Mechanical properties of epoxy polymers¶

Overview¶

This advanced ReaxFF tutorial is based on Radue, Jensen, Gowtham, Klimek-McDonald, King and Odegard, J. Polym. Sci. B, 56, 255-264 (2018) [1]. It will demonstrate how to calculate stress-strain curves of an epoxy polymer.

Contents:

• Setting up a strain rate
• Calcuate the atomic stresses
• Results: stress-strain curves, Young’s modulus, yield points…

Setting up¶

The polymer used in this tutorial is referred to as Tetra(-epoxy) in [2] since it was build from the tetrafunctional resin epoxy TGDDM (tetra-glycidyl-4,4 0 - diaminodiphenylmethane, Araldite MY 721) and DETDA as hardener. The following cross linking reaction was used to create the polymer structure:

Start by importing the polymer structure into AMSinput

Click here to download the .xyz file tetra_epoxy.xyz

Import the coordinates in AMSinput:

File → Import Coordinates

Before setting up the strain rate, start with the general molecular dynamics settings. Begin by selecting a force field

Force field dispersion/CHONSSi-lg.ff

Click on next to Molecular Dynamics

Select 2000000 as Number of steps (500 ps)

Select 2000 as Sample frequency

Next we set up the thermo- and barostat

Click on next to Thermostat

Click on the

Select Berendsen from the menu Thermostat

Set the Temperature to 300.15 K and the Damping constant to 100 fs

Click on next to MD main options

Click on next to Barostat

Select Berendsen from the menu Barostat

Set the Pressure to 101000 Pa and the Damping constant to 1500 fs

From the Scale menu, select YZ

Setting up the strain rate¶

The publication [2] put a linear strain of 20% over the course of 1 ns. Since we are simulating only 500 ps, for the sake of computational efficiency, the total strain reduces to 10%.

The straightforward way to defining this strain is by defining the strain type to be linear, followed by the final length of the vector at the end of the straining.

Let’s first find and note the length of the a-lattice vector.

Model → Lattice

The length of the a-lattice vector a (\(\mid\vec{a}\mid\)) is found to be 37.59793 Å. The endpoint, after stretching it 10%, will then be 41.36 Å. To define this strain, change to the MD deformation panel

Model → MD deformation

Click on

Enter 2000000 as the final step

Enter 41.36,``0``,``0`` as the final lengths of the lattice vectors

Save the input files with a suitable name, e.g. tetra_strain_a, and run the calculation. On 16 cores, it will typically take a bit less than 1 day to compute the trajectory depending on your hardware.

Results¶

Once the calculation has finished, the stress-strain curves can be extracted from the binary results file with the help of a Python script using the PLAMS library.

The script called stress_strain_curve.py can be run from the command line:

$AMSBIN/amspython stress_strain_curve.py tetra_strain_a

Be sure to match the job name correctly.

The stress-strain curve is written to a file called stress-strain-curve.csv:

# strain_x, strain_y, strain_z, stress_xx, stress_yy, stress_zz
0.0001 -0.0012 0.0016 -0.0126 0.0107 -0.0142
0.0002 0.0003 0.0025 ...

It can be plotted with any graph plotting software, e.g. gnuplot or qtiplot.

The following example shows how to obtain the mechanical properties from stress-strain plot for an uniaxial strain in y-direction:

A Young’s modulus of 6.10 GPa was calculated from the slope of a linear fit to the small strain regime (< 0.03). The Yield point is then found as the intersection between the smoothed blue curve (moving window average, 200 points for smoothing) and a 0.2% offset line of the linear fit.

Poisson’s ratio is obtained from the ratio of transverse and uniaxial strains, i.e. plotting column #1 and #3 against column #2 (the system was strained in y-direction)

Since the system is amorphous, Poisson’s ratio becomes (0.54 + 0.20)/2 = 0.37.

Lit.:

[1] M. S. Radue, B. D. Jensen, S. Gowtham, D. R. Klimek‐McDonald, J. A. King and G. M. Odegard, Comparing the mechanical response of di‐, tri‐, and tetra‐functional resin epoxies with reactive molecular dynamics, Inc. J. Polym. Sci., Part B: Polym. Phys. 56, 255–264 (2018).