Coupled thermo-mechanical modelling of bulk-metallic glasses: Theory, finite-element simulations and experimental verification

Research output: Contribution to journalArticle

56 Citations (Scopus)

Abstract

A three-dimensional, finite-deformation-based constitutive model to describe the behavior of metallic glasses in the supercooled liquid region has been developed. By formulating the theory using the principles of thermodynamics and the concept of micro-force balance [Gurtin, M., 2000. On the plasticity of single crystals: free energy, microforces, plastic-strain gradients. J. Mech. Phys. Solids 48, 989-1036], a kinetic equation for the free volume concentration is derived by augmenting the Helmholtz free energy used for a conventional metallic alloy with a flow-defect free energy which depends on the free volume concentration and its spatial gradient. The developed constitutive model has also been implemented in the commercially available finite-element program ABAQUS/Explicit (2005) by writing a user-material subroutine. The constitutive parameters/functions in the model were calibrated by fitting the constitutive model to the experimental simple compression stress-strain curves conducted under a variety of strain-rates at a temperature in the supercooled liquid region [Lu, J., Ravichandran, G., Johnson, W., 2003. Deformation behavior of the Zr-Ti-Cu-Ni-Be bulk metallic glass over a wide range of strain-rates and temperatures. Acta Mater. 51, 3429-3443]. With the model calibrated, the constitutive model was able to reproduce the simple compression stress-strain curves for jump-in-strain-rate experiments to good accuracy. Furthermore stress-strain responses for simple compression experiments conducted at different ambient temperatures within the supercooled liquid region were also accurately reproduced by the constitutive model. Finally, shear localization studies also show that the constitutive model can reasonably well predict the orientation of shear bands for compression experiments conducted at temperatures within the supercooled liquid region [Wang, G., Shen, J., Sun, J., Lu, Z., Stachurski, Z., Zhou, B., 2005. Compressive fracture characteristics of a Zr-based bulk metallic glass at high test temperatures. Mater. Sci. Eng. A 398, 82-87].

Original languageEnglish
Pages (from-to)1236-1273
Number of pages38
JournalJournal of the Mechanics and Physics of Solids
Volume55
Issue number6
DOIs
Publication statusPublished - Jun 2007
Externally publishedYes

Fingerprint

Metallic glass
metallic glasses
Constitutive models
Free energy
Strain rate
simulation
Free volume
Liquids
Stress-strain curves
strain rate
free energy
Temperature
liquids
Shear bands
Experiments
Subroutines
high temperature tests
ABAQUS
shear
subroutines

Keywords

  • Constitutive behavior
  • Finite elements
  • Finite strain
  • Glass material
  • Viscoplasticity

ASJC Scopus subject areas

  • Mechanical Engineering
  • Mechanics of Materials
  • Condensed Matter Physics

Cite this

@article{a007f1640df449cc9df9a4ba60c136a7,
title = "Coupled thermo-mechanical modelling of bulk-metallic glasses: Theory, finite-element simulations and experimental verification",
abstract = "A three-dimensional, finite-deformation-based constitutive model to describe the behavior of metallic glasses in the supercooled liquid region has been developed. By formulating the theory using the principles of thermodynamics and the concept of micro-force balance [Gurtin, M., 2000. On the plasticity of single crystals: free energy, microforces, plastic-strain gradients. J. Mech. Phys. Solids 48, 989-1036], a kinetic equation for the free volume concentration is derived by augmenting the Helmholtz free energy used for a conventional metallic alloy with a flow-defect free energy which depends on the free volume concentration and its spatial gradient. The developed constitutive model has also been implemented in the commercially available finite-element program ABAQUS/Explicit (2005) by writing a user-material subroutine. The constitutive parameters/functions in the model were calibrated by fitting the constitutive model to the experimental simple compression stress-strain curves conducted under a variety of strain-rates at a temperature in the supercooled liquid region [Lu, J., Ravichandran, G., Johnson, W., 2003. Deformation behavior of the Zr-Ti-Cu-Ni-Be bulk metallic glass over a wide range of strain-rates and temperatures. Acta Mater. 51, 3429-3443]. With the model calibrated, the constitutive model was able to reproduce the simple compression stress-strain curves for jump-in-strain-rate experiments to good accuracy. Furthermore stress-strain responses for simple compression experiments conducted at different ambient temperatures within the supercooled liquid region were also accurately reproduced by the constitutive model. Finally, shear localization studies also show that the constitutive model can reasonably well predict the orientation of shear bands for compression experiments conducted at temperatures within the supercooled liquid region [Wang, G., Shen, J., Sun, J., Lu, Z., Stachurski, Z., Zhou, B., 2005. Compressive fracture characteristics of a Zr-based bulk metallic glass at high test temperatures. Mater. Sci. Eng. A 398, 82-87].",
keywords = "Constitutive behavior, Finite elements, Finite strain, Glass material, Viscoplasticity",
author = "{G. Thamburaja}, {T Prakash} and R. Ekambaram",
year = "2007",
month = "6",
doi = "10.1016/j.jmps.2006.11.008",
language = "English",
volume = "55",
pages = "1236--1273",
journal = "Journal of the Mechanics and Physics of Solids",
issn = "0022-5096",
publisher = "Elsevier Limited",
number = "6",

}

TY - JOUR

T1 - Coupled thermo-mechanical modelling of bulk-metallic glasses

T2 - Theory, finite-element simulations and experimental verification

AU - G. Thamburaja, T Prakash

AU - Ekambaram, R.

