Viscoelasticity Tab

Setting Item

Notes

Defined by

Selectable from No viscoelasticity, Prony series [coefficient input], Dynamic modulus [freq response], Dynamic modulus [temp/freq characteristics], and Relaxation modulus.

Relaxation Type

Enterable for Prony series [coefficient input], Dynamic modulus [freq characteristics], Dynamic modulus [temp/freq response], and Relaxation modulus.

Available types are Shear and bulk, Shear only, and Bulk only.

Relaxation Table (Prony Series)

By clicking the Relaxation table button for Prony series [coefficient input]., the dialog box below will appear.

Enter Coefficient of modulus βi and Relaxation time Ti [s].

The sum of βi needs to be 1 or less.

See [Analysis of Viscoelastic Materials] for more details of Prony series.

Click the Graph button to see the relaxation modulus with time and
the frequency characteristics of dynamic modulus.

Relaxation Table (Dynamic Modulus)

By clicking the Relaxation table button for Dynamic modulus[freq characteristics] and Dynamic modulus[temp/freq response], the dialog box below will appear.

- In the case of Dynamic modulus [freq response]

Fill in the table with the data of Frequency, Storage modulus and Loss modulus.
Use the modulus below for each relaxation type.

These moduli are interchangeable
as explained in [Analysis of Viscoelastic Materials].

- In the case of Dynamic modulus [temp/freq response]

In most cases, material property of viscoelastic material is measured with dynamic moduli (storage and loss) over temperatures and frequencies.

Measured data can be directly entered.

Fill in the table with the data of Temperature, Frequency, Storage modulus and Loss modulus.
Follow the rule below.

- Fill in either table depending on the relaxation type.
- Enter multiple frequencies as one set.

- Frequencies can be entered either in incremental or decremental order, but do not mix the orders in the table.
One set of data ends and another set begins where the order of temperature changes from incremental to decremental or the other way round.

- Constant temperature is preferable for one set of data but the variation is allowed, in which case the average temperature will be treated as typical value.

- Temperature should be either in incremental or decremental order in the table. Do not mix.

Example:

Press the Frequency Graph button to see the frequency characteristics of dynamic moduli (storage and loss)

The Temperature Graph button is selectable for Dynamic modulus[freq response].

You can see the temperature characteristics of dynamic moduli (storage and loss).

To understand Master Curve Setting and Curve Fitting fully,
please read [Analysis of Viscoelastic Materials] and [Converting the Measurement Data of Viscoelastic Materials].

Use The default setting unless you are absolutely sure.

Reference temperature is required for master curve.
You can use the initial temperature or you can set it yourself.
If [Initial temperature to be the reference] is selected, the average of temperatures of 1st set will be the reference temperature.
If [Set the reference temperature] is selected, you enter the value in Reference temperature.

If [Remove irregular data] is selected,
the master curve will be plotted ignoring irregular data in the cases where
the master curve creation failed due to the irregular data or
the shift factor goes higher in the rising temperature which is opposite the tendency of the general materials.

Master Curve button will show the frequency characteristics of dynamic moduli (storage and loss)..
If the data of each temperature are on one trace, the master curve is successfully created.

Shift Function Graph button will show the temperature characteristics of shift factor.

The number of elements per frequency digit is used to calculate the number of elements for Prony series.
The number of elements = The number of elements per frequency digit * (log10[Max freq] - log10[Min freq])
More elements means better accuracy but more memory consumption.

Weight yielding to the loss modulus can be set for better curve fitting. The default is 0 and no loss modulus is taken into account.

If 1.0 is entered, storage and loss moduli are treated equally.

Curve Fit button will let you compare the original master curve and the curve-fitted master curve.
(Frequency characteristics graph of the dynamic moduli (storage and loss))
Comparison is also possible for the relaxation modulus transformed from the master curve by the Ninomiya-Ferry equation and the curve-fitted relaxation modulus given by Prony series.
(Time dependency graph of the relaxation moduli.)
If the curves match, curve fitting is considered to be successful.

Output Data in File button will let you compare
the sum of elastic moduli, number of elements, reference temperature, master curve,
curve-fitted master curve, relaxation modulus given by the Ninomiya-Ferry equation, the curve-fitted relaxation modulus,
the Prony series, and the shift function.

Relaxation Table (Relaxation Modulus)

Buy clicking the Relaxation table button for Relaxation modulus, the dialog box below will appear.

Fill in the table with the data of time and relaxation modulus.
Use the modulus below for each relaxation type.

These moduli are interchangeable
as explained in [Analysis of Viscoelastic Materials].

The number of elements per time digit is used to calculate the number of elements for Prony series.
The number of elements = The number of elements per time digit * (log10[Max time] - log10[Min time])
More elements means better accuracy but more memory consumption.

Curve Fit button will let you compare the input data and the curve-fitted relaxation modulus. (Time dependency graph of the relaxation modulus)
If the curves match, curve fitting is considered to be successful.
Dynamic modulus will be shown as well after curve fitting. (Frequency characteristics graph of the dynamic modulus)

Output Data in File will let you compare
the sum of elastic moduli, the number of elements, the input data, the curve-fitted relaxation modulus,
the curve-fitted dynamic modulus, and the Prony series.

Temperature Dependency and Shift Function

Selectable when Thermal load is selected in the Analysis Condition Setting dialog box and either Prony series [coefficient input] or Dynamic modulus [freq response] is selected on the Viscoelasticity tab.

Shift factor aT indicates the temperature dependency of relaxation time.

Common logarithm is entered.

For example, log10aT = -1 means the relaxation time is 1/10.

See also [Analysis of Viscoelastic Materials].

Select one from WLF, Arrhenius law and User to define.

By clicking the Shift Function Graph button, the temperature dependency of the entered shift factor will be graphed.