Inverse optimal design of cooling conditions for continuous quenching processes

This paper presents an inverse design methodology to obtain a required yield strength with an optimal cooling condition for the continuous quenching of precipitation hardenable sheet alloys. The yield strength of a precipitation hardenable alloy can be obtained by allowing solute to enter into solid solution at a proper temperature and rapidly cooling the alloy to hold the solute in the solid solution. An aging process may be needed for the alloy to develop the nal mechanical property. The objective of the design is to optimize the quenching process so that the required yield strength can be achieved. With the inverse design method, the required yield strength is speci ed and the sheet thermal pro le at the exit of the quenching chamber can also be speci ed. The conjugate gradient method is used to optimize the cooling boundary condition during quenching. The adjoint system is developed to compute the gradient of the objective functional. An aluminium sheet quenching problem is presented to demonstrate the inverse design method