphous Metallic Alloys. London: Butterworths, 1983. [2] Klement W, Willens RH, P D. Nature 1960;187:869. 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Lett. 2009;80:134115. 136 Appendix The failure data of samples made from four BMG alloys (Zr0.48Cu0.45Al0.07)100-xYx (x=0, 0.5, 1, 2) were subjected to the 3-parameter Weibull statistical study in Chapter 2. The following Table a1, a2, a3 and a4 list the failure stress (σi) and the failure probability (Fi) of all samples for alloys (Zr0.48Cu0.45Al0.07)100-xYx at x=0, x=0.5, x=1 and x=2, respectively. Table a1. The failure stress (σi) and the failure probability (Fi) of all samples for alloy Zr48Cu45Al7. Rank σi (MPa) Fi Rank σi (MPa) Fi 10 11 12 13 14 1790.6 1799.8 1817.2 1820 1822.3 1827.1 1834.6 1837 1844 1845.4 1845.8 1852.1 1852.7 1867.5 0.017857 0.053571 0.089286 0.125 0.160714 0.196429 0.232143 0.267857 0.303571 0.339286 0.375 0.410714 0.446429 0.482143 15 16 17 18 19 20 21 22 23 24 25 26 27 28 1867.7 1868.5 1873 1878.5 1880.6 1883.6 1884.1 1885.2 1886.5 1887.7 1892.2 1895.2 1897.1 1897.9 0.517857 0.553571 0.589286 0.625 0.660714 0.696429 0.732143 0.767857 0.803571 0.839286 0.875 0.910714 0.946429 0.982143 137 Table a2. The failure stress (σi) and the failure probability (Fi) of all samples for alloy (Zr0.48Cu0.45Al0.07)99.5Y0.5. Rank σi (MPa) Fi 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 1666.5 1698 1713 1714 1714.8 1715.3 1727.2 1731.6 1741.9 1750.1 1750.5 1755 1756.5 1756.6 1758.7 1763.8 1766.8 1767.5 1770.7 1778.7 1788.2 1790.5 1792.1 1793.5 1802.2 1816.4 1837.8 0.018519 0.055556 0.092593 0.12963 0.166667 0.203704 0.240741 0.277778 0.314815 0.351852 0.388889 0.425926 0.462963 0.5 0.537037 0.574074 0.611111 0.648148 0.685185 0.722222 0.759259 0.796296 0.833333 0.87037 0.907407 0.944444 0.981481 138 Table a3. The failure stress (σi) and the failure probability (Fi) of all samples for alloy (Zr0.48Cu0.45Al0.07)99Y1. Rank σi (MPa) Fi 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 1636 1639.1 1671.3 1678.3 1690.3 1704.3 1705.9 1713.5 1730.4 1736.8 1741.2 1757 1762.7 1765 1772.2 1772.8 1774.1 1776.7 1777.3 1792.5 1794.3 1802.5 1805 1808.5 1811.9 1823.9 1824.9 1842.8 1856.5 1882.7 0.016667 0.05 0.083333 0.116667 0.15 0.183333 0.216667 0.25 0.283333 0.316667 0.35 0.383333 0.416667 0.45 0.483333 0.516667 0.55 0.583333 0.616667 0.65 0.683333 0.716667 0.75 0.783333 0.816667 0.85 0.883333 0.916667 0.95 0.983333 139 Table a4. The failure stress (σi) and the failure probability (Fi) of all samples for alloy (Zr0.48Cu0.45Al0.07)98Y2. Rank σi (MPa) Fi Rank σi (MPa) Fi 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 1430.4 1471.5 1493.1 1518.5 1528 1531.5 1541.7 1568.8 1581.3 1586.3 1597.2 1601.6 1621.1 1622 1624 1628.2 1636.2 1640.8 1645.7 1646.3 1654.7 1657.6 1658.2 1659.5 0.010638 0.031915 0.053191 0.074468 0.095745 0.117021 0.138298 0.159574 0.180851 0.202128 0.223404 0.244681 0.265957 0.287234 0.308511 0.329787 0.351064 0.37234 0.393617 0.414894 0.43617 0.457447 0.478723 0.5 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 1660.5 1663.6 1675.3 1676.7 1681.8 1683.1 1686 1689.7 1698.9 1702 1708 1708.7 1717.3 1718.5 1718.9 1724.3 1730.3 1733 1739.2 1743.9 1747.4 1750.7 1779.7 0.521277 0.542553 0.56383 0.585106 0.606383 0.62766 0.648936 0.670213 0.691489 0.712766 0.734043 0.755319 0.776596 0.797872 0.819149 0.840426 0.861702 0.882979 0.904255 0.925532 0.946809 0.968085 0.989362 140 [...]... Wei and H J Gao An instability index of shear band for plasticity in metallic glasses Acta Materialia, 2009, 57: 1367 5 Z Han and Y Li Cooperative shear and catastrophic fracture of bulk metallic glasses from a shear-band instability perspective Journal of Materials Research, 2009, 24: 3620 6 Z Han, L C Tang, J Xu and Y Li A three-parameter Weibull statistical analysis of the strength variation of bulk. .. 