PSI - Issue 35

Onkar Salunkhe et al. / Procedia Structural Integrity 35 (2022) 261–268 Onkar Salunkhe, Par g Tandaiy / Structural In egrity Proc dia 00 (20 1) 000–000

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(a) (b) Fig. 2. Uniaxial tension of 3D slab with VUMAT. (a) Contour plot of maximum principal logarithmic plastic strain ln λ p

1 at an overall strain of

1.7% and, (b) nominal stress-strain curve.

on symmetry planes and loading is done by prescribing displacements at the top surface nodes. The continuum, three dimensional, 8 noded, hexahedral finite element, C3D8RH, available in ABAQUS is employed. This element employs a hybrid formulation which prevents the mesh locking e ff ects due to BMG’s near-plastic incompressibility. The mate rial properties used are the same as those mentioned in Section 2. However, the initial value of cohesion is statistically distributed among the finite elements in the mesh. The initial cohesion values are taken from a Gaussian distribution with c 0 as mean and 3% of the mean value as standard deviation. These values are randomly assigned to the finite elements in the mesh. This spatial perturbation of initial cohesion triggers strain localization in the mesh. The bar is deformed at an engineering strain rate of 10 − 4 s − 1 till an overall strain of 5%. Figure 1(a) shows the contour plot of maximum principal logarithmic plastic strain ln λ p 1 at an overall compressive engineering strain of 1.5%. It can be seen from Fig. 1(b) that multiple shear bands are formed at 3% compressive engineering strain and the plastic strain intensifies inside the shear bands at 5% engineering strain (see Fig. 1(c)). This would lead to potential failure inside a dominant shear band. Tensile loading also leads to similar shear band formation. Figure 1(d) shows the comparison of nominal stress-strain curves for the prismatic bar under uniaxial tension and uniaxial compression. It can be observed that the yield strength in compression is higher than the yield strength in tension which is as observed in BMGs in experiments and is a characteristic of pressure dependent plastic solids. To observe and predict not only the shear band formation but also fracture in BMGs, simulations of uniaxial tension using VUMAT subroutine are also carried out invoking the ductile damage model. The material properties used for the simulation are the same as before except in VUMAT additional damage parameters are considered. The values of damage parameters γ c and γ f are chosen in such a way that damage occurs at the desired strain. For the simulation of the slab model under tension the values γ c = 0 . 05 and γ f = 0 . 15 are chosen as in Anand and Su (2005). To predict the formation of the dominant shear band and failure of BMG matrix at this dominant shear band a 3D slab model (1 mm × 2 mm × 0.2 mm) is simulated. Total number of finite elements used are 10000 of the type C3D8R. Figure 2(a) shows that a prominent shear band forms in the slab at an angle close to 45 ◦ with the loading axis. While the rest of the part far from the dominant shear band has not reached the desired maximum principal strain for failure. This is known as failure by shear localization. Fig. 2(b) displays the nominal stress-strain curve which indicates that the failure of BMG occurs at 1.7% strain as the curve suddenly drops at that strain. This simulates the catastrophic nature of failure of monolithic BMGs. BMGs being quasi-brittle in nature they tend to fail catastrophically. 3.2. Rectangular slab under uniaxial tension

3.3. Plane strain compression of monolithic BMG and thin Copper coated BMG composite

Similar to the 3D slab model, a rectangular plane strain model is simulated under compression using the same material properties and same damage parameters. The continuum CPE4R elements available in ABAQUS are used