Quench Process Modeling and Optimization

"We optimize continuous quench process parameters to produce a desired precipitate distribution in aluminum alloy extrudates. To perform this task, an optimization problem is defined and solved using a standard nonlinear programming algorithm. Ingredients of this algorithm include a cost function, constraint functions and their sensitivities with respect to the process parameters. These functions are dependent on the temperature and precipitate size which are obtained by balancing energy to determine the temperature distribution and by using a reaction-rate theory to determine a discrete precipitate particle size distribution. Both the temperature and the precipitate models are solved via the finite element method. Since we use a discrete particle size model, there are as many as 105 degrees-of-freedom per finite element node. After we compute the temperature and precipitate size distributions, we must also compute their sensitivities. This seemingly intractable computational task is resolved by using an element-by-element discontinuous Galerkin finite element formulation and a direct differentiation sensitivity analysis which allows us to perform all of the computations on a PC.1 IntroductionThis work addresses the need for an integrated design capability that links microstructure evolution to the process parameters. It is motivated by the manufacture of lightweight aluminum-alloy extrusions for use in automotive structures. Aluminum alloys offer obvious benefits, however, care must be taken to manufacture favorable microstructures that ensure acceptable structural performance. For example, the manufacturing process for 6000-series components involves hot extrusion of cast aluminum billets followed by either an air or water quench process. The bill~t's initial grain structure is dramatically altered during extrusion by massive mechanical deformations and recrystallization processes. The microstructure continues to evolve during the quench, as complex chemical processes determine the formation of precipitates. The control of the precipit'ate size distribution is vital. Indeed, large precipitates located on grain boundaries serve as crack initiation sites which adversely effect structural crash· worthiness."