Adiabatic Shear Band Formation in Metallic Glasses

Shank S. Kulkarni

### Abstract

Metallic glasses (MGs) are widely used in many applications due to their unique and attractive properties such as high strength, high elastic limit and good corrosion resistance. Experiments have shown that deformation in MGs is governed by either shear banding or cavitation process leading to a ductile or brittle material response, respectively. In this chapter, shear band formation process in metallic glasses is modeled using free volume theory in infinitesimal deformation. According to the free volume theory, local free volume concentration is considered as order parameter which can be changed by three processes, namely diffusion, annihilation and stress driven creation. Equations are set up for the evolution of free volume and stresses based on conservation of free volume, and mechanical equilibrium, respectively. Another important parameter to consider while modeling the shear bands is temperature as the temperature inside the shear band can reach up to glass transition temperature. This can be achieved by assuming shear band formation process as an adiabatic process whereby evolution equation for temperature is also included with plastic work as the heat source. Example of quasi-static deformation in thin MG strip is solved using this proposed formulation. Formation of the shear band and resulting stresses are studied through the introduction of small inhomogeneity along the thickness direction in the strip.

Keywords: metallic glasses, shear bands, adiabatic process, free volume theory, inhomogeneous deformation

### 1. Introduction

The basic difference between any conventional metal and metallic glass (MG) is their arrangement of atoms in the solid state. When any solid is cooled below its melting point it tries to arrange in the crystalline lattice which is the structure with minimum energy. Atoms of every conventional metal arrange themselves in this crystalline manner just below the melting point and this process is very quick. On the other hand, glass takes a lot more time to arrange in a crystalline manner and glass liquid can be cooled below melting point before glass transition temperature is reached. Due to which atoms in glass remain in a random position and do not have any preferential arrangement.

Earlier, Turnbull and Cech [1, 2] predicted that by rapid cooling, crystallization can be suppressed. In the late 1960s, it was discovered by Jun et al. [3] at California Institute of Technology that it is possible to keep atoms of metal in random packing in the solid state either by increasing the time required to form crystal or by cooling the liquid so fast that there will not be sufficient time to form the crystal. By this method, the liquid solidifies as MG, which is metal without any particular arrangement of atoms. When Jun et al. [3] performed their classic experiment of rapidquenching on Al-Si alloys MGs came to reality. MGs are opaque, shiny, smooth, gray in color and less brittle than conventional glass. Yield strength of MGs is reported to be as high as 1.9 GPa [4] and is found to be more resistant to fracture than ceramics. As there are no grain boundaries in MGs they are resistant to corrosion and wear. They have high electrical sensitivity which leads to low eddy current losses. Also, MGs formed from alloys of Fe, Co, or Ni has soft magnetic properties as well.

1.2 Deformation mechanism

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

fracture surface.

development.

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modeling of shear bands causing ductile failure.

must be dependent upon local atomic arrangements.

1.3 Microscopic deformation models

Fracture toughness of MGs exhibits a very wide range from 1 to 140 MPa ffiffiffiffi

[6]. Lewandowski et al. [7] found that the fracture toughness can be correlated with Poisson's ratio. As Poisson's ratio decreases fracture energy decreases resulting in brittle fracture. Brittle fracture surface shows very fine corrugations of the length scale of nanometers on the other hand ductile fracture surface shows a coarse pattern with deep impressions of the length scale of micrometers. Thus higher Poisson's ratio implies higher fracture toughness and a critical Poisson's ratio around 0.34 is found for the transition between brittle and ductile behavior [8]. In order to understand the effect of Poisson's ratio on the deformation mechanism of MGs, Murali et al. [8] conducted atomic scale simulations on two MGs, FeP and CuZr with Poisson's ratio 0.33 and 0.39, respectively. They found that FeP with Poisson's ratio 0.33 fractures in brittle fashion according to cavitation mechanism. Cavitation is the process of nucleation of voids inside a solid. In brittle fracture, the crack propagates by continuous series of nucleation of voids in front of the crack tip. This nucleation of void takes place in void-free solid when hydrostatic stress at any point reaches a critical value known as cavitation stress σc. Firstly, single void nucleates and grows and after sufficient growth of the void, next one nucleates at some distance from the new crack tip and crack propagation continuous. On the other hand, in CuZr with Poisson's ratio 0.39 instead of the propagation of crack tip, they observed blunting of the crack tip. Shear bands were formed near the crack tip as the applied strain was increased. This extensive shear banding near crack tip gives rise to ductile failure at large strains. There could be a large amount of dissipation of energy inside shear bands which can cause localized melting observed on the ductile

