- Original Article
- Open Access
Numerical Study on the Stress–Strain Cycle of Thermal Self-Compressing Bonding
© The Author(s) 2018
- Received: 6 November 2016
- Accepted: 6 August 2018
- Published: 20 August 2018
Thermal self-compressing bonding (TSCB) is a new solid-state bonding method pioneered by the authors. With electron beam as the non-melted heat source, previous experimental study performed on titanium alloys has proved the feasibility of TSCB. However, the thermal stress–strain process during bonding, which is of very important significance in revealing the mechanism of TSCB, was not analysed. In this paper, finite element analysis method is adopted to numerically study the thermal elasto-plastic stress–strain cycle of thermal self-compressing bonding. It is found that due to the localized heating, a non-uniform temperature distribution is formed during bonding, with the highest temperature existed on the bond interface. The expansion of high temperature materials adjacent to the bond interface are restrained by surrounding cool materials and rigid restraints, and thus an internal elasto-plastic stress–strain field is developed by itself which makes the bond interface subjected to thermal compressive action. This thermal self-compressing action combined with the high temperature on the bond interface promotes the atom diffusion across the bond interface to produce solid-state joints. Due to the relatively large plastic deformation, rigid restraint TSCB obtains sound joints in relatively short time compared to diffusion bonding.
- Thermal self-compressing bonding
- Locally non-melted heating
- Thermal elasto-plastic stress–strain
- Atom diffusion
- Solid-state bonding
- Finite element analysis
With the rapid development of aviation industry, the requirements of excellent performance, long life and high reliability for both civil and military aircraft become increasingly strict [1, 2]. To satisfy these requirements, advanced structural materials, such as composite materials, titanium alloys and aluminum alloys, with high specific strength, high specific stiffness and other perfect mechanical and physical properties are developed [3–5]. Meanwhile, welding technique, as an inevitable process for aeronautical manufacturing, also meet the challenge of achieving outstanding welding and joining quality to fulfill the increasingly strict requirements.
Fusion welding process uses the heat source such as arc, laser, and electron beam to heat and melt the materials to be joined. Although perpetual joint with acceptable tensile strength can be attained in some cases, fusion welding still has inherent disadvantages. Due to the influence of high temperature thermal cycle by centralized heat source during fusion welding, solidification problems, such as as-cast microstructure and weld defects are always occurred in the weld seams as reported by Kou , Li et al.  and Chen et al. . This non-homogeneous microstructure combined with weld defects and residual stresses is probably harmful to the mechanical performance of fusion joints, especially to the fatigue property [8–10]. Thus, time-consuming and costly post-weld heat treatment has to be adopted sometimes to improve the comprehensive mechanical properties of fusion joints [11–13].
Compared with fusion welding, solid-state welding method, such as diffusion bonding , linear fraction welding  and friction stir welding , has many outstanding advantages. The first one is solid state joint is attained, which avoid the as-cast microstructure and metallurgical defects such as pores and cracks emerged in the fusion joints. Therefore, sound joints with excellent comprehensive mechanical properties are attained. Furthermore, solid-state welding method, especially diffusion welding, can be used to join dissimilar and refractory materials that cannot be welded by fusion welding process [17, 18].
At present, with EB as the non-melted heat source, previous experimental study performed on titanium alloys has proved the feasibility of rigid restraint TSCB . Sound solid-state joints with homogeneous microstructure and good comprehensive mechanical properties were obtained. A comparative study on the microstructure and mechanical properties of the Ti6Al4V joints produced by Electron beam welding and rigid restraint TSCB shown that rigid restraint TSCB joint has better combination of strength and ductility than electron beam welded joint . Meanwhile, rigid restraint TSCB also presented the feasibility of joining dissimilar materials . However, the thermal stress–strain process during bonding, which is of very important significance in revealing the mechanism of TSCB, was not analysed systematically. In this study, finite element analysis method was adopted to numerically study the distributions and developing histories of temperature, stress and strain during rigid restraint TSCB of Ti6Al4V titanium alloys. And then, the bonding mechanism and characteristics of rigid restraint TSCB were investigated.
2.1 Geometry Model and Mesh Generation
2.2 Materials Properties
2.3 Thermal Analysis
Parameters employed in the thermal analysis
Beam voltage Ub (kV)
Beam current Ib (mA)
Heating time tH (s)
Heat efficiency η
Length of the heat source l (mm)
The effective radius of the heat source R (mm)
Fourier heat conduction equation was used to describe heat propagation. In addition, because the bonding process was carried out in a vacuum, only the heat loss resulting from radiation were taken into account in the model.
2.4 Mechanical Analysis
Sequentially coupled thermal and elasto-plastic analyses were employed in present model. Results of calculated temperature field were employed as input conditions for the next mechanical analysis. The material behavior of Ti6Al4V alloy were assumed to be governed by thermal elasto-plastic theory. The von Mises yield criterion and the associated flow rule were adopted in the current work.
Rigid restraint is accomplished through the use of stainless steel plates restrained by a serious of bolts of welding fixture, so the displacement along y direction of the side face S1 of the restraint was defined as 0, while with respect to the bond interface the symmetry condition is considered. Other in-plane and out-of-plane displacement boundary conditions are imposed to prevent the rigid movement and rotation of the specimen and rigid restraints as well.
2.5 Verification of Finite Element Model
It can be seen that slight differences exist in the values between experimental and calculated results. Considering the existence of testing error, it can be suggested that the calculated result is in reasonable agreement with the experimental one. Therefore, present model is reliable to analysis the thermal stress–strain process of rigid restraint TSCB.
