- Email: [email protected]
Brazed residual stress in a hollow-tube stacking: Numerical simulation and experimental investigation
Journal of Manufacturing Processes 31 (2018) 35–45
Contents lists available at ScienceDirect
Journal of Manufacturing Processes journal homepage: www.elsevier.com/locate/manpro
Research Paper
Brazed residual stress in a hollow-tube stacking: Numerical simulation and experimental investigation Yu-Cai Zhang a , Wenchun Jiang a,∗ , Huiqin Zhao a , Zhiquan Wei a , Shan-Tung Tu b a
State Key Laboratory of Heavy Oil Processing, College of Chemical Engineering, China University of Petroleum (East China), Qingdao, 266580, PR China Key Laboratory of Pressure System and Safety (MOE), School of Mechanical and Power Engineering, East China University of Science and Technology, Shanghai 200237, PR China b
a r t i c l e
i n f o
Article history: Received 2 May 2017 Received in revised form 24 October 2017 Accepted 2 November 2017 Key words: Hollow-tube stacking Brazed joint Residual stress Finite element method X-Ray diffraction
a b s t r a c t In this study, the residual stresses of a hollow-tube stacking made of 316L stainless steel by brazing technology have been analyzed by finite element method and X-ray diffraction method. The results show that simulated results are in good agreement with the experimental data, reflecting the feasibility of finite element method to calculate the residual stress. Large tensile stresses are generated in the brazing filler metal, decreasing the cooling rate can decrease the residual stress. With the tube diameter, brazing filler metal thickness increasing, or tube length decreasing, the residual stresses in the filler metal decrease. Increasing the wall thickness can decrease the transverse stress at the middle region of the brazing filler metal, while it can increase the longitudinal stress at the vicinity of brazing fillet. The matrix size of the hollow-tube stacking has little effect on the stress distribution of the 316L/BNi-2 brazed joint. When the tube diameter is increased to 8 mm, the residual stress in the fillet transforms into compressive stress and thus can decrease the cracking sensitivity in the fillet. It is proposed that the diameter of tube should not be less than 8 mm from the viewpoint of generating compressive stress. © 2017 Published by Elsevier Ltd on behalf of The Society of Manufacturing Engineers.
1. Introduction Hollow-tube stacking, a kind of cellular structure, is very promising as lightweight aeronautical frames since it has superior specific mechanical properties such as structural or impact resistance [1,2]. The core of the hollow-tube stacking is fabricated by the brazing technology, and plenty of brazed joints are generated between the hollow-tubes. For many metallic cellular materials, a lot of cracks will be generated in the brazed joints, which named as node failure. Sun and Gao [3] studied the mechanical behaviour of a composite pyramidal truss core sandwich panel. The results indicate that two kinds of failure modes are observed in the sandwich panel: the strut fracture and node rupture. Xiong et al. [4] also found that the node failure and the strut buckling are the main failure modes for carbon fiber pyramidal truss sandwich panel. There are mainly two reasons are generalized for the node failure. One is that the deformation of strut leads to the stress concentration at the node due to the geometrical discontinuity. In order to decrease this type of stress concentration, Queheillalt [5] proposed a liquid interface diffusion bonding approach to form a large fillet between
∗ Corresponding author. E-mail address: [email protected] (W. Jiang).
the truss and face-sheet interface, which is helpful to decrease the stress concentration and increase the interfacial strength. Jiang et al. [6] also found that a larger fillet can decrease the stress concentration and increase the tensile strength for brazed plate-fin structure. The other reason is that the brazed residual stresses generated by the mismatching of mechanical properties between the brazing filler metal and substrate metal [7]. The brazed residual stresses have a great effect on the structure fracture [8–10] and buckling [11–13]. Therefore, it is very important to decrease the brazed residual stress for ensuring the structure integrity. The brazing filler metal is surrounded by the base metal, the whole brazed joint like a kind of sandwich structure. The thickness of brazing filler metal is only about 30–100 m, while the thickness of base metal is several millimeters or even more thick. Therefore, it is a challenging question to measure the residual stress accurately in the brazed joint, especially for the stress characterization of the brazing filler metal. X-ray diffraction (XRD) [14,15] and neutron diffraction method [16] are widely used to measure the residual stress. Although the XRD cannot measure the inner stress of the brazed joint directly limited by the penetrate capability [17], stress gradients can be characterized in combination with the layer removal by electrochemical polishing technique. Neutron diffraction can penetrate into the material and test the residual stress directly due to the higher penetrate capability. However, it is a pity
https://doi.org/10.1016/j.jmapro.2017.11.002 1526-6125/© 2017 Published by Elsevier Ltd on behalf of The Society of Manufacturing Engineers.
36
Y.-C. Zhang et al. / Journal of Manufacturing Processes 31 (2018) 35–45
that both the two methods cannot measure the stress in the filler metal for the limitation of gauge volume. At present the minimum gauge volume of X-Ray and neutron beam is about 1 ∼ 2 mm, which is much larger than the thickness of brazing filler metal [18]. Some researchers adopted the neutron diffraction to measure the brazed residual stress [19], however, the measured position located in the base metal rather than the brazing filler metal. Nano-indentation can measure the stress in the micro-region, but it requires a good smooth surface, and the cutting and grinding process will relax the residual stress in the brazed joint [20]. Hamilton et al. [21] pointed out that the validation of brazed residual stress is still further required. Therefore, it is very difficult to determine the brazed residual stress in the brazing filler metal by experimental method up to now. With the development of computer technology, finite element method (FEM) is widely used to predict the residual stress in the brazed joint [22–24], and the residual stress in any region of the brazed joint can be obtained directly by the FEM. Zhang et al. [25] studied the residual stress in a brazed joint between the alumina and 304 stainless steel by FEM. The results demonstrated that Ni and Ni-Cr filler metals are compliant layers, and they are suitable to relieve the residual stress. Riccardo et al. [26] investigated the brazed residual stress in hybrid package for integrated substrate packaging applications, it is found that the residual stress in the substrate decreases with the thickness of barrier layer increases. Hamilton et al. [27] found that the thermal autofrettage can decrease the residual stress in brazed joint. Barrena et al. [28] studied the residual stress in the brazed joint between 90MnCrV8 steel and cemented carbide by FEM. The results illustrated that the residual stresses are very large and they can significantly decrease the joint strength. The maximum peak stress is located in the brazing filler metal-cemented carbide interface. Increase the brazing time can decrease the residual stress and thus improve the shear strength of the brazed joint. However, an excessive brazing time can generate intermetallic compound in the brazed joint, and in turn, decrease the strength of the brazed joint. He et al. [29] examined the residual stresses in Si3 N4 CGM filler alloy-42CrMo joints by FEM. The effects of gradient material compositions, layer numbers and thicknesses on residual stresses have been discussed. It depicted that the CTE mismatch between the joined materials and the ability of plastic deformation in the brazing filler metal were the two factors that determine the residual stresses level in brazing joint. Jiang et al. [24,30] studied the effect of structure dimensions on residual stress in the compact plate-fin heat exchanger by FEM, which provides a guidance to improve the joint performance. For the hollow-tube stacking, V. Marcadon et al. [1] analyzed the mechanical behaviour by experimental characterization and modelling. It is found that the heterogeneity of the brazed joints generates stress concentration in the fillet. However, the distribution of brazed residual stress and how to decrease the residual stress are still need to be investigated. In this paper, the residual stress in a brazed hollow-tube stacking was investigated by finite element and experimental method, and the effects of tube diameter and cooling rate on the residual stress magnitude and distribution were fully discussed. Based on the calculated results, it is proposed to generate the compressive residual stress in the brazed joint by the self-expansion of tube to improve the strength of the whole joint.
2. Finite element modeling 2.1. Fabrication introduction of the hollow-tube stacking Fig. 1 shows a hollow-tube stacking consists of two sheets and a tube-stacking core. Tubes were stacked in a graphite die lined
Fig. 1. Schematic of a hollow-tube stacking.
with sheets which positioned at the top and bottom. The brazing filler metal of BNi-2 was pre-positioned between the tubes and face plates. Then the assembly was clamped tightly to prevent the free movement of the substrate materials and brazing filler metal. The stacking was formed by high temperature brazing at a vacuum furnace, the assembly was firstly heated to 800 ◦ C within 50 min and the temperature was held for about 30 min. Then it was heated to the brazing temperature of 1100 ◦ C within 30 min and the temperature was lasted for about 25 min. At last, the assembly was cooled to the ambient temperature in the furnace. The melting temperature of filler metal BNi-2 is about 1020 ◦ C. At the brazing temperature of 1100 ◦ C, the brazing filler metal is liquid while the tube and plate are still solid. The filler metal flows into the gap between the two plates by wetting and capillary action. After cooling to the environmental temperature the assembly are joined together to form the stacking. The materials of the tube and plates are 316L stainless steel. Due to the constraint and difference of mechanical properties between the tube and BNi-2, large residual stresses will be generated in the joint. In this paper, we developed a sequential coupling finite element method to study the brazing temperature and residual stress. The brazing temperature field was firstly simulated by a thermal analysis, and then the residual stresses were calculated by a thermal-elastic-plastic constitutive model.
2.2. Finite element model and meshing As shown in Fig. 1, the outer diameter and thickness of tubes are 2 mm and 0.2 mm, respectively. The joint width is around 0.7 mm. The tube length is 10 mm. The plate length, width and thickness are 10 mm, 8 mm and 0.2 mm, respectively. The stacking is four tubes wide and five tubes high. Finite element software ABAQUS was used to calculate the temperature distribution and residual stress. Fig. 2 shows the finite element meshing of the hollow-tube stacking. Dissimilar materials are assumed to be perfectly bonded at interfaces. The number of element and node are 201330 and 246977, respectively. The element type of temperature calculation is DC3D8, and stress analysis type is C3D8. In order to improve the calculation accuracy and save calculation time, the meshing around the brazed joints is refined and the other parts away from the joint are relatively coarse.