PY - 2007/6

Y1 - 2007/6

N2 - A three-dimensional, finite-deformation-based constitutive model to describe the behavior of metallic glasses in the supercooled liquid region has been developed. By formulating the theory using the principles of thermodynamics and the concept of micro-force balance [Gurtin, M., 2000. On the plasticity of single crystals: free energy, microforces, plastic-strain gradients. J. Mech. Phys. Solids 48, 989-1036], a kinetic equation for the free volume concentration is derived by augmenting the Helmholtz free energy used for a conventional metallic alloy with a flow-defect free energy which depends on the free volume concentration and its spatial gradient. The developed constitutive model has also been implemented in the commercially available finite-element program ABAQUS/Explicit (2005) by writing a user-material subroutine. The constitutive parameters/functions in the model were calibrated by fitting the constitutive model to the experimental simple compression stress-strain curves conducted under a variety of strain-rates at a temperature in the supercooled liquid region [Lu, J., Ravichandran, G., Johnson, W., 2003. Deformation behavior of the Zr-Ti-Cu-Ni-Be bulk metallic glass over a wide range of strain-rates and temperatures. Acta Mater. 51, 3429-3443]. With the model calibrated, the constitutive model was able to reproduce the simple compression stress-strain curves for jump-in-strain-rate experiments to good accuracy. Furthermore stress-strain responses for simple compression experiments conducted at different ambient temperatures within the supercooled liquid region were also accurately reproduced by the constitutive model. Finally, shear localization studies also show that the constitutive model can reasonably well predict the orientation of shear bands for compression experiments conducted at temperatures within the supercooled liquid region [Wang, G., Shen, J., Sun, J., Lu, Z., Stachurski, Z., Zhou, B., 2005. Compressive fracture characteristics of a Zr-based bulk metallic glass at high test temperatures. Mater. Sci. Eng. A 398, 82-87].

AB - A three-dimensional, finite-deformation-based constitutive model to describe the behavior of metallic glasses in the supercooled liquid region has been developed. By formulating the theory using the principles of thermodynamics and the concept of micro-force balance [Gurtin, M., 2000. On the plasticity of single crystals: free energy, microforces, plastic-strain gradients. J. Mech. Phys. Solids 48, 989-1036], a kinetic equation for the free volume concentration is derived by augmenting the Helmholtz free energy used for a conventional metallic alloy with a flow-defect free energy which depends on the free volume concentration and its spatial gradient. The developed constitutive model has also been implemented in the commercially available finite-element program ABAQUS/Explicit (2005) by writing a user-material subroutine. The constitutive parameters/functions in the model were calibrated by fitting the constitutive model to the experimental simple compression stress-strain curves conducted under a variety of strain-rates at a temperature in the supercooled liquid region [Lu, J., Ravichandran, G., Johnson, W., 2003. Deformation behavior of the Zr-Ti-Cu-Ni-Be bulk metallic glass over a wide range of strain-rates and temperatures. Acta Mater. 51, 3429-3443]. With the model calibrated, the constitutive model was able to reproduce the simple compression stress-strain curves for jump-in-strain-rate experiments to good accuracy. Furthermore stress-strain responses for simple compression experiments conducted at different ambient temperatures within the supercooled liquid region were also accurately reproduced by the constitutive model. Finally, shear localization studies also show that the constitutive model can reasonably well predict the orientation of shear bands for compression experiments conducted at temperatures within the supercooled liquid region [Wang, G., Shen, J., Sun, J., Lu, Z., Stachurski, Z., Zhou, B., 2005. Compressive fracture characteristics of a Zr-based bulk metallic glass at high test temperatures. Mater. Sci. Eng. A 398, 82-87].

KW - Constitutive behavior

KW - Finite elements

KW - Finite strain

KW - Glass material

KW - Viscoplasticity

UR - http://www.scopus.com/inward/record.url?scp=34047139868&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34047139868&partnerID=8YFLogxK

U2 - 10.1016/j.jmps.2006.11.008

DO - 10.1016/j.jmps.2006.11.008

M3 - Article

AN - SCOPUS:34047139868

VL - 55

SP - 1236

EP - 1273

JO - Journal of the Mechanics and Physics of Solids

JF - Journal of the Mechanics and Physics of Solids

SN - 0022-5096

IS - 6

ER -