Abstract
Metallic glasses, made of metallic elements yet possessing an amorphous structure, have attracted considerable interest due to their unique mechanical properties and excellent net-shape forming ability. In terms of mechanical properties, they are extraordinary in elastic limit and strength but inferior in ductility at room temperature, where the inhomogeneous deformation characteristics of shear banding, flow serration, and sometimes cavitation prevail. The net-shape forming ability surfaces when the temperature rises above Tg (i.e., the glass transition temperature), where metallic glasses deform in a homogeneous manner. Understanding both the homogeneous and inhomogeneous deformation in metallic glasses is pivotal for promoting their potential applications. In this course, the continuum mechanics constitutive modeling has played a critical role. The constitutive modeling can be used for either predicting the mechanical responses of metallic glasses under various loading conditions or guiding material, product, and process designs. In this chapter, a number of important constitutive models for metallic glasses are reviewed; their applications in predicting both the homogeneous and inhomogeneous plastic flows are presented; and finally, the attempts of using the constitutive modeling to assist the design of ductility and net-shape forming processes are discussed.
References
Abaqus manual (Version 6.13-2) (2013) Dassault Systémes Simulia Corp, Providence
An ZN, Li WD, Liu FX, Liaw PK, Gao YF (2012) Interface constraints on shear band patterns in bonded metallic glass films under microindentation. Metall Mater Trans A 43:2729–2741
Anand L, Su C (2005) A theory for amorphous viscoplastic materials undergoing finite deformations, with application to metallic glasses. J Mech Phys Solids 53:1362–1396
Anand L, Su C (2007) A constitutive theory for metallic glasses at high homologous temperatures. Acta Mater 55:3735–3747
Argon AS (1979) Plastic deformation in metallic glasses. Acta Metall 27:47–58
Ashby MF (2005) Materials selection in mechanical design, 3rd edn. Butterworth-Heinemann, Burlington
Bergman TL, Incropera FP, DeWitt DP, Lavine AS (2011) Fundamentals of heat and mass transfer, 6th edn. Wiley, Danvers
Bower AF (2009) Applied mechanics of solids. CRC Press, Boca Raton
Chen HM, Huang JC, Song SX, Nieh TG, Jang JSC (2009) Flow serration and shear-band propagation in bulk metallic glasses. Appl Phys Lett 94:141914
Cohen MH, Turnbull D (1959) Molecular transport in liquids and glasses. J Chem Phys 31:1164–1169
De Hey P, Sietsma J, van den Beukel A (1998) Structural disordering in amorphous Pd40Ni40P20 induced by high temperature deformation. Acta Mater 46:5873–5882
Dieter GE, Bacon DJ (1986) Mechanical metallurgy. McGraw-Hill, New York
Dubach A, Dalla Torre FH, Löffler JF (2009) Constitutive model for inhomogeneous flow in bulk metallic glasses. Acta Mater 57:881–892
Dunne F, Petrinic N (2005) Introduction to computational plasticity. Oxford University Press, Oxford
Ekambaram R, Thamburaja P, Yang H, Li Y, Nikabdullah N (2010) The multi-axial deformation behavior of bulk metallic glasses at high homologous temperatures. Int J Solids Struct 47:678–690
Ekambaram R, Thamburaja P, Nikabdullah R (2011) Shear localization and damage in metallic glasses at high homologous temperatures. Int J Struct Changes Solids 1:15–29
Flores KM, Suh D, Dauskardt RH, Asoka-Kumar P, Sterne PA, Howell RH (2011) Characterization of free volume in a bulk metallic glass using positron annihilation spectroscopy. J Mater Res 17:1153–1161
Gao YF (2006) An implicit finite element method for simulating inhomogeneous deformation and shear bands of amorphous alloys based on the free-volume model. Model Simul Mater Sci Eng 14:1329
Gao YF, Yang B, Nieh TG (2007) Thermomechanical instability analysis of inhomogeneous deformation in amorphous alloys. Acta Mater 55:2319–2327
Gao YF, Wang L, Bei H, Nieh TG (2011) On the shear-band direction in metallic glasses. Acta Mater 59:4159–4167
Greer AL, Cheng YQ, Ma E (2013) Shear bands in metallic glasses. Mater Sci Eng R 74:71–132
Guan P, Lu S, Spector MJB, Valavala PK, Falk ML (2013) Cavitation in amorphous solids. Phys Re Lett 110:185502
Henann D, Anand L (2008) A constitutive theory for the mechanical response of amorphous metals at high temperatures spanning the glass transition temperature: application to microscale thermoplastic forming. Acta Mater 56:3290–3305
