| Abstract Scope |
Sofía Salazar Torres, Patricio F. Mendez
Email: sofiaisa@ualberta.ca
Key Words:
Friction stir welding, High-speed Deformation, Temperature profile, Scaling Analysis, Shear layer
Abstract
The present work presents an improvement in the coupled model of heat transfer and plastic deformation in friction stir welding (FSW). The study develops a heat transfer balance model to understand the interaction between the pin-shoulder tool and the base plate. To develop a mathematical model and establish its correlation with reality, it is crucial to have an understanding of thermal energy transfer and material deformation during the welding process. The model generated allows for an understanding of the problem in one dimension, the temperature profile along the base plate, the shear rate relation with the temperature, and the constitutive behavior in the shear layer. By focusing on four common conditions of FSW, consisting of the relatively slow translation movement of the tool, high rotation velocities, a thin shear layer, and the influence of the shoulder on the maximum temperature, four equations were derived to explain the FSW process. The results are a set of updated closed-form expressions for the maximum temperature, the thickness of the shear layer, the shear stress around the pin, torque and thermal effect of the shoulder, applicable to all metals. A relation between the differences of temperature reached in the plate, the Zenner-Hollomon constants, efficiency of the process, speed, Bessel function and Peclet number was generated for different materials typically used in FSW. These relationships can be used to study the influence of torque on the temperature attained in the process, estimate the thickness of the shear layer according to the parameters established in the process, and the temperature necessary to plastically deform the materials. This model is important from both an academic and industrial perspective, as it improves our understanding of FSW in terms of heat transfer, physics, and the relation between the plastic deformation temperature and the melting temperature.
The predictions from this model are verified against a comprehensive database of published experiments, which include the variables of rotational and travel speed, the radius of the pin and shoulder, the material being welded, and its properties such as the specific heat, plate thickness, density, thermal conductivity, melting temperature, RPM, the height of the shoulder. Other considerations were taken such as the heat losses on top and under the plate, the Peclet number, Zenner-Hollomon constants, the preheat temperature given by the shoulder, and the efficiency. All the material properties were revisited before the calculations were made.
To assess the accuracy of the model, the results obtained from experiments were compared to the ones calculated from the model. The ratio of these two sets of results was plotted against the assumptions used to formulate the model, enabling precision analysis. Most of the experimental results grouped closely around a value of one, indicating that the model was successful in predicting the experimental outcomes. In the maximum temperature, the model tended to underestimate the estimation by approximately 7%. The primary objective is to minimize the discrepancy between the model and experimental results.
In conclusion, the study provides valuable insights into the heat transfer and thermodynamics involved in the FSW process. The development of a heat transfer balance model has allowed for a better understanding of the interaction between the pin-shoulder tool and the base plate. The generated mathematical model, along with the obtained equations and relationships, has provided a deeper insight into this welding technique, including the maximum temperature attained, torque, shear layer thickness, heat transfer, and the influence of different materials on the process. This model has proven to be accurate in predicting experimental outcomes with a few minor discrepancies. Overall, this model can be useful for both academic and industrial purposes to improve the understanding of FSW. |