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39附 录A 英 文 文 献 翻 译Numerical Simulation of Linear Friction Welding Based on ABAQUS Environment: Challenges and PerspectivesWenya Li, Feifan Wang, Shanxiang Shi, and Tiejun Ma(Submitted April 10, 2012; in revised form July 5, 2013; published online November 14, 2013)In order to investigate the complicated thermomechanically coupled process of linear friction welding (LFW), three different numerical methods were developed using the ABAQUS software. LFW steel and Ti-6Al-4V were calculated by using a 2D model with the explicit and implicit methods, respectively, and the calculated results were validated by experiments. In addition, a 3D model for LFW Ti-5Al-2Sn-2Zr-4Mo- 4Cr was rstly acquired by using the newly developed explicit-implicit alternate method and the calculated ash seemed more like the real one. Furthermore, a few open questions and perspectives in LFW modeling are discussed and concluded.Keywords ： linear friction welding, map solution, numerical simulation, thermos mechanically coupled model1. IntroductionLinear friction welding (LFW) is a solid state welding process, in which the workpieces are joined together with the help of the normal pressure and the frictional heat generated from the linear reciprocating movement of one component relative to the other under certain amplitude and frequency of oscillation. Compared to other welding techniques, LFW has four distinct phases (Ref 1) which include the initial phase, transition phase, equilibrium phase, and deceleration (or forging) phase. LFW has been applied to non-round or complex geometry components, such as aircraft engine blades to discs (blisks). However, as a relatively new, with very few research centers equipped for it worldwide but promising welding technique, LFW still requires further investigation. These studies may be difcult to study merely by experiments, as for example, the complex and dynamic thermos mechanically coupled process directly inuences the plastic ow of metal and the metallurgical behavior of joint during the welding process. With the development of numerical techniques that can use the computer technology available today, the nite element method has become a powerful and reliable tool for the prediction of temperature and stress elds within the welded parts. In this context, the nite element method was used to model the LFW process in association with experiments.Vairis and Frost (Ref 2) established a numerical model taking the nonlinear material behavior and complex boundary condi- tions into account. Additionally, they analyzed the thermome-chanically coupled relationship and obtained the temperature rise of the initial stage of LFW. Tao et al. (Ref 3) studied the heating and cooling processes of LFW Ti-6Al-4V (Ti64) through轴 承 座 的 结 构 分 析 及 优 化40a thermomechanically coupled model based on the DEFORM software. They found that the highest temperature of about 1340 C appeared at the centre of the welding interface, which is veried in experiments. Moreover, Ceretti et al. (Ref 4) built a 2D model for LFW AISI1045 steel by the DEFORM software. Results showed that the maximum temperature of the joint is about 900 C. In our previous work (Ref 5), a 2D thermome- chanically coupled model for LFW Ti-6Al-4V was developed using ABAQUS. The effects of processing parameters (oscilla- tion amplitude and frequency, axial pressure) were systematically examined and the temperature contours in the specimen at different friction times were calculated. Sorina-Mu ller et al. (Ref6) developed a 3D thermomechanical model for LFW of Ti-6Al- 2Sn-4Cr-6Mo using ANSYS to explore the temperature distri- bution in the rubbing interface. Recently, Turner et al. (Ref 7) formulated a 2D nite element model for LFW Ti64 using FORGE to study the extrusion phase of the process. They found that the calculated temperature agrees with experiments with the highest temperature on the interface being at about 1100 C. Grujicic et al. (Ref 8) established a 3D fully coupled thermome- chanical nite element model using ABAQUS and a typical temperature distribution over the contact interface was obtained.In order to understand the bonding nature for this complex and strongly thermomechanically coupled deformation process, the LFW group at Northwestern Polytechnical University (NPU) has performed extensive numerical analyses with different materials. In this paper, the developed 2D and 3D numerical analyses are demonstrated and the simulation perspectives are discussed.2. Numerical Methods 2D ModelBased on the A characteristics of the LFW process, it is difcult to model the whole LFW process with a single numerical model for its complex interface contact and huge computation effort it requires during the material extrusion phase. Therefore, some simplications to the model are necessary. According to experiments (Ref 9), the workpieces deformed in a symmetric manner during the welding process. In addition, it has been shown that a deformable part with a rigid surface/body is acceptable and reasonable to study the temperature eld (Ref 5). For the analyses performed as partof this work, the developed 2D model is shown in Fig. 141 The Explicit Method.The 2D explicit method used with the ABAQUS/Explicit package and the Arbitrary Lagrangian-Eulerian (ALE) adaptive mesh control was used to cope with the excessively element distortion. As shown in Fig. 1, the deformable specimen had a width of 18 mm and height of 40 mm. The rigid surface was used to model the opposite oscillating specimen. For ease of creating a mesh and applying constraints to the model, the deformable specimen was partitioned into three parts, where the upper part of 10 mm length has a mesh size of 0.5 mm and the lower part of 25 mm length has a mesh size of 3 mm, while the middle part of the remaining 10 mm has a gradually changing mesh size. The mesh was created by using the four-node quad element