1 Introduction

Linear friction welding (LFW) is a solid state joining process in which two flat-edged components are joined together using a relative reciprocating motion under axial (compressive) force [1, 2]. The process is divided into four distinct phases, which include the initial phase, the transition phase, the equilibrium phase and the deceleration phase [3, 4]. The temperature during the process does not reach the melting point of the parent material (PM), thus, solidification problems (e.g., hot cracking, porosity, segregation) are avoided [3, 5]. A number of additional advantages such as no spatter, no need for filler material and gas protection [6-8], have made LFW an important technology to manufacture and repair blisks in aeroengines [9, 10]. Furthermore, LFW has been demonstrated to be effective in welding similar or dissimilar joints of titanium alloys, steels, nickel alloys and aluminum alloys [11-14]. In particular, titanium alloys, such as Ti6Al4V (Ti-64), with excellent integrated performance, are one of the most important materials in aeroengines [15].

Residual stresses are expected to develop at the end of process as a result of the large deformations during LFW. The thermal strain results in steep temperature gradients on the weld line. The significance of residual stresses is that they may greatly influence the material and component performance through various mechanisms: ductility exhaustion, creep rupture, etc. [2]. Tensile residual stresses may reduce the performance or cause failure of components as they affect fatigue strength, creep or environmental degradation. Compressive residual stresses, on the other hand, are mostly beneficial at the expense of reduced bucklingloads. Therefore, it is important to identify the residual stress fields generated in LFW.

At present, a few papers about residual stresses in LFW have been published, but most of these papers focused on experimental measurements rather than numerical simulations [16-20]. Frankel et al. [19] studied the levels of residual stresses in the vicinity of LFW in Ti-64 and Ti6Al2Sn4Zr2Mo (Ti-6242). Measurements were taken using high energy synchrotron X-ray diffraction and were compared to those destructively made using the contour method. The peak tensile residual stresses introduced by the welding process were found to be greater for Ti-6242 (750 MPa) than for Ti-64 (650 MPa). The weld residual stresses were found to be the largest in the non-reciprocating direction (y) with those parallel to the reciprocating direction (x)30%smaller.The stresses normal to the weld (z direction) were found to be much lower still. Romero et al. [20] investigated the influence of forging pressure on the microstructure, microhardness, and residual stress development in LFWed Ti-64. Energy dispersive synchrotron X-ray diffraction scans were performed in the three principle directions across the welds to characterize the residual stress development. The experimental data identified a strong relationship between forging pressure and residual stresses and weld microstructure, whereby the residual stresses, the width of the weld region, and the α-Ti texture strength in the weld region generally decreased with the increase of forging pressure. Turner et al. [3] investigated the sensitivity of predicted residual stress to the applied forge load and compared them with measurements with X-ray diffraction methods. It was found that only small changes in residual stress were predicted for large changes in forge load, supporting the hypothesis that the welding process is only of secondary importance to residual stress formation, after the cooling process.

As a result of the operating requirements of aero engines and the importance of stress on component lifetime estimation, it is of considerable interest to investigate the magnitude and the influence factor of the residual stress from LFW. However, previous investigations of the residual stress development in Ti-64 welds using measuring means, such as, neutron and synchrotron X-ray diffraction is difficult to reach certain accuracy. Therefore, in this study in order to further understand the residual stresses in LFW joints, we investigated the effects of applied forging pressure and temperature field at the end of the oscillating stages on the residual stresses within the joints using the numerical method.

2 Numerical methods 2.1 Finite element model

According to research on residual stresses of Ti-64 after LFW by Frankel et al. [19], a coupled thermomechanical model was built with ABAQUS [11], as shown in Fig. 1, with some simple flash formed around the weld. The whole specimen had a length of 140 mm, width of 13 mm and height of 26 mm. For meshing and constraint reasons, the specimen was partitioned into two regions, where the center region has a meshing size of 1 mm and the other region has a graduated meshing size. The meshing was conducted with 8-node hex elements with coupled temperature and displacement, reduced integration and hourglass control. The model consisted of 22 698 elements in total.

