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Numerical simulation of residual stresses in aluminum alloy welded joints
Journal of Manufacturing Processes 50 (2020) 380–393
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Numerical simulation of residual stresses in aluminum alloy welded joints a,
a
a
b
T
b
Yaohui Lu *, Shengchang Zhu , Zhitang Zhao , Tianli Chen , Jing Zeng a b
School of Mechanical Engineering, Southwest Jiaotong University, Chengdu, Sichuan 610031, China Traction Power State Key Laboratory, Southwest Jiaotong University, Chengdu, Sichuan 610031, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Welded joint Residual stress Thermal elastic–plastic method Inherent strain method Finite element method
The lightweight design makes thin-plate welded structures used widely, especially for the aluminum alloy thinplate welded structure, it is very important to study the fatigue fracture properties of the structure considering the influence of residual stress. A solid model of a butt joint of aluminum alloy with a double-pass weld is established. Both the welding temperature fields and residual stress fields are simulated through the thermal elastic–plastic method. The welding experiment is also performed with the corresponding joint, which is welded by means of metal inert-gas (MIG) welding. Consequently, the computational and experimental results of residual stress are in good agreement. Moreover, the thermal elastic–plastic method is employed to calculate the residual stress fields of typical welded joints. Based on the inherent strain theory, the transverse and longitudinal inherent strain of the joints are decomposed from the total strains and applied to both solid and shell models of the three types of joints to calculate the residual stress fields of them. The results of the solid and shell models using the two methods are practically consistent, which indicates that the inherent strain method can predict the residual stress on the shell model efficiently and accurately. Thus, the method of predicting the welding residual stress of thin-plate structures based on the inherent strain is proposed, which provides a reference for the structural fatigue assessment under the influence of residual stress.
1. Introduction Welded structures are widely used in vehicles, pressure vessels, marine structures and other fields due to its good connectivity and high production efficiency [1]. During the welding process, a large amount of local heat input causes a large temperature difference inside the material, and then, with the subsequent uneven cooling, the residual stress will be inevitably generated at the weld zone [2]. In addition, due to the limitations of welding procedure, crack-like defects such as pores and slags may appear at the weld seam. The tensile residual stress will promote the crack growth at the weld zone and reduce the structural load-bearing capacity, which makes it prone to fatigue failure; while compressive residual stress may effectively slow down crack growth and enhance the fatigue performance of the welded structure and thus can improve the service life [3,4]. It is particularly important to conduct research on welding residual stress and distortion in order to improve the safety and reliability of welded components so that they can be utilized in engineering practice for an extended period of time. With the development of computer technology and the finite element theory, numerical simulation technology has been widely utilized to predict welding temperature, residual stress, and distortion. The commonly employed numerical simulation techniques are the thermal ⁎
elastic–plastic method and inherent strain method. The thermal elasticplastic method simulates the welding residual stress and the welding distortion caused by the heat transfer process, the melting and solidification of the metal, and the phase change during welding. Japanese scholars, Ueda and Yamakawa [5], applied the thermal elastic–plastic finite element method to two-dimensional and three-dimensional models for predicting the dynamic welding stress–strain fields for the first time. Thereafter, the thermal elastic–plastic method was applied to the prediction of residual stress of welded structures such as steel plate [6,7], marine propeller [8] and impeller [9]. Huang et al. [6] studied the effects of laser welding heat input on residual stress of stainless steel sheets by a highly efficient and accurate approach—hybrid iterative substructure and adaptive mesh method. The authors made accurate predictions and verified their correctness and rationality through experimental measurements. Rong et al. [8] studied the residual stress in hybrid laser arc girth welds of a large marine propeller; thereafter, they simulated the laser heat flux and arc power in the weld zone. The best welding sequence was obtained by analyzing the equivalent residual stress. In these researches, the thermal elastic–plastic method can obtain both the temperature field and stress field relatively accurately, but it is only suitable for predicting the residual stress of small structures because of its complex calculation process, high hardware
Corresponding author. E-mail addresses: [email protected], [email protected] (Y. Lu).
https://doi.org/10.1016/j.jmapro.2019.12.056 Received 15 April 2019; Received in revised form 25 November 2019; Accepted 27 December 2019 1526-6125/ © 2019 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.
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Fig. 1. Butt joint models: (a) geometric model; (b) finite element model. Table 1 Material parameters of A7N01 aluminum alloy. Temperature (°C)
Density (kg m−3)
Specific heat (J kg−1 °C−1)
Thermal conductivity (W m−1 °C−1)
Thermal expansion coefficient (°C−1)
Yield stress (MPa)
Young's modulus (Pa)
Heat transfer coefficient (W m−2 °C−1)
20 100 250 400 550 700 850 1000
2780 2760 2730 2700 2660 2450 2430 2420
869 912 981 1040 1189 1110 1066 1015
156 164 174 182 189 88 92 105
2.38E-5 2.42E-5 2.52E-5 2.65E-5 2.71E-5 2.76E-5 2.81E-5 2.90E-5
295 285 125 48 12 5 5 5
7.00E10 6.60E10 5.65E10 2.60E10 1.07E10 5.00E9 3.80E9 3.00E9
8.2 10.9 18.5 33.6 49.1 55.9 57.9 60.2
Table 2 Welding conditions of A7N01 aluminum alloy welded joint for numerical simulation. Weld bead
Voltage (V)
Current (A)
Welding speed (mm s-1)
Thermal efficiency of arc
First welding Second welding
20 19
170 155
5 10
0.75 0.75
requirements, and lengthy processing time. However, the inherent strain method was more suitable for large and complex structures. Ueda et al. [10,11] introduced the concept of inherent strains, they stated that the weld residual stress and distortion that are generated during the welding process were caused by the inherent strain. For large and complex structures, only the inherent strain need to be calculated, and then the residual stress can be obtained by using one linear elastic calculation. Thereafter, the inherent strain was used in the prediction of welding distortion [12,13] and residual stress
Fig. 2. Involved nodes and boundary conditions.
[14–17]. To predict residual stresses in butt joints, Khurram and Shehzad [14] employed the equivalent load method based on inherent strains; the simulation results agreed well with the experimental values. Ueda et al. [16] experimentally verified the validity and practical application of predicting three-dimensional residual stresses in T-type 381
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Fig. 3. Transient temperature fields of butt joint: (a) 23.2 s; (b) 125.8 s; (c) 165.2 s; (d) 4755.0 s.
fillet welds using inherent strains. These references indicated that both the inherent strain analysis and thermal elastic–plastic analysis were effective in evaluating residual stress. In this study, the inherent strain was applied to predict the residual stress in shell models of welded joints; this provided a basis for predicting the residual stress in large complex thin-plate welded structures. By applying the thermal elastic–plastic method, which involves the birth and death element technique and the indirect thermal-mechanical coupling method, the process of adding solder to the components during welding is simulated. In order to show the residual stress clearly, the small deformation is not presented considering that residual stress and plastic deformation are related. This paper focuses on the value and distribution of residual stress by applying a finite element commercial software. In Section 2, the welding temperature field and residual stress field of a butt joint are simulated and analyzed. In the experiment, the joint is welded by means of the MIG welding, and the corresponding data are compared with the simulation data. In Section 3, both the
Fig. 4. Temperature history of involved nodes.
Fig. 5. Residual stress fields of butt joint: (a) longitudinal; (b) transverse. 382
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Fig. 6. Experimental equipment: (a) ABB/ IRB 1410 welding robot; (b) X-ray residual stress analyzer; (c) butt joint for residual stress measurement.
Fig. 7. Comparison of residual stress obtained by experiment and simulation: (a) longitudinal stress along line A; (b) transverse stress along line A; (c) longitudinal stress along line B; (d) transverse stress along line B.
edge is 1 mm, and the gap between the two plates is 1.6 mm. During the actual welding process, the temperature of the weld and the heat-affected zone in the vicinity drastically changed; on the other hand, the change in temperature away from the base metal of the weld is relatively gradual. In order to improve the convergence of computational results, the joint is divided into 2 mm segments along the weld direction. To accomplish this, a mapped grid discrete model is used while taking into consideration the relative balance between numerical simulation accuracy and economics. The joint along the vertical weld direction is divided into eight segments; the heat-affected zone and the adjacent parent metal mesh size are determined as 2 mm, 3 mm, and 5 mm. Solid70, which has a 3D thermal conduction capability, is used as
thermal elastic–plastic method and inherent strain method are used to simulate and analyze the stress fields of different welded joints with solid models and shell models. The main conclusions are summarized in Section 4.
