Prediction of cure-induced spring-in of an angle bracket

The tool is made of steel, with properties as listed in Table 1. The bracket material is modeled with LY5052 epoxy reinforced with 55% E-glass fiber. Table 2 lists the properties of the E-glass, which are based on those in Table 1.

The cure characteristics of LY5052 are based on those in Saseendran and Wysocki (2016). The Kamal definition is used for the cure kinetics, and the standard DiBenedetto equation is used to compute the glass transition temperature from the degree of cure. Table 3 and Table 4 list the Kamal coefficients and the parameters in the DiBenedetto equation, respectively. Another important aspect of the cure reaction is that a considerable amount of energy can be released during curing, which can result in exothermal temperature peaks and drastic changes in temperature and degree of cure. The cure heat generation is set to 4.82e5 J/Kg (Saseendran and Wysocki (2016)).

During the curing process, the cure temperature in the resin changes with time. With this change, the resin material undergoes two transformations. The first one is a transformation from a liquid to a solid, which is called gelation. At this point, the material is in a rubbery state. As the glass transition temperature increases and eventually exceeds the cure temperature, the material transforms from a rubbery state to a glassy state. This second transformation is called vitrification. Table 5 and Table 6 list the properties of the resin at the glassy state and the rubbery state.

The mechanical constitutive relationship of the resin material can be modeled as linear viscoelastic with thermorheologically simple effects. For simplicity, a simple shift function proposed by Svanverg (2002) is used:

With this simplified shift function (see Temperature Effects), the resin material reaches full relaxation instantaneously in the rubbery state and has no relaxation once it reaches the glassy state. In the shift function definition, 10⁻²⁰ is used for the rubbery state and 10³⁰ is used for the glassy state. The relaxation of the modulus is adapted from Prony series coefficients in Kim and White (1996).

During the curing process, the resin material undergoes permanent shrinkage due to the cross-linking reaction. Cure shrinkage, thermal strain, and residual stresses developed during the curing process are the main contributing factors to the shape distortion of the composite part after tool removal. The thermal strain in this example is modeled in the following rate:

in which $\alpha$ is the thermal expansion coefficient given by in which ${\alpha }^r$ and ${\alpha }^g$ are, respectively, the thermal expansion coefficient of the rubbery state and the glassy state. The thermal expansion coefficient is assumed to be zero before gelation—the degree of cure is less than 0.5. Two approaches are used to model the thermal expansion: one is through user subroutine UEXPAN, and the other is through a tabular tangent definition (see Thermal Expansion). The cure shrinkage is modeled with a similar rate formulation (see Cure Shrinkage Strain).

Two approaches are demonstrated to model the local fiber directions. In the first approach, the composite is modeled as a unidirectional fiber reinforced composite, and the local fiber direction is specified in the 1- and 2-direction in alternate layers of the mesh. In the second approach, the composite is modeled with a single woven material, which contains two inclusions that are orthogonal to each other.