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

263

(a)

(b)

(c)

(d)

Fig. 1. Uniaxial compression of a 3D bar. Contour plots of maximum principal logarithmic plastic strain (ln λ p 3% and, (c) 5%. (d) Nominal stress-strain curves for monolithic prismatic bar under uniaxial compression and tension.

1 ) at an overall strain of (a) 1.5%, (b)

b e − 1

η η cv − 1 ,

e 1 −

c = c cv +

(4)

where, η is the plastic volumetric strain. As the plastic deformation progresses, η increases from zero and saturates to a value of η cv while simultaneously β decreases from its initial value g 0 to 0, and c decreases from c 0 to c cv . The initial cohesion is given by c 0 = c cv + b . (5) The above constitutive model has been numerically implemented in a thoroughly tested and benchmarked user mate rial subroutine UMAT for the commercial finite element software ABAQUS by Tandaiya et al. (2010). In this work, the above model has also been implemented in a user material subroutine VUMAT for ABAQUS / Explicit software employing an explicit integration procedure. In this VUMAT implementation, a linear ductile damage model proposed in Anand and Su (2005) has also been implemented. This damage model is capable of simulating cracking inside shear bands due to accumulation of plastic shear strain inside it. Once the damage is complete in any finite element, it is removed from the calculations. von Mises plasticity model is used to represent the plastic behavior of Copper coating. Nonlinear isotropic hardening for Copper is taken from literature and supplied to ABAQUS in tabular form. Table 1 lists the salient material properties of Vitreloy-105 BMG and Copper which are used in the present simulations. The values of other material parameters involved in the Anand and Su (2005) model for this BMG are assumed to be same as in Raut et al. (2018) and are mentioned in Section 3.5.

Table 1. Material properties Material properties

BMG

Copper

Young’s Modulus

107 GPa

110 GPa

Poisson’s ratio

0.38

0.3

Yield strength (In compression)

1.93 GPa

0.114 GPa

3. Results and discussion

3.1. Uniaxial compression and tension of a 3D bar

In order to first test the capability of the code to simulate multiple shear bands in a three-dimensional (3D) speci men, simulations of uniaxial loading of a 3D prismatic bar made of monolithic BMG are carried out. Fig. 1(a) shows the finite element mesh of the 3D bar (15 mm × 5 mm × 5 mm). The mesh is prepared in such a way that it has 20 elements along the small edges and 60 elements along the long edge. Appropriate boundary conditions are applied