2. Residual stress in butt joint 2.1. Finite element modeling and calculation As shown in Fig. 1, a 250 × 300 × 8 mm3 double-pass welded butt joint made of aluminum alloy A7N01 is fabricated; this is based on the actual joint used in the welding experiment. The groove is 70°, the blunt 383
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be extremely high and would not match actual scenarios. The latent heat of phase change is treated through heat enthalpy of materials at different temperatures. The weldment is subjected to a large amount of local heat input during the welding process that produces a considerably uneven temperature field. During the molten pool formation, the heat source transfers heat to the weldment particularly through radiation and convection. After the temperature of the base metal in the heat-affected zone increases, the heat is mainly transmitted to the area away from the weld through conduction. The numerical model of the welding temperature field is a typical nonlinear transient heat conduction problem. Its constitutive equation is as follows:
Table 3 Parameters and welding conditions of typical welded joints. Thickness (mm)
Number of weld beads
Angle of the groove (°)
Voltage (V)
Current (A)
Welding speed (mm s-1)
Butt joints
t3.5 + t3.5 t4.5 + t4.5 t7.0 + t7.0
1 1 2
70 70 70
20 25 20 21
150 160 152 180
6 6 10 6
T-joints
t4.0 + t4.0 t6.0 + t6.0
1 2
45 45
20 22 25
140 165 180
6 10 6
Lap joints
t3.0 t4.0 t6.0 t8.0
1 1 1 1
None
24 25 25 25
150 155 185 195
5 5 5 5
+ + + +
t4.7 t4.0 t7.0 t8.0
cρ
∂T ∂ ⎛ ∂T ⎞ ∂ ⎛ ∂T ⎞ ∂ ⎛ ∂T ⎞ = + + λ λ λ + Q˙ ∂t ∂x ⎝ ∂x ⎠ ∂y ⎝ ∂y ⎠ ∂z ⎝ ∂z ⎠ ⎜
⎟
(1)
where c is the specific heat capacity; ρ is the density; λ is the thermal •
conductivity; T is the function of temperature field; Q is the rate of internal heat generation; t is the heat transfer time. In this study, the internal heat generation rate heat source model combined with the birth and death element technology is used to simulate the movement of the welding heat source and the filling process of the weld. The internal heat generation rate is a body load in the thermal analysis; moreover, it can be assigned to the elements in the molten pool. It is expressed as follows:
the temperature field solution. The elements are replaced by equivalent structural elements, such as Solid185, when the model is structurally analyzed. In the numerical simulation of welding, the value of each performance parameter of the material as a function of temperature is required. The material used in this study is A7N01 aluminum alloy; its material parameters are summarized in Table 1. Besides, the initial temperature of the weld is 20 °C and the Poisson's ratio is 0.33. For the welding temperature field analysis, it is necessary to identify thermal physical parameters as follows: thermal conductivity, convection coefficient, density, specific heat, melting point, and initial component temperature. Moreover, for the stress and strain field simulation, determining Poisson's ratio, Young's modulus, thermal expansion coefficient, and yield limit is necessary. During the welding process, the metal at the molten pool of the component underwent melting and solidification. No temperature change is observed during the solid–liquid phase transition because of the latent heat of phase change. If this is not taken into consideration, the temperature of the simulation would
HGEN = UIη /(Aweld × v × dt )
(2)
where HGEN is the heat generation rate applied for each load step; U is the welding voltage; I is the welding current; η is the thermal efficiency of the arc; Aweld is the cross-sectional area of the weld; v is the welding speed; dt is the time step for each load step. According to literature [18], the thermal efficiency of the MIG welding arc is 0.75 in this simulation. The welding conditions are listed in Table 2. During the welding process, both the weldment and the heat source exchange heat with the surrounding medium by convection. In the solution of temperature field, the convective heat transfer and thermal radiation are considered as the heat transfer coefficients of the material.
Fig. 8. Models of Typical joints: (a) butt joint; (b) T-joint; (c) lap joint. 384
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Fig. 9. Residual stress fields in typical joints: (a) longitudinal stress in butt joint with 4.5-mm thickness; (b) transverse stress in butt joint with 4.5-mm thickness; (c) longitudinal stress in T-joint with 6.0-mm thickness; (d) transverse stress in T-joint with 6.0-mm thickness; (e) longitudinal stress in lap joint with 6.0–7.0-mm thickness; (f) transverse stress in lap joint with 6.0–7.0-mm thickness.
Fig. 10. Lines of joints: (a) T-joint (b) lap joint.
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Fig. 11. Residual stress along lines of T-joint: (a) longitudinal stress along line 1; (b) transverse stress along line 1; (c) longitudinal stress along line 2; (d) transverse stress along line 2.
of metallic materials in the plastic zone obeys the plastic flow and strain hardening law. Temperature-dependent mechanical properties and stress strains vary linearly over a small time increment. The obtained temperature field is applied as a body load to the weldment to calculate the welding stress field. The material undergoes deformation during the welding process. The total strain at a certain point consists of several components as follows:
All the outer surfaces of the model are considered as heat transfer surfaces, and they are selected for the application of material parameters to simulate the entire heat transfer process. The heat transferred is taken into consideration as follows:
qc = −β (Ts − T0)
(3)
where β is the surface heat transfer coefficient; Ts is the surface temperature of the weldment; T0 is the temperature of the surrounding medium. In this simulation, the entire welding process is divided into two processes: heating and cooling. For the first welding, the heating and cooling times are 50 s and 60 s, respectively; both heating and cooling have a time step of 0.4 s. For the second welding, the heating and cooling times are 25 s and 6000 s, respectively, both with a time step of 0.2 s. The entire welding simulation process lasts 6165 s. In calculating the stress fields, it is necessary to impose constraints on the model. The basic principles are as follows: the rigid displacement of the model must be eliminated, and the degree of freedom must not be overconstrained. As illustrated in Fig. 2, the boundary conditions in this simulation are as follows: a full constraint is applied to one edge of the lower surface of the butt joint, and one edge imposes a constraint along the plate thickness direction. To improve the convergence of stress field results, the complete Newton–Raphson method is implemented. The welding thermal stress process is considerably complicated. In order to improve the calculation accuracy, the welding thermal stress field is simplified to a nonlinear transient problem of the material. The elastic–plastic mechanical model is used for finite element calculation. The yield of the material follows the Von Mises criterion. The behavior
εt = εe + εp + εth
(4)
where εe is the elastic strain; εp is the plastic strain; εth is the thermal strain, which relates to thermal expansion coefficient and rate of temperature change. The elastic strain–stress relationship is modeled using the isotropic Hooke’s law. The material parameters (such as Young's modulus, yield strength) used in the mechanical analysis are summarized in Table 1. 2.2. Analysis of results From the calculation results of the transient temperature field of the welded joint, the temperature fields of 23.2 s, 125.8 s, 165.2 s, and 4755.0 s are selected, as depicted in Fig. 3. In the middle of the first welding process and that of second welding process, the welding temperature field is uniform. Because of the short heating time, the temperature field is mainly concentrated in the weld and its vicinity. At the beginning of the cooling process, the cooling rate is faster, and the heat is transmitted from the vicinity of the weld to the base metal of the component. During the welding process, the temperature changes, and the 386
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Fig. 12. Residual stress along lines of lap joint: (a) longitudinal stress along line 1; (b) transverse stress along line 1; (c) longitudinal stress along line 2; (d) transverse stress along line 2.
joint is sufficiently cooled. A portable X-ray residual stress analyzer, μ-X360n , manufactured by Pulstec in Japan, is the welding residual stress instrument used (Fig. 6b); its advantages include high precision and portability. In order to verify the accuracy of the numerical results, the welding test is performed on the same model size with the same material. The welded joint is shown in Fig. 6c, and the residual stress is measured accordingly. The welding conditions are consistent with those in the numerical simulation, as listed in Table 2. Residual stresses are measured on the joint along lines A and B, as shown in Fig. 6c. The X-ray tube angle of the instrument should be adjusted to 25° to measure the residual stress in the aluminum alloy. When the X-ray tube is parallel to the measurement line, the gauged value is the longitudinal residual stress, whereas that measured in the vertical direction is the transverse residual stress. After the adjustment, the red spot is aligned with the measuring point to determine the residual stress values. The stresses obtained by simulation along lines A and B are presented in Fig. 7. The longitudinal residual stress on line A in the weld and some areas near the heat-affected zone is tensile stress; it is practically symmetric with respect to the centerline of the weld. Two peaks appear in the heat-affected zone; these peaks are 250 MPa and 259 MPa, which do not exceed the yield stress of the material. The heataffected zone away from the center of the weld and a part of the base metal exhibit compressive residual stress; most values are approximately 10 MPa. The transverse residual stress on line A is symmetrically distributed along the center line of the weld, and is tensile stress in most areas. Furthermore, in the heat-affected zone, there are two peak values, 12.9 MPa and 13.3 MPa. Compressive residual stress appears at the center of the weld and nearby areas with a peak value of less than
stresses at different locations in the joint are not consistent. To understand the temperature field of the model more clearly, the results of several positions are observed, as shown in Fig. 2. For the second welding, nodes A, B, C, and D are selected on the center line along the weld direction; the distance between each node and the welding start point is 20 mm, 50 mm, 80 mm, and 110 mm, respectively. The temperature profiles are exhibited in Fig. 4; the cooling process is eliminated. It can be observed that with the movement of the heat source during the welding process, the temperature at each point of the component initially increases and thereafter decreases because the welding heat source is loaded twice. The temperature at a node initially increases to the highest temperature and thereafter drops. The rate of temperature increase is significantly larger than the rate at which the temperature decreases. The temperature at each node tends to be constant during the cooling process. The residual stress along the weld direction is called the longitudinal residual stress, whereas that along the vertical weld direction is called the transverse residual stress. Only the residual stress on the upper surface of the model is extracted, as shown in Fig. 5. 2.3. Experimental verification In this study, the welding experiment equipment utilized is the ABB/IRB1410 welding robot, which is produced by ABB Group in Switzerland (Fig. 6a). This robot has adaptive current and voltage functions, and it can be operated for automatic welding only after certain necessary parameters (such as welding starting position, welding line, welding end position, and moving speed of the welding gun) are defined. A residual stress test is performed after the welded 387
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Fig. 13. Shell models: (a) butt joint; (b) T-joint; (c) lap joint.
