In this study, the finite element method was applied for analyzing the effect of annealing temperatures on residual stress in the diffusion zone of AZ31 Mg and 6061 Al alloys. The microstructure and mechanical behavior of the diffusion zone were also investigated. Simulations on the annealing of the welded specimens at 200°C, 250°C, and 300°C were conducted. Moreover, experiments such as diffusion bonding and annealing, analysis of residual stress by X-ray diffraction, elemental analysis using an electron probe microanalyzer, and microstructure investigation via scanning electron microscopy were performed for further investigation of the diffusion layers. According to the results of the simulations and experiments, the diffusion layers widen with increasing annealing temperatures, and the results of the simulations are in good agreement with those of the experiments. The microstructure and elemental distribution were the most uniform and the residual stress was the least for samples annealed at 250°C. Thus, 250°C was found to be the most appropriate annealing temperature.
The finite element method (FEM) has many applications in modern industry and technology because of the extensive use of computers [
In addition, FEM is used in plastic forming and can simulate the press forming of aluminum by selecting appropriate forming parameters for the material, such as pressure force and falling speed of the punch [
Recently, many investigations on the welding of Mg/Al alloys have been conducted using FEM, especially on the analysis of residual stress during welding, because magnesium and aluminum alloys are widely used in aerospace, automotive, machine, electrical, and chemical industries owing to their superior properties [
However, most studies have focused on the analysis of residual stress during butt welding, laser beam welding, or friction stir welding [
In this study, AZ31 magnesium alloy and 6061 aluminum alloy were used for diffusion bonding and annealing. Simulations and experiments were performed to analyze residual stress and evaluate the microstructure.
During diffusion bonding and annealing, microstructures of the alloys vary with temperature, and at the same time, thermal stress is induced. If the stress exceeds the elastic limit, plastic deformation occurs. A series of varieties do not emerge individually but interact with each other. The theory for analyzing the interaction is called metallo-thermomechanics, which is the foundation of thermal treatment analysis.
When the AZ31 magnesium alloy and 6061 aluminum alloy are welded by diffusion bonding, diffusion between Mg and Al should be considered. The diffusion phenomenon can be analyzed by Fick’s law and can be expressed by the following equation:
If the energy of the object is represented as
If the Fourier law (
When plastic materials are subjected to loading, they undergo elastic or plastic deformation. Hooke’s law is applicable to three-dimensional stress and strain and can be expressed as
First, the definition of the mixture and the mixing rule are explained. Intermetallic compounds, such as Al3Mg2 and Mg17Al12, are formed during diffusion bonding between magnesium and aluminum alloys. It is assumed that many microstructures are present in the mixture. Further, the mixture contains
If the properties of composition
In the intermetallic compounds of Mg and Al alloys, the ratio of atomic quantity can be expressed as the following equation:
The molar concentration of Mg is expressed as follows:
So the volume ratio of Mg to Al can be expressed as follows:
According to the mixing rule and the volume ratio of Mg to Al, the coefficients of simulations can be calculated. Thermal-stress coupling field of ANSYS was applied to simulate stress at different temperatures during the diffusion process and annealing process. The element type was “Coupled Field, Vector Quad 13,” and the material model was “Structural” and “Thermal.” Temperature conditions were 200°C, 250°C, 300°C, and room temperature (20°C). It was assumed that the interface could not move during the diffusion process. Therefore, a fixed boundary condition was applied to the contact surface, and then the simulations were performed. The model is shown in Figure
Analysis model.
The finite element mesh is shown in Figure
Finite element mesh.
The AZ31 magnesium alloy sheets and 6061 aluminum alloy sheets were successfully welded using vacuum diffusion bonding. The joining temperature was 440°C. After vacuum diffusion bonding, the samples were annealed at 200, 250, and 300°C. After heat treatment, the samples were cooled to room temperature in an electric furnace.
XRD was used to investigate the residual stress distribution of the specimens annealed at different temperatures. Based on the testing principle of residual stress, the X-ray was adjusted. Initially, the specimen was radiated, and the corresponding diffraction angle 2
For the 6061 Al alloy, 2
Furthermore, the microstructure and elemental distribution of the diffusion zone were investigated by SEM and EPMA.
The Mises stress data were obtained after completion of the simulation. The simulation results of stress distribution are shown in Figures
Results of simulations: (a) without annealing and annealing at 200°C (b), 250°C (c), and 300°C (d), previously presented in [
Figure
In this paper, stress distribution along the line crossing the edge of the interface was investigated (the measuring line is shown in Figure
Distribution of residual stress obtained by simulation, previously presented in [
Residual stress is a vector, and in this study, its direction was along the axial direction of the specimens. According to material mechanics, tensile stress is positive, while compressive stress is negative. Therefore, it could be concluded from Figure
The residual stress measured by XRD is shown in Figure
Residual stress of specimens annealed at different temperatures.
The stress of the untreated specimens was about 65 MPa, while that of the specimens annealed at 300°C and 200°C was 51 MPa and 59 MPa, respectively. However, when the specimens were annealed at 250°C, the stress was approximately 44 MPa. During the experiments, the diffraction peak for the (311) plane of Al appeared at a 2
The above results showed that 250°C is the most appropriate annealing temperature. This could be further confirmed by microstructure investigation. The results of the elemental analysis are shown in Figures
Results of elemental analysis, surface scanning: (a) without annealing and annealing at (b) 200°C, (c) 250°C, and (d) 300°C.
Results of elemental analysis, line scanning: (a) without annealing and annealing at (b) 200°C, (c) 250°C, and (d) 300°C.
As shown in Figures
To verify the above results, the microstructures of the specimens annealed at different temperatures were investigated. The microstructures of the joints are shown in Figure
SEM micrographs of joints: (a) without annealing and annealing at (b) 200°C, (c) 250°C, and (d) 300°C; layer A: Al3Mg2, layer B: Mg17Al12, and layer C: Mg-based solid solution.
The diffusion layers, including layers A, B, and C, which were investigated and confirmed to be Al3Mg2, Mg17Al12, and Mg-based solid solutions, respectively, could be clearly observed. Moreover, the width of the diffusion layers increased with increasing annealing temperature. However, the microstructure of the specimens annealed at 250°C was more uniform than that of those annealed at other conditions, thus confirming the results of the elemental distribution analysis.
As shown in Figure
Elemental distribution of Zn, line scanning: (a) without annealing and annealing at (b) 200°C, (c) 250°C, and (d) 300°C.
The following results were obtained from the simulations and experiments: Annealing temperatures have a great effect on the microstructure and elemental distribution. The most appropriate annealing temperature for the diffusion-bonded Mg/Al alloy is 250°C. It is difficult to obtain a sufficiently high-quality diffusion zone by diffusion bonding magnesium and aluminum alloy sheets because of the formation of intermetallic compound layers. However, this study used annealing to improve the microstructure, thus achieving such a diffusion zone. The outcomes obtained by FEM are in good agreement with those of the experiments; thus, the accuracy of FEM for analyzing residual stress during annealing is reliable.
The authors declare that they have no conflicts of interest.
This research work has been partially supported by the grant subsidy of the “Nano Project” for Private Universities: 2011–2014 from MEXT, Japan. This study was also supported by the “Advanced Science Research Laboratory” in Saitama Institute of Technology.