Inverse Optimal Design of the Continuous Sheet Quenching Process

"An inverse design method is developed to obtain the optimal cooling conditions for the continuous quenching of precipitation hardenable sheet alloys to achieve the required yield strength. The yield strength of a precipitation hardenable alloy is obtained by allowing solute to enter into solid solution at a proper temperature and rapidly cooling the alloy to retain the solute in the solid solution. An aging process may be needed for the alloy to develop the final mechanical properties.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 specified and the sheet thermal profile at the exit of the quenching chamber can also be specified. 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 aluminum sheet quenching problem is presented to demonstrate feasibility of the inverse design method.IntroductionQuenching is a critical step in metal production to achieve desired material properties, such as yield strength, hardness, etc., for precipitation hardenable alloys. In most cases, rapid quenching from the solution heat treatment temperature is necessary to obtain the required material properties, but rapid quenching may cause other problems such as excessive distortions of the quenched materials.In a solution heat treatment, the alloy is heated to a suitable temperature, held at that temperature to allow the soluble alloying elements to enter into the solid solution, and cooled rapidly (quenching) to retain the alloy elements in the solid solution. An aging process, which controls precipitation of fine particles at room (natural aging) or elevated temperatures (artificial aging), is generally followed after the quenching process to develop the final mechanical properties of the heat treated alloys."