because the instrument used in the test has a shallow incident depth. The surface quality near the weld is poor after welding; consequently, even the data at the center of the weld and its nearby areas cannot be measured. The distribution trend of experiment and simulation is basically the same, which indicates the rationality of predicting residual stress with the thermal elastic-plastic method for aluminum alloys.
50 MPa. The transverse residual stress in the middle section is considerably less than the longitudinal residual stress. The longitudinal stress on line B is basically tensile stress, and a uniform value appears in the middle of the weld. The peak value reaches 250 MPa, and the compressive stress is generated only near the arcing end. The transverse residual stress on line B exhibits compressive stress on the entire component. From the beginning of the arcing end, the stress initially increases before a uniform region appears; thereafter, the stress decreases. The stress along the uniform region reaches approximately 50 MPa, which is still significantly smaller than the longitudinal residual stress at this location. The difference indicates that the transverse residual stress rapidly decreases along the vertical direction of the weld. In summary, the longitudinal residual stress is more uniform than the transverse residual stress. The former stress is more uniform because the heat in the welding process is applied along the direction of the weld, and the heat constraints of the component are larger than those in the other directions. On the other hand, in the latter stress, the formation mechanism is more complicated; it generally has two parts. One part is caused by the longitudinal shrinkage of the weld and the nearby heat-affected zone, and the other is caused by the difference between the transverse shrinkage of the weld and the nearby plastic zone. In general, in the cross-section of the weld direction, the transverse residual stress caused by the longitudinal shrinkage appears as compressive stress at the arcing and extinction end of the weld, whereas the tensile stress appears in the middle; as a result, a uniform region occurs. Therefore, the farther the weld, the smaller the stress. There will be a time difference during the welding heating process and cooling process, which will lead to the uneven distribution of temperature and stress perpendicular to the welding direction and eventually cause the transverse shrinkage of the weld joint. In Fig. 7, it can be observed that the residual stress profile that is obtained through numerical simulation is consistent with the trend of the experimental data; the values are approximately the same. This is
3. Residual stress in typical joints After the parameters (Table 3) of the welded joint model in the welding process of an aluminum alloy carbody are determined, finite element models are established to calculate the stress in every joint by employing the thermal elastic–plastic method. 3.1. Thermal elastic–plastic method Three types of joint models (Table 3) are built, as shown in Fig. 8. The length and width of the butt joints are 300 mm and 150 mm, respectively. The mesh size in the weld direction is 1.5 mm, and their sizes in the vertical weld direction are 1 mm, 2 mm, and 3 mm. The Tjoints have a web size of 300 × 150 mm2 and a flange size of 300 × 300 mm2. The mesh size in the weld direction is 1.5 mm, and their sizes in the vertical weld direction are 0.5 mm, 1 mm, 2 mm, and 3 mm. The length and width of each plate of the lap joint are 150 mm and 100 mm, respectively. The mesh size in the weld direction is 2 mm, and the sizes in the vertical weld direction are 2 mm, 3 mm, and 4 mm. The welding conditions for the simulation of the welding residual stress fields of various joints are listed in Table 3. Referring to Kirchhoff plate theory, a thin plate is a structure that possesses one dimension that is far smaller than the other two [19]. For most welded sheets in Table 3, the height is far smaller than the length and width and thus it can be considered as a thin plate. For each type of joint, only one figure is shown. The residual stress 388
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Fig. 14. Comparison of residual stresses along the lines of butt joint with a 3.5-mm thickness: (a) longitudinal stress along line 1; (b) transverse stress along line 1; (c) longitudinal stress along line 2; (d) transverse stress along line 2. (TEPM = Thermal elastic–plastic method; ISM = Inherent strain method).
fields of butt joint, T-joint, and lap joint with thicknesses of 4.5 mm, 6.0 mm, and 6.0–7.0 mm are illustrated in Fig. 9. It can be observed in Fig. 9 that the longitudinal residual stress values of the three joints are considerably larger than those of the transverse residual stresses, and the maximum longitudinal residual stress in each joint does not exceed the yield stress of the material. In fact, the contours of the same type of joints have similarities with regard to their longitudinal and transverse stresses; moreover, thickness affects the values of residual stress. For the butt joint, the longitudinal residual stress decreases as the thickness increases, whereas the transverse residual stress increases as the thickness increases. To clearly illustrate the stress results, the lines presented in Fig. 10 are the sections where the stresses are extracted. Because the results of the butt joint are similar to those of the numerical simulation exhibited in Fig. 7, these results no longer require illustration; thus, in Fig. 10, only the T-joint and lap joint are taken as examples. It can be observed in Fig. 11 that the longitudinal residual stress on line 1 of the T-joint single-pass welding model is larger than that of the double-pass welding model. The stress profile of the single-pass welding has only one peak in the heat-affected zone, whereas two peaks are observed in that of the double-pass welding. Because the welds of the Tjoint are located only on one side, the residual stress on that side is significantly larger than that without the weld. The longitudinal residual stress on line 2 of the T-joint is compressive at the arcing and extinction end of the weld. At the middle position of the weld, tensile stress and a uniform area occur. The residual stress value of the doublepass welding joint is smaller than that of the single-pass welding joint. The transverse residual stress in the double-pass welding on line 1 is tensile stress in the heat-affected zone, and the compressive stress
occurs at the center of the weld. Both tensile and compressive stresses are observed at the heat-affected zone of the single-pass welding joint. The transverse residual stress on line 2 is more consistent than that on line 1. Except for the arcing end where the compressive stress is approximately 125 MPa, practically no residual stress in the remaining parts is observed; moreover, a uniform area appears in the middle of the weld. It can be observed in Fig. 12 that the longitudinal residual stress on line 1 of the lap joint has no distinct double-peak; the residual stress value decreases with the increase in the thickness, and the residual stress profiles are considerably similar. Among these, the maximum longitudinal residual stress in the lap joint that has 3.0–4.7 mm thickness is 230 MPa. Similar to T-joints, the residual stress value on the side with the weld is significantly larger than the side without the weld. The profiles of the transverse residual stress on line 1 are also practically the same; the value does not change considerably with thickness. The longitudinal residual stress on line 2 is compressive at the arcing and extinction end of the weld; the tensile stress in the middle of the weld and a uniform area simultaneously appear. The residual stress value is inversely proportional to the thickness of the lap joint. The transverse residual stress on line 2 of the lap joint increases with the increase in thickness, and a long uniform compressive stress region appears in the middle of the weld. The stresses at the arcing and extinction end of the weld are mostly compressive stresses.