with coupled displacement and temperature and reduced integration.In this model, the external boundary of the lower 30 mm part was allowed to move in the Y direction and constrained in the X direction. Pressure was applied to the bottom surface of the specimen in the Y direction. The rigid surface on top was only permitted to move in the X direction in a sinusoidal mode with a specic amplitude and frequency of oscillation. The thermal radiation and convection coefcient between the workpiece and surroundings were set to 50 W/(m2 C) as it does not change much with temperature, and the thermal conductance between the workpiece and xture changed with temperature from a maximum value of 20,000 W/(m2 C) at 800 C to a minimum of 1000 W/(m2 C) at room temperature in a linear manner. During the LFW process, the welding interface faces sliding and sticking friction conditions (Ref 10) which produce the necessary frictional heat. Due to the complicated friction process of LFW, Coulomb friction was adopted in this simulation for numerical convenience, rather than being physically correct. In the sliding friction stage, the friction coefcient of steel increases with increasing interface temperature, and does not exceed 0.577 (Ref 11). With further increases in the interface temperature, the sticking friction regime dominates, and limiting shear stress was used in this case. As indicated by Maalekian (Ref 10), the temperature for full sticking friction to occur is about 0.6 Tm for steel, and therefore, 800 C was adopted as the starting temperature for sticking friction in this work. A temperature-dependent friction coefcient (as listed in Table 1) at the interface taking sliding and sticking friction into account was used in these analyses.轴 承 座 的 结 构 分 析 及 优 化 The Implicit Method.ALE is usually employed for maintaining a high-quality mesh throughout an analysis, even when large deformation or loss of material occurs, but the ALE adaptive meshing does not alter the topology (elements and connectivity) of the mesh. This limits the ability of this method to maintain a high-quality mesh in extreme deformation conditions (Ref 12). The 2D implicit method was used in the ABAQUS/Standard package with the map solution technique to cope with excessive element distortion and rem eshing the distorted shape.The geometric model in the 2D implicit method was the same as that in the explicit method as shown in Fig. 1. The heatinput at the interface was given by the user-dened subroutine (DFLUX) (Ref 12): where l is the friction coefcient (here was set at 0.577),p the friction pressure and v the linear oscillation velocity.Table 2 Specimen dimensions and processing parameters used in the experiments2.2 3D ModelIn order to improve the process model of this complicated thermomechanically coupled process a 3D model was devel- oped as shown in Fig. 2. As mentioned previously, the ALE can maintain a high-quality mesh and the map solution technique can alter the topology of the mesh, and it was used in this model combined with the HYPERWORKS software.In the model developed, the deformable specimen was 40 mm in height, 10 mm in width, and 75 mm in length and a rigid body with the same width and length was used in place of the42symmetrical workpiece. To ease the creation of the mesh and application of constraints, the specimen was split into three parts, with the upper 28 mm part having a mesh size of 3 mm, the lower 5 mm part a mesh size of 1 mm, and the middle 7 mm part a gradually changing mesh size. The mesh was lled with eight-node brick elements with coupled displacement and temperature, reduced integration, and hourglass control. In the model, the external boundary of the upper 28 mm part was allowed to move in the Y direction. Pressure was applied to the upper surface of the specimen in the Y direction. The rigid body was only allowed to move in the X direction in a sinusoidal mode with an amplitude and frequency of oscillation. The coefcient of friction between the workpiece and the rigid body followed a temperature-dependent law as in Ref 5 and was used to generate frictional heat.Fig. 3 Calculated temperature eld at different friction times for LFW 20 steel2.3 Material ModelAlthough phase transformations may signicantly affect the thermoplastic behavior of the specimens, to simplify the analysis it is ignored in this preliminary analysis. The accurate representation of the dependence of material ow stress on temperature, strain, and strain rate is essential for the modeling of the LFW process. The materials deformation was initially assumed to follow the Johnson and Cook plasticity model, which accounts for strain hardening, strain rate hardening, and thermal softening effects. The ow stress (r) of material is expressed as follows (Ref 12):where A, B, n, C, m are material constants, ep the effective plastic strain (PEEQ), and e_ m the effective plastic strain rate normalized with respect to a reference strain rateT* is a homologous temperature dened as (Ref 12):where Tm is the melting point and Tr the43轴 承 座 的 结 构 分 析 及 优 化reference or transi- tion temperature.3. ExperimentTo validate these models, LFW experiments were per- formed with mild steel (20 steel in Chinese classication) and Ti-5Al-2Sn-2Zr-4Mo-4Cr (Ti17) using the LFW machine (type XMH-160) developed in NPU. The specimen dimensions and processing parameters used in the experiments are shown in Table 2. In order to obtain the useful temperature information of the 20 steel, the K-type thermocouples (error range between0.2 and 0.2 % of the measured temperature) with an outer diameter of 1 mm were embedded in a blind hole with 5.5 mm in depth and 4 mm away from the weld interface. For obtaining the interface and the ash temperature of Ti17 an infrared thermometer (Infra Tec, VarioCAMhr head-HS), with an error range between 1.5 and1.5 C, was used in the welding experiment.Fig. 4 Comparison between the estimated and experimental