Optimal Cool Down in Nonlinear Thermoviscoelasticity With Application to Graphite/Peek (APC-2) Laminates

Many thermoplastic resin composite laminates, such as those made of APC-2, undergo a substantial temperature drop during their post-manufacturing cool down. This thermal excursion induces significant residual thermal stresses into the laminate due to the mutual geometric constraints among the multidirectional plies. In view of the considerable time-dependent relaxation which occurs during the cooling process, the residual thermal stresses exhibit strong dependence on the temperature history. However, in view of the high magnitudes of those stresses, the relaxation behavior is viscoelastically nonlinear. This paper demonstrates that it is possible to obtain an optimal cool-down path which minimizes the residual thermal stresses in APC-2 composites upon the termination of the cooling process.

Optimal Cool-Down in Linear Viscoelasticity

An optimal temperature path is derived for a thin viscoelastic plate which is cooled from a stress-free state against geometric constraints. The optimal path, which minimizes the final residual stress due to cool down, is shown to possess discontinuities at the initial and final times and to be smooth and continuous during all intermediate times. An iterative convergent scheme is provided for a wide class of linear viscoelastic responses and typical paths are determined for two specific cases. In addition, a time-temperature path which maintains constant stress values during cool-down is derived. The problem is motivated by the cooling process of composite materials.