3.2. Inherent strain method The inherent strain can be divided into two categories: longitudinal and transverse. The longitudinal inherent strain is along the direction of 389
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Fig. 15. Comparison of residual stresses along the lines of T-joint with 4.0-mm thickness: (a) longitudinal stress along line 1; (b) transverse stress along line 1; (c) longitudinal stress along line 2; (d) transverse stress along line 2. (TEPM = Thermal elastic–plastic method; ISM = Inherent strain method).
strain; h is the plate thickness; z is the coordinate in the thickness direction. When the inherent distortion of a welding component is known, the corresponding inherent strain can be identified. When the inherent strain is used in elastic finite element, it is usually assumed to be evenly distributed on the weld. Therefore, the average value of the inherent strain in the joints is used to represent the approximate inherent strain distribution in the entire welded joint. The average values of inherent strains in joints are calculated by the following equations [20]:
the weld; this causes the component to produce shrinkage distortion and transverse residual stress along the weld. On the other hand, the longitudinal inherent strain is along the vertical direction of the weld. This causes the component to produce shrinkage distortion and longitudinal residual stress along the vertical direction of the weld; moreover, it causes angular distortion on the welding component. The transverse inherent strain is generally considerably smaller than the longitudinal inherent strain. The inherent strain values of the weld and its adjacent areas are applied as initial loads to the welded component, and residual stress fields and weld distortion can be obtained through elastic calculation. Based on experimental observations and theoretical analysis, it is found that the total welding distortion in the welded structure is mainly composed of four parts: longitudinal shrinkage, δx ; transverse shrinkage, δ y ; longitudinal bending, θx ; transverse bending, θy . These four main parts are called inherent distortions. According to the results of the thermal elastic–plastic method, the four abovementioned inherent distortions of a certain cross-section along the weld can be calculated by the following equations:
1 δx = h
∫∫
εxp dydz
(5)
∫ ∫ εyp dydz
(6)
δy =
1 h
θx =
12 h3
∫ ∫ εxp (z − h 2 ) dydz
θy =
12 h3
∫ ∫ εyp (z − h 2 ) dydz
where
εxp
is the longitudinal plastic strain;
∫0
L
1 δ¯y = Lw
∫0
L
1 θ¯x = Lw
∫0
L
1 θ¯y = Lw
∫0
L
δx dx δ y dx θx dx θy dx
(9) (10) (11) (12)
where L w is the length of the weld; L is the length of the component. Strain values cannot be applied directly to the weld and its adjacent elements as loads. The anisotropic thermal expansion coefficient provided by the finite element analysis software can be used to generate a different weld shrinkage along the longitudinal and transverse directions. The load is applied by using a unit temperature load. The solid models of the three types of joints are described above. In order to apply the inherent strain method more accurately, the shell element is used due to its applicability to thin-plate structures, and the shell models of the three types of joints are established according to the mesh sizes of the solid models illustrated in Fig. 13. The plastic strain
(7) (8)
ε yp
1 δ¯x = Lw
is the transverse plastic 390
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Fig. 16. Comparison of residual stresses along the lines of lap joint with 3.0–4.7-mm thickness: (a) longitudinal stress along line 1; (b) transverse stress along line 1; (c) longitudinal stress along line 2; (d) transverse stress along line 2. (TEPM = Thermal elastic–plastic method; ISM = Inherent strain method).
stress value, and that obtained through the inherent strain method of the shell model is the smallest. This is because the maximum stress position of the joint is generally on the upper surface of the component. When the inherent strain is applied to solid models, the average plastic strain in all the weld joints is calculated. Therefore, the surface stress obtained by using the inherent strain method is smaller than that yielded by the thermal elastic–plastic method. In addition, the shell models simplified the details of the weld; this results in a smaller stress value than that of the inherent strain applied to the solid. The tensile stress obtained by the inherent strain method is smaller than that yielded by the thermal elastic–plastic method for the longitudinal residual stress profile of line 1. This is because the inherent strain is only applied to the weld zone. Because the residual stress value outside the weld zone is small, it can be ignored. For the profiles of the transverse stress on line 2, the results of the inherent strain method are more moderate than those of the thermal elastic–plastic method. Moreover, the uniform areas in the middle of the weld are larger in the thermal elastic–plastic method; this is because the average plastic strain is applied. The accuracy can be verified to predict the residual stress in welded joints through the use of the inherent strain method and shell models. The inherent strain method, which is economical and efficient, is generally applied to predict the residual stress for full-scale complex thin-walled structures. Considering a train carbody as an example in terms of geometric characteristics, the length, width, and height of the aluminum alloy profiles used in it are approximately 25,000 mm, 3500 mm, and 3600 mm. Evidently, these dimensions are considerably larger than its thickness of 3–12 mm. Accordingly, the shell model is adopted for the finite element analysis, as shown in Fig. 17. It can be observed that the carbody has various joints, such as butt joint, lap joint, and T-
Fig. 17. The shell model of a train carbody and some welded joint details.
values extracted from the calculation results of the thermal elastic–plastic method of solid models are applied to both solid and shell models; the residual stress results of the inherent strain method are obtained. The lines in Figs. 6c and 10 show the extracted stresses of the three types of joints. Because there are numerous joints, only the butt joint with a 3.5 mm thickness, the T-joint with a 4.0 mm thickness, and the lap joint with a 3.0–4.7 mm thickness are considered; the residual stress along the lines are shown in Figs. 14–16. The residual stress distributions of the butt joint, T-joint, and lap joint in the middle section and the centerline of the weld are consistent in the two calculation methods, and their stress values are not considerably different, which can show that the trend is basically the same. The thermal elastic–plastic method of the solid models yields the largest 391
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Fig. 18. The residual stress distribution of the train carbody.
References
joint. According to the results of the shell models of joints, the inherent strain is applied to the train carbody to predict the welding residual stress. The distribution of residual stress is shown in Fig. 18. Based on this, the influence of residual stress on the fatigue and fracture performance of the carbody can be evaluated further. This provides a basis for the post-weld adjustment of the residual stress in a large carbody structure and the accurate analysis of the influence of welding residual stress on fatigue fracture performance. In recent research, the author [21] studied the effect of welding residual stress on the fatigue strength of aluminum alloy carbody of a high speed train. It is found that under the influence of welding residual stress, the average stress of the weld zone was obviously increased, which made the carbody easy to fatigue failure. In addition, the residual stress significantly changed the direction of the maximum principal stress at the weld zone.
[1] Zhang WY, Jiang WC, Zhao X, Tu ST. Fatigue life of a dissimilar welded joint considering the weld residual stress: experimental and finite element simulation. Int J Fatigue 2018;109:182–90. [2] Aliha MRM, Gharehbaghi H. The effect of combined mechanical load/welding residual stress on mixed mode fracture parameters of a thin aluminum cracked cylinder. Eng Fract Mech 2017;180:213–28. [3] James MN. Residual stress influences on structural reliability. Eng Failure Anal 2011;18:1909–20. [4] Coules HE, Horne GCM, Kabra S, Colegrove P, Smith DJ. Three-dimensional mapping of the residual stress field in a locally-rolled aluminium alloy specimen. J Manuf Process 2017;26:240–51. [5] Ueda Y, Yamakawa T. Analysis of thermal elastic–plastic stress and strain during welding by finite element method. Trans Jpn Weld Soc 1971;2:186–96. [6] Huang H, Tsutsumi S, Wang J, Li L, Murakawa H. High performance computation of residual stress and distortion in laser welded 301l stainless sheets. Finite Elem Anal Des 2017;135:1–10. [7] Deng D, Zhou Y, Bi T, Liu X. Experimental and numerical investigations of welding distortion induced by CO2 gas arc welding in thin-plate bead-on joints. Mater Des 2013;52:720–9. [8] Rong Y, Chang Y, Xu J, Huang Y, Lei T, Wang C. Numerical analysis of welding deformation and residual stress in marine propeller nozzle with hybrid laser-arc girth welds. Int J Pressure Vessels Pip 2017;158:51–8. [9] Zhang Z, Ge P, Zhao GZ. Numerical studies of post weld heat treatment on residual stresses in welded impeller. Int J Pressure Vessels Pip 2017;153:1–14. [10] Ueda Y, Fukuda K, Nakacho K, Endo S. A new measuring method of residual stresses with the aid of finite element method and reliability of estimated values. Trans JWRI 1975;4(2):123–31. [11] Ueda Y, Fukuda K. A selection method of observing positions for highly accurate measurement of residual stresses. Trans JWRI 1980;9(1):101–6. [12] Deng D, Murakawa H, Liang W. Numerical simulation of welding distortion in large structures. Comput Meth Appl Mech Eng 2007;196(45-48):4613–27. [13] Lu YH, Wu XW, Zeng J, Wu PB. Study on FEM numerical simulation method for the welding distortion. Mater Sci Forum 2012;704–705:1316–21. [14] Khurram A, Shehzad K. FE simulation of welding distortion and residual stresses in butt joint using inherent strain. Int J Appl Phys Math 2012;2(6):405–8. [15] Ueda Y, Yuan MG, Mochizuki M, Umezawa S, Enomoto K. Experimental verification of a method for prediction of welding residual stresses in T joints using inherent strains 4th report: method for prediction using source of residual stress. Weld Int 1993;7(11):863–9. [16] Ueda Y, Ma NX, Koki R, Wang YS. Measurement of residual stresses in single-pass and multi-pass fillet welds using inherent strains: methods for estimation and measurement of residual stresses by functional representation of inherent strains (5th Report). Weld Int 1996;10(4):302–11. [17] Mochizuki M. Evaluation of through thickness residual stress in multipass buttwelded joint by using inherent strain. Sci Technol Weld Joining 2006;11(5):496–501. [18] Lu YH, Lu C, Zhang DW, Chen TL, Zeng J, Wu PB. Numerical computation methods of welding deformation and their application in bogie frame for high-speed trains. J Manuf Process 2019;38:204–13. [19] Bauchau OA, Craig JI. Kirchhoff plate theory. Bauchau OA, Craig JI, editors.
