Paper Title
Modeling and Optimization of Submerged Friction Stir Welding of AA 2219-T6 Alloy

In many fields, such as the aerospace industry, acquiring high-quality weld is considered challenging with conventional joining techniques. This issue appears at some materials, especially those that have low melting temperature. Friction stir welding (FSW) is a promising joining technique for welding lightweight materials. FSW is an environmentallyfriendly technique, which involves versatility and energy efficiency used to generate a good collection of mechanical properties and microstructure. This process is an innovative solid-state joining technique. FSW processes were first applied on aluminum alloys because of their low melting temperatures; and were found to be an effective technique. Submerged Friction Stir Welding has been conducted successfully in joining different alloys. The objective of the present paper is to develop a model, optimize the submerged FSW process, and compare with experimental data published in the literature. The optimization problem is formulation using the Lagrange multiplier method and the optimality conditions are verified using Karush-Kuhn-Tucker (KKT) theorem. Keywords- KKT, Karush-Kuhn-Tucker, FSW, Friction Stir Welding, Underwater, UFSW, AA 2219-T6, Aluminum Alloys.