Master Curve Generation

A master curve is fit to viscoelastic data. The master curve is found by reading in the raw data, shifting it, and fitting the shifted data points. Curve fitting is accomplished with the MasterCurve object, as demonstrated in the cells to follow.



In [1]:

    
%pylab inline
%load_ext autoreload
%autoreload 2
from matmodlab2 import *
from matmodlab2.fitting.mcgen import *









    



Populating the interactive namespace from numpy and matplotlib
Setting up the Matmodlab notebook environment

Import the Data

Data is imported in to the MasterCurve object by the Import factory method. The MasterCurve.plot method plots the data. The keyword raw indicates that raw, unshifted data is to be plotted.



In [2]:

    
mc = MasterCurve.Import('mcgen.csv', yvar='E_r', yunits='psi')
mc.plot(raw=True)

Fitting Data

The data are fit with the MasterCurve.fit method. By default, the shifted data is fit to a Prony series.



In [3]:

    
mc.fit()
mc.plot()

The master curve fit is plotted by setting the keyword show_fit=True



In [4]:

    
mc.plot(show_fit=True)

A description of the fit is printed to the screen with the MasterCurve.description property



In [5]:

    
mc.description









    



mcgen Version 1.2
Curve Fitter: Prony
Curve Fitting Information
tau_1,tau_2,tau_3,tau_4,tau_5,tau_6,tau_7
0.000100000000000000,0.001000000000000000,0.010000000000000000,0.100000000000000006,1.000000000000000000,10.000000000000000000,100.000000000000000000
y_1,y_2,y_3,y_4,y_5,y_6,y_7,y_inf
3151.792989217418835324,1999.638114092092564533,810.563266079318964330,435.084289976046534321,239.322095377840781794,114.163294480146703336,97.133449550873024236,238.101825181011406585
Fit Error
39.581373201190061195
WLF C1,WLF C2
6.793113271188959246,331.323540165617146158

The optimized $C_1$ and $C_2$ WLF coefficients are in the MasterCurve.wlf_opt attribute



In [6]:

    
mc.wlf_opt









    Out[6]:





array([   6.79311327,  331.32354017])

It is often necessary to supply initial guesses to the WLF coefficients, do so by passing to MasterCurve.fit the wlf_coeffs keyword



In [7]:

    
mc.fit(wlf_coeffs=[2, 300])
mc.plot(show_fit=True)

Other master curve fit types are available



In [8]:

    
mc.fit(fitter=MODIFIED_POWER)
mc.plot(show_fit=True)
mc.fiterr









    












    Out[8]:





40.523176401110035



In [9]:

    
mc.fit(fitter=POLYNOMIAL, order=4)
mc.plot(show_fit=True)
mc.fiterr









    












    Out[9]:





38.999755327133464



In [10]:

    
mc.fit(fitter=POWER)
mc.plot(show_fit=True)
mc.fiterr









    












    Out[10]:





87.182941021048947

Exporting Fitted Data

Data can be exported to a number of file formats



In [11]:

    
mc.fit()
mc.Export('foo.csv')
#mc.Export('foo.xlsx')