Numerical analysis of both front- and back-side deformation of fully-penetrated GTAW weld pool surfaces

The profile of the free surface deformation of a weld pool gives information about the extent of penetration depth, and weld bead appearance. Calculating the surface deformation of the weld pool is of great significance to the task of welding process modeling and simulation. Two nonlinear partial differential equations for describing both front- and back-side deformation of weld pool surfaces are derived in detail to make the physical terms and the sign of Lagrange multiplier in two equations be with one accord. Under some practical welding conditions, the secant method is used to determine the value of Lagrange multiplier, and the coupled equations are numerically solved to calculate both front and back free surfaces' deformation of fully-penetrated three-dimensional weld pools. The influence of the welding current on the surface depression of weld pool is examined. It shows that the predicted weld pool deformation is in agreement with the measurements.