axial shortening4. Results and Discussion 2D Explicit MethodIn this numerical analysis the 20 steel was taken as an example, welded with parameters shown in Table 2. The calculated temperature eld at different process times is shown in Fig. 3. It can be seen that the temperature at the interface quickly increases to about 1000 C at 1 s, which is in agreement with experimental results of orbital friction welding steel (Ref 10). But the high temperature developed is limited only in the center. The temperature reaches about 400 C at the edges (at 1 s). Further into the process up until 2 s, the maximum interface temperature increases slowly while the area of high temperature becomes larger. At the same time, the ash is generated and axial shortening begins to appear as shown in Fig. 4. After about 2 s, the interface temperature changes very little and the LFW process reaches a quasi-steady state where the plasticized metal is continuously extruded. The calculated rate of change of axial shortening is similar to that of the experiment (Ref 9), where it changes exponentially with friction time. In addition, the total unilateral axial shortening is about 2.6 mm which is in agreement with the experiment (about 2.7 mm) as shown in Fig. 4.The recorded temperature history of the embedded thermo- couple at 1 is shown in Fig. 5. It is evident that the calculated temperature (both the welding and coo ling phases) is also in good44agreement with the experiment. In addition, the calculated maximum temperature of the interface (767 C) is also comparable to the experimental one (755 C).Therefore, this method is suitable for modeling LFW of this small model based on temperature and axial shortening experimental data.Fig. 5 Comparison between the estimated and experimentally recorded temperatures at hole 1 2D Implicit MethodIn this numerical analysis, Ti64 was used as an example. The welding parameters used in the analysis are shown in Table 2. The calculated temperature eld at different times during the friction process is shown in Fig. 6. It can be seen that the temperature at the interface increases quickly to about 1100 C within 0.1 s, which is faster than the example with the explicit method for the different forms of heat input. Further into the process, the maximum interface temperature increases slowly while the area of high temperature is becoming larger. After 2 s, ash begins to be generated along the oscillation direction and becomes longer with friction time until 3 s. When studying the interface temperature as shown in Fig. 7, it can be seen that the temperature at the interface center increases rapidly to about 1100 C and changes a little after that, which is comparable with previous works (Ref 5, 7, 8).Fig. 6 Calculated temperature eld at different friction times for LFW Ti64Compared with the explicit method, it can be found that the ash calculated with the implicit method has a different shape with the map solution technique used, while the implicit method requires much longer computational time. 3D Explicit-Implicit Alternate Method45轴 承 座 的 结 构 分 析 及 优 化In this analysis, the Ti17 alloy was used as an example. The calculated temperature contours at different process times are shown in Fig. 8. It can be seen that the temperature at the interface increases rapidly for the rst 2 s while the area of maximum temperature expands, but the maximum temperature is restricted to the center. Until 3 s into the process the maximum temperature reaches a quasi-steady state, where this zone increases slowly in the Y direction. In addition to these, no extrusion has formed in the rst 3 s. After 3 s, the ash is extruded from all four sides. It should be pointed out that the ash in the non-oscillatory sides of the specimen is larger than that in the sides of the specimen which oscillate, as in the experiments. And the temperature eld and joint deformation is not symmetrical along the width of the workpieces.Figure 9 shows the calculated and experimentally recorded temperatures at the weld interface during the friction stage. It can be clearly seen that the calculated temperature history is in good agreement with the experiments, and both reach about 1400 C.Compared to the 2D methodology, this 3D model can represent the LFW process better, especially when the model size is very large. Comparison of Different MethodsBased on the calculated results, the different methods are compared in Table 3. Judging them in terms of computation time required, it can be concluded that the 3D model takes longer than the 2D one for a larger model. It should be noted that the 2D implicit method requires much more computation time (about 6 h) than the 2D explicit method. With regards to the accuracy of the models, the 3D model is superior to 2D. The 2D implicit method shows an average accuracy, possibly because the user-dened subroutine does not express the heat input accurately. All three studied methods can be used to investigate temperature and axial shortening of LFW. In addition, the 3D model can simulate the residual stresses. Although 2D models show good accuracy for a low computational cost, there are some limitations. In the 2D models, a section of workpieces was modeled instead of the three dimensional structure, making them suitable when the object to be modeled is not very big.5. Open Questions and PerspectivesIn the previous sections, three mature numerical methods for 2D and 3D models are used to investigate the LFW process. The calculated temperature and axial shortening correspond to experimental values. However, a lot of modeling work still remains. The following open ended46questions need to be addressed in the future for successful modeling of the process. Excessive Element DistortionLFW is a process where large strains develop in small areas of the specimens with the very large plastic deformation appearing in the weld z
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