Y.-C. Zhang et al. / Journal of Manufacturing Processes 31 (2018) 35–45
37
Fig. 2. FE meshing of the hollow-tube stacking.
where s is the volume of the heat source, the material density, C the specific heat, T the temperature, t the time, and K the conductivity. The heat convection was calculated by
˚ = hA tw − tf
(2)
where ˚ is the heat transfer in unit time, h the convective heat transfer coefficient, A the contacting area, tw the temperature of solid surface and tf the temperature of fluid surface. It is should be mentioned that h is a non-physical property parameter and related with the ambient. The size of brazed joint is small compared to the space of brazing environment, so the value of h can be considered as a constant, h = 10W/(m2 ◦ C) in present paper. The heat radiation was calculated by: q = εAω((Ts + 273.15)4 − (Tfurn + 273.15)4 )
(3)
where q is the irradiance, ε the emissivity (the value is about 0.8 in the brazing furnace), Ts the temperature of brazed parts and Tfurn the temperature of high vacuum furnace. ω is the Stefan-Boltzmann constant (ω = 5.67e − 8W m−2 K−4 ).
Fig. 3. Boundary conditions of the hollow-tube stacking.
2.3. Boundary conditions
2.5. Residual stress analysis
In order to accurately simulate the as-brazed residual stress of the hollow-tube stacking, the proper boundary conditions which correspond with the actual brazing process should be applied on the finite element model. Fig. 3 depicts the boundary conditions applied on the hollow-tube stacking finite element model. During the brazing process, the tubes were constrained tightly by the vertical baffle to prevent the free movement. Therefore during the simulation process, the displacements of the surfaces which contact the vertical baffle were constrained in X-direction (Face 1: U1 = 0) and Z-direction (Face 2: U3 = 0), respectively. And the displacement of the bottom plate face was constrained in Y-direction (U2 = 0). A pressure load of 1 MPa was applied on the top face to keep a tight contact between the components.
The residual stress was calculated by thermal-elastic-plastic model, and the temperature field used for the stress calculation was called the data obtained from the thermal analysis. The total strain is decomposed into elastic strain, plastic strain and thermal strain:
2.4. Brazing temperature simulation The brazing temperature simulation was carried out by considering thermal conduction, heat convection and radiation. Three-dimensional heat conduction was calculated by:
s=−
C
∂T + ∇ (K ∇ T ) ∂t
(1)
{dε} = {dε}p + {dε}e + {dε}T
(4)
where {dε} is the total strain, {dε}p the plastic strain, {dε}e the elastic strain, {dε} T the thermal strain. Elastic strain was modeled using the isotropic Hooke’s law with temperature-dependent Young’s modulus and Poisson’s ratio. The thermal strain was calculated using the temperature-dependent coefficient of thermal expansion (CTE). For the plastic strain, a rate-independent plastic model was employed with Von Mises yield surface, temperature-dependent mechanical properties and isotropic hardening model. The temperature dependent material properties are listed in Tables 1 and 2 [31,32]. 3. Experimental testing XRD plays a prominent role in the stress measurement due to its simplicity of operation and high accuracy [16]. Although the XRD
38
Y.-C. Zhang et al. / Journal of Manufacturing Processes 31 (2018) 35–45
Table 1 Thermal properties of 316L steel and BNi-2. Material
Temperature (◦ C)
Conductivity (W/(m ◦ C))
Density (Kg/m3 )
Specific heat (J/(◦ C kg))
316 L
20 400 900 20 400 900
13.3 19.5 26.33 25.6 29.2 33.6
7966 7966 7966 7850 7850 7850
492 538 659 469 577 1161
BNi-2
Table 2 Mechanical properties of 316L steel and BNi-2. Material
Temperature (◦ C)
Young’s modulus (GPa)
Poisson’s ratio
CTE (1/◦ C)
Yield strength (MPa)
316 L
20 400 900 20 400 800
196.5 172.6 116.8 205.1 183.2 161.0
0.29 0.29 0.29 0.296 0.306 0.328
1.46 × 10−5 1.74 × 10−5 1.90 × 10−5 1.35 × 10−5 1.68 × 10−5 19.9 × 10−5
243 163 99 300 220 160
BNi-2
Fig. 4. Schematic illustration of the brazed joint.
Fig. 5. Residual stress along P3 by FEM and XRD.
cannot measure the residual stress in the brazing filler metal of the brazed joint, the stress in the substrate metal can be characterized in combination with the layer removal by electrochemical polishing technique. Based on the stress distribution in the substrate and the stress balance of the whole brazed joint, the stress distribution in the brazing filler metal can be deduced. However, constrained by the measuring space of the XRD, it is hardly to test the as-brazed residual stress of the hollow-tube staking directly. Therefore, the simulation method was used to analyze the residual stress of the hollow-tube stacking. In order to verify the feasibility of the finite element method to calculate the as-brazed residual stress, for testing purpose, two pieces of 316L stainless steel plates with 10 mm thickness, 12 mm length and 6 mm width were brazed together by the sheet-shaped brazing filler metal BNi-2 with 40 m thickness, as shown in Fig. 3. For comparison, the materials and brazing technology are the same as those mentioned in Section 2. Before the test, electrolytic polishing was used to process the surface of samples before test, which could avoid the surface compressive stress layer resulting from machinery grinding. The high voltage of the X-ray tube is 24.0 KV and the current is 5.0 mA. Mn-K␣ X-ray was launched on the crystalline phase (311) of the sample. The theory of residual stress measurement by X-ray diffraction method is based on the Bragg’s equation: = 2dsin
(5)
Where is the wave length, d the interatomic lattice spacing and the diffraction angle [33].
The method of was used to calculate the residual stress and the values of were 0.0◦ , 15.0◦ , 30.0◦ , 45.0◦ , respectively. The residual stress can be calculated according to the following equation [34,35]: = KM K =−
E cot 0 180 2(1 + v)
M=
(6)
∂ 2p
(7)
∂(sin2 )
(8)
where 0 is the diffraction angle under a stress-free state, the angle between the normal of the crystal surface and the material surface, K the stress constant of X-ray, and M the slope of the linear relationship between the position of diffraction angle 2p and sin2 at different values of . The test points are located on path P3, see as Fig. 4, and the distance interval is 1.5 mm. The tested residual stress will be used to analyze the stress distribution of the 316L/BNi-2 brazed joint and also to verify the feasibility and rationality of the FEM to calculate the residual stress in present paper. The simulation technologies of the tested specimen are the same as those used to the hollow-tube staking in Section 2, so they are not described in this Section.
Y.-C. Zhang et al. / Journal of Manufacturing Processes 31 (2018) 35–45
39
Fig. 6. Contour of the transverse (TD), normal (ND) and longitudinal stress (LD).
4. Results and discussion 4.1. Residual stress distribution Fig. 5 depicts the residual stress distributions measured by XRD and FEM method along P3. The residual stresses in X, Y and Z directions are defined as transverse (TD), normal (ND) and longitudinal (LD) stresses, respectively. The maximum value (355 ± 46 MPa) of the TD stress measured by XRD is located at the middle region of path P3, and it decreases gradually from the middle region to both sides of the path P3. While the maximum value measured by FEM is 293 MPa in the same position. For the ND stress, the results measured by XRD and FEM are 285 ± 43 MPa and 250 MPa, respectively. From the above analysis, it can be seen that there is a small difference between the results from XRD and FEM. Since the materials, brazing technological parameters of the specimen used in the
experimental test and the simulation technology are the same as those used in the hollow-tube staking, therefore, the well agreed experimental and simulation data in the Fig. 5 demonstrate that the FEM method used in present paper can be used effectively to predict the as-brazed residual stress of the hollow-tube staking. Fig. 6 shows the residual stress distribution of the hollow-tube staking. Since the single tube is axisymmetric, as clearly illustrated in Fig. 6a and b, the transverse and normal stresses have a similar distribution. Both the maximum of TD stress and ND stress are around 218 MPa, which are located in the horizontal and vertical brazing joints, respectively. The residual stresses in the brazing filler metal are tensile stresses, which are balanced by the compressive stress in the adjacent tubes. The maximum compressive stress is 121 MPa. For the LD stress (See Fig. 6c), the maximum value is 304 MPa, which located at the fillet of the brazing filler metal. It is also balanced by the compressive stress (the maximum value is
40
Y.-C. Zhang et al. / Journal of Manufacturing Processes 31 (2018) 35–45
Fig. 7. Residual stress distribution along path P1 (a) and P2 (b).
