Three-dimensional heat and material flow during friction stir welding of mild steel

Abstract

Three-dimensional viscoplastic flow and heat transfer during friction stir welding of mild steel were investigated both experimentally and theoretically. The equations of conservation of mass, momentum and energy were solved in three dimensions using spatially variable thermo-physical properties and a methodology adapted from well-established previous work in fusion welding. Non-Newtonian viscosity for the metal flow was calculated considering temperature and strain rate dependent flow stress. The computed results showed significant viscoplastic flow near the tool surface, and convection was found to be the primary mechanism of heat transfer in this region. Also, the results demonstrated the strong three-dimensional nature of the transport of heat and mass, reaffirming the need for three-dimensional calculations. The streamlines of plastic flow indicated that material was transported mainly along the retreating side. The computed temperatures were in good agreement with the corresponding experimentally determined values.

Introduction

Friction stir welding (FSW) is a solid-state welding process. The tool usually has a large-diameter shoulder and a smaller threaded pin. The plates to be welded are aligned together and clamped using fixtures. A cylindrical hole is drilled at one end of the workpiece on the centerline and the pin is inserted into the hole, with the shoulder in contact with the top surface of the workpiece. The tool is rotated at high speed as it is moved along the weld centerline. Heat is generated by friction between the tool and the workpiece and by the plastic deformation of the workpiece material. A schematic diagram of the FSW system is shown in Fig. 1. The heat transfer and plastic flow depend on material properties as well as welding variables like the rotational and translational speeds of the tool and the tool design. The complex interactions between the various simultaneously occurring physical processes affect the heating and cooling rates and the structure and properties of the welded joints.

The FSW process was discovered in 1991 at TWI [1]. Since then FSW has been widely studied both experimentally and theoretically to better understand both the welding process and the welded materials. Most of the early quantitative studies were based on heat conduction and ignored the plastic flow near the tool [2], [3]. Several heat generation models were proposed to quantitatively describe the frictional heat generation at the interface between the tool and the workpiece and the internal heat generation within the workpiece due to plastic deformation [4], [5]. Several researchers [6], [7] investigated the partitioning of heat between the tool and the workpiece for the FSW of different engineering alloys. Khandkar et al. [8] developed a three-dimensional thermal model where the heat generation was modeled based on experimentally measured torque distribution. They adjusted the bottom heat transfer coefficient to achieve good agreement between the computed and the measured temperatures. Although the heat conduction models provided important insight about the FSW process, these initial models ignored convective heat transfer due to viscoplastic flow of metals.

Work on the development of rigorous models of heat transfer in FSW considering materials flow is just beginning. Seidel and Reynolds [9] developed a two-dimensional thermal model based on laminar, viscous and non-Newtonian flow around a circular cylinder. They observed that significant vertical mixing occurred during FSW, particularly at low values of welding speed to rotational speed ratios. This fact indicates the need for three-dimensional models. Colegrove and Shercliff [10], [11] used a commercial CFD software, FLUENT, to develop a three-dimensional heat and material flow model during friction stir welding of 7075 Al alloy. They used the thermal and materials flow model to investigate tool design. Interestingly, the different tool designs did not result in any significant changes in either the heat input or the power requirement. In another study [12] they examined the effect of tool orientation on the traversing force.

Smith et al. [13] experimentally determined viscosity as a function of shear rate and temperature for the AA 6061-T6 alloy, which was then incorporated into a three-dimensional coupled heat and material flow model for the FSW of 6061 aluminum alloy. Ulysse [14] modeled the effects of tool speeds, both rotational and linear, on forces and plate temperatures during FSW of thick aluminum plates, based on a three-dimensional viscoplastic model. Most recently, Nandan et al. reported results of a three-dimensional material flow and heat transfer model during FSW of 6061 aluminum alloy [15] and 304 austenitic stainless steel [16]. They calculated the temperature fields, cooling rates, plastic flow fields and the geometry of the thermomechanically affected zone (TMAZ) using spatially variable heat generation rates, non-Newtonian viscosity as a function of local strain rate and temperature, and temperature-dependent thermal conductivity, specific heat and yield stress. The computed temperature fields and TMAZ agreed well with the corresponding independent experimental data.

Although several numerical models of FSW of aluminum alloy have been reported in the literature, most of these were not concerned with the FSW of steel. There are a few exceptions. Zhu and Chao [17] proposed a three-dimensional thermal model without considering plastic flow for 304L stainless steel. Two-dimensional steady-state heat transfer and fluid flow near the tool pin was modeled by Cho et al. [18] for the FSW of 304L stainless steel. They used a simplified Hart’s model [19] to calculate the flow stress and non-Newtonian viscosity. Isotropic strain hardening was included in the finite element solution procedure. The workpiece temperatures were computed assuming various tool temperatures and heat transfer coefficients. They found that higher tool temperatures and heat transfer coefficients resulted in higher workpiece temperatures. The experimental and the computed results indicated that the temperatures were about 100 K higher on the advancing side than on the retreating side.

Here we present a detailed numerical analysis of three-dimensional material flow and heat transfer during FSW of mild steel. In particular, we examine the temperature fields, cooling rates and plastic flow fields by solving the equations of conservation of mass, momentum and energy in three dimensions with appropriate boundary conditions. The computed values of strain rates, viscosity, velocities and temperatures during FSW of steel are compared with the corresponding values typically obtained during the FSW of aluminum alloys. The nature of materials flow around the pin is understood through the examination of streamlines. The model considers spatially variable heat generation rates, non-Newtonian viscosity as a function of local strain rate, temperature and the nature of the material, and temperature-dependent thermal conductivity, specific heat and yield stress. Numerically computed temperature fields and the total torque on the tool were compared with the corresponding experimentally measured values.