**1. Introduction**

Nanotechnology provides applications in an increasing number of engineering fields, with tailor manufactured products for everyday use. Mobile phones, medical sensors and solar cells are examples of well-established application areas. However, since it is an experimentally verified fact that nanosized structures respond differently on mechanical loading than macroscopic structures of the same material, design and dimensioning of nanocomponents lack a solid ground corresponding to traditional dimensioning handbook rules at the macroscale.

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

The reason for traditional engineering dimensioning rules becoming obsolete at small enough metric scales is that, with decreasing structural size, the number of surface close atoms as compared to number of bulk atoms increases and, at some point, no longer is negligible. Electron redistribution close to the surfaces will leave the surface close atoms in energy states deviating from those of bulk atoms. This influences the interatomic bonding forces and, thereby, the material response to mechanical loading as discussed by e.g., [1–3]. This effect is accentuated if the atoms are placed at, or close to, corners and edges of the structure, e.g., [4]. As a consequence, the material properties will vary with size for small enough structures, and the effects become obvious below about 50–100 nm.

Also, the crystallographic orientation is of uttermost importance for the material properties, e.g., [5, 6]. The crystallographic orientation imposes anisotropy in the structure and also decides the surface topology which influences the mechanical properties. The orientation further sets the preferred slip plane directions and, thereby, influences the plasticity development.

The atoms in between the clamped ends are free to move in all directions without constraints. The beams are loaded in tension along the *x*-axis until final rupture. The load is displacement

**Figure 1.** (a) Beam configuration and coordinate system. (b) and (c) Crystallographic orientations.

For the simulations, the molecular dynamics free-ware LAMMPS has been employed and the

In the simulations, an NVT-ensemble, with constant number of particles N, constant volume V and absolute temperature T, kept at a constant temperature of 0.01 K through a Nosé-Hoover thermostat as found in [9] is employed. Before load application, relaxation of the atomic ensemble in order to reach the equilibrium state is imposed during 5000 time steps, with each time step equal to 5 fs. This gives the relaxation time equal to 25 ps, which was found to be sufficiently long to reach equilibrium with good accuracy as judged from the variations in axial

To calculate the atomic interactions, an embedded atom method (EAM) potential according to [10, 11] is employed. The potential has one pair-wise repulsive and one N-body attractive

where *rij* is the distance between atoms *i* and *j*, *φ* is a pair-wise potential function, *ρ* is the contribution to the electron charge density from atom *j* at the location of atom *i* and *f* is an embedding function that represents the energy required to place atom *i* into the electron cloud. For the present study, the potential file Cu\_u3.eam, provided by LAMMPS and devel-

−*x*-directions at all atoms within the clamped ends using a constant time step of 5 fs.

of atom *i* is given by:

( ∑ *j*≠*i ρ*(*rij*) ) <sup>+</sup> \_\_1 <sup>2</sup> ∑ *j*≠*i*

in the +*x*- and –*x*-directions to all atoms

Effects of Voids in Tensile Single-Crystal Cu Nanobeams http://dx.doi.org/10.5772/intechopen.74169 63

/200/ps is imposed in the +*x*- and

*φ*(*rij*) (1)

controlled through applying a constant velocity, *vend*,

atomic images are produced using OVITO, developed by [8].

stress with time. Thereafter, a constant velocity of *vend* = *a*<sup>0</sup>

**3. Molecular dynamic simulations**

within the clamped beam ends.

**3.1. Simulation procedure**

**3.2. Interatomic potential**

oped by [12], is used.

part and the potential energy *Ei*

*Ei* = *f*

Here, the tensile response of single-crystal nanosized Cu beams, holding square-shaped, through-the-thickness voids, will be investigated with respect to elastic and plastic behavior and eventual size dependence in the mechanical response. The rational for this investigation is that even if defect-free structures might be intended at manufacturing, defects will always be present to some extent. If their presence influences the mechanical response of the structure, the product functionality might be at risk.

To this end, 3D single-crystal nanosized Cu beams of different cross section sizes, holding throughthe-thickness voids of different sizes, will be investigated using the molecular dynamics free-ware large-scale atomic/molecular massively parallel simulator (LAMMPS), see [7]. The loading will be displacement controlled tension along the length direction, and two different crystallographic orientations will be considered and compared.
