PSI - Issue 2_B

Aylin Ahadi et al. / Procedia Structural Integrity 2 (2016) 1343–1350 Ahadi, Hansson and Melin./ Structural Integrity Procedia 00 (2016) 000–000

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Staring with MD for the [010]-orientation, Fig. 5 (left), slip is seen along the closed packed <110>-directions, with an angle of 45° to the y -axis. In Fig. 5 (right) the atomic pattern for the [011]-direction is found. Also in this case slip occurs in <110>-directions, but in this case this includes one direction coinciding with the y -axis, resulting in a different deformation pattern with almost no deformation directly beneath the center of the indenter. Similar deformation patterns have previously been studied by Hansson (2014, 2015). The distribution of the material particles as found from the PD simulations for the same indentation depths as in the MD simulations are presented in Fig. 6. The particle distributions seem quite realistic for both orientations, with typical pile-up effects present. For the [101]-orientation, Fig. 6 (left), the slip occurs with an angle of 45° to the y axis, similar to the results from MD simulation. The deformation pattern for the orientation [011] in Fig 6 (right) shows also similarities to the deformation pattern from the MD simulation, with slip occurring along the y -axes. 4. Summary and conclusions Molecular dynamic simulations, that are well confirmed to capture nanoscale phenomena, were used as reference in investigating to what extent PD can capture nanoscale features. Nanoindentation in a thin single-crystal copper coating have been modelled using both MD and PD, with the code LAMMPS as a common framework. The crystal orientations in the loading direction were [010] or [011]. It was shown that a small increase in size of the unit cell in PD rapidly reduces the number of particles, i.e. the degrees of freedom, in the simulations as compared to MD simulations, thereby considerably reducing the computational costs. Force-displacement curves obtained from PD was fitted with good accuracy to the force-displacement curves obtained from MD simulation for both crystallographic orientations. The distributions of the material particles from the PD simulations are realistic, with typical formation of slip patterns below the indenter. The agreement is somewhat surprisingly good despite that no orientation dependence exists in the PD model. This suggests that PD is well suited to describe phenomena at the nanoscale and model features derived from the atomic scale to a very low computational cost. Ahadi, A., Melin, S., 2016, Capturing nano scale effects by peridynamics, report Division of mechanics, Lund University, submitted for publication. Ahadi, A., Melin, S. 2016, Size dependence of the Poisson’s ratio in single-crystal fcc copper nanobeam, Computational Materials Science, 111, 322-327. Bourreau, S., Roca, H., Ahadi, A., Melin, S. 2014, Elastic nanobeam modelled using peridynamics - length scale effects”, Proceedings to NSCM 27, Stockholm, Sweden. Ellad, B. T., Miller, R. E., 2011. Modeling Materials Continuum, Atomistic and Multiscale Techniques. Cambridge University press. Foiles S. M, Baskes M. I, Daw M. S 1986, Embedded-atom-method functions for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys, Physical review B 33(12). Hansson, P., 2014, Influence of the cryctallographic orientation of thin copper coating during Nano indentation, Procedia Material Science, 20th Europian Conference on Fracture (ECF20). Hansson, P., 2015, Influence of the cryctallographic orientation and thickness of thin copper coating during nanoindentation, Engineering Fracture Mechanics 150, 143-152. Holian, B.L., Ravelo, R., 1995, Fracture simulation using large-scale molecular dynamics, Phys. Rev. B 51 17 11275-11288. LAMMPS, http://lammps.sandia.gov. Stukowski, A, 2010, Visualization and analysis of atomistic simulation data with OVITO–the Open Visualization Tool. Modelling Simul. Mater. Sci. Eng. 18. Parks, M.L., Seleson, P., Plimpton, S.J., Silling, S.A., Lehoucq, R.B, 2013. Peridynamics with LAMMPS: A User Guide v0.3 Beta, Sandia National Laboratories. Silling,S.A. 2000, Reformulation of Elasticity Theory for Discontinuities and Long-Range Forces, J. Mech. Phy. of Solids, vol 48, p 175—209. Silling, S.A., Askari, E., 2005. Meshfree method based on the peridynamic model of solid mechanics, Computers and Structures 83, 1526–1535. References