4. Conclusions The main conclusions are as follows: (1) The longitudinal residual stress and the transverse residual stress were generally tensile stresses in the weld areas and the adjacent heat-affected zone; the transverse residual stress was considerably smaller than the longitudinal residual stress. The numerical simulation results were in good agreement with the experimental results. (2) The residual stress in the middle section of different joints and along the centerline of the weld was consistent using the two calculation methods; the trend of the stress values was basically the same, which indicated the accuracy of the inherent strain method for the prediction of welding residual stress fields. (3) The residual stresses of the shell and solid models of joints were consistent, and the inherent strain method was economical and efficient, which suggested that the application of shell models and inherent strains was practicable for thin-plate welded structures.
Acknowledgments This work was supported by the Sichuan Province Science and Technology Support Program (Grant No. 2018HH0072) and National Natural Science Foundation of China (Grant No. 51275428). 392
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[21] Lu YH, Zhang DW, Zhao ZT, Liu JJ, Lu C. Influence of welding residual stress on fatigue strength for EMU aluminum alloy carbody. J Traffic Transp Eng 2019;19(4):94–103. (in Chinese).
Structural analysis. Solid mech its appl, 163. Dordrecht: Springer; 2009. p. 819–914. [20] Deng D, Murakawa H. Prediction of welding distortion and residual stress in a thin plate butt-welded joint. Comput Mater Sci 2008;43(2):353–65.
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Contents lists available at ScienceDirect
Journal of Manufacturing Processes journal homepage: www.elsevier.com/locate/manpro
Numerical simulation of residual stresses in aluminum alloy welded joints a,
a
a
b
T
b
Yaohui Lu *, Shengchang Zhu , Zhitang Zhao , Tianli Chen , Jing Zeng a b
School of Mechanical Engineering, Southwest Jiaotong University, Chengdu, Sichuan 610031, China Traction Power State Key Laboratory, Southwest Jiaotong University, Chengdu, Sichuan 610031, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Welded joint Residual stress Thermal elastic–plastic method Inherent strain method Finite element method
The lightweight design makes thin-plate welded structures used widely, especially for the aluminum alloy thinplate welded structure, it is very important to study the fatigue fracture properties of the structure considering the influence of residual stress. A solid model of a butt joint of aluminum alloy with a double-pass weld is established. Both the welding temperature fields and residual stress fields are simulated through the thermal elastic–plastic method. The welding experiment is also performed with the corresponding joint, which is welded by means of metal inert-gas (MIG) welding. Consequently, the computational and experimental results of residual stress are in good agreement. Moreover, the thermal elastic–plastic method is employed to calculate the residual stress fields of typical welded joints. Based on the inherent strain theory, the transverse and longitudinal inherent strain of the joints are decomposed from the total strains and applied to both solid and shell models of the three types of joints to calculate the residual stress fields of them. The results of the solid and shell models using the two methods are practically consistent, which indicates that the inherent strain method can predict the residual stress on the shell model efficiently and accurately. Thus, the method of predicting the welding residual stress of thin-plate structures based on the inherent strain is proposed, which provides a reference for the structural fatigue assessment under the influence of residual stress.
1. Introduction Welded structures are widely used in vehicles, pressure vessels, marine structures and other fields due to its good connectivity and high production efficiency [1]. During the welding process, a large amount of local heat input causes a large temperature difference inside the material, and then, with the subsequent uneven cooling, the residual stress will be inevitably generated at the weld zone [2]. In addition, due to the limitations of welding procedure, crack-like defects such as pores and slags may appear at the weld seam. The tensile residual stress will promote the crack growth at the weld zone and reduce the structural load-bearing capacity, which makes it prone to fatigue failure; while compressive residual stress may effectively slow down crack growth and enhance the fatigue performance of the welded structure and thus can improve the service life [3,4]. It is particularly important to conduct research on welding residual stress and distortion in order to improve the safety and reliability of welded components so that they can be utilized in engineering practice for an extended period of time. With the development of computer technology and the finite element theory, numerical simulation technology has been widely utilized to predict welding temperature, residual stress, and distortion. The commonly employed numerical simulation techniques are the thermal ⁎
elastic–plastic method and inherent strain method. The thermal elasticplastic method simulates the welding residual stress and the welding distortion caused by the heat transfer process, the melting and solidification of the metal, and the phase change during welding. Japanese scholars, Ueda and Yamakawa [5], applied the thermal elastic–plastic finite element method to two-dimensional and three-dimensional models for predicting the dynamic welding stress–strain fields for the first time. Thereafter, the thermal elastic–plastic method was applied to the prediction of residual stress of welded structures such as steel plate [6,7], marine propeller [8] and impeller [9]. Huang et al. [6] studied the effects of laser welding heat input on residual stress of stainless steel sheets by a highly efficient and accurate approach—hybrid iterative substructure and adaptive mesh method. The authors made accurate predictions and verified their correctness and rationality through experimental measurements. Rong et al. [8] studied the residual stress in hybrid laser arc girth welds of a large marine propeller; thereafter, they simulated the laser heat flux and arc power in the weld zone. The best welding sequence was obtained by analyzing the equivalent residual stress. In these researches, the thermal elastic–plastic method can obtain both the temperature field and stress field relatively accurately, but it is only suitable for predicting the residual stress of small structures because of its complex calculation process, high hardware
Corresponding author. E-mail addresses: [email protected], [email protected] (Y. Lu).
https://doi.org/10.1016/j.jmapro.2019.12.056 Received 15 April 2019; Received in revised form 25 November 2019; Accepted 27 December 2019 1526-6125/ © 2019 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.
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Fig. 1. Butt joint models: (a) geometric model; (b) finite element model. Table 1 Material parameters of A7N01 aluminum alloy. Temperature (°C)
Density (kg m−3)
Specific heat (J kg−1 °C−1)
Thermal conductivity (W m−1 °C−1)
Thermal expansion coefficient (°C−1)
Yield stress (MPa)
Young's modulus (Pa)
Heat transfer coefficient (W m−2 °C−1)
20 100 250 400 550 700 850 1000
2780 2760 2730 2700 2660 2450 2430 2420
869 912 981 1040 1189 1110 1066 1015
156 164 174 182 189 88 92 105
2.38E-5 2.42E-5 2.52E-5 2.65E-5 2.71E-5 2.76E-5 2.81E-5 2.90E-5
295 285 125 48 12 5 5 5
7.00E10 6.60E10 5.65E10 2.60E10 1.07E10 5.00E9 3.80E9 3.00E9
8.2 10.9 18.5 33.6 49.1 55.9 57.9 60.2
Table 2 Welding conditions of A7N01 aluminum alloy welded joint for numerical simulation. Weld bead
Voltage (V)
Current (A)
Welding speed (mm s-1)
Thermal efficiency of arc
First welding Second welding
20 19
170 155
5 10
0.75 0.75
requirements, and lengthy processing time. However, the inherent strain method was more suitable for large and complex structures. Ueda et al. [10,11] introduced the concept of inherent strains, they stated that the weld residual stress and distortion that are generated during the welding process were caused by the inherent strain. For large and complex structures, only the inherent strain need to be calculated, and then the residual stress can be obtained by using one linear elastic calculation. Thereafter, the inherent strain was used in the prediction of welding distortion [12,13] and residual stress
Fig. 2. Involved nodes and boundary conditions.
[14–17]. To predict residual stresses in butt joints, Khurram and Shehzad [14] employed the equivalent load method based on inherent strains; the simulation results agreed well with the experimental values. Ueda et al. [16] experimentally verified the validity and practical application of predicting three-dimensional residual stresses in T-type 381
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Fig. 3. Transient temperature fields of butt joint: (a) 23.2 s; (b) 125.8 s; (c) 165.2 s; (d) 4755.0 s.
fillet welds using inherent strains. These references indicated that both the inherent strain analysis and thermal elastic–plastic analysis were effective in evaluating residual stress. In this study, the inherent strain was applied to predict the residual stress in shell models of welded joints; this provided a basis for predicting the residual stress in large complex thin-plate welded structures. By applying the thermal elastic–plastic method, which involves the birth and death element technique and the indirect thermal-mechanical coupling method, the process of adding solder to the components during welding is simulated. In order to show the residual stress clearly, the small deformation is not presented considering that residual stress and plastic deformation are related. This paper focuses on the value and distribution of residual stress by applying a finite element commercial software. In Section 2, the welding temperature field and residual stress field of a butt joint are simulated and analyzed. In the experiment, the joint is welded by means of the MIG welding, and the corresponding data are compared with the simulation data. In Section 3, both the
Fig. 4. Temperature history of involved nodes.
