Example 01: Relaxation experiment

This script provides an example of fitting of a relaxation experiment. First import the packages.

using RHEOSafm
using RHEOS

using Plots
using Plots.PlotMeasures
gr();

Next, the output file provided by the JPK software is imported. The file contains the time-force-displacement values and they are automatically converted into time-stress-strain. The function importJPK requires the file path, the radious of the indenter, and the segments of the curve to upload (i.g. extend, pause, retract).

input_file = joinpath(@__DIR__, "assets", "AFM_relaxation.txt")
R = 150e-9; # Radious of the indenter
interface = AFM(R);
data = importJPK(input_file, interface, sections = ["extend", "pause"]);

Beware!

Currently RHEOSafm makes use of the Hertz contact model to convert force-displacement to stress-strain. Additional tip geometries will be added in next updates.

plot(data.t, data.σ, legend = false, xlabel = "Time", ylabel = "Stress", guidefont= 10, size = (300,300), lw=3, margin=16mm)

To detect the point at which approximately contact occurs using RHEOSafm it is possible to:

define a force threshold
apply Hertz spherical contact model

In this example the "threshold" method is used. An application of the Hertz method is availabel in example 02.

data_contact = contact_point(data, interface, "threshold", (threshold = 1e-8,));

Note

From this point, RHEOS functionalities are used. For more information refer to RHEOS documentation.

To speed up the fitting procedure, the data points are downsampled.

d_downsample = resample(data_contact, -20);

The relaxation curve is then fitted using a Fractional Standard Linear Solid model

SLS_model = modelstepfit(d_downsample, FractSLS_Zener, strain_imposed);

┌ Warning: Initial values for model parameters are set to [0.5, 0.5, 0.5, 0.5] by default
└ @ RHEOS ~/.julia/packages/RHEOS/UUrax/src/processing.jl:250
Time: 74.807872373 s, Why: FORCED_STOP, Parameters: [6.525747251001682e8, 0.04408093765119187, 2.8051408580771286e7, -2.6135959849098466e7], Error: 3.2168867230898936e16

Now we can extract the strain pattern

SLS_predict = extract(data_contact, strain_only);

and calculate the stress based on the fitted model

SLS_predict = modelpredict(SLS_predict, SLS_model);

Now we can plot data and model together for comparison

plot(data_contact.t, data_contact.σ, legend = true, xlabel = "Time", ylabel = "Stress", label = "Experimental data", guidefont= 10, size = (500,500), lw=3, margin=16mm)
plot!(SLS_predict.t, SLS_predict.σ, label = "Fitted",guidefont= 10, size = (400,400), lw=2)

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