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Temperature Dependence

Temperature Dependence

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Temperature Dependence

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Viscosity is a strong function of temperature. HyperXtrude has five user options for specifying the temperature dependence of polymer viscosity. These options are:

None
Exp(Q/RT)
Exp(Tb/T)
Exp(-Beta(DeltaT))
WLF

Besides polymer viscosity, other material parameters can also be specified as a function of temperature using the Function/Table format.

 

TemperatureDependence="None"

No additional parameters are required for this option. This option implies that viscosity is not a function of temperature and depends only on the shear rate. This option is chosen if the analysis is isothermal or if the variation of viscosity with temperature is negligibly small.

td_none

 

Parameter

Description

Units

Data Type

Typical Value

TemperatureDependence

Specifies one of the five functions available in HyperXtrude for computing temperature dependence of viscosity.

None

String

"None"

 

TemperatureDependence="Exp(Q/RT)"

The following equation describes this temperature dependence which is also known as Arrhenius function. R is the universal constant and its value is 8.314 in SI units. The only parameter that needs to be experimentally determined is the activation energy Q. This function is one of the commonly used methods to describe the variation of a property with respect to temperature.

td1

 

The parameters associated with this function are summarized in the following table.

 

Parameter

Description

Units

Data Type

Typical Value

TemperatureDependence

Specifies one of the five functions available in HX for computing temperature dependence of viscosity.

None

String

"Exp(Q/RT)"

ReferenceTemperature

Temperature at which data is calculated for the initialization step.

K

Constant

533

FreezeTemperature

This is the no flow temperature. Below this temperature material ceases to flow.

K

Constant

350

ActivationEnergy

Experimentally determined parameter to define the temperature sensitivity.

J/mol

Constant

16628

UniversalGasConstant

A parameter from state equation PV = nRT, R is universal Gas constant.

J/mol/K

Constant

8.314

 

TemperatureDependence="WLF"

The William-Landel-Ferry (WLF) equation is often used with semi-crystalline polymers. This function describes the variation in the property with respect to the data at the glass transition temperature (Tg). It is important to note that C1 is a constant and has no units. The parameter C2 is like temperature difference (deltaT) and its value is same in K and deg C.

td_wlf

 

Parameter

Description

Units

Data Type

Typical Value

TemperatureDependence

Specifies one of the five functions available in HX for computing temperature dependence of viscosity.

None

String

"WLF"

ReferenceTemperature

Temperature at which data is calculated for the initialization step.

K

Constant

533

FreezeTemperature

This is the no flow temperature. Below this temperature material ceases to flow.

K

Constant

350

WLFConstant1

Constant C1 of WLF model

None

Constant

17.44

WLFConstant2

Constant C2 of WLF model. This is like DeltaT, hence the value is same in K and Celsius.

K

Constant

51.6

GlassTransitionTemperature

Temperature below with polymer molecules ceases to move (frozen). There are few definitions of this term.

K

Constant

320

 

TemperatureDependence="Exp(-Beta(DeltaT))"

This function is mostly used in academic examples and is not as popular as the Arrhenius and the WLF functions. Variation in the viscosity is expressed with reference to the ReferenceTemperature T_0. The parameter beta is experimentally determined.

td_2

 

Parameter

Description

Units

DataType

Typical Value

TemperatureDependence

Specifies one of the five functions available in HX for computing temperature dependence of viscosity.

None

String

"Exp(-Beta(DeltaT))"

ReferenceTemperature

Temperature at which data is calculated for the initialization step.

K

Constant

533

FreezeTemperature

This is the no flow temperature. Below this temperature material ceases to flow.

K

Constant

350

Beta

Parameter in the relationship Exp(-Beta(DeltaT))

None

Constant

0.005

 

TemperatureDependence="Exp(Tb/T)"

This function is very similar to the Arrhenius function, with Q/R replaced by a more intuitive Tb. The temperature sensitivity Tb has the units of temperature.

td_3

 

Parameter

Description

Units

Data Type

Typical Value

TemperatureDependence

Specifies one of the five functions available in HX for computing temperature dependence of viscosity.

None

String

"Exp(Tb/T)"

ReferenceTemperature

Temperature at which data is calculated for the initialization step.

K

Constant

533

FreezeTemperature

This is the no flow temperature. Below this temperature material ceases to flow.

K

Constant

350

TemperatureSensitivity

A derived parameter which has the same physical meaning as Q/R.

K

Constant

2000 K

 

 

See Also:

Polymer Material Properties