Fig. 5. Residual stress fields of butt joint: (a) longitudinal; (b) transverse. 382
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Fig. 6. Experimental equipment: (a) ABB/ IRB 1410 welding robot; (b) X-ray residual stress analyzer; (c) butt joint for residual stress measurement.
Fig. 7. Comparison of residual stress obtained by experiment and simulation: (a) longitudinal stress along line A; (b) transverse stress along line A; (c) longitudinal stress along line B; (d) transverse stress along line B.
edge is 1 mm, and the gap between the two plates is 1.6 mm. During the actual welding process, the temperature of the weld and the heat-affected zone in the vicinity drastically changed; on the other hand, the change in temperature away from the base metal of the weld is relatively gradual. In order to improve the convergence of computational results, the joint is divided into 2 mm segments along the weld direction. To accomplish this, a mapped grid discrete model is used while taking into consideration the relative balance between numerical simulation accuracy and economics. The joint along the vertical weld direction is divided into eight segments; the heat-affected zone and the adjacent parent metal mesh size are determined as 2 mm, 3 mm, and 5 mm. Solid70, which has a 3D thermal conduction capability, is used as
thermal elastic–plastic method and inherent strain method are used to simulate and analyze the stress fields of different welded joints with solid models and shell models. The main conclusions are summarized in Section 4.
2. Residual stress in butt joint 2.1. Finite element modeling and calculation As shown in Fig. 1, a 250 × 300 × 8 mm3 double-pass welded butt joint made of aluminum alloy A7N01 is fabricated; this is based on the actual joint used in the welding experiment. The groove is 70°, the blunt 383
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be extremely high and would not match actual scenarios. The latent heat of phase change is treated through heat enthalpy of materials at different temperatures. The weldment is subjected to a large amount of local heat input during the welding process that produces a considerably uneven temperature field. During the molten pool formation, the heat source transfers heat to the weldment particularly through radiation and convection. After the temperature of the base metal in the heat-affected zone increases, the heat is mainly transmitted to the area away from the weld through conduction. The numerical model of the welding temperature field is a typical nonlinear transient heat conduction problem. Its constitutive equation is as follows:
Table 3 Parameters and welding conditions of typical welded joints. Thickness (mm)
Number of weld beads
Angle of the groove (°)
Voltage (V)
Current (A)
Welding speed (mm s-1)
Butt joints
t3.5 + t3.5 t4.5 + t4.5 t7.0 + t7.0
1 1 2
70 70 70
20 25 20 21
150 160 152 180
6 6 10 6
T-joints
t4.0 + t4.0 t6.0 + t6.0
1 2
45 45
20 22 25
140 165 180
6 10 6
Lap joints
t3.0 t4.0 t6.0 t8.0
1 1 1 1
None
24 25 25 25
150 155 185 195
5 5 5 5
+ + + +
t4.7 t4.0 t7.0 t8.0
cρ
∂T ∂ ⎛ ∂T ⎞ ∂ ⎛ ∂T ⎞ ∂ ⎛ ∂T ⎞ = + + λ λ λ + Q˙ ∂t ∂x ⎝ ∂x ⎠ ∂y ⎝ ∂y ⎠ ∂z ⎝ ∂z ⎠ ⎜
⎟
(1)
where c is the specific heat capacity; ρ is the density; λ is the thermal •
conductivity; T is the function of temperature field; Q is the rate of internal heat generation; t is the heat transfer time. In this study, the internal heat generation rate heat source model combined with the birth and death element technology is used to simulate the movement of the welding heat source and the filling process of the weld. The internal heat generation rate is a body load in the thermal analysis; moreover, it can be assigned to the elements in the molten pool. It is expressed as follows:
the temperature field solution. The elements are replaced by equivalent structural elements, such as Solid185, when the model is structurally analyzed. In the numerical simulation of welding, the value of each performance parameter of the material as a function of temperature is required. The material used in this study is A7N01 aluminum alloy; its material parameters are summarized in Table 1. Besides, the initial temperature of the weld is 20 °C and the Poisson's ratio is 0.33. For the welding temperature field analysis, it is necessary to identify thermal physical parameters as follows: thermal conductivity, convection coefficient, density, specific heat, melting point, and initial component temperature. Moreover, for the stress and strain field simulation, determining Poisson's ratio, Young's modulus, thermal expansion coefficient, and yield limit is necessary. During the welding process, the metal at the molten pool of the component underwent melting and solidification. No temperature change is observed during the solid–liquid phase transition because of the latent heat of phase change. If this is not taken into consideration, the temperature of the simulation would
HGEN = UIη /(Aweld × v × dt )
(2)
where HGEN is the heat generation rate applied for each load step; U is the welding voltage; I is the welding current; η is the thermal efficiency of the arc; Aweld is the cross-sectional area of the weld; v is the welding speed; dt is the time step for each load step. According to literature [18], the thermal efficiency of the MIG welding arc is 0.75 in this simulation. The welding conditions are listed in Table 2. During the welding process, both the weldment and the heat source exchange heat with the surrounding medium by convection. In the solution of temperature field, the convective heat transfer and thermal radiation are considered as the heat transfer coefficients of the material.
Fig. 8. Models of Typical joints: (a) butt joint; (b) T-joint; (c) lap joint. 384
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Fig. 9. Residual stress fields in typical joints: (a) longitudinal stress in butt joint with 4.5-mm thickness; (b) transverse stress in butt joint with 4.5-mm thickness; (c) longitudinal stress in T-joint with 6.0-mm thickness; (d) transverse stress in T-joint with 6.0-mm thickness; (e) longitudinal stress in lap joint with 6.0–7.0-mm thickness; (f) transverse stress in lap joint with 6.0–7.0-mm thickness.
Fig. 10. Lines of joints: (a) T-joint (b) lap joint.
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Fig. 11. Residual stress along lines of T-joint: (a) longitudinal stress along line 1; (b) transverse stress along line 1; (c) longitudinal stress along line 2; (d) transverse stress along line 2.
of metallic materials in the plastic zone obeys the plastic flow and strain hardening law. Temperature-dependent mechanical properties and stress strains vary linearly over a small time increment. The obtained temperature field is applied as a body load to the weldment to calculate the welding stress field. The material undergoes deformation during the welding process. The total strain at a certain point consists of several components as follows:
All the outer surfaces of the model are considered as heat transfer surfaces, and they are selected for the application of material parameters to simulate the entire heat transfer process. The heat transferred is taken into consideration as follows:
qc = −β (Ts − T0)
(3)
where β is the surface heat transfer coefficient; Ts is the surface temperature of the weldment; T0 is the temperature of the surrounding medium. In this simulation, the entire welding process is divided into two processes: heating and cooling. For the first welding, the heating and cooling times are 50 s and 60 s, respectively; both heating and cooling have a time step of 0.4 s. For the second welding, the heating and cooling times are 25 s and 6000 s, respectively, both with a time step of 0.2 s. The entire welding simulation process lasts 6165 s. In calculating the stress fields, it is necessary to impose constraints on the model. The basic principles are as follows: the rigid displacement of the model must be eliminated, and the degree of freedom must not be overconstrained. As illustrated in Fig. 2, the boundary conditions in this simulation are as follows: a full constraint is applied to one edge of the lower surface of the butt joint, and one edge imposes a constraint along the plate thickness direction. To improve the convergence of stress field results, the complete Newton–Raphson method is implemented. The welding thermal stress process is considerably complicated. In order to improve the calculation accuracy, the welding thermal stress field is simplified to a nonlinear transient problem of the material. The elastic–plastic mechanical model is used for finite element calculation. The yield of the material follows the Von Mises criterion. The behavior
εt = εe + εp + εth
(4)
where εe is the elastic strain; εp is the plastic strain; εth is the thermal strain, which relates to thermal expansion coefficient and rate of temperature change. The elastic strain–stress relationship is modeled using the isotropic Hooke’s law. The material parameters (such as Young's modulus, yield strength) used in the mechanical analysis are summarized in Table 1. 2.2. Analysis of results From the calculation results of the transient temperature field of the welded joint, the temperature fields of 23.2 s, 125.8 s, 165.2 s, and 4755.0 s are selected, as depicted in Fig. 3. In the middle of the first welding process and that of second welding process, the welding temperature field is uniform. Because of the short heating time, the temperature field is mainly concentrated in the weld and its vicinity. At the beginning of the cooling process, the cooling rate is faster, and the heat is transmitted from the vicinity of the weld to the base metal of the component. During the welding process, the temperature changes, and the 386
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Fig. 12. Residual stress along lines of lap joint: (a) longitudinal stress along line 1; (b) transverse stress along line 1; (c) longitudinal stress along line 2; (d) transverse stress along line 2.
