Reaction Kinetics
The degree of cure (or conversion) of a material is characterized by a normalized quantity, α , with a value changing from 0 (corresponding to the uncured state; that is, no bonds) to 1 (corresponding to the fully cured material).
The cure reaction kinetics control the rate of conversion, ˙α , as a function of α and temperature. The Kamal equation provides a well accepted description of the cure reaction kinetics that is known to produce accurate results, particularly for epoxy resins. It is given by the following rate form:
where N is the number of terms, Zi are rate constants, Ei are activation energies, mi and ni are reaction constants, θZ is the absolute zero on the temperature scale used, and R is the universal gas constant. The material constants, bi , are introduced to allow a nonzero initial conversion rate by setting at least one of them to a small positive value. Alternatively, you can specify a nonzero initial conversion value, α|t=0 , using initial conditions (see Solution-Dependent State Variables). If you do not define bi or α|t=0 , the degree of cure (conversion) remains equal to zero throughout the analysis.
The constant, αmax , controls the maximum degree of cure. By default, αmax=1 . You can define a different value, as described in Maximum Conversion.
In addition to the Kamal equation, you can specify the rate of conversion, ˙α , in a tabular format. This format allows you to express the rate as a function of conversion and, optionally, temperature and field variables:
Curing is an irreversible process; therefore, the value of the degree of cure that Abaqus computes never decreases. The value either increases or remains constant.
Input File Usage
Use the following options to define the conversion rate in the Kamal equation:
PHYSICAL CONSTANTS, UNIVERSAL GAS CONSTANT=R, ABSOLUTE ZERO=θZ MATERIAL PARAMETER TABLE, TYPE="ABQ_Cure_ReactionKinetics_Kamal" Z1, E1, m1, n1, b1 Z2, E2, m2, n2, b2 … ZN, EN, mN, nN, bN
Use the following options to define the conversion rate in tabular form:
MATERIAL PROPERTY TABLE, TYPE="ABQ_Cure_ReactionKinetics_Tabular", TEMPERATURE ˙α, α, θ
Maximum Conversion
In general, the degree of cure can reach a maximum value of 1 (corresponding to a fully cured material). However, at lower temperatures, the reaction might slow down considerably, and a fully cured state might not be reached (corresponding to αmax<1 ). You can specify the maximum conversion as a function of temperature. The default is αmax=1 .
Input File Usage
Use the following option to specify the maximum conversion:
MATERIAL PROPERTY TABLE, TYPE="ABQ_Cure_ReactionKinetics_MaxConversion" αmax