This is a two parameter model and it is described by the following equation.
This model describes the viscosity using a powerlaw relationship. The exponent n determines the nature of the relationship.
n < 1 Shear thinning or Pseudoplastic
n > 1 Shear thickening or dilalatant
n = 1 Newtonian
For most polymers, Exponent n is less than 1. When the exponent is less than 1, viscosity of the polymer decreases with increase in the shear rate. This behavior is called shear thinning. On the other hand, when the exponent is greater than 1, viscosity increases with shear rate and this behavior is called shear thickening. The following figure shows viscosity as a function of exponent (consistency = 1.05e+04)
One of the disadvantages of the powerlaw model is, as the shear rate tends to zero (when the exponent is less than 1) the viscosity tends to infinity. This setback is overcome in HyperXtrude by defining a ZeroShearRateLimit. Typically, this value is chosen based on the experimental data used to determine the model coefficients. For instance, if the ZeroShearRateLimit is set to 10.0, then HyperXtrude will use this value to compute the viscosity whenever the effective shear rate of the flow field is less than the ZeroShearRateLimit. The following figure shows this effect for a powerlaw model with consistency 1.05e+04 and exponent 0.34.
In addition to this, a few additional parameters arise due the temperature dependence of material data; these variables are discussed in Temperature Dependence.
Syntax
Syntax of the data packet Polymer is as follows:
Polymer 
PolymerName 
{ 

ConstitutuveModel = 
"PowerLaw" 

Density = 
ρ 

SpecificHeat = 
Cp(T) 

Conductivity = 
K(T) 

CoeffOfThermalExpansion = 
βT 

VolumetricHeatSource = 
Qvol 

Consistency = 
A 

Exponent = 
n 

ZeroShearRate = 
γ0 

TemperatureDependence = 
"None" } 
Parameter 
Description 
Units 
Data Type 
Condition 
Typical Value 
ConstitutiveModel 
Describes the model used 
None 
String 
Required 
"PowerLaw" 
Density 
Density of the polymer 
kg/m^3 
Constant 
Required 
995.0 
SpecificHeat 
Specific heat at constant pressure 
J/kg/K 
Constant / F(T) 
Required 
2000.0 
Conductivity 
Thermal conductivity 
W/m/K 
Constant / F(T) 
Required 
0.167 
CoeffOfThermalExpansion 
Indicates the change in volume with change in temperature 
1/K 
Constant 
Required 
1.0e05 
VolumetricHeatSource 
Heat generated/ removed in the volume by methods like electrical heating 
W/m^3 
Constant 
Required 
0.0 
Consistency 
One of the parameters of the power law model. When n=1 it is same as viscosity. 
Pa s^n 
Constant 
Required 
1.0e+04 
Exponent 
Power law index, defines the dependency of viscosity on shear rate. 
None 
Constant 
Required 
0.66 
ZeroShearRateLimit 
See above 
1/s 
Constant 
Required 
0.01 
TemperatureDependence 
None 
String 
Required 
"Exp(Beta(DeltaT))" 

ReferenceTemperature 
Temperature at which data is calculated for the initialization step. 
K 
Constant 
Required only if TD is not "None" 
533 
FreezeTemperature 
This is the no flow temperature. Below this temperature, material ceases to flow. 
K 
Constant 
Required only if TD is not "None" 
350 
ActivationEnergy 
A parameter required by Arrhenius model. 
J/mol 
Constant 
Required only if TD is Exp(Q/RT) 
16628 
UniversalGasConstant 
A parameter from state equation PV = nRT, R is universal Gas constant. 
J/mol/K 
Constant 
Required only if TD is Exp(Q/RT) 
8.314 
TemperatureSensitivity 
A derived parameter which has the same physical meaning as Q/R. 
K 
Constant 
Required only if TD is Exp(Tb/T) 
2000 K 
WLFConstant1 
Constant C1 of WLF model 
None 
Constant 
Required only if TD is WLF 
17.44 
WLFConstant2 
Constant C2 of WLF model. This is like DeltaT, hence the value is same in K and Celsius. 
K 
Constant 
Required only if TD is WLF 
51.6 
GlassTransitionTemperature 
Temperature below with polymer molecules ceases to move (frozen). There are few definitions of this term. 
K 
Constant 
Required only if TD is WLF 
320 
Beta 
Parameter in the relationship Exp(Beta(DeltaT)) 
None 
Constant 
Required only if TD is Exp(Beta(DeltaT)) 
0.005 
F(T)  Function of Temperature. Can be specified as a TABLE1 or TCL function.
TD  TemperatureDependence