111 xvii List of Publications 1 Z Han, J Zhang and Y Li Quaternary Fe-based bulk metallic glasses with a diameter of 5 mm Intermetallics, 2007, 15: 1447 2 Z Han, H Yang, W F Wu and Y Li Invariant critical stress for shear banding in a bulk metallic glass Applied Physics Letters, 2008, 93: 231912 3 W F Wu, Z Han and Y Li Size-dependent "malleable-to-brittle" transition in a bulk metallic glass Applied... curves of 1:1 samples measured for a range of controlled values of sample size (d) and machine stiffness (κM) 86 Figure 4.11 SEM micrographs of 4 mm 1:1 samples tested at a machine stiffness of (a) 31300 N/mm, exhibiting an unstable behavior of shear banding by forming one dominant shear band, and (b) 159000 N/mm, exhibiting a stable behavior of shear banding by forming dense shear bands, and thus... strain rate, and each element of the glass is able to contribute to the deformation The deformation map was later revisited by Argon [46,47] Recently, Lu [48] and Schuh [49] updated this map in terms of bulk metallic glass instead of amorphous ribbons In this thesis, we only focus on the region of inhomogeneous deformation of bulk metallic glasses Before describing the mechanical behaviors and interpreting... alloys were the first examples of bulk metallic glasses (BMGs) During the late 1980s, the Inoue group found exceptional glass forming ability in Mg [5-7] and Ln-based [8-10] ternary alloys and fabricated fully glassy rods and bars with the thickness of several millimeters The availability of MGs in bulk form permits detailed studies of their amorphous microstructures and mechanical behaviors Inoue’s... will go to infinity, and D is known as the fragility parameter which identifies the property of liquid The change of viscosity of a liquid as a function of supercooling reflects the change of mobility of atoms during the period, and thus can be used to characterize different liquids Figure 1.3 [44] compares the viscosities of some BMGs with a selection of typical glass-forming non -metallic liquids in... temperature and high strain rate Deformation is localized in discrete, thin shear bands, leaving the rest of the material plastically undeformed Upon yielding, metallic glasses often show plastic flow without work hardening, and tend to show work softening which leads to shear localization; (2) Homogeneous deformation, in which metallic glasses deform at relatively high 11 1 Introduction temperature and low... variation of bulk metallic glasses Scripta Materialia, 2009, 61: 923 7 Y Q Cheng, Z Han, E Ma and Y Li Cold versus hot shear banding in bulk metallic glass Physical Review B, 2009, 80: 134115 xviii 1 Introduction Chapter 1 Introduction The widespread enthusiasm for research on metallic glasses (MGs) is driven by both a fundamental interest in the structure and properties of disordered materials and their unique... behaviors of shear banding The sample diameter (d) and testing machine stiffness (κM) are both indicated in each curve The enlarged views of the plastic part of two representative curves showing a positive slope and a negative slope, respectively, are provided 77 Figure 4.5 SEM micrographs of the deformed 1 mm samples tested at a machine stiffness of 81200 N/mm (a) The side view and top view of the... plasticity of ~1%, and no tensile ductility [50] As shown in Figure 1.6, Zr-based bulk metallic glass samples fracture along one dominant shear band, which is near the maximum shear stress plane, exhibiting plastic strain of less than 1% under compression and zero plasticity under tension [53] Generally, the lack of the intrinsic strain-hardening mechanism leads to a strong tendency for instability of the . STRENGTH, PLASTICITY, AND FRACTURE OF BULK METALLIC GLASSES HAN ZHENG (B. Eng, Beihang Univ.) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY. Wei and H. J. Gao. An instability index of shear band for plasticity in metallic glasses. Acta Materialia, 2009, 57: 1367. 5. Z. Han and Y. Li. Cooperative shear and catastrophic fracture of bulk. statistical analysis of the strength variation of bulk metallic glasses. Scripta Materialia, 2009, 61: 923. 7. Y. Q. Cheng, Z. Han, E. Ma and Y. Li. Cold versus hot shear banding in bulk metallic glass.