Henann DL, Anand L (2009) Fracture of metallic glasses at notches: effects of notch-root radius and the ratio of the elastic shear modulus to the bulk modulus on toughness. Acta Mater 57:6057–6074
Huang R, Suo Z, Prevost JH, Nix WD (2002) Inhomogeneous deformation in metallic glasses. J Mech Phys Solids 50:1011–1027
Ichitsubo T, Matsubara E, Kai S, Hirao M (2004) Ultrasound-induced crystallization around the glass transition temperature for Pd40Ni40P20 metallic glass. Acta Mater 52:423–429
Inoue A, Zhang T, Masumoto T (1989) Al-La-Ni amorphous alloys with a wide supercooled liquid region. Mater Trans, JIM 30:965–972
Inoue A, Zhang T, Masumoto T (1990) Zr-Al-Ni amorphous alloys with high glass transition temperature and significant supercooled liquid region. Mater Trans, JIM 31:177–183
Inoue A, Kato A, Zhang T, Kim SG, Masumoto T (1991) Mg-Cu-Y amorphous alloys with high mechanical strengths produced by a metallic mold casting method. Mater Trans, JIM 32:609–616
Jia HL, Liu FX, An ZN, Li WD, Wang GY, Chu JP, Jand JSC, Gao YF, Liaw PK (2014) Thin-film metallic glasses for substrate fatigue-property improvements. Thin Solid Films 561:2–27
Jia HL, Zheng LL, Li WD, Li N, Qiao JW, Wang GY, Ren Y, Liaw PK, Gao YF (2015) Insights from the lattice-strain evolution on deformation mechanisms in metallic-glass-matrix composites. Metall Mater Trans A 46:2431–2442
Jiang Y, Sun L, Wu Q, Qiu K (2017) Enhanced tensile ductility of metallic glass matrix composites with novel microstructure. J Non-Cryst Solids 459:26–31
Klement W, Willens RH, Duwez P (1960) Non-crystalline structure in solidified gold-silicon alloys. Nature 187:869–870
Langer JS (2006) Shear-transformation-zone theory of deformation in metallic glasses. Scripta Mater 54:375–379
Lewandowski JJ, Greer AL (2005) Temperature rise at shear bands in metallic glasses. Nat Mater 5:15–18
Li WD, Bei H, Tong Y, Dmowski W, Gao YF (2013) Structural heterogeneity induced plasticity in bulk metallic glasses: from well-relaxed fragile glass to metal-like behavior. Appl Phys Lett 103:171910
Li WD, Gao YF, Bei H (2015) On the correlation between microscopic structural heterogeneity and embrittlement behavior in metallic glasses. Sci Rep 5:14786
Li WD, Bei H, Gao YF (2016a) Effects of geometric factors and shear band patterns on notch sensitivity in bulk metallic glasses. Intermetallics 79:12–19
Li WD, Gao YF, Bei H (2016b) Instability analysis and free volume simulations of shear band directions and arrangements in notched metallic glasses. Sci Rep 6:34878
Li WD, Liaw KP, Gao YF (2016c) Fracture resistance of high entropy alloys: a review. Intermetallics 99:69–83
Liu MC, Huang JC, Chen KW, Lin JF, Li WD, Gao YF, Nieh TG (2012) Is the compression of tapered micro- and nanopillar samples a legitimate technique for the identification of deformation mode change in metallic glasses? Scripta Mater 66:817–820
Murali P, Guo TF, Zhang YW, Narasimhan R, Li Y, Gao HJ (2011) Atomic scale fluctuations govern brittle fracture and cavitation behavior in metallic glasses. Phys Rev Lett 107:215501
Pan J, Zhou HF, Wang ZT, Li Y, Gao HJ (2015) Origin of anomalous inverse notch effect in bulk metallic glasses. J Mech Phys Solids 84:85–94
Peker A, Johnson WL (1993) A highly processable metallic glass: Zr41.2Ti13.8Cu12.5Ni10.0Be22.5. Appl Phys Lett 63:2342–2344
Ruan HH, Zhang LC, Lu J (2011) A new constitutive model for shear banding instability in metallic glass. Int J Solids Struct 48:3112–3127
Rudnicki JW, Rice JR (1975) Conditions for the localization of deformation in pressure-sensitive dilatant materials. J Mech Phys Solids 23:371–394
Sarac B, Wilmers J, Bargmann S (2014) Property optimization of porous metallic glasses via structural design. Mater Lett 134:306–310
Schuh CA, Nieh TG (2003) A nanoindentation study of serrated flow in bulk metallic glasses. Acta Mater 51:87–99
Schuh CA, Hufnagel TC, Ramamurty U (2007) Mechanical behavior of amorphous alloys. Acta Mater 55:4067–4109
Singh I, Guo TF, Murali P, Narasimhan R, Zhang YW, Gao HJ (2013) Cavitation in materials with distributed weak zones: implications on the origin of brittle fracture in metallic glasses. J Mech Phys Solids 61:1047–1064
Singh I, Guo TF, Narasimhan R, Zhang YW (2014) Cavitation in brittle metallic glasses – effects of stress state and distributed weak zones. Int J Solids Struct 51:4373–4385
Singh I, Narasimhan R, Ramamurty U (2016) Cavitation-induced fracture causes nanocorrugations in brittle metallic glasses. Phys Rev Lett 117:044302