−92 MPa) in the adjacent tubes. In general, the residual stress in the hollow-tube structure shows a self-equilibrating distribution: large tensile residual stresses are generated in the brazing filler metal and balanced by the compressive stress in the adjacent tube. Fig. 7 displays the residual stress distributions along path P1 and P2 in the brazed joint. P1 is the centerline of brazing filler metal in the horizontal filler metal, and P2 is along the thickness from tube-to-tube, as shown in Fig. 7a. The stresses in the three directions along P1 present M shape distribution. For the TD and LD stress, the magnitude stresses on the fillet surface are about 90 MPa and 20 MPa, respectively, and the maximum stresses along the P1 are about 170 MPa and 160 MPa, respectively. For the ND stress, it is compressive stress (−76 MPa) on the fillet surface, increases to −20 MPa at 0.12 mm and then keeps stable in the middle region. Along P2, ND stress in the tube and brazing filler metal is very small. TD and LD stresses in the tubes are about −40 MPa and −20 MPa, respectively. However, the two types of stress jump to 140 MPa and 160 MPa in the brazing filler metal, respectively. Fig. 8 shows the effect of tube diameter on residual stress of the hollow-tube staking. For the TD stress, as shown in Fig. 8a, the stress decrease with the increasing of the tube diameter. When the diameter is 4 mm, the TD stress on the fillet surface decreases to compressive stress. As the diameter is 8 mm, TD stress on the fillet further decreases to −230 MPa, and in the middle of joint TD stress decreases to a small value of 40 MPa. For the ND stress, as shown in Fig. 8b, it is compressive stress at the region of the brazing fillet, and the magnitude of the compressive stress increase with the increasing of the tube diameter. When the tube diameter is 8 mm, the TD
Fig. 8. Effect of tube diameter on transverse (a) normal (b) and longitudinal (c) residual stress.
stress at the brazing fillet surface is about −200 MPa. At the middle region of the P1, the stress is compressive stress when the tube diameter is 2 mm. With the increasing of the tube diameter, the stress in the middle region of the P1 is gradually from compressive stress changed into tensile stress, but the magnitude of the tensile stress is small compared to the TD stress, it is only about 40 MPa when the tube diameter is 8 mm. With the diameter increasing, LD stress in the fillet decreases, while in the middle region it changes a little. As the diameter increases from 2 mm to 8 mm, the LD stress in the fillet decreases from 190 MPa to −15 MPa, as shown in Fig. 8c. It is concluded from the Fig. 8 that increasing the tube diameter
Y.-C. Zhang et al. / Journal of Manufacturing Processes 31 (2018) 35–45
41
Fig. 9. Effect of brazing filler metal thickness on transverse (a) normal (b) and longitudinal (c) residual stress.
Fig. 10. Effect of tube wall thickness on transverse (a) normal (b) and longitudinal (c) residual stress.
of the hollow-tube stacking can decrease the stress in the brazing filler metal of the brazed joint, thus the strength of the brazed joint can be improved. Since the brazing joint is similar to a sandwich structure, the stresses in the brazing filler metal and the substrate metal constraint with each other due to the stress balance of the whole joint. Therefore, different brazing filler metal thicknesses can cause the different stress distributions in the brazing joint. Fig. 9 depicts the effect of the brazing filler metal thickness on the stress distribution along P1. The brazing filler metal thickness of 0.03 mm, 0.05 mm and 0.08 mm was adopted in present study. From the Fig. 2, it can
be seen that the fillet radius of the brazed joint will increase with the increasing of the brazing filler metal thickness. The corresponding brazing fillet radius with the thickness of 0.03 mm, 0.05 mm and 0.08 mm are 0.13 mm, 0.15 mm and 0.17 mm, respectively. Generally, all the TD stress ND stress and LD stress decrease with the increasing of the brazing filler metal thickness/fillet radius. For the TD stress, the stress along the P1 is tensile stress, and the peak stress locates at 0.2 mm of the P1 length from the brazing fillet surface, as shown in Fig. 9a. For the ND stress, all the stresses at the brazing fillet surface for the three thicknesses are compressive stress, and they are −65 MPa, −70 MPa and −110 MPa, respectively. When the
42
Y.-C. Zhang et al. / Journal of Manufacturing Processes 31 (2018) 35–45
Fig. 11. Effect of tube length on transverse (a) normal (b) and longitudinal (c) residual stress.
brazing filler metal thickness is 0.03 mm, the ND stress at the middle region of the path P1 is changed from 10 MPa to about −20 MPa. While the brazing filler metal thickness increasing to 0.05 mm or 0.08 mm, all the stresses along the P1 are changed into compressive stresses. For the LD stress, the variation tendency is similar to that the TD stress, all the stresses are tensile stress and they decrease with the increasing of the brazing filler metal thickness. The stress at the brazing fillet surface decreases from 96 MPa to 68 MPa when the thickness increases from 0.03 mm to 0.08 mm. Generally, from the Fig. 9, it can be concluded that increasing the brazing filler metal thickness can reduce the residual stress in the brazed joint. However, it does not mean that the thicker of the brazing filler metal, the
Fig. 12. Effect of matrix size of the hollow-tube stacking on transverse (a) normal (b) and longitudinal (c) residual stress.
better for the brazed joint. As we known, when the thickness of the brazing filler metal is very large, the chemical elements in the brazing filler metal cannot diffusion uniformly at the brazing process, and also some brittle phases will be generated, thus the strength of the brazing filler metal will be greatly reduced although the residual stress can be decreased. Therefore, the thickness of the brazing filler metal should be determined by considering both the residual stress distribution and the chemical element diffusion. Fig. 10 describes the effect of the tube wall thickness on the stress in the brazing filler metal. The wall thickness of 0.18 mm,
Y.-C. Zhang et al. / Journal of Manufacturing Processes 31 (2018) 35–45
43
Fig. 13. Observed cracks [1] (a) and equivalent plastic strain (b) in the braze joint.
Fig. 14. Effect of tube diameter on deformation. Fig. 15. Effect of tube diameter on the thickness of filler metal.
0.20 mm, 0.22 mm and 0.24 mm are adopted. For the TD stress, the wall thickness has almost no effect on the residual stress of the brazing fillet surface, while at the middle region of the P1, the stress decreases with the increasing of the wall thickness. For the ND stress, increasing the wall thickness can reduce the magnitude of the compressive stress at the brazing fillet surface, while at the middle region of the P1, when the wall thickness is 0.2 mm, the magnitude of the compressive stress is the largest. For the LD stress, all the stresses are the tensile stress. Based on the variation of the TD, ND and LD stress under the different wall thicknesses, it recommends that the wall thickness of 0.2 mm is the best choice from the viewpoint of reducing the residual stress. Fig. 11 shows the effect of the tube length on the residual stress distribution in the brazing filler metal. For the TD stress, the stress at the brazing fillet surface increases with the increasing of the tube length, but the effect is not obvious. The variation tendency is contrast to that of the stress at the brazing fillet surface, decreases with the increasing of the tube length. For the ND and LD stress, both the two types of the stress increase with the increasing of the tube length. It can be concluded from the Fig. 11 that reasonably reduce the tube length can decrease the residual stress of the 316L/BNi-2 brazing joint. Fig. 12 shows the effect of the hollow-tube stacking matrix size on the residual stress distribution along path P1. The matrix size of 3 × 4, 4 × 5 and 5 × 6 are chosen as the research object. Both the TD stress and LD stress are tensile stress, the magnitude of the peak stresses of these two type stresses are nearly the same, about 170 MPa. For the ND stress, most region of the path P1 is compressive stress, the tensile stress region can be observed from Fig. 12b, it is about 0.1 mm–0.18 mm away from the brazing fillet surface. The maximum value of the ND stress is only about 10 MPa. In general, the matrix size of the hollow-tube stacking has little effect on the stress distribution of the 316L/BNi-2 brazed joint.
4.2. Discussion As described above, large residual stress is generated in the brazing filler metal due to the mismatching of material properties and constraint. Especially, the residual stress is concentrated on the fillet due to the geometrical discontinuity. It is found that the fillet of the brazed joint contains more brittle phases than that in the middle region of the brazed joint, and the microstructure in the middle region is also more homogeneous [6]. Therefore, the vicinity region of the brazing fillet is the weakest region of the whole brazed joint, and the crack will initiate from this region and lead to the node failure, as shown in Fig. 13. Hence it is significantly important to decrease the residual stress in the fillet. As it is found above, the tube diameter, brazing filler metal thickness, tube length and tube wall thickness have a great effect on residual stress. Here we choose the parameter of tube diameter to deeply explain the effect mechanism of the as-brazed residual stress. With the tube radius increasing, both the radial and hoop deformations increase, as shown in Fig. 14. Since that there is a high constraint during the brazing, with the tube diameter increasing, the brazing filler metal is compressed by the tube expansion because of the deformation coordination. As a result, the residual stress in the brazing filler metal is decreased. Fig. 15 shows the effect of tube diameter on the thickness of filler metal. The results reveal that the filler metal thickness decreases with the tube diameter increasing, which proves that the brazing filler metal is compressed by the increased tube diameter and leads to the corresponding decrease of residual stress. As the tube diameter increasing to 8 mm, the residual stress in the fillet of the brazed joint has been changed to compressive stress, which is helpful to increase the load-bearing of the fillet. Thus, it is concluded that the improving tube diameter can increase the strength of hollow-tube staking.
44
Y.-C. Zhang et al. / Journal of Manufacturing Processes 31 (2018) 35–45
Fig. 16. The variation of temperature and residual stress with time.