The ABAQUS/Standard package was used to model the LFW process [11]. To simplify the calculation, in this model, three steps were set up: the first one was for forging at the end of movement for 10 s; the second one was for cooling for 100 s without pressure where the sample was clamped; and in the third one the clamp was released after 10 s. The forging pressures used in the model are based on previous experiments, which are 60 MPa, 120 MPa and 180 MPa, respectively. To simplify the simulation, the friction process was omitted and an initial temperature field was applied to the weld with a simple distribution as a function of distance from the weld interface as used previously [21] (see Eq. (1): Gaussian variance, σ, is 0.003 5; constant, a, is 10.20). Temperature changes were along the z-direction and the maximum temperature at the interface was calculated to be 1 183 ℃.

During LFW, different welding parameters, e.g., amplitude, frequency and friction time, result in different temperature fields at the end of the oscillating stages (different temperature gradients and high-temperature zone). As it is known, for the Gaussian distribution, a decrease of variance, σ, increases the concentration of the distribution. Taking into account the effect of temperature field at the end of the oscillating stages on the residual stresses within the joints, we changed the σ to 0.002 5 and 0.004 5. Meanwhile, based on previous simulation results [22], the constant, a, in Eq. (1) was changed to ensure that the maximum temperature at the interface kept 1 183 ℃. The values for different parameters are listed in Table 1. The temperature field at the end of oscillating stages used in the finite element model is shown in Fig. 2.

2.2 Material properties

The density, Young’s modulus and Poisson’s ratio of Ti-64 are 4 430 kg/m³, 114 GPa and 0.34 GPa, respectively [22]. The material properties such as temperature-dependent thermal conductivity, specific heat and thermal expansion coefficient were taken from Ref. [22]. The Johnson-Cook material model was used to describe the flow stress as a function of strain, strain rate and temperature, as given in Eq. (2).

where ε_p is strain, strain rate, reference strain rate, T_r reference temperature, T_m melting point; A, B, C, n, m are material constants.

3 Results and discussions 3.1 Representative simulation results

Typical parameters in the Ti-64 LPW were used, i.e., forging pressure 60 MPa and variance σ 0.003 5, to investigate residual stresses. The contours of equivalent von Mises stress, x-direction stress, y-direction stress and z-direction stress are shown in Fig. 3. It is worth noting that within 120 s, the temperature of sample reaches room temperature, thus the residual stresses at 120 s are regarded as the final ones in this study. It can be found from Fig. 3 that very large residual stresses have developed across the weld line in a non-uniform manner. The residual tensile stresses can be seen at the center of the weld, while compressive stresses are present at the vicinity of the heat affected zone (HAZ), in the x-, y-and z-directions. The residual tensile stresses at the weld interface are largest in the y-direction (see Fig. 3c), while the largest compressive stresses appear at the flash root in the z-direction (see Fig. 3d).

The von Mises stress and the z-direction stress at different stages of the model are shown in Figs. 4 and 5. The sequence provides an illustration of how the residual stresses evolve in the model. It can be seen that the von Mises stress and the z-direction stresses change significantly at different stages. As shown in Fig. 4, from the forging stage to the cooling stage, the von Mises stress increases remarkably and the region of high von Mises stress (300-452 MPa) enlarges. Once the release stage begins, the von Mises stress gradually reduces, while its minimum value also becomes smaller, from the forging stage to the release stage.

For the z-direction stress (the forging direction), the maximum tensile stress rose from 378 MPa to 586 MPa, and then down to 224 MPa, from the forging stage to the release stage. On the contrary, the maximum compressive stresses decreased from 340 MPa to 107 MPa, and then rose to 469 MPa. It is worth pointing out that strong compressive stresses always appear at the flash root in all stages.