3.1 Thermal Cycle and Temperature Distribution during Rigid Restraint TSCB
Tensile properties of base metal and present joint
Ultimate tensile strength σb (MPa)
Elongation δ (%)
3.2 Thermal Stress–strain Evolution during Rigid Restraint TSCB
In the earlier period during heating process, longitudinal and transversal compressive stresses, σx and σy, respectively, are increased quickly by virtue of the fast enhanced thermal compressive effect with the increase of heating time. At the moment of t = 48.7 s, transversal compressive stress is increased to the peak with the value of − 244.3 MPa which is equal to the yield strength of materials at corresponding temperature; and thus plastic deformation is occurred. From this time onwards, compressive stress is decreased gradually with the increase of heating time due to the decreased strength of materials along with the further improvement of temperature. Finally, transversal stress is approximately − 63.2 MPa at the end of heating time. However, the transversal plastic deformation is increased gradually during the whole heating period. During the following cooling process, since the temperature of bond interface decreases more rapidly than that of the region nearby, bond interface is stretched by the surrounding metals. And then the transit compressive stress is transformed to tensile stress. During further cooling process, the longitudinal and transversal tensile stresses on the bond interface increased gradually. With regard to normal stress, the value is very small during the whole bonding process. However, the normal plastic deformation is notable; formed during the whole bonding process and the value of it is almost equal to that of transversal compressive plastic deformation. The whole stress–strain process is under the plane stress state.
3.3 Bonding Mechanism of Rigid Restraint TSCB
The heat source in present experimental of rigid restraint TSCB is same to electron beam fusion welding. However, the bonding mechanism of rigid restraint TSCB is notably different from electron beam fusion welding which is dependent on the solidification and crystallization of the welding pool to attain permanent joints while no materials is melted during rigid restraint TSCB. According to above numerical analysis, it can be seen clearly that transversal compressive stress and plastic deformation are developed on the entire bond interface during heating period; meanwhile temperature of materials adjacent to bond interface is high. And thus the requirements of pressure and temperature for atom diffusion are met. Notable atom diffusion between butt-welded specimens is occurred, which promote the formation of permanent solid-state joints. On the other hand, unlike diffusion bonding relied on external force, present method utilizes self-established internal thermal elasto-plastic stress–strain field to promote the atom diffusion between butt-specimens. Therefore it is a thermal self-compressing bonding process.
On the basis of above analysis, it is found that two requirements are needed in order to produce this kind of atom diffusion effect during rigid restraint TSCB. The first one is the internal thermal elasto-plastic stress–strain field established by localized non-melted heating which makes the bond interface subjected to long time compressive action during heating. The other one is that materials at the bond interface should be heated to a high temperature as the atom diffusion coefficient is large at elevated temperature.
In addition, it can be seen that the dwell time over high temperature is short as shown in Figure 6; meanwhile the whole bonding time is only 300 s. Compared to diffusion bonding which also relies on atom diffusion effect, the bonding time of rigid restraint TSCB is relatively short. The main reason may be the relatively large plastic deformation occurred on the bond interface during TSCB process which significantly improves the atom diffusion between materials to be bonded. Therefore, sound solid-state joints can be attaint in a short time by rigid restraint TSCB.
A three-dimensional model based on ABAQUS finite element analysis software was built to analyse the thermal stress–strain process during rigid restraint TSCB of Ti6Al4V titanium alloys.
Due to the localized heating, a non-uniform temperature distribution is formed during rigid restraint TSCB, with the highest temperature existed on the bond interface.
The high temperature materials adjacent to the bond interface is restrained by surrounding cool materials and rigid restraints, and thus an internal elasto-plastic stress–strain field is developed by itself which makes the bond interface subjected to thermal compressive action. This thermal self-compressing action combined with the high temperature on the bond interface promotes the atom diffusion across the bond interface to produce solid-state joints.
In comparison with diffusion bonding, the bonding time of rigid restraint TSCB is short due to the relatively large plastic deformation at the bond interface during rigid restraint TSCB.
Y-HD and QG were in charge of the whole trial; Y-HD wrote the manuscript; JT and BW assisted with sampling and laboratory analyses. All authors read and approved the final manuscript.
Yun-Hua Deng, born in 1987, is currently an engineer at Aeronautical Key Laboratory for Welding and Joining Technologies, AVIC Beijing Aeronautical Manufacturing Technology Research Institute, China. He received his PhD degree on materials processing engineering from Beihang University, China, in 2016. His research interests include solid-state bonding, brazing, electron beam welding and numerical simulation.
Qiao Guan, born in 1935, is currently an academician of the Chinese Academy of Engineering. He received his PhD degree from Bauman Moscow State Technical University, Russia, in 1963. His research interests include aeronautical non-conventional welding/joining techniques, welding mechanics, welding structures and additive manufacturing.
Jun Tao, born in 1977, is currently a senior engineer at Aeronautical Key Laboratory for Welding and Joining Technologies, AVIC Beijing Aeronautical Manufacturing Technology Research Institute, China. He received his PhD degree from Harbin Institute of Technology, China, in 2006. His research interests include fraction welding and numerical simulation.
Bing Wu, born in 1979, is currently a senior engineer at Science and Technology on Power Beam Process Laboratory, AVIC Beijing Aeronautical Manufacturing Technology Research Institute, China. She received her master degree from Tianjin University, China, in 2004. Her research interests include electron beam welding and integrity assessment of welded structures.
The authors declare that they have no competing interests.
Supported by National Natural Science Foundation of China (Grant No. 51705491).
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