Non-Dimensional Characterization of the Friction Stir/Spot Welding Process Using a Simple Couette Flow Model Part I:Constant Property Bingham Plastic Solution

摘要

A simplified model for the material flow created during a friction stir/spot welding process has been developed using a boundary driven cylindrical Couette flow model with a specified heat flux at the inner cylinder for a Bingham plastic material.Non-dimensionalization of the constant property governing equations identified three parameters that influence the velocity and temperature fields.Analytic solutions to these equations are presented and some representative results from a parametric study(parameters chosen and varied over ranges expected for the welding of a wide variety of metals)are discussed.The results also provide an expression for the critical radius(location of vanishing material velocity)as functions of the relevant non-dimensional parameters.A final study was conducted in which values for the non-dimensional heat flux parameter were chosen to produce peak dimensional temperatures on the order of 80% of the melting temperature for a typical 2000 series aluminum.Under these conditions it was discovered that the ratio of the maximum rate of shear work within the material(viscous dissipation)to the rate of energy input at the boundary due to frictional heating,ranged from about 0.0005 % for the lowest pin tool rotation rate,to about 1.3 % for the highest tool rotation rate studied.Curve fits to previous Gleeble data taken for a number of aluminum alloys provide reasonable justification for the Bingham plastic constitutive model,and although these fits indicate a strong temperature dependence for critical flow stress and viscosity,this work provides a simple tool for more sophisticated model validation.Part II of this study will present numerical solutions for velocity and temperature fields resulting from the non-linear coupling of the momentum and energy equations created by temperature dependent transport properties.