Fig. 16 shows the development of temperature and residual stress for a finite element node in the middle of joint. From 0–150s, the temperature increases to 400 ◦ C; LD and TD stresses increase to 65 and 30 MPa, respectively because of the thermal expansion. From 150s-1140s, the temperature increases to 750 ◦ C; the filler metal is compressed by the tube expansion, and as a result, LD and TD stress decrease to −157 and −90 MPa, respectively. From 1140–4300s, the temperature was held and the residual stresses change little. As the temperature increases to brazing temperature, the filler metal is melted to liquid state, leading to a decrease of residual stress. During the cooling as the temperature decreases from 1100 ◦ C to room temperature, the LD and TD residual stresses increase to 250 MPa and 120 MPa, respectively. Therefore, the residual stress in the brazing filler metal is mainly generated during the cooling stage. Fig. 17 shows the effect of cooling rate on residual stress. It shows that the quick cooling (1.35 ◦ C/s) induces larger residual stresses, which may induce the crack in the fabrication stage. It is found by us that micro cracks are generated in the joint for quick cooling [36]. As the cooling rate increases from 0.1 ◦ C/s to 1.35 ◦ C/s, the maximum LD and TD stresses in the joint have been increased from 260 MPa to 340 MPa and 209 MPa to 309 MPa, respectively. Therefore, a slower cooling rate should be used to avoid the generation of larger residual stress in the joint. 5. Conclusions In this study, the brazed residual stresses of a hollow-tube stacking made of 316L stainless steel have been analyzed by XRD and FEM. The effects of tube diameter, brazing filler metal thickness, tube wall thickness, tube length, matrix size and cooling rate on residual stress have also been investigated. Based on the obtained results, the following conclusions are drawn. (1) Due to the constraint and mismatching of material properties, large tensile residual stresses are generated in the brazing filler metal, and they are balanced by the compressive stress in the adjacent tube of hollow-tube stacking. The peak residual stresses and the maximum plastic strain locate at the fillet of the brazed joint, and therefore, the fillet of the brazing filler metal is the weakest region. (2) Increasing the tube diameter, brazing filler metal thickness, or reducing the tube length of the hollow-tube stacking can decrease the stress in the brazing filler metal of the 316L/BNi2 brazing joint. Increasing the wall thickness can decrease the TD stress at the middle region of the brazing filler metal, while it can increase the LD stress. The matrix size of the hollowtube stacking has little effect on the stress distribution of the 316L/BNi-2 brazed joint.
Fig. 17. Effect of cooling rate on transverse (a) and longitudinal (b) residual stress.
(3) The residual stresses are mainly generated during the brazing cooling process, and decreasing the cooling rate can decrease the residual stress. (4) The residual stress in the hollow-tube structure shows a selfequilibrating distribution. With the tube diameter increasing, the expansion deformation of tube increases and it compresses the filler metal due to the deformation coordination. As a result, the residual stresses in the filler metal decrease. When the tube diameter increased to 8 mm, the residual stresses in the fillet of the brazing filler metal transform into compressive stress. It is proposed that the diameter should not be less than 8 mm from the viewpoint of generating compressive stress. Acknowledgments The authors gratefully acknowledge the support provided by the China Postdoctoral Science Foundation (2017M612373), Qingdao Postdoctoral Applied Research Project (2016000101), UPC project (YJ201601054), the Taishan Scholar Foundation (ts201511018), the National Natural Science Foundation of China (51105380) and Fundamental Research Funds for the Central Universities (17CX05019). References [1] Marcadon V, Davoine C, Passilly B, Boivin D, Popoff F, Rafray A, et al. Mechanical behaviour of hollow-tube stackings: experimental characterization and modelling of the role of their constitutive material behaviour. Acta Mater 2012;60:5626–44. [2] Luo X, Xu JY, Nie L, Gao Y, Zhu J, Li W. The mechanical behavior of thin-walled tube filled with hollow metal spheres. Compos Struct 2015;133:124–30. [3] Sun Y, Gao L. Mechanical behavior of all-composite pyramidal truss cores sandwich panels. Mech Mater 2013;65:56–65.
Y.-C. Zhang et al. / Journal of Manufacturing Processes 31 (2018) 35–45 [4] Xiong J, Ma L, Pan S, Wu L, Papadopoulos J, Vaziri A. Shear and bending performance of carbon fiber composite sandwich panels with pyramidal truss cores. Acta Mater 2012;60:1455–66. [5] Queheillalt DT, Wadley HNG. Titanium alloy lattice truss structures. Mater Design 2009;30:1966–75. [6] Jiang W, Gong J, Tu ST. A study of the effect of filler metal thickness on tensile strength for a stainless steel plate-fin structure by experiment and finite element method. Mater Design 2010;31:2387–96. [7] Jiang W, Gong J, Tu S, Fan Q. A comparison of brazed residual stress in plate–fin structure made of different stainless steel. Mater Design 2009;30:23–7. [8] Ghovanlou MK, Jahed H, Khajepour A. Cohesive zone modeling of fatigue crack growth in brazed joints. Eng Fract Mech 2014;120:43–59. [9] Yang X, Dong C, Shi D, Zhang L. Experimental investigation on both low cycle fatigue and fracture behavior of DZ125 base metal and the brazed joint at elevated temperature. Mater Sci Eng A 2011;528:7005–11. [10] Ghovanlou MK, Jahed H, Khajepour A. Cohesive zone modeling of ductile tearing process in brazed joints. Eng Fract Mech 2013;102:156–70. [11] Wang J, Ma N, Murakawa H. An efficient FE computation for predicting welding induced buckling in production of ship panel structure. Mar Struct 2015;41:20–52. [12] Lee CH, Chang KH. Influence of the residual stresses and distortions on the structural behavior of girth-welded cylindrical steel members. Constr Build Mater 2013;41:766–76. [13] Gong W, Chen J, Patterson EA. Buckling and delamination growth behaviour of delaminated composite panels subject to four-point bending. Compos Struct 2015;138:122–33. [14] Pamnani R, Sharma GK, Mahadevan S, Jayakumar T, Vasudevan M, Rao BPC. Residual stress studies on arc welding joints of naval steel (DMR-249A). J Manuf Process 2015;20:104–11. [15] Bajpei T, Chelladurai H, Ansari MZ. Experimental investigation and numerical comparison of residual stresses and distortions in GMA welding of thin dissimilar AA5052-AA6061 plates. J Manuf Process 2016:25. [16] Ding W, Zhang L, Li Z, Zhu Y, Su H, Xu J. Review on grinding-induced residual stresses in metallic materials. Int J Adv Manuf Tech 2016:1–30. [17] Pala Z, Ganev N. The impact of various cooling environments on the distribution of macroscopic residual stresses in near-surface layers of ground steels. Mat Sci Eng: A 2008;497:200–5. [18] Woo W, Em V, Hubbard CR, Lee HJ, Park KS. Residual stress determination in a dissimilar weld overlay pipe by neutron diffraction. Mater Sci Eng A 2011;528:8021–7. [19] Wang XL, Hubbard CR, Spooner S, David SA, Rabin BH, Williamson RL. Mapping of the residual stress distribution in a brazed zirconia-iron joint. Mater Sci Eng A 1996;211:45–53. [20] Hang Y, Liu G, Huang K, Jin W. Mechanical properties and interfacial adhesion of composite membranes probed by in-situ nano-indentation/scratch technique. J Membr Sci 2015;494:205–15.
45
[21] Hamilton NR, Robbie MO, Wood J, Galloway A, Katramados I, Milnes J. The challenges in predicting the fatigue life of dissimilar brazed joints and initial finite element results for a tungsten to EUROFER97 steel brazed joint. Fusion Eng Des 2011;86:1642–5. [22] Zhu Y, Ding W, Xu J, Yang C. An investigation of residual stresses in brazed cubic boron nitride abrasive grains by finite element modelling and raman spectroscopy. Mater Design 2015;87:342–51. [23] Ding W, Zhu Y, Zhang L, Xu J, Fu Y, Liu W, et al. Stress characteristics and fracture wear of brazed CBN grains in monolayer grinding wheels. Wear 2015;332:800–9. [24] Jiang W, Chen H, Gong JM, Tu ST. Numerical modelling and nanoindentation experiment to study the brazed residual stresses in an X-type lattice truss sandwich structure. Mater Sci Eng A 2011;528:4715–22. [25] Zhang JX, Chandel RS, Chen YZ, Seow HP. Effect of residual stress on the strength of an alumina–steel joint by partial transient liquid phase (PTLP) brazing. J Mater Process Tech 2002;122:220–5. [26] Monti R, Coppola F, Gasbarri P, Lecci U. Residual stress brazing process induced in hybrid package for ISP applications. Acta Astronaut 2010;66:897–913. [27] Hamilton NR, Wood J, Easton D, Robbie MBO, Zhang Y, Galloway A. Thermal autofrettage of dissimilar material brazed joints. Mater Design 2015;67:405–12. [28] Barrena MI, Salazar JMGD, Gómez-Vacas M. Numerical simulation and experimental analysis of vacuum brazing for steel/cermet. Ceram Int 2014;40:10557–63. [29] He Y, Zhang J, Pan F, Liu C, Li X. Uncovering the critical factor in determining the residual stresses level in Si3N4–GM filler alloy–42CrMo joints by FEM analysis and experiments. Ceram Int 2013;39:709–18. [30] Jiang W, Gong J, Tu ST, Chen H. Effect of geometric conditions on residual stress of brazed stainless steel plate-fin structure. Nucl Eng Des 2008;238:1497–502. [31] Chen LY, Wang GZ, Tan JP, Xuan FZ, Tu ST. Effects of residual stress on creep damage and crack initiation in notched CT specimens of a Cr–Mo–V steel. Eng Fract Mech 2013;97:80–91. [32] Muránsky O, Hamelin CJ, Smith MC, Bendeich PJ, Edwards L. The effect of plasticity theory on predicted residual stress fields in numerical weld analyses. Comp Mater Sci 2012;54:125–34. [33] Ahmed II, Adebisi JA, Abdulkareem S, Sherry AH. Investigation of surface residual stress profile on martensitic stainless steel weldment with X-ray diffraction. J King Saud Univ 2016 (in Press). [34] Zhang DQ. Basic knowledge of stress determination by X-Ray- Lecture No.1 basic concept of residual stress. Phys Test Chem Anal 2007;43(4):211–3 (in Chinese). [35] Zhang DQ. Basic knowledge of stress determination by X-ray- lecture No.2 basic concept of stress determination by X-ray. Phys Test Chem Anal 2007;43(5):263–5 (in Chinese). [36] Jiang W, Gong J, Tu ST. A new cooling method for vacuum brazing of a stainless steel plate–fin structure. Mater Design 2010;31:648–53.