joint is sufficiently cooled. A portable X-ray residual stress analyzer, μ-X360n , manufactured by Pulstec in Japan, is the welding residual stress instrument used (Fig. 6b); its advantages include high precision and portability. In order to verify the accuracy of the numerical results, the welding test is performed on the same model size with the same material. The welded joint is shown in Fig. 6c, and the residual stress is measured accordingly. The welding conditions are consistent with those in the numerical simulation, as listed in Table 2. Residual stresses are measured on the joint along lines A and B, as shown in Fig. 6c. The X-ray tube angle of the instrument should be adjusted to 25° to measure the residual stress in the aluminum alloy. When the X-ray tube is parallel to the measurement line, the gauged value is the longitudinal residual stress, whereas that measured in the vertical direction is the transverse residual stress. After the adjustment, the red spot is aligned with the measuring point to determine the residual stress values. The stresses obtained by simulation along lines A and B are presented in Fig. 7. The longitudinal residual stress on line A in the weld and some areas near the heat-affected zone is tensile stress; it is practically symmetric with respect to the centerline of the weld. Two peaks appear in the heat-affected zone; these peaks are 250 MPa and 259 MPa, which do not exceed the yield stress of the material. The heataffected zone away from the center of the weld and a part of the base metal exhibit compressive residual stress; most values are approximately 10 MPa. The transverse residual stress on line A is symmetrically distributed along the center line of the weld, and is tensile stress in most areas. Furthermore, in the heat-affected zone, there are two peak values, 12.9 MPa and 13.3 MPa. Compressive residual stress appears at the center of the weld and nearby areas with a peak value of less than
stresses at different locations in the joint are not consistent. To understand the temperature field of the model more clearly, the results of several positions are observed, as shown in Fig. 2. For the second welding, nodes A, B, C, and D are selected on the center line along the weld direction; the distance between each node and the welding start point is 20 mm, 50 mm, 80 mm, and 110 mm, respectively. The temperature profiles are exhibited in Fig. 4; the cooling process is eliminated. It can be observed that with the movement of the heat source during the welding process, the temperature at each point of the component initially increases and thereafter decreases because the welding heat source is loaded twice. The temperature at a node initially increases to the highest temperature and thereafter drops. The rate of temperature increase is significantly larger than the rate at which the temperature decreases. The temperature at each node tends to be constant during the cooling process. The residual stress along the weld direction is called the longitudinal residual stress, whereas that along the vertical weld direction is called the transverse residual stress. Only the residual stress on the upper surface of the model is extracted, as shown in Fig. 5. 2.3. Experimental verification In this study, the welding experiment equipment utilized is the ABB/IRB1410 welding robot, which is produced by ABB Group in Switzerland (Fig. 6a). This robot has adaptive current and voltage functions, and it can be operated for automatic welding only after certain necessary parameters (such as welding starting position, welding line, welding end position, and moving speed of the welding gun) are defined. A residual stress test is performed after the welded 387
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Fig. 13. Shell models: (a) butt joint; (b) T-joint; (c) lap joint.
because the instrument used in the test has a shallow incident depth. The surface quality near the weld is poor after welding; consequently, even the data at the center of the weld and its nearby areas cannot be measured. The distribution trend of experiment and simulation is basically the same, which indicates the rationality of predicting residual stress with the thermal elastic-plastic method for aluminum alloys.
50 MPa. The transverse residual stress in the middle section is considerably less than the longitudinal residual stress. The longitudinal stress on line B is basically tensile stress, and a uniform value appears in the middle of the weld. The peak value reaches 250 MPa, and the compressive stress is generated only near the arcing end. The transverse residual stress on line B exhibits compressive stress on the entire component. From the beginning of the arcing end, the stress initially increases before a uniform region appears; thereafter, the stress decreases. The stress along the uniform region reaches approximately 50 MPa, which is still significantly smaller than the longitudinal residual stress at this location. The difference indicates that the transverse residual stress rapidly decreases along the vertical direction of the weld. In summary, the longitudinal residual stress is more uniform than the transverse residual stress. The former stress is more uniform because the heat in the welding process is applied along the direction of the weld, and the heat constraints of the component are larger than those in the other directions. On the other hand, in the latter stress, the formation mechanism is more complicated; it generally has two parts. One part is caused by the longitudinal shrinkage of the weld and the nearby heat-affected zone, and the other is caused by the difference between the transverse shrinkage of the weld and the nearby plastic zone. In general, in the cross-section of the weld direction, the transverse residual stress caused by the longitudinal shrinkage appears as compressive stress at the arcing and extinction end of the weld, whereas the tensile stress appears in the middle; as a result, a uniform region occurs. Therefore, the farther the weld, the smaller the stress. There will be a time difference during the welding heating process and cooling process, which will lead to the uneven distribution of temperature and stress perpendicular to the welding direction and eventually cause the transverse shrinkage of the weld joint. In Fig. 7, it can be observed that the residual stress profile that is obtained through numerical simulation is consistent with the trend of the experimental data; the values are approximately the same. This is
3. Residual stress in typical joints After the parameters (Table 3) of the welded joint model in the welding process of an aluminum alloy carbody are determined, finite element models are established to calculate the stress in every joint by employing the thermal elastic–plastic method. 3.1. Thermal elastic–plastic method Three types of joint models (Table 3) are built, as shown in Fig. 8. The length and width of the butt joints are 300 mm and 150 mm, respectively. The mesh size in the weld direction is 1.5 mm, and their sizes in the vertical weld direction are 1 mm, 2 mm, and 3 mm. The Tjoints have a web size of 300 × 150 mm2 and a flange size of 300 × 300 mm2. The mesh size in the weld direction is 1.5 mm, and their sizes in the vertical weld direction are 0.5 mm, 1 mm, 2 mm, and 3 mm. The length and width of each plate of the lap joint are 150 mm and 100 mm, respectively. The mesh size in the weld direction is 2 mm, and the sizes in the vertical weld direction are 2 mm, 3 mm, and 4 mm. The welding conditions for the simulation of the welding residual stress fields of various joints are listed in Table 3. Referring to Kirchhoff plate theory, a thin plate is a structure that possesses one dimension that is far smaller than the other two [19]. For most welded sheets in Table 3, the height is far smaller than the length and width and thus it can be considered as a thin plate. For each type of joint, only one figure is shown. The residual stress 388
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Fig. 14. Comparison of residual stresses along the lines of butt joint with a 3.5-mm thickness: (a) longitudinal stress along line 1; (b) transverse stress along line 1; (c) longitudinal stress along line 2; (d) transverse stress along line 2. (TEPM = Thermal elastic–plastic method; ISM = Inherent strain method).
fields of butt joint, T-joint, and lap joint with thicknesses of 4.5 mm, 6.0 mm, and 6.0–7.0 mm are illustrated in Fig. 9. It can be observed in Fig. 9 that the longitudinal residual stress values of the three joints are considerably larger than those of the transverse residual stresses, and the maximum longitudinal residual stress in each joint does not exceed the yield stress of the material. In fact, the contours of the same type of joints have similarities with regard to their longitudinal and transverse stresses; moreover, thickness affects the values of residual stress. For the butt joint, the longitudinal residual stress decreases as the thickness increases, whereas the transverse residual stress increases as the thickness increases. To clearly illustrate the stress results, the lines presented in Fig. 10 are the sections where the stresses are extracted. Because the results of the butt joint are similar to those of the numerical simulation exhibited in Fig. 7, these results no longer require illustration; thus, in Fig. 10, only the T-joint and lap joint are taken as examples. It can be observed in Fig. 11 that the longitudinal residual stress on line 1 of the T-joint single-pass welding model is larger than that of the double-pass welding model. The stress profile of the single-pass welding has only one peak in the heat-affected zone, whereas two peaks are observed in that of the double-pass welding. Because the welds of the Tjoint are located only on one side, the residual stress on that side is significantly larger than that without the weld. The longitudinal residual stress on line 2 of the T-joint is compressive at the arcing and extinction end of the weld. At the middle position of the weld, tensile stress and a uniform area occur. The residual stress value of the doublepass welding joint is smaller than that of the single-pass welding joint. The transverse residual stress in the double-pass welding on line 1 is tensile stress in the heat-affected zone, and the compressive stress
occurs at the center of the weld. Both tensile and compressive stresses are observed at the heat-affected zone of the single-pass welding joint. The transverse residual stress on line 2 is more consistent than that on line 1. Except for the arcing end where the compressive stress is approximately 125 MPa, practically no residual stress in the remaining parts is observed; moreover, a uniform area appears in the middle of the weld. It can be observed in Fig. 12 that the longitudinal residual stress on line 1 of the lap joint has no distinct double-peak; the residual stress value decreases with the increase in the thickness, and the residual stress profiles are considerably similar. Among these, the maximum longitudinal residual stress in the lap joint that has 3.0–4.7 mm thickness is 230 MPa. Similar to T-joints, the residual stress value on the side with the weld is significantly larger than the side without the weld. The profiles of the transverse residual stress on line 1 are also practically the same; the value does not change considerably with thickness. The longitudinal residual stress on line 2 is compressive at the arcing and extinction end of the weld; the tensile stress in the middle of the weld and a uniform area simultaneously appear. The residual stress value is inversely proportional to the thickness of the lap joint. The transverse residual stress on line 2 of the lap joint increases with the increase in thickness, and a long uniform compressive stress region appears in the middle of the weld. The stresses at the arcing and extinction end of the weld are mostly compressive stresses.
