PSI - Issue 23

Solveig Melin et al. / Procedia Structural Integrity 23 (2019) 137–142 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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gradually changes. This is due to the increase in the number surface atoms as compared to the number of bulk atoms, giving impact on the material properties. For the surface atoms, lacking some of their neighbors, a redistribution of the electron clouds puts the surface atoms in energy states different from what applies to bulk atoms. To an increasing extent we are thus surrounded by products with properties determined at the atomic scale, and traditional dimensioning of such structures according to handbook recommendations no longer apply. The mechanical response at the nanoscale is determined by discrete events at the atomic level and continuum mechanics modelling fails. Instead one should lean against atomistic simulations. At the nanoscale, lattice irregularities that can be sources for dislocation emission or act as dislocation traps are of special interest since they rules the plasticity built-up in the structure. In this paper we investigate the effects of a boundary between two grains in Cu beams subjected to tensile loading by molecular dynamic simulations. Nanobeams of Cu, with clamped ends and subjected to displacement controlled, tensile loading are considered. A beam has the length L = 100 a 0 and a quadratic cross section with side length s = 12 a 0 , with a 0 denoting the lattice parameter for Cu, here put to a 0 = 3.615Å , cf. Fig. 1a. At the center of the beam a grain boundary is introduced perpendicular to the loading direction x by abruptly changing the lattice orientation, thus creating two grains, cf. Fig 1. The grain boundaries investigated are between grains with lattice orientations [100], [110] and [111] in their respective x -direction and thus, in all, three different grain boundary configurations are considered, [left grain orientation]-[right grain orientation]: [100]-[110], [100]-[111] and [110]-[111]. Figure 1b shows the atomic configuration near a relaxed [100]-[110] grain boundary. For each two-grain configuration as well as for single crystal beams with lattice orientations [100], [110] and [111], tensile stress-strain curves and dislocation developments are monitored until rupture. 2. Statement of the problem 2.1. Geometrical arrangements

Fig. 1. a) Geometrical configuration with a central grain boundary, GB and b) atomic positions near the grain boundary after relaxation. Red color corresponds to the [100] orientation and blue to the [110] orientation.

2.2. Molecular dynamics For the simulations the molecular dynamics freeware LAMMPS (http://lammps.sandia.gov) have been employed and the illustrations are produced using OVITO, developed by Stukowski (2010). The interaction between the Cu atoms is described by an EAM-potential, giving the potential energy of an atom. The potential chosen in this study is provided by LAMMPS under file name Cu_u3.eam and was developed by Foiles et al. (1986). For all simulations, an NVT-ensemble with a Nosé -Hoover thermostat according to Ellard and Miller (2011), with a constant temperature of 0.1K, was used. Initially, the beam is relaxed to its equilibrium state during 50000 time steps with time step 5fs. Thereafter an axial elongation is applied by putting a constant velocity of 0.018075 Å /ps, corresponding to a strain rate of 10 8 /s, in the + x - and – x -directions at the ends of the beam, whereas zero velocities are applied in the y - and z -directions for these atoms. This mimics clamped ends of the beam. The atoms in-between the clamped regions are free to move without constraints.