Contents lists available at ScienceDirect
Journal of Manufacturing Processes journal homepage: www.elsevier.com/locate/manpro
Research Paper
Brazed residual stress in a hollow-tube stacking: Numerical simulation and experimental investigation Yu-Cai Zhang a , Wenchun Jiang a,∗ , Huiqin Zhao a , Zhiquan Wei a , Shan-Tung Tu b a
State Key Laboratory of Heavy Oil Processing, College of Chemical Engineering, China University of Petroleum (East China), Qingdao, 266580, PR China Key Laboratory of Pressure System and Safety (MOE), School of Mechanical and Power Engineering, East China University of Science and Technology, Shanghai 200237, PR China b
a r t i c l e
i n f o
Article history: Received 2 May 2017 Received in revised form 24 October 2017 Accepted 2 November 2017 Key words: Hollow-tube stacking Brazed joint Residual stress Finite element method X-Ray diffraction
a b s t r a c t In this study, the residual stresses of a hollow-tube stacking made of 316L stainless steel by brazing technology have been analyzed by finite element method and X-ray diffraction method. The results show that simulated results are in good agreement with the experimental data, reflecting the feasibility of finite element method to calculate the residual stress. Large tensile stresses are generated in the brazing filler metal, decreasing the cooling rate can decrease the residual stress. With the tube diameter, brazing filler metal thickness increasing, or tube length decreasing, the residual stresses in the filler metal decrease. Increasing the wall thickness can decrease the transverse stress at the middle region of the brazing filler metal, while it can increase the longitudinal stress at the vicinity of brazing fillet. The matrix size of the hollow-tube stacking has little effect on the stress distribution of the 316L/BNi-2 brazed joint. When the tube diameter is increased to 8 mm, the residual stress in the fillet transforms into compressive stress and thus can decrease the cracking sensitivity in the fillet. It is proposed that the diameter of tube should not be less than 8 mm from the viewpoint of generating compressive stress. © 2017 Published by Elsevier Ltd on behalf of The Society of Manufacturing Engineers.
1. Introduction Hollow-tube stacking, a kind of cellular structure, is very promising as lightweight aeronautical frames since it has superior specific mechanical properties such as structural or impact resistance [1,2]. The core of the hollow-tube stacking is fabricated by the brazing technology, and plenty of brazed joints are generated between the hollow-tubes. For many metallic cellular materials, a lot of cracks will be generated in the brazed joints, which named as node failure. Sun and Gao [3] studied the mechanical behaviour of a composite pyramidal truss core sandwich panel. The results indicate that two kinds of failure modes are observed in the sandwich panel: the strut fracture and node rupture. Xiong et al. [4] also found that the node failure and the strut buckling are the main failure modes for carbon fiber pyramidal truss sandwich panel. There are mainly two reasons are generalized for the node failure. One is that the deformation of strut leads to the stress concentration at the node due to the geometrical discontinuity. In order to decrease this type of stress concentration, Queheillalt [5] proposed a liquid interface diffusion bonding approach to form a large fillet between
∗ Corresponding author. E-mail address: [email protected] (W. Jiang).
the truss and face-sheet interface, which is helpful to decrease the stress concentration and increase the interfacial strength. Jiang et al. [6] also found that a larger fillet can decrease the stress concentration and increase the tensile strength for brazed plate-fin structure. The other reason is that the brazed residual stresses generated by the mismatching of mechanical properties between the brazing filler metal and substrate metal [7]. The brazed residual stresses have a great effect on the structure fracture [8–10] and buckling [11–13]. Therefore, it is very important to decrease the brazed residual stress for ensuring the structure integrity. The brazing filler metal is surrounded by the base metal, the whole brazed joint like a kind of sandwich structure. The thickness of brazing filler metal is only about 30–100 m, while the thickness of base metal is several millimeters or even more thick. Therefore, it is a challenging question to measure the residual stress accurately in the brazed joint, especially for the stress characterization of the brazing filler metal. X-ray diffraction (XRD) [14,15] and neutron diffraction method [16] are widely used to measure the residual stress. Although the XRD cannot measure the inner stress of the brazed joint directly limited by the penetrate capability [17], stress gradients can be characterized in combination with the layer removal by electrochemical polishing technique. Neutron diffraction can penetrate into the material and test the residual stress directly due to the higher penetrate capability. However, it is a pity
https://doi.org/10.1016/j.jmapro.2017.11.002 1526-6125/© 2017 Published by Elsevier Ltd on behalf of The Society of Manufacturing Engineers.
36
Y.-C. Zhang et al. / Journal of Manufacturing Processes 31 (2018) 35–45
that both the two methods cannot measure the stress in the filler metal for the limitation of gauge volume. At present the minimum gauge volume of X-Ray and neutron beam is about 1 ∼ 2 mm, which is much larger than the thickness of brazing filler metal [18]. Some researchers adopted the neutron diffraction to measure the brazed residual stress [19], however, the measured position located in the base metal rather than the brazing filler metal. Nano-indentation can measure the stress in the micro-region, but it requires a good smooth surface, and the cutting and grinding process will relax the residual stress in the brazed joint [20]. Hamilton et al. [21] pointed out that the validation of brazed residual stress is still further required. Therefore, it is very difficult to determine the brazed residual stress in the brazing filler metal by experimental method up to now. With the development of computer technology, finite element method (FEM) is widely used to predict the residual stress in the brazed joint [22–24], and the residual stress in any region of the brazed joint can be obtained directly by the FEM. Zhang et al. [25] studied the residual stress in a brazed joint between the alumina and 304 stainless steel by FEM. The results demonstrated that Ni and Ni-Cr filler metals are compliant layers, and they are suitable to relieve the residual stress. Riccardo et al. [26] investigated the brazed residual stress in hybrid package for integrated substrate packaging applications, it is found that the residual stress in the substrate decreases with the thickness of barrier layer increases. Hamilton et al. [27] found that the thermal autofrettage can decrease the residual stress in brazed joint. Barrena et al. [28] studied the residual stress in the brazed joint between 90MnCrV8 steel and cemented carbide by FEM. The results illustrated that the residual stresses are very large and they can significantly decrease the joint strength. The maximum peak stress is located in the brazing filler metal-cemented carbide interface. Increase the brazing time can decrease the residual stress and thus improve the shear strength of the brazed joint. However, an excessive brazing time can generate intermetallic compound in the brazed joint, and in turn, decrease the strength of the brazed joint. He et al. [29] examined the residual stresses in Si3 N4 CGM filler alloy-42CrMo joints by FEM. The effects of gradient material compositions, layer numbers and thicknesses on residual stresses have been discussed. It depicted that the CTE mismatch between the joined materials and the ability of plastic deformation in the brazing filler metal were the two factors that determine the residual stresses level in brazing joint. Jiang et al. [24,30] studied the effect of structure dimensions on residual stress in the compact plate-fin heat exchanger by FEM, which provides a guidance to improve the joint performance. For the hollow-tube stacking, V. Marcadon et al. [1] analyzed the mechanical behaviour by experimental characterization and modelling. It is found that the heterogeneity of the brazed joints generates stress concentration in the fillet. However, the distribution of brazed residual stress and how to decrease the residual stress are still need to be investigated. In this paper, the residual stress in a brazed hollow-tube stacking was investigated by finite element and experimental method, and the effects of tube diameter and cooling rate on the residual stress magnitude and distribution were fully discussed. Based on the calculated results, it is proposed to generate the compressive residual stress in the brazed joint by the self-expansion of tube to improve the strength of the whole joint.
2. Finite element modeling 2.1. Fabrication introduction of the hollow-tube stacking Fig. 1 shows a hollow-tube stacking consists of two sheets and a tube-stacking core. Tubes were stacked in a graphite die lined
Fig. 1. Schematic of a hollow-tube stacking.
with sheets which positioned at the top and bottom. The brazing filler metal of BNi-2 was pre-positioned between the tubes and face plates. Then the assembly was clamped tightly to prevent the free movement of the substrate materials and brazing filler metal. The stacking was formed by high temperature brazing at a vacuum furnace, the assembly was firstly heated to 800 ◦ C within 50 min and the temperature was held for about 30 min. Then it was heated to the brazing temperature of 1100 ◦ C within 30 min and the temperature was lasted for about 25 min. At last, the assembly was cooled to the ambient temperature in the furnace. The melting temperature of filler metal BNi-2 is about 1020 ◦ C. At the brazing temperature of 1100 ◦ C, the brazing filler metal is liquid while the tube and plate are still solid. The filler metal flows into the gap between the two plates by wetting and capillary action. After cooling to the environmental temperature the assembly are joined together to form the stacking. The materials of the tube and plates are 316L stainless steel. Due to the constraint and difference of mechanical properties between the tube and BNi-2, large residual stresses will be generated in the joint. In this paper, we developed a sequential coupling finite element method to study the brazing temperature and residual stress. The brazing temperature field was firstly simulated by a thermal analysis, and then the residual stresses were calculated by a thermal-elastic-plastic constitutive model.