Hence two different type of fracture mechanism were observed depending on Poisson's ratio. Brittle MGs shows crack propagation while ductile shows crack blunting with extensive shear banding. In this chapter, the focus will be on the

A large amount of research has been done to understand the nature of mecha-

In the late 1970s, two classic theories were developed for the understanding of deformation in case of MGs assuming that the fundamental process responsible for deformation is a local arrangement of atoms which accommodates the local shear strain. The first theory is known as the shear transformation zone model by Argon. This model depends on the shear transformation zone (STZ) which is a local cluster of atoms undergoing plastic shear distortion. Argon [14] was first to develop a model of STZ where he treated the problem as an Eshelby inclusion. When MGs undergoes uniform stress STZ will be selected on the basis of energies which in turn

nism which causes shear band, but still, it is not totally clear. Gilman [9, 10] modeled shear bands in MGs in terms of glide of dislocations. After that Chaudhari et al. [11] and Shi [12] investigated the stability of dislocations in MGs but results did not follow the results came from theoretical work. They found that both edge and screw dislocations are rather stable. Recently Takeuchi and Edagawa [13] did some atomic simulations to review so far proposed deformation models and to understand deformation induced softening, shear band formation and its

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In spite of all the attractive properties, commercial use of MGs was not possible until the 1990s. This is due to the fact that it was not practically possible to attain required cooling rate (10<sup>6</sup> °C/s) so that there will not be any time for crystallization [4]. Even if the cooling rates were attained, the thickness of MGs that was cast was very small because of slow heat conduction. The main focus was on how to decrease the cooling rate and simultaneously increase the casting thickness. Finally, researchers found that if a different metal alloy is added to the liquid metal, then the amorphous structure can be achieved at lower cooling rates. Presence of more number of elements increases the size and complexity of the unit cell which leads to amorphous formation. If there is a large difference between sizes of a radius of different atoms then packing density increases which again favors amorphous arrangement. Using this technique, around 1990, first commercial MG was developed and named "Vitreloy," also known as Liquidmetal [4]. Following the success of "Vitreloy," there was tremendous development in reducing the critical cooling rate (minimum rate to suppress the formation of crystalline lattice). Due to the increase in the achievable thickness (>1 cm) of MGs, they are also known as bulk metallic glasses (BMGs) [5]. A large variety of BMGs is found out using different alloys in varying proportions.

#### 1.1 Applications of MGs

MGs are used in golf club heads, baseball bats and tennis rackets due to low damping and ability to transfer a large fraction of impact energy to the ball. Its high strength to weight ratio allows the mass to be distributed differently, which means different shapes can be achieved for club heads. They are also used in bicycle frames, hunting bows, fishing equipment and guns.

As a result of being very good corrosion and wear resistant, use of MGs in luxurious items is increasing day by day. Also, they have excellent scratch resistance along with smooth and shiny surface which makes them ideal for watch cases, spectacle frames, rings, pens and mobile cases.

MGs are biocompatible with a non-allergenic form which allows using it as a knee-replacement device or pacemaker casing. Also, they are used in surgical blades as they are less expensive than diamond blades as well as sharper and long-lasting than steel. Due to the lack of grain structure, a blade can be sharpened to an exceptional edge. They can also be used in razor blades and knives.

Micro electro mechanical systems offer a very wide range of application for MGs. They are used in micromirrors used in digital light processor (DLP) technology for data projectors. MGs are lighter, stronger and easily molded due to which they are used in components of liquid crystal display (LED), ultra-personal computer screens and casing of cameras. Also, high hardness and lack of grain structure allow it to use as information storage of digital data.
