The effect of material orientation on void growth

In this work, we have brought to light the effect of material orientation on void growth. For that purpose, we have performed finite element calculations using a cubic unit-cell model with a spherical void at its center and subjected to periodic boundary conditions. The behavior of the material is described with an elastic isotropic, plastic orthotropic constitutive model with yielding defined by Yld2004-18p criterion (Barlat et al., 2005). We have used the multi-point constraint subroutine developed by Dakshinamurthy et al. (2021) to enforce constant values of macroscopic stress triaxiality and Lode parameter in calculations that have been carried out for different stress states resulting from the combination of T=0.33, 1 and 2, with L=-1, 0 and 1 (axisymmetric tension, generalized shear and axisymmetric compression, respectively). Firstly, we have performed numerical simulations in which the loading directions are collinear with the orthotropy axes of the material, so that the principal directions of macroscopic stress and strain are parallel. Investigation of the cases for which the minor loading axis coincides either with the rolling, the transverse or the normal direction, has shown that the initially spherical void turns into an ellipsoid whose rate of growth and eccentricity depend on both stress state and material orientation. A key result is that for specific material orientations the anisotropy switches the effect of Lode parameter on void growth, reversing the trends obtained for isotropic von Mises materials. Secondly, we have carried out calculations using a novel strategy which consists of including angular misalignments within the range 0<\theta<90, so that one loading direction is parallel to one of the symmetry axes of the material, and \theta is the angle formed between the other two loading directions and the second and third orthotropy axes. In fact, to the authors’ knowledge, these are the first unit-cell calculations ever reported in which the material is modeled using a macroscopic anisotropic yield function with prescribed misalignment between loading and material axes and, at the same time, the macroscopic stress triaxiality and the Lode parameter are controlled to be constant during loading. The finite element calculations have shown that the misalignment between loading and material axes makes the void and the faces of the unit-cell to rotate and twist during loading. Moreover, the main contribution of this work is the identification of an intermediate value of the angle for which the growth rate of the void reaches an extreme value (minimum or maximum), so that the numerical results indicate that material orientation and angular misalignment can be strategically exploited to control void growth, and thus promote or delay localization and fracture of anisotropic metal products. The conclusions of this research have been shown to be valid for three different materials (aluminum alloys 2090-T3, 6111-T4 and 6013) and selected comparisons have also been performed using two additional yield criteria (CPB06ex2 and Yld2011-27p).

RESIADUAL STRESS RELAXATION IN DECAHEDRAL PARTICLES THROUGH THE FORMATION OF A CENTRAL SPHERICAL VOID

Small metal particles with a body-centered crystal lattice (BCC) often take the form of polyhedrons with fifth-order symmetry axes such as the icosahedron, decahedron, and pentagonal prism. The quintic symmetry axes, forbidden by the traditional crystallography laws, cause inhomogeneous elastic stress and strain in these particles. Under certain conditions, these stress and strain could relax through the change in the particle structure: the formation of partial and perfect dislocations, misfit layers, and the nucleation of cracks and voids. Within the quasi-equilibrium energy approach, the authors proposed a theoretical model of residual stress relaxation in decahedral particles due to the formation of a central spherical void. The explicit analytical expressions for energies of solid and hollow decahedral particles are found. The elastic energy of a hollow decahedral particle is defined as the work spent on the nucleation of a positive wedge disclination with the power ω≈0.0163 rad (≈7°20') in the elastic spherical shell under its own stress field. The authors determined the change in the surface energy due to the formation of a void considering the influence of the relaxation effect of the first coordination sphere surrounding the vacancy on the particle volume change. The energy change of decahedral particles during the formation of a spherical void is calculated and the optimal and critical parameters of this process are determined. The study shows that there some critical radius of a particle, if reached the formation of the central spherical void becomes energetically favorable. Moreover, the study shows that a pore germ will grow until it reaches a certain optimal size corresponding to the greatest change in the system energy. The numerical calculations correspond with experimental observations of unstable voids in the rather small silver and gold decahedral particles with the diameter of 30–40 nm and stable voids in relatively large copper decahedral particles with the diameter of ~1 μm.

Modelling of Void Collapse with Molecular Dynamics in Pure Sn

This work simulates the collapse of a spherical void in pure Sn during melting using molecular dynamics (MD). Simulations were performed for two temperatures with a modified embedded atom method (MEAM) potential, which was reported to be in good agreement with respect to melting point and elastic constants. Solutions of the Rayleigh–Plesset (RP) equation are used for comparison under the assumption of macroscopic surface tension and liquid viscosity. Despite a qualitative correlation, longer collapse times were observed in MD simulations, which arose from partial solid structures and the incubation time for melting.

Redshift-space effects in voids and their impact on cosmological tests. Part I: the void size function

ABSTRACT Voids are promising cosmological probes. Nevertheless, every cosmological test based on voids must necessarily employ methods to identify them in redshift space. Therefore, redshift-space distortions (RSD) and the Alcock–Paczyński effect (AP) have an impact on the void identification process itself generating distortion patterns in observations. Using a spherical void finder, we developed a statistical and theoretical framework to describe physically the connection between the identification in real and redshift space. We found that redshift-space voids above the shot noise level have a unique real-space counterpart spanning the same region of space, they are systematically bigger and their centres are preferentially shifted along the line of sight. The expansion effect is a by-product of RSD induced by tracer dynamics at scales around the void radius, whereas the off-centring effect constitutes a different class of RSD induced at larger scales by the global dynamics of the whole region containing the void. The volume of voids is also altered by the fiducial cosmology assumed to measure distances, this is the AP change of volume. These three systematics have an impact on cosmological statistics. In this work, we focus on the void size function. We developed a theoretical framework to model these effects and tested it with a numerical simulation, recovering the statistical properties of the abundance of voids in real space. This description depends strongly on cosmology. Hence, we lay the foundations for improvements in current models of the abundance of voids in order to obtain unbiased cosmological constraints from redshift surveys.