2.2. Finite element model and meshing As shown in Fig. 1, the outer diameter and thickness of tubes are 2 mm and 0.2 mm, respectively. The joint width is around 0.7 mm. The tube length is 10 mm. The plate length, width and thickness are 10 mm, 8 mm and 0.2 mm, respectively. The stacking is four tubes wide and five tubes high. Finite element software ABAQUS was used to calculate the temperature distribution and residual stress. Fig. 2 shows the finite element meshing of the hollow-tube stacking. Dissimilar materials are assumed to be perfectly bonded at interfaces. The number of element and node are 201330 and 246977, respectively. The element type of temperature calculation is DC3D8, and stress analysis type is C3D8. In order to improve the calculation accuracy and save calculation time, the meshing around the brazed joints is refined and the other parts away from the joint are relatively coarse.
Y.-C. Zhang et al. / Journal of Manufacturing Processes 31 (2018) 35–45
37
Fig. 2. FE meshing of the hollow-tube stacking.
where s is the volume of the heat source, the material density, C the specific heat, T the temperature, t the time, and K the conductivity. The heat convection was calculated by
˚ = hA tw − tf
(2)
where ˚ is the heat transfer in unit time, h the convective heat transfer coefficient, A the contacting area, tw the temperature of solid surface and tf the temperature of fluid surface. It is should be mentioned that h is a non-physical property parameter and related with the ambient. The size of brazed joint is small compared to the space of brazing environment, so the value of h can be considered as a constant, h = 10W/(m2 ◦ C) in present paper. The heat radiation was calculated by: q = εAω((Ts + 273.15)4 − (Tfurn + 273.15)4 )
(3)
where q is the irradiance, ε the emissivity (the value is about 0.8 in the brazing furnace), Ts the temperature of brazed parts and Tfurn the temperature of high vacuum furnace. ω is the Stefan-Boltzmann constant (ω = 5.67e − 8W m−2 K−4 ).
Fig. 3. Boundary conditions of the hollow-tube stacking.
2.3. Boundary conditions
2.5. Residual stress analysis
In order to accurately simulate the as-brazed residual stress of the hollow-tube stacking, the proper boundary conditions which correspond with the actual brazing process should be applied on the finite element model. Fig. 3 depicts the boundary conditions applied on the hollow-tube stacking finite element model. During the brazing process, the tubes were constrained tightly by the vertical baffle to prevent the free movement. Therefore during the simulation process, the displacements of the surfaces which contact the vertical baffle were constrained in X-direction (Face 1: U1 = 0) and Z-direction (Face 2: U3 = 0), respectively. And the displacement of the bottom plate face was constrained in Y-direction (U2 = 0). A pressure load of 1 MPa was applied on the top face to keep a tight contact between the components.
The residual stress was calculated by thermal-elastic-plastic model, and the temperature field used for the stress calculation was called the data obtained from the thermal analysis. The total strain is decomposed into elastic strain, plastic strain and thermal strain:
2.4. Brazing temperature simulation The brazing temperature simulation was carried out by considering thermal conduction, heat convection and radiation. Three-dimensional heat conduction was calculated by:
s=−
C
∂T + ∇ (K ∇ T ) ∂t
(1)
{dε} = {dε}p + {dε}e + {dε}T
(4)
where {dε} is the total strain, {dε}p the plastic strain, {dε}e the elastic strain, {dε} T the thermal strain. Elastic strain was modeled using the isotropic Hooke’s law with temperature-dependent Young’s modulus and Poisson’s ratio. The thermal strain was calculated using the temperature-dependent coefficient of thermal expansion (CTE). For the plastic strain, a rate-independent plastic model was employed with Von Mises yield surface, temperature-dependent mechanical properties and isotropic hardening model. The temperature dependent material properties are listed in Tables 1 and 2 [31,32]. 3. Experimental testing XRD plays a prominent role in the stress measurement due to its simplicity of operation and high accuracy [16]. Although the XRD
38
Y.-C. Zhang et al. / Journal of Manufacturing Processes 31 (2018) 35–45
Table 1 Thermal properties of 316L steel and BNi-2. Material
Temperature (◦ C)
Conductivity (W/(m ◦ C))
Density (Kg/m3 )
Specific heat (J/(◦ C kg))
316 L
20 400 900 20 400 900
13.3 19.5 26.33 25.6 29.2 33.6
7966 7966 7966 7850 7850 7850
492 538 659 469 577 1161
BNi-2
Table 2 Mechanical properties of 316L steel and BNi-2. Material
Temperature (◦ C)
Young’s modulus (GPa)
Poisson’s ratio
CTE (1/◦ C)
Yield strength (MPa)
316 L
20 400 900 20 400 800
196.5 172.6 116.8 205.1 183.2 161.0
0.29 0.29 0.29 0.296 0.306 0.328
1.46 × 10−5 1.74 × 10−5 1.90 × 10−5 1.35 × 10−5 1.68 × 10−5 19.9 × 10−5
243 163 99 300 220 160
BNi-2
Fig. 4. Schematic illustration of the brazed joint.
Fig. 5. Residual stress along P3 by FEM and XRD.
cannot measure the residual stress in the brazing filler metal of the brazed joint, the stress in the substrate metal can be characterized in combination with the layer removal by electrochemical polishing technique. Based on the stress distribution in the substrate and the stress balance of the whole brazed joint, the stress distribution in the brazing filler metal can be deduced. However, constrained by the measuring space of the XRD, it is hardly to test the as-brazed residual stress of the hollow-tube staking directly. Therefore, the simulation method was used to analyze the residual stress of the hollow-tube stacking. In order to verify the feasibility of the finite element method to calculate the as-brazed residual stress, for testing purpose, two pieces of 316L stainless steel plates with 10 mm thickness, 12 mm length and 6 mm width were brazed together by the sheet-shaped brazing filler metal BNi-2 with 40 m thickness, as shown in Fig. 3. For comparison, the materials and brazing technology are the same as those mentioned in Section 2. Before the test, electrolytic polishing was used to process the surface of samples before test, which could avoid the surface compressive stress layer resulting from machinery grinding. The high voltage of the X-ray tube is 24.0 KV and the current is 5.0 mA. Mn-K␣ X-ray was launched on the crystalline phase (311) of the sample. The theory of residual stress measurement by X-ray diffraction method is based on the Bragg’s equation: = 2dsin
(5)
Where is the wave length, d the interatomic lattice spacing and the diffraction angle [33].
The method of was used to calculate the residual stress and the values of were 0.0◦ , 15.0◦ , 30.0◦ , 45.0◦ , respectively. The residual stress can be calculated according to the following equation [34,35]: = KM K =−
E cot 0 180 2(1 + v)
M=
(6)
∂ 2p
(7)
∂(sin2 )
(8)
where 0 is the diffraction angle under a stress-free state, the angle between the normal of the crystal surface and the material surface, K the stress constant of X-ray, and M the slope of the linear relationship between the position of diffraction angle 2p and sin2 at different values of . The test points are located on path P3, see as Fig. 4, and the distance interval is 1.5 mm. The tested residual stress will be used to analyze the stress distribution of the 316L/BNi-2 brazed joint and also to verify the feasibility and rationality of the FEM to calculate the residual stress in present paper. The simulation technologies of the tested specimen are the same as those used to the hollow-tube staking in Section 2, so they are not described in this Section.
Y.-C. Zhang et al. / Journal of Manufacturing Processes 31 (2018) 35–45
39
Fig. 6. Contour of the transverse (TD), normal (ND) and longitudinal stress (LD).
4. Results and discussion 4.1. Residual stress distribution Fig. 5 depicts the residual stress distributions measured by XRD and FEM method along P3. The residual stresses in X, Y and Z directions are defined as transverse (TD), normal (ND) and longitudinal (LD) stresses, respectively. The maximum value (355 ± 46 MPa) of the TD stress measured by XRD is located at the middle region of path P3, and it decreases gradually from the middle region to both sides of the path P3. While the maximum value measured by FEM is 293 MPa in the same position. For the ND stress, the results measured by XRD and FEM are 285 ± 43 MPa and 250 MPa, respectively. From the above analysis, it can be seen that there is a small difference between the results from XRD and FEM. Since the materials, brazing technological parameters of the specimen used in the
experimental test and the simulation technology are the same as those used in the hollow-tube staking, therefore, the well agreed experimental and simulation data in the Fig. 5 demonstrate that the FEM method used in present paper can be used effectively to predict the as-brazed residual stress of the hollow-tube staking. Fig. 6 shows the residual stress distribution of the hollow-tube staking. Since the single tube is axisymmetric, as clearly illustrated in Fig. 6a and b, the transverse and normal stresses have a similar distribution. Both the maximum of TD stress and ND stress are around 218 MPa, which are located in the horizontal and vertical brazing joints, respectively. The residual stresses in the brazing filler metal are tensile stresses, which are balanced by the compressive stress in the adjacent tubes. The maximum compressive stress is 121 MPa. For the LD stress (See Fig. 6c), the maximum value is 304 MPa, which located at the fillet of the brazing filler metal. It is also balanced by the compressive stress (the maximum value is
40
Y.-C. Zhang et al. / Journal of Manufacturing Processes 31 (2018) 35–45
Fig. 7. Residual stress distribution along path P1 (a) and P2 (b).
