Multiphysics simulation and optimization of the curing process of thick thermosetting epoxy samples : multi-objective genetic algorithm and a conversion rate driven approach

Abstract

Over the last decades, due to higher specific strength and stiffness, low weight, and good resistance to corrosion, thermoset resin composite materials have been replacing conventional materials in aerospace, maritime, automotive and several other high performance engineering applications. These composites are usually produced in an autoclave by carrying out a cure schedule to crosslink the resin. However, for the case of thick thermosets, the manufacturer’s recommended cure (MRC) schedule cannot be followed, once it is generally intended to thin parts. When applied to thick components, the MRC schedule usually results in cures either that are unnecessarily too long or that overheat the material internally, due to the thermoactived and exothermic aspects of the curing reaction associated to the thermal insulating property of the thermoset. This local overheating results in high gradients in the thermoset properties during the cure that may create residual stresses and structural defects, such as bubbles and cracks. To avoid this and find optimal cure schedules, this work simulated the cure process of a thermoset using the finite element software COMSOL Multiphysics and implemented two optimization methods in MATLAB, connected to the simulations via the COMSOL LiveLink for MATLAB. The first method is an authorial conversion rate driven (CRD) strategy based on cure kinetics, which has a single objective: minimize the cure time. The second one is a multi-objective genetic algorithm (GA) with three conflicting objectives: minimize cure time, minimize the gradient of degree of cure after gel point (AGP) and minimize the gradient of temperature AGP, reflecting the existing trade-off between manufacturing speed and product quality. As constraints for both methods, the minimum degree of cure in the final cured part was set as 0.854, in order to achieve the same material properties achieved by the MRC schedule; and the maximum temperature inside the composite during the cure was limited to 155°C, to avoid material degradation. Both methods searched for optimal two-step cure schedules with a constant heating rate of 3°C/min. The decision variables for the GA optimization and CRD strategy were the first and second plateau temperatures and the duration of the first plateau. The free MATLAB-based software package GOSET was used as the basis to execute an elitist GA, with 20 generations and 50 individuals per generation. The thermoset polymer selected for the study was the LY-556 epoxy resin system, cured in a cylindrical geometry with a height of 60 mm and a diameter of 32 mm. It was found that, in comparison to the MRC schedule, the CRD strategy and GA reduced the cure time by almost the same amount: 87% and 88%, respectively; whereas the gradients of degree of cure and temperature AGP were reduced by the GA by 6% and 31%, respectively. Thus, the methods presented in this work were shown to be effective tools to optimize the cure schedule of thermosets, depending on the objective selected.