5. Conclusions

This chapter presents a theoretical framework for modeling of shear band formation in homogeneous and inhomogeneous deformation in MGs by considering shear banding process as an adiabatic process and adopting free volume as an order parameter. A problem of infinitely long thin strip undergoing shear strain is solved for four different scenarios namely: (1) homogeneous isothermal, (2) homogeneous adiabatic, (3) inhomogeneous isothermal and (4) inhomogeneous adiabatic deformation, undergoing infinitesimal deformation.

Shear bands observed in case of MGs can be modeled by using free volume theory effectively. When shear banding is considered as an adiabatic process temperature keeps on increasing and therefore free volume concentration keeps on reducing as annihilation process dominates due to increased temperature. Hence, although the assumption of shear banding process as isothermal process reduces the complexity of theory considerably but still effect of temperature should also be considered as it is an important parameter and alters result by a large amount. In homogeneous case MG always attain a steady state where shear stress does not vary with time and MG flows like a liquid. When free volume concentration is not uniform throughout the material which is the most practical case, inhomogeneity grows to cause the formation of the shear band where free volume concentration is higher initially. Shear strain inside shear band grows rapidly and can reach a critical value of strain which may cause crack initiation leading to full fracture.

## Acknowledgements

The author greatly acknowledges the guidance of Prof. Tanmay K. Bhandakkar from Indian Institute of Technology of Bombay, Mumbai, India. This work would not be possible without the helpful discussions with him.

Author details

Shank S. Kulkarni

83

shankkulkarni1316@gmail.com

provided the original work is properly cited.

The University of North Carolina at Charlotte, Charlotte, USA

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

\*Address all correspondence to: skulka17@uncc.edu;

Adiabatic Shear Band Formation in Metallic Glasses DOI: http://dx.doi.org/10.5772/intechopen.87437

#### Abbreviations


Adiabatic Shear Band Formation in Metallic Glasses DOI: http://dx.doi.org/10.5772/intechopen.87437

As seen in this section solution varies drastically with the change in parameters,

This chapter presents a theoretical framework for modeling of shear band formation in homogeneous and inhomogeneous deformation in MGs by considering shear banding process as an adiabatic process and adopting free volume as an order parameter. A problem of infinitely long thin strip undergoing shear strain is solved for four different scenarios namely: (1) homogeneous isothermal, (2) homogeneous adiabatic, (3) inhomogeneous isothermal and (4) inhomogeneous adiabatic defor-

Shear bands observed in case of MGs can be modeled by using free volume theory effectively. When shear banding is considered as an adiabatic process temperature keeps on increasing and therefore free volume concentration keeps on reducing as annihilation process dominates due to increased temperature. Hence, although the assumption of shear banding process as isothermal process reduces the complexity of theory considerably but still effect of temperature should also be considered as it is an important parameter and alters result by a large amount. In homogeneous case MG always attain a steady state where shear stress does not vary with time and MG flows like a liquid. When free volume concentration is not uniform throughout the material which is the most practical case, inhomogeneity grows to cause the formation of the shear band where free volume concentration is higher initially. Shear strain inside shear band grows rapidly and can reach a critical

value of strain which may cause crack initiation leading to full fracture.

not be possible without the helpful discussions with him.

The author greatly acknowledges the guidance of Prof. Tanmay K. Bhandakkar from Indian Institute of Technology of Bombay, Mumbai, India. This work would

therefore a selection of parameters should be done very carefully.

mation, undergoing infinitesimal deformation.

5. Conclusions

Metallic Glasses

Acknowledgements

Abbreviations

82

MGs metallic glasses BMGs bulk metallic glasses STZ shear transformation zone

1D one-dimensional 2D two-dimensional

ODE ordinary differential equation PDE partial differential equation