−92 MPa) in the adjacent tubes. In general, the residual stress in the hollow-tube structure shows a self-equilibrating distribution: large tensile residual stresses are generated in the brazing filler metal and balanced by the compressive stress in the adjacent tube. Fig. 7 displays the residual stress distributions along path P1 and P2 in the brazed joint. P1 is the centerline of brazing filler metal in the horizontal filler metal, and P2 is along the thickness from tube-to-tube, as shown in Fig. 7a. The stresses in the three directions along P1 present M shape distribution. For the TD and LD stress, the magnitude stresses on the fillet surface are about 90 MPa and 20 MPa, respectively, and the maximum stresses along the P1 are about 170 MPa and 160 MPa, respectively. For the ND stress, it is compressive stress (−76 MPa) on the fillet surface, increases to −20 MPa at 0.12 mm and then keeps stable in the middle region. Along P2, ND stress in the tube and brazing filler metal is very small. TD and LD stresses in the tubes are about −40 MPa and −20 MPa, respectively. However, the two types of stress jump to 140 MPa and 160 MPa in the brazing filler metal, respectively. Fig. 8 shows the effect of tube diameter on residual stress of the hollow-tube staking. For the TD stress, as shown in Fig. 8a, the stress decrease with the increasing of the tube diameter. When the diameter is 4 mm, the TD stress on the fillet surface decreases to compressive stress. As the diameter is 8 mm, TD stress on the fillet further decreases to −230 MPa, and in the middle of joint TD stress decreases to a small value of 40 MPa. For the ND stress, as shown in Fig. 8b, it is compressive stress at the region of the brazing fillet, and the magnitude of the compressive stress increase with the increasing of the tube diameter. When the tube diameter is 8 mm, the TD
Fig. 8. Effect of tube diameter on transverse (a) normal (b) and longitudinal (c) residual stress.
stress at the brazing fillet surface is about −200 MPa. At the middle region of the P1, the stress is compressive stress when the tube diameter is 2 mm. With the increasing of the tube diameter, the stress in the middle region of the P1 is gradually from compressive stress changed into tensile stress, but the magnitude of the tensile stress is small compared to the TD stress, it is only about 40 MPa when the tube diameter is 8 mm. With the diameter increasing, LD stress in the fillet decreases, while in the middle region it changes a little. As the diameter increases from 2 mm to 8 mm, the LD stress in the fillet decreases from 190 MPa to −15 MPa, as shown in Fig. 8c. It is concluded from the Fig. 8 that increasing the tube diameter
Y.-C. Zhang et al. / Journal of Manufacturing Processes 31 (2018) 35–45
41
Fig. 9. Effect of brazing filler metal thickness on transverse (a) normal (b) and longitudinal (c) residual stress.
Fig. 10. Effect of tube wall thickness on transverse (a) normal (b) and longitudinal (c) residual stress.
of the hollow-tube stacking can decrease the stress in the brazing filler metal of the brazed joint, thus the strength of the brazed joint can be improved. Since the brazing joint is similar to a sandwich structure, the stresses in the brazing filler metal and the substrate metal constraint with each other due to the stress balance of the whole joint. Therefore, different brazing filler metal thicknesses can cause the different stress distributions in the brazing joint. Fig. 9 depicts the effect of the brazing filler metal thickness on the stress distribution along P1. The brazing filler metal thickness of 0.03 mm, 0.05 mm and 0.08 mm was adopted in present study. From the Fig. 2, it can
be seen that the fillet radius of the brazed joint will increase with the increasing of the brazing filler metal thickness. The corresponding brazing fillet radius with the thickness of 0.03 mm, 0.05 mm and 0.08 mm are 0.13 mm, 0.15 mm and 0.17 mm, respectively. Generally, all the TD stress ND stress and LD stress decrease with the increasing of the brazing filler metal thickness/fillet radius. For the TD stress, the stress along the P1 is tensile stress, and the peak stress locates at 0.2 mm of the P1 length from the brazing fillet surface, as shown in Fig. 9a. For the ND stress, all the stresses at the brazing fillet surface for the three thicknesses are compressive stress, and they are −65 MPa, −70 MPa and −110 MPa, respectively. When the
42
Y.-C. Zhang et al. / Journal of Manufacturing Processes 31 (2018) 35–45
Fig. 11. Effect of tube length on transverse (a) normal (b) and longitudinal (c) residual stress.
brazing filler metal thickness is 0.03 mm, the ND stress at the middle region of the path P1 is changed from 10 MPa to about −20 MPa. While the brazing filler metal thickness increasing to 0.05 mm or 0.08 mm, all the stresses along the P1 are changed into compressive stresses. For the LD stress, the variation tendency is similar to that the TD stress, all the stresses are tensile stress and they decrease with the increasing of the brazing filler metal thickness. The stress at the brazing fillet surface decreases from 96 MPa to 68 MPa when the thickness increases from 0.03 mm to 0.08 mm. Generally, from the Fig. 9, it can be concluded that increasing the brazing filler metal thickness can reduce the residual stress in the brazed joint. However, it does not mean that the thicker of the brazing filler metal, the
Fig. 12. Effect of matrix size of the hollow-tube stacking on transverse (a) normal (b) and longitudinal (c) residual stress.
better for the brazed joint. As we known, when the thickness of the brazing filler metal is very large, the chemical elements in the brazing filler metal cannot diffusion uniformly at the brazing process, and also some brittle phases will be generated, thus the strength of the brazing filler metal will be greatly reduced although the residual stress can be decreased. Therefore, the thickness of the brazing filler metal should be determined by considering both the residual stress distribution and the chemical element diffusion. Fig. 10 describes the effect of the tube wall thickness on the stress in the brazing filler metal. The wall thickness of 0.18 mm,
Y.-C. Zhang et al. / Journal of Manufacturing Processes 31 (2018) 35–45
43
Fig. 13. Observed cracks [1] (a) and equivalent plastic strain (b) in the braze joint.
Fig. 14. Effect of tube diameter on deformation. Fig. 15. Effect of tube diameter on the thickness of filler metal.
0.20 mm, 0.22 mm and 0.24 mm are adopted. For the TD stress, the wall thickness has almost no effect on the residual stress of the brazing fillet surface, while at the middle region of the P1, the stress decreases with the increasing of the wall thickness. For the ND stress, increasing the wall thickness can reduce the magnitude of the compressive stress at the brazing fillet surface, while at the middle region of the P1, when the wall thickness is 0.2 mm, the magnitude of the compressive stress is the largest. For the LD stress, all the stresses are the tensile stress. Based on the variation of the TD, ND and LD stress under the different wall thicknesses, it recommends that the wall thickness of 0.2 mm is the best choice from the viewpoint of reducing the residual stress. Fig. 11 shows the effect of the tube length on the residual stress distribution in the brazing filler metal. For the TD stress, the stress at the brazing fillet surface increases with the increasing of the tube length, but the effect is not obvious. The variation tendency is contrast to that of the stress at the brazing fillet surface, decreases with the increasing of the tube length. For the ND and LD stress, both the two types of the stress increase with the increasing of the tube length. It can be concluded from the Fig. 11 that reasonably reduce the tube length can decrease the residual stress of the 316L/BNi-2 brazing joint. Fig. 12 shows the effect of the hollow-tube stacking matrix size on the residual stress distribution along path P1. The matrix size of 3 × 4, 4 × 5 and 5 × 6 are chosen as the research object. Both the TD stress and LD stress are tensile stress, the magnitude of the peak stresses of these two type stresses are nearly the same, about 170 MPa. For the ND stress, most region of the path P1 is compressive stress, the tensile stress region can be observed from Fig. 12b, it is about 0.1 mm–0.18 mm away from the brazing fillet surface. The maximum value of the ND stress is only about 10 MPa. In general, the matrix size of the hollow-tube stacking has little effect on the stress distribution of the 316L/BNi-2 brazed joint.
4.2. Discussion As described above, large residual stress is generated in the brazing filler metal due to the mismatching of material properties and constraint. Especially, the residual stress is concentrated on the fillet due to the geometrical discontinuity. It is found that the fillet of the brazed joint contains more brittle phases than that in the middle region of the brazed joint, and the microstructure in the middle region is also more homogeneous [6]. Therefore, the vicinity region of the brazing fillet is the weakest region of the whole brazed joint, and the crack will initiate from this region and lead to the node failure, as shown in Fig. 13. Hence it is significantly important to decrease the residual stress in the fillet. As it is found above, the tube diameter, brazing filler metal thickness, tube length and tube wall thickness have a great effect on residual stress. Here we choose the parameter of tube diameter to deeply explain the effect mechanism of the as-brazed residual stress. With the tube radius increasing, both the radial and hoop deformations increase, as shown in Fig. 14. Since that there is a high constraint during the brazing, with the tube diameter increasing, the brazing filler metal is compressed by the tube expansion because of the deformation coordination. As a result, the residual stress in the brazing filler metal is decreased. Fig. 15 shows the effect of tube diameter on the thickness of filler metal. The results reveal that the filler metal thickness decreases with the tube diameter increasing, which proves that the brazing filler metal is compressed by the increased tube diameter and leads to the corresponding decrease of residual stress. As the tube diameter increasing to 8 mm, the residual stress in the fillet of the brazed joint has been changed to compressive stress, which is helpful to increase the load-bearing of the fillet. Thus, it is concluded that the improving tube diameter can increase the strength of hollow-tube staking.
44
Y.-C. Zhang et al. / Journal of Manufacturing Processes 31 (2018) 35–45
Fig. 16. The variation of temperature and residual stress with time.