Slipenyuk A, Eckert J (2004) Correlation between enthalpy change and free volume reduction during structural relaxation of Zr55Cu30Al10Ni5 metallic glass. Scripta Mater 50:39–44
Song SX, Nieh TG (2009) Flow serration and shear-band viscosity during inhomogeneous deformation of a Zr-based bulk metallic glass. Intermetallics 17:762–767
Song SX, Wang XL, Nieh TG (2010) Capturing shear band propagation in a Zr-based metallic glass using a high-speed camera. Scripta Mater 62:847–850
Spaepen F (1977) A microscopic mechanism for steady state inhomogeneous flow in metallic glasses. Acta Metall 25:407–415
Steif PS, Spaepen F, Hutchinson JW (1982) Strain localization in amorphous metals. Acta Metall 30:447–455
Su C, Anand L (2006) Plane strain indentation of a Zr-based metallic glass: experiments and numerical simulation. Acta Mater 54:179–189
Suryanarayana C, Inoue A (2017) Bulk metallic glasses. CRC Press, Boca Raton
Tandaiya P, Narasimhan R, Ramamurty U (2007) Mode I crack tip fields in amorphous materials with application to metallic glasses. Acta Mater 55:6541–6552
Tandaiya P, Ramamurty U, Narasimhan R (2009) Mixed mode (I and II) crack tip fields in bulk metallic glasses. J Mech Phys Solids 57:1880–1897
Telford M (2004) The case for bulk metallic glass. Mater Today 7:36–43
Thamburaja P, Ekambaram R (2007) Coupled thermo-mechanical modelling of bulk-metallic glasses: theory, finite-element simulations and experimental verification. J Mech Phys Solids 55:1236–1273
Wang G et al (2007) Nanoscale periodic morphologies on the fracture surface of brittle metallic glasses. Phys Rev Lett 98:235501
Wang G, Chan KC, Xu XH, Wang WH (2008) Instability of crack propagation in brittle bulk metallic glass. Acta Mater 56:5845–5860
Wang L, Bei H, Gao YF, Lu ZP, Nieh TG (2011) Effect of residual stresses on the hardness of bulk metallic glasses. Acta Mater 59:2858–2864
Wang Y, Li M, Xu J (2016) Toughen and harden metallic glass through designing statistical heterogeneity. Scripta Mater 113:10–13
Wang Y, Li M, Xu J (2017a) Free volume gradient effect on mechanical properties of metallic glasses. Scripta Mater 130:12–16
Wang Y, Li M, Xu J (2017b) Mechanical properties of spinodal decomposed metallic glass composites. Scripta Mater 135:41–45
Xi XK, Zhao DQ, Pan MX, Wang WH, Wu Y, Lewandowski JJ (2006) Periodic corrugation on dynamic fracture surface in brittle bulk metallic glass. Appl Phys Lett 89:181911
Yang B, Liaw PK, Wang G, Morrison M, Liu CT, Buchanan RA, Yokoyama Y (2004) In-situ thermographic observation of mechanical damage in bulk-metallic glasses during fatigue and tensile experiments. Intermetallics 12:1265–1274
Yang B, Morrison ML, Liaw PK, Buchanan RA, Wang G, Liu CT, Denda M (2005) Dynamic evolution of nanoscale shear bands in a bulk-metallic glass. Appl Phys Lett 86:141904
Yang Q, Mota A, Ortiz M (2006) A finite-deformation constitutive model of bulk metallic glass plasticity. Comput Mech 37:194–204
Yavari AR, Moulec AL, Inoue A, Nishiyama N, Lupu N, Matsubara E, Botta WJ, Vaughan G, Michiel MD, Kvick A (2005) Excess free volume in metallic glasses measured by X-ray diffraction. Acta Mater 53:1611–1619
Yousfi MA, Hajlaoui K, Tourki Z, Yavari AR (2013) Serrated flow model for metallic glasses under compressive loading. Acta Metall Sin 26:503–508
Zhao M, Li M (2011a) A constitutive theory and modeling on deviation of shear band inclination angles in bulk metallic glasses. J Mater Res 24:2688–2696
Zhao M, Li M (2011b) Local heating in shear banding of bulk metallic glasses. Scripta Mater 65:493–496
Zhao M, Li M (2012) Comparative study of elastoplastic constitutive models for deformation of metallic glasses. Metals 2:488
Zhao M, Li M, Zheng YF (2011) Assessing the shear band velocity in metallic glasses using a coupled thermo-mechanical model. Philos Mag Lett 91:705–712
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Section Editor information
Rights and permissions
Copyright information
© 2018 Springer Nature Switzerland AG
About this entry
Cite this entry
Li, W. (2018). Constitutive Modeling in Metallic Glasses for Predictions and Designs. In: Andreoni, W., Yip, S. (eds) Handbook of Materials Modeling. Springer, Cham. https://doi.org/10.1007/978-3-319-50257-1_103-1
Download citation
DOI: https://doi.org/10.1007/978-3-319-50257-1_103-1
Received:
Accepted:
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-50257-1
Online ISBN: 978-3-319-50257-1
eBook Packages: Springer Reference Physics and AstronomyReference Module Physical and Materials ScienceReference Module Chemistry, Materials and Physics