Modeling of rotary friction welding process based on maximum entropy production principle

Abstract

The interfacial transition point isolated by maximum entropy production principle (MEPP) was used to construct a two-dimensional (2D) finite element (FE) model of continuous-drive rotary friction welding (RFW) with GH4169 superalloy. The transition point from sliding friction to shear friction was calculated based on the equal entropy of these two kinds of heat liberation mechanisms at this point. The FE model was shown valid by the consistency of comparison between simulation and experiment. The simulation issued an interfacial distribution of non-uniform heat intensity that determined the corona bond, which corresponded to higher temperature zone over the transition temperature. The influences of linear speed and friction pressure on welding time were examined, which showed that a shorter welding time could be acquired when the linear speed was about 1.96 m/s and the friction pressure is larger.

Introduction

Rotary friction welding (RFW) is a solid state welding method that one workpiece rotates at a constant speed while the other keeps stationary under an axial force. When sufficient temperature has arrived at the friction interface, the viscoplastic metal is ejected from the weld region and the coalescence of metal is produced by solid phase bonding [[1], [2], [3], [4]]. During the welding process, heat liberated by relative friction motion contributes to softening the narrow region in the vicinity of the interface and provides permanent bonding energy. Thus, the insight into the mechanisms of heat liberation and evolution of temperature field in welding joint becomes a stringent and significant requirement.

Considering the complicated thermal-mechanical coupling involved in the welding process, it is difficult to explore the temperature field evolution and plastic deformation in the internal weld joint [5]. Thus a feasible and simplified way has been adopted by researchers to investigate the friction behavior on the welding region. At an earlier time, Rykalin et al. [6] and Vill [1] established the thermal analytical model by deeming the heat liberation as a constant sliding friction. It revealed the inhomogeneity of interfacial heat intensity which has been adopted by many investigators [[7], [8], [9], [10]] However, the ignorance of shear friction at high temperature constrained its applicability.

The experimental study provided a theoretical basis for the friction behavior of the interface. Hasegawa et al. [11] and Kimura et al. [12,13] demonstrated that the local dominated friction mechanism gradually transferred from sliding friction to shear friction as the process going on. The friction mechanism at different radial position was determined by temperature and strain rate. Therefore, how to define the local transition of these two friction mechanisms has become a critical problem in the establishment of heat liberation modeling.

Originally, Moal and Massoni [14] [Moal, 1995 #520] proposed that the evolution of shear stress was dependent on rotational speed, which provided a new idea for the distinction of friction behavior. Then, in 2008, Maalekian et al. [15] proposed a sliding-shear model to describe the friction mechanism in orbital friction welding (OFW). While the friction stress was smaller than the shear yield stress, pure sliding friction according to Coulomb’s friction law was in dominant. Otherwise, full plasticity at the interface was presented and the entire heat liberation came from shear friction. Maalekian et al. [15] assumed the transition temperature at about 0.6T_m (T_m is the melting temperature), which falls around the dynamic recrystallization temperature. However, this criterion of transition temperature was only dependent on the nature of the material and temperature, which ignored the influence of heat liberation inhomogeneity at the interface. To date, this criterion was widely recognized as a reasonable theory and accepted by many researchers [[16], [17], [18], [19]]. Zhang et al. [16] built a three-dimensional (3D) finite element (FE) model in which the heat liberation was kept two different friction mechanisms. Li et al. [17] and Wang et al. [19] constructed the heat flux boundary condition by considering the coexistence stage of two friction mechanisms. More recently, Shailesh et al. [18] presented a thermomechanical model of thixocast A356 aluminum alloy to predict temperature field and optimize the process parameters. Yet, there was short of a method to characterize the transition point based upon comprehensive consideration of the process parameters.

The transition point, which indicates the heat liberation mechanism from sliding friction to shear friction, is resulted from the accumulation of sliding friction process. As one may have noticed that RFW is a severe deformation process, the friction mechanism was determined by process parameters, which brought greater deviation in simulation. Thus the state variable entropy is introduced in RFW to handle the comprehensive effect of strain rate, stress, temperature and so on [19]. The second law of thermodynamics indicates that any irreversible process develops always in the direction of increasing entropy. So Maximum Entropy Production Principle (MEPP) is introduced into RFW process to judge the thermodynamic state of friction welding joint at different time and the evolution of the process in the next step [20,21].

This paper focused on developing an accurate FE model of GH4169 in RFW to simulate the thermal-mechanical coupling process using DEFORM software, in which the interfacial transition point was calculated based on the equal entropy of sliding friction and shear friction. The validation of the model was conducted by comparing simulation with experiment. Based on the simulation, the evolution of joint morphology (i.e., corona bond [22]), which means the full plastic deformed zone under thermal-mechanical coupling, was acquired according to temperature field. The effects of linear speed and friction pressure on welding time was also investigated. This study focuses on the construction of more accurate FE model to provide an effective method for RFW research. Thus unlike other study [23,24], the evolution of microstructure and mechanical property are not discussed here.