3.2. Inherent strain method The inherent strain can be divided into two categories: longitudinal and transverse. The longitudinal inherent strain is along the direction of 389
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Fig. 15. Comparison of residual stresses along the lines of T-joint with 4.0-mm thickness: (a) longitudinal stress along line 1; (b) transverse stress along line 1; (c) longitudinal stress along line 2; (d) transverse stress along line 2. (TEPM = Thermal elastic–plastic method; ISM = Inherent strain method).
strain; h is the plate thickness; z is the coordinate in the thickness direction. When the inherent distortion of a welding component is known, the corresponding inherent strain can be identified. When the inherent strain is used in elastic finite element, it is usually assumed to be evenly distributed on the weld. Therefore, the average value of the inherent strain in the joints is used to represent the approximate inherent strain distribution in the entire welded joint. The average values of inherent strains in joints are calculated by the following equations [20]:
the weld; this causes the component to produce shrinkage distortion and transverse residual stress along the weld. On the other hand, the longitudinal inherent strain is along the vertical direction of the weld. This causes the component to produce shrinkage distortion and longitudinal residual stress along the vertical direction of the weld; moreover, it causes angular distortion on the welding component. The transverse inherent strain is generally considerably smaller than the longitudinal inherent strain. The inherent strain values of the weld and its adjacent areas are applied as initial loads to the welded component, and residual stress fields and weld distortion can be obtained through elastic calculation. Based on experimental observations and theoretical analysis, it is found that the total welding distortion in the welded structure is mainly composed of four parts: longitudinal shrinkage, δx ; transverse shrinkage, δ y ; longitudinal bending, θx ; transverse bending, θy . These four main parts are called inherent distortions. According to the results of the thermal elastic–plastic method, the four abovementioned inherent distortions of a certain cross-section along the weld can be calculated by the following equations:
1 δx = h
∫∫
εxp dydz
(5)
∫ ∫ εyp dydz
(6)
δy =
1 h
θx =
12 h3
∫ ∫ εxp (z − h 2 ) dydz
θy =
12 h3
∫ ∫ εyp (z − h 2 ) dydz
where
εxp
is the longitudinal plastic strain;
∫0
L
1 δ¯y = Lw
∫0
L
1 θ¯x = Lw
∫0
L
1 θ¯y = Lw
∫0
L
δx dx δ y dx θx dx θy dx
(9) (10) (11) (12)
where L w is the length of the weld; L is the length of the component. Strain values cannot be applied directly to the weld and its adjacent elements as loads. The anisotropic thermal expansion coefficient provided by the finite element analysis software can be used to generate a different weld shrinkage along the longitudinal and transverse directions. The load is applied by using a unit temperature load. The solid models of the three types of joints are described above. In order to apply the inherent strain method more accurately, the shell element is used due to its applicability to thin-plate structures, and the shell models of the three types of joints are established according to the mesh sizes of the solid models illustrated in Fig. 13. The plastic strain
(7) (8)
ε yp
1 δ¯x = Lw
is the transverse plastic 390
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Fig. 16. Comparison of residual stresses along the lines of lap joint with 3.0–4.7-mm thickness: (a) longitudinal stress along line 1; (b) transverse stress along line 1; (c) longitudinal stress along line 2; (d) transverse stress along line 2. (TEPM = Thermal elastic–plastic method; ISM = Inherent strain method).
stress value, and that obtained through the inherent strain method of the shell model is the smallest. This is because the maximum stress position of the joint is generally on the upper surface of the component. When the inherent strain is applied to solid models, the average plastic strain in all the weld joints is calculated. Therefore, the surface stress obtained by using the inherent strain method is smaller than that yielded by the thermal elastic–plastic method. In addition, the shell models simplified the details of the weld; this results in a smaller stress value than that of the inherent strain applied to the solid. The tensile stress obtained by the inherent strain method is smaller than that yielded by the thermal elastic–plastic method for the longitudinal residual stress profile of line 1. This is because the inherent strain is only applied to the weld zone. Because the residual stress value outside the weld zone is small, it can be ignored. For the profiles of the transverse stress on line 2, the results of the inherent strain method are more moderate than those of the thermal elastic–plastic method. Moreover, the uniform areas in the middle of the weld are larger in the thermal elastic–plastic method; this is because the average plastic strain is applied. The accuracy can be verified to predict the residual stress in welded joints through the use of the inherent strain method and shell models. The inherent strain method, which is economical and efficient, is generally applied to predict the residual stress for full-scale complex thin-walled structures. Considering a train carbody as an example in terms of geometric characteristics, the length, width, and height of the aluminum alloy profiles used in it are approximately 25,000 mm, 3500 mm, and 3600 mm. Evidently, these dimensions are considerably larger than its thickness of 3–12 mm. Accordingly, the shell model is adopted for the finite element analysis, as shown in Fig. 17. It can be observed that the carbody has various joints, such as butt joint, lap joint, and T-
Fig. 17. The shell model of a train carbody and some welded joint details.
values extracted from the calculation results of the thermal elastic–plastic method of solid models are applied to both solid and shell models; the residual stress results of the inherent strain method are obtained. The lines in Figs. 6c and 10 show the extracted stresses of the three types of joints. Because there are numerous joints, only the butt joint with a 3.5 mm thickness, the T-joint with a 4.0 mm thickness, and the lap joint with a 3.0–4.7 mm thickness are considered; the residual stress along the lines are shown in Figs. 14–16. The residual stress distributions of the butt joint, T-joint, and lap joint in the middle section and the centerline of the weld are consistent in the two calculation methods, and their stress values are not considerably different, which can show that the trend is basically the same. The thermal elastic–plastic method of the solid models yields the largest 391
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Fig. 18. The residual stress distribution of the train carbody.
References
joint. According to the results of the shell models of joints, the inherent strain is applied to the train carbody to predict the welding residual stress. The distribution of residual stress is shown in Fig. 18. Based on this, the influence of residual stress on the fatigue and fracture performance of the carbody can be evaluated further. This provides a basis for the post-weld adjustment of the residual stress in a large carbody structure and the accurate analysis of the influence of welding residual stress on fatigue fracture performance. In recent research, the author [21] studied the effect of welding residual stress on the fatigue strength of aluminum alloy carbody of a high speed train. It is found that under the influence of welding residual stress, the average stress of the weld zone was obviously increased, which made the carbody easy to fatigue failure. In addition, the residual stress significantly changed the direction of the maximum principal stress at the weld zone.
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4. Conclusions The main conclusions are as follows: (1) The longitudinal residual stress and the transverse residual stress were generally tensile stresses in the weld areas and the adjacent heat-affected zone; the transverse residual stress was considerably smaller than the longitudinal residual stress. The numerical simulation results were in good agreement with the experimental results. (2) The residual stress in the middle section of different joints and along the centerline of the weld was consistent using the two calculation methods; the trend of the stress values was basically the same, which indicated the accuracy of the inherent strain method for the prediction of welding residual stress fields. (3) The residual stresses of the shell and solid models of joints were consistent, and the inherent strain method was economical and efficient, which suggested that the application of shell models and inherent strains was practicable for thin-plate welded structures.
Acknowledgments This work was supported by the Sichuan Province Science and Technology Support Program (Grant No. 2018HH0072) and National Natural Science Foundation of China (Grant No. 51275428). 392
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[21] Lu YH, Zhang DW, Zhao ZT, Liu JJ, Lu C. Influence of welding residual stress on fatigue strength for EMU aluminum alloy carbody. J Traffic Transp Eng 2019;19(4):94–103. (in Chinese).
Structural analysis. Solid mech its appl, 163. Dordrecht: Springer; 2009. p. 819–914. [20] Deng D, Murakawa H. Prediction of welding distortion and residual stress in a thin plate butt-welded joint. Comput Mater Sci 2008;43(2):353–65.
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