PSI - Issue 35

Onkar Salunkhe et al. / Procedia Structural Integrity 35 (2022) 261–268 Onkar Salunkhe, Parag Tandaiya / Structural Integrity Procedia 00 (2021) 000–000

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2

forms at much lower cooling rates which resulted in section thicknesses in excess of 1 mm. Such materials were called as Bulk Metallic Glasses (BMGs). Due to lack of crystalline structure and consequently absence of crystal defects such as point or line defects, BMGs have very high strength ( ≈ 2 GPa), moderate fracture toughness, and high resilience. Also, since there are no grain boundaries, corrosion and wear resistances of BMGs are superior as compared to conventional alloys. This makes BMGs attractive candidates for replacing conventional materials in structural applications. However, the use of BMGs in load bearing applications is limited by their lack of ductility under uniaxial loading. This is due to localization of plastic flow into narrow regions that are often referred to as shear bands (SBs) (Schuh et al., 2007) which led to cracking and catastrophic fracture. Material scientists have proposed several methods (intrinsic and extrinsic) for improving the ductility of BMGs by making composites. One of the methods explored in literature is to coat a thin layer of a ductile polycrystalline metal on the surface of a BMG cylinder to make a composite (Sun et al., 2016). Such a composite was tested under compression by Sun et al. (2016) and found that a thin layer of Copper coating enhances the strain to failure of the composites significantly as compared to the monolithic BMG. Other researchers such as Ren et al. (2015a) and Ren et al. (2015b) also investigated this e ff ect through experiments. However, the mechanics based understanding of this observed enhancement in strain to failure due to Copper coating is lacking in literature. In the present work, our objective is to perform Finite Element Modelling and Simulations of loading of Copper coated BMG composite specimens and investigate the mechanics and mechanisms of their deformation and failure and predict potential enhancement of strain to failure. The novelty of the present work is that, to the best of authors’ knowledge, this is the first attempt at finite element modelling and simulation of mechanics of deformation and failure of Copper coated BMG composites. The present results can enable design of BMG composites with improved strain to failure suitable for load bearing structural applications. BMGs being amorphous are isotropic down to the atomic scale and don’t have any preferred directions in the microstructure. In this work, the finite deformation, viscoplastic, Mohr-Coulomb based constitutive model for BMGs proposed by Anand and Su (2005) is employed. According to this model, the inelastic deformation in BMGs occurs via simultaneous shearing and dilatation on six potential ‘slip systems’ defined with respect to the principal directions of stress. The original constitutive equations proposed by Anand and Su (2005) have been reformulated and implemented using an implicit numerical integration scheme by Tandaiya et al. (2010). In the following, some key equations in the model have been briefly summarized. The elastic part of the constitutive relation is defined by an isotropic Hooke’s law which governs the relation between the principal Kirchho ff stresses and the principal logarithmic elastic strains (Anand, 1979). The deformation gradient is multiplicatively decomposed into elastic and plastic parts, F = F e F p . The flow rule is written for the plastic part of the spatial velocity gradient in the form: 2. Constitutive model

6 α = 1

˙ v ( α ) ( s ( α ) ⊗ m ( α ) ) + β ( m ( α ) ⊗ m ( α ) )

l p =

(1)

where, β is the dilatancy function, s ( α ) and m ( α ) are the unit slip direction and the unit slip plane normal vectors for the α th potential slip system. These are defined in terms of the principal directions of stress. v ( α ) is the viscoplastic shearing rate for the α th slip system. The viscoplastic law for the shearing rate is taken as:

0

τ ( α ) c + µσ ( α ) 1 m

˙ v ( α ) = ˙ v

(2)

where, ˙ v 0 is a reference plastic shear strain rate. Here, τ ( α ) and σ ( α ) are resolved shear traction and normal traction (compressive is taken positive) on the α th slip system, respectively. c is cohesion which signifies the yield strength in pure shear. µ is the coe ffi cient of internal material friction, and when τ ( α ) = c + µσ ( α ) , ˙ v ( α ) = ˙ v 0 for m > 0. m is the strain rate sensitivity parameter. The dilatancy function β and cohesion c are taken as:

g 0 e − 1

η η cv − 1

e 1 −

(3)

β =