Since in 1991, Friction Stir welding (FSW) was invented by TWI in UK, it has been researched for decades and widely applied in the manufacturing industry including aerospace industry. For normal fusion welding, flaws like porosity and solidification or liquidation cracking are inevitable. However, friction stir welding is a solid-state process, which avoids the normal defects of fusion welding. It makes the defect-free welding of metals like Al 2xxx and 7xxx become possible, which is widely used in the aerospace industry.Even if FSW has achieved mature applications in the manufacturing industry, there are still many issues to be discussed, one of which is to study how to build a mathematical model for the coupled thermal and mechanical phenomena. Most of researches remain on a numerical level, which is often case-specific. People from the industry find proper parameters by trial and error. Thus, the presentation will focus on building a scaling model of the mechanical and thermal process, which will make prediction of state variables (e.g. maximum temperature) possible. It will also help people understand the process of FSW better and provide more information for improvement of welding process to avoid defects in the future.
In order to make FSW process be described by the existing physical formulas, four assumptions are introduced, which is also proved to be reasonable later.1)The pin travels slowly along the welding direction and thus can be considered as a steady-state, slow-moving heat source. 2)The amount of incoming mass is much less than the mass rotated around the pin.3)The thickness of shear layer is small.4)The maximum temperature does not depend on the shoulder. Based on above assumptions, FSW process can be considered a one-dimension problem and the thermal effect of the shoulder is weak. For the temperature field in the shear layer, a 1D heat conduction equation with the heat generation formula from plastic deformation can describe it well. A constitutive equation transferred from the hot deformation mechanism is applied to describe the relationship between the shear rate, temperature and shear stress, which is a coupled thermal and mechanical equation. For heat conduction outside the shear layer, we use Rothental’s solution of a moving heat source on the thin plate. The solution calculates the temperature of different positions relative to the heat source. After investigation, we have four equations (three differential equations) with four independent variables. For avoiding solving any differential equation, scaling analysis is applied to all the equations. It allows us to have four linear equations describing the mathematical relationship between four characteristic values of FSW process, which includes shear stress(toque), thickness of the shear layer, generated heat and maximum temperature. Simple mathematical solutions are derived from those linear equations, which predict values of those characteristic variables. We collected data of FSW from other literatures as much as possible and compare them with the predicted value from those derived equations. For the prediction of maximum temperature, the model overpredicts it by approximately 34%. The prediction of torque is underpredicted by approximately 36% and the thickness of shear layer is underpredicted by around 30%. Correction factors can be applied as a function of four assumptions and make estimations much closer to real data. In order to verify self-consistency of the model, we plot the prediction values against those assumption values and find those assumptions are valid in most cases. However, there is still some violations of assumptions and will be discussed in the future work. By using the scaling method, the coupled behavior of heat and metal flow during FSW process is modeled as four closed-form linear equations. Those equations are able to predict the shear stress, the thickness of the shear layer, the maximum temperature and the volumetric heat generation, without measured temperature or torque. After comparing the estimated values and experimental data, we can conclude that the scaling model achieve an excellent performance predicting the thermal and mechanical properties during FSW process. It catches the right order of magnitude and trends without calibration. This model will provide a powerful method to evaluate the welding parameters of FSW and help researchers have a deeper understanding of friction stir welding. In the future, it will be combined with mathematical models related to the welding defects of FSW and helpful to improve the welding quality.