3.2 Effect of the forging pressure on residual stresses

How the residual stresses are affected by the welding parameters is of great importance. An important process parameter is the forging pressure [20-22]. Therefore, in order to facilitate comparison, the residual stresses, contours are listed in Table 2. The influence of the forging pressure on the residual stresses can be clearly seen for all three directions in Fig. 6.

As shown in the contours of Table 2, the maximum tensile stresses reduce with increasing forging pressure. The compressive stresses at both sides of the welds in the y-direction (S₂₂) and at the flash root in the z-direction (S₃₃) reduce with the increase of forging pressure. It is observed from Figs. 6a-c that, as the forging pressure increases the residual stresses reduce significantly. These results are to some extent comparable to those measured by Frankel et al. [19] (see Fig. 6d) and Romero et al. [20] (see Fig. 6e). It is worth noting that the low-pressure weld shows residual stresses about four times higher than the high-pressure weld, in the x-direction (see Fig. 6a). The forging pressure appears to have a greater influence on the residual tensile stress in the x-direction compared to those in the y-and z-directions. In addition, the highest tensile stresses develop towards the weld line in the y-direction (see Fig. 6b), which is consistent with the observation made by Turner et al. [3] and Frankel et al. [19].

3.3 Effect of the temperature field on residual stresses

In addition to the forging pressure, the temperature gradients and the zone of high-temperature also affect the distribution of the final residual stresses in LFW. The final residual stress contours for different temperature fields are shown in Table 3. Figure 7 shows the final residual stresses in three directions with different σ values.

It can be seen that the value of σ affects the magnitude of residual stresses. As shown in Table 3, with the increase of σ, the maximum tensile stresses in all three directions reduce. The maximum compressive stresses in the x-direction and the z-direction gradually increase with σ, while the maximum compressive stresses in the y-direction reduce. In Fig. 7a, it can be seen that for a large change in σ (e.g., 0.002 5-0.004 5) there is a large variation (approximately 116 MPa) in the maximum residual tensile stress in the x-direction at the weld center. Additionally, the temperature field has a smaller influence on the residual tensile stress in z-direction (see Fig. 7c).

These results are similar to those obtained in the case of different forging pressures. From the results presented, it seems that the σ value decreases, the temperature gradient increases, as well as the residual stresses.

4 Conclusions

In this work, the model for calculating residual stresses in the LFW of Ti-64 has been developed. The following conclusions can be drawn:

(ⅰ)  A numerical model considering the forging, cooling and release stages of LFW has been developed using ABAQUS based on previous experiments. It shows a good agreement between simulation results and experimental data.

(ⅱ)  Strong residual tensile stresses can be found at the weld center, while the compressive stresses are present in the vicinity of HAZ in x-, y-and z-directions. The residual tensile stresses at the welding interface in the y-direction are the largest, while the largest compressive stresses are present in the flash root in the z-direction. From the forging to the cooling stage, von Mises stresses increase and the region of high von Mises stresses (300-452 MPa) becomes larger. Once the release stage begins, the von Mises stress gradually reduces.

(ⅲ)  The forging pressure strongly affects the magnitude of the final residual stresses. The larger forging pressure produces the lower residual stresses in the weld plane in all three directions (x-, y-, and z-directions). The forging pressure appears to have a larger influence on the residual tensile stress in the x-direction, compared to the y-and z-directions. In addition, it generally develops the highest tensile stresses towards the weld line in the y-direction.

(ⅳ) Similarly, the variance, σ, which decides the Gaussian distribution of temperature field at the stop of friction, also significantly affects the residual stresses. With a decrease in σ value, the temperature gradient increases as well as the residual stresses.

Acknowledgements The authors would like to acknowledge the financial support from the National Natural Science Foundation of China (Grant No. 51405389), the Fundamental Research Funds for the Central Universities (Grant No. 3102014JC02010404) and the Research Fund of the State Key Laboratory of Solidification Processing (Grant No. 122-QZ-2015).