Perform Nanoindentation on Al-Mg Alloy

Perform Nanoindentation on an Aluminum-Magnesium Alloy

Yifan Wang

Created May 2017

This tutorial explains how to create an FCC sample of Al-Mg alloy and perform nanoindentation on the sample in LAMMPS.

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Prerequisite

For this simulation, we will use the LAMMPS 5 Nov 2016 version. The newer version may have changes of the commands. When compiling LAMMPS, please switch on the package MANYBODY in order to use the EAM potential. More details about compiling LAMMPS, please see the manual page (http://lammps.sandia.gov/doc/Section_start.html) for more information.

Prepare The Al-Mg Alloy Sample

In this note, we will use the following geometric parameters as an example, to show how to perform nanoindentation MD simulation in LAMMPS:

Weight percentage: 0.6% (~0.67% atomic percentage)

Simulation Box: 32.4x32.4x32.4nm (free surface on z-direction, pbc on x- and y-directions)

Indenter radius: 16.2nm

Thermodynamics

According to the phase diagram of Al-Mg alloy (Fig.1), the solubility of Mg in Al is smaller than 1% at room temperature. For our case, since the atomic concentration is 0.67%, we can generate the sample by first creating pure FCC Al metal, and then randomly exchange required Al atoms to Mg.

Fig.1 Phase Diagram of Aluminum-Magnesium (Murray, 1982)

Fig.2 Size Factors of Al-Mg solid solution (Cai&Nix, 2016)

However, the size factor of Mg as the solute in Al is not negligible (Fig.2). We have to consider the volume change of the sample by adding Mg into pure Al. There are two ways to account for the size effect:

1. Relax the sample under zero pressure after we generate the Al-Mg alloy.
2. Estimate the volume change theoretically from the size factor.

Although the first method is more correct in the physical sense, the relaxation process will create surface steps on the free surface which will interfere the nanoindentation process. Here we estimate the volume change by correcting the lattice constant:

$a_{\text{alloy}}=a_{\text{Al}}(1+\chi _{\text{Mg}}l_{sf})$.

For now, we use the linear size factor from King's table. For a more accurate value, a constant pressure relaxation can be performed to determine the size factor.

Perform MD Simulation of Nanoindentation on The Alloy Sample

You need first to build the GPU library. Go to your lammps/lib/gpu folder. Copy the generic linux makefile

cd ~/Codes/LAMMPS/lib/gpu
cp Makefile.linux Makefile.sherlock

You have to modify 3 lines in this file. Open it and replace the values of CUDA_HOME, CUDA_ARCH and CUDA_PREC with the following

vi Makefile.sherlock

CUDA_HOME = /share/sw/free/cuda/6.5
CUDA_ARCH = -arch=sm_35
CUDA_PREC = -D_DOUBLE_DOUBLE