Fig. 16 shows the development of temperature and residual stress for a finite element node in the middle of joint. From 0–150s, the temperature increases to 400 ◦ C; LD and TD stresses increase to 65 and 30 MPa, respectively because of the thermal expansion. From 150s-1140s, the temperature increases to 750 ◦ C; the filler metal is compressed by the tube expansion, and as a result, LD and TD stress decrease to −157 and −90 MPa, respectively. From 1140–4300s, the temperature was held and the residual stresses change little. As the temperature increases to brazing temperature, the filler metal is melted to liquid state, leading to a decrease of residual stress. During the cooling as the temperature decreases from 1100 ◦ C to room temperature, the LD and TD residual stresses increase to 250 MPa and 120 MPa, respectively. Therefore, the residual stress in the brazing filler metal is mainly generated during the cooling stage. Fig. 17 shows the effect of cooling rate on residual stress. It shows that the quick cooling (1.35 ◦ C/s) induces larger residual stresses, which may induce the crack in the fabrication stage. It is found by us that micro cracks are generated in the joint for quick cooling [36]. As the cooling rate increases from 0.1 ◦ C/s to 1.35 ◦ C/s, the maximum LD and TD stresses in the joint have been increased from 260 MPa to 340 MPa and 209 MPa to 309 MPa, respectively. Therefore, a slower cooling rate should be used to avoid the generation of larger residual stress in the joint. 5. Conclusions In this study, the brazed residual stresses of a hollow-tube stacking made of 316L stainless steel have been analyzed by XRD and FEM. The effects of tube diameter, brazing filler metal thickness, tube wall thickness, tube length, matrix size and cooling rate on residual stress have also been investigated. Based on the obtained results, the following conclusions are drawn. (1) Due to the constraint and mismatching of material properties, large tensile residual stresses are generated in the brazing filler metal, and they are balanced by the compressive stress in the adjacent tube of hollow-tube stacking. The peak residual stresses and the maximum plastic strain locate at the fillet of the brazed joint, and therefore, the fillet of the brazing filler metal is the weakest region. (2) Increasing the tube diameter, brazing filler metal thickness, or reducing the tube length of the hollow-tube stacking can decrease the stress in the brazing filler metal of the 316L/BNi2 brazing joint. Increasing the wall thickness can decrease the TD stress at the middle region of the brazing filler metal, while it can increase the LD stress. The matrix size of the hollowtube stacking has little effect on the stress distribution of the 316L/BNi-2 brazed joint.
Fig. 17. Effect of cooling rate on transverse (a) and longitudinal (b) residual stress.
(3) The residual stresses are mainly generated during the brazing cooling process, and decreasing the cooling rate can decrease the residual stress. (4) The residual stress in the hollow-tube structure shows a selfequilibrating distribution. With the tube diameter increasing, the expansion deformation of tube increases and it compresses the filler metal due to the deformation coordination. As a result, the residual stresses in the filler metal decrease. When the tube diameter increased to 8 mm, the residual stresses in the fillet of the brazing filler metal transform into compressive stress. It is proposed that the diameter should not be less than 8 mm from the viewpoint of generating compressive stress. Acknowledgments The authors gratefully acknowledge the support provided by the China Postdoctoral Science Foundation (2017M612373), Qingdao Postdoctoral Applied Research Project (2016000101), UPC project (YJ201601054), the Taishan Scholar Foundation (ts201511018), the National Natural Science Foundation of China (51105380) and Fundamental Research Funds for the Central Universities (17CX05019). References [1] Marcadon V, Davoine C, Passilly B, Boivin D, Popoff F, Rafray A, et al. Mechanical behaviour of hollow-tube stackings: experimental characterization and modelling of the role of their constitutive material behaviour. Acta Mater 2012;60:5626–44. [2] Luo X, Xu JY, Nie L, Gao Y, Zhu J, Li W. The mechanical behavior of thin-walled tube filled with hollow metal spheres. Compos Struct 2015;133:124–30. [3] Sun Y, Gao L. Mechanical behavior of all-composite pyramidal truss cores sandwich panels. Mech Mater 2013;65:56–65.
Y.-C. Zhang et al. / Journal of Manufacturing Processes 31 (2018) 35–45 [4] Xiong J, Ma L, Pan S, Wu L, Papadopoulos J, Vaziri A. Shear and bending performance of carbon fiber composite sandwich panels with pyramidal truss cores. Acta Mater 2012;60:1455–66. [5] Queheillalt DT, Wadley HNG. Titanium alloy lattice truss structures. Mater Design 2009;30:1966–75. [6] Jiang W, Gong J, Tu ST. A study of the effect of filler metal thickness on tensile strength for a stainless steel plate-fin structure by experiment and finite element method. Mater Design 2010;31:2387–96. [7] Jiang W, Gong J, Tu S, Fan Q. A comparison of brazed residual stress in plate–fin structure made of different stainless steel. Mater Design 2009;30:23–7. [8] Ghovanlou MK, Jahed H, Khajepour A. Cohesive zone modeling of fatigue crack growth in brazed joints. Eng Fract Mech 2014;120:43–59. [9] Yang X, Dong C, Shi D, Zhang L. Experimental investigation on both low cycle fatigue and fracture behavior of DZ125 base metal and the brazed joint at elevated temperature. Mater Sci Eng A 2011;528:7005–11. [10] Ghovanlou MK, Jahed H, Khajepour A. Cohesive zone modeling of ductile tearing process in brazed joints. Eng Fract Mech 2013;102:156–70. [11] Wang J, Ma N, Murakawa H. An efficient FE computation for predicting welding induced buckling in production of ship panel structure. Mar Struct 2015;41:20–52. [12] Lee CH, Chang KH. Influence of the residual stresses and distortions on the structural behavior of girth-welded cylindrical steel members. Constr Build Mater 2013;41:766–76. [13] Gong W, Chen J, Patterson EA. Buckling and delamination growth behaviour of delaminated composite panels subject to four-point bending. Compos Struct 2015;138:122–33. [14] Pamnani R, Sharma GK, Mahadevan S, Jayakumar T, Vasudevan M, Rao BPC. Residual stress studies on arc welding joints of naval steel (DMR-249A). J Manuf Process 2015;20:104–11. [15] Bajpei T, Chelladurai H, Ansari MZ. Experimental investigation and numerical comparison of residual stresses and distortions in GMA welding of thin dissimilar AA5052-AA6061 plates. J Manuf Process 2016:25. [16] Ding W, Zhang L, Li Z, Zhu Y, Su H, Xu J. Review on grinding-induced residual stresses in metallic materials. Int J Adv Manuf Tech 2016:1–30. [17] Pala Z, Ganev N. The impact of various cooling environments on the distribution of macroscopic residual stresses in near-surface layers of ground steels. Mat Sci Eng: A 2008;497:200–5. [18] Woo W, Em V, Hubbard CR, Lee HJ, Park KS. Residual stress determination in a dissimilar weld overlay pipe by neutron diffraction. Mater Sci Eng A 2011;528:8021–7. [19] Wang XL, Hubbard CR, Spooner S, David SA, Rabin BH, Williamson RL. Mapping of the residual stress distribution in a brazed zirconia-iron joint. Mater Sci Eng A 1996;211:45–53. [20] Hang Y, Liu G, Huang K, Jin W. Mechanical properties and interfacial adhesion of composite membranes probed by in-situ nano-indentation/scratch technique. J Membr Sci 2015;494:205–15.
45
[21] Hamilton NR, Robbie MO, Wood J, Galloway A, Katramados I, Milnes J. The challenges in predicting the fatigue life of dissimilar brazed joints and initial finite element results for a tungsten to EUROFER97 steel brazed joint. Fusion Eng Des 2011;86:1642–5. [22] Zhu Y, Ding W, Xu J, Yang C. An investigation of residual stresses in brazed cubic boron nitride abrasive grains by finite element modelling and raman spectroscopy. Mater Design 2015;87:342–51. [23] Ding W, Zhu Y, Zhang L, Xu J, Fu Y, Liu W, et al. Stress characteristics and fracture wear of brazed CBN grains in monolayer grinding wheels. Wear 2015;332:800–9. [24] Jiang W, Chen H, Gong JM, Tu ST. Numerical modelling and nanoindentation experiment to study the brazed residual stresses in an X-type lattice truss sandwich structure. Mater Sci Eng A 2011;528:4715–22. [25] Zhang JX, Chandel RS, Chen YZ, Seow HP. Effect of residual stress on the strength of an alumina–steel joint by partial transient liquid phase (PTLP) brazing. J Mater Process Tech 2002;122:220–5. [26] Monti R, Coppola F, Gasbarri P, Lecci U. Residual stress brazing process induced in hybrid package for ISP applications. Acta Astronaut 2010;66:897–913. [27] Hamilton NR, Wood J, Easton D, Robbie MBO, Zhang Y, Galloway A. Thermal autofrettage of dissimilar material brazed joints. Mater Design 2015;67:405–12. [28] Barrena MI, Salazar JMGD, Gómez-Vacas M. Numerical simulation and experimental analysis of vacuum brazing for steel/cermet. Ceram Int 2014;40:10557–63. [29] He Y, Zhang J, Pan F, Liu C, Li X. Uncovering the critical factor in determining the residual stresses level in Si3N4–GM filler alloy–42CrMo joints by FEM analysis and experiments. Ceram Int 2013;39:709–18. [30] Jiang W, Gong J, Tu ST, Chen H. Effect of geometric conditions on residual stress of brazed stainless steel plate-fin structure. Nucl Eng Des 2008;238:1497–502. [31] Chen LY, Wang GZ, Tan JP, Xuan FZ, Tu ST. Effects of residual stress on creep damage and crack initiation in notched CT specimens of a Cr–Mo–V steel. Eng Fract Mech 2013;97:80–91. [32] Muránsky O, Hamelin CJ, Smith MC, Bendeich PJ, Edwards L. The effect of plasticity theory on predicted residual stress fields in numerical weld analyses. Comp Mater Sci 2012;54:125–34. [33] Ahmed II, Adebisi JA, Abdulkareem S, Sherry AH. Investigation of surface residual stress profile on martensitic stainless steel weldment with X-ray diffraction. J King Saud Univ 2016 (in Press). [34] Zhang DQ. Basic knowledge of stress determination by X-Ray- Lecture No.1 basic concept of residual stress. Phys Test Chem Anal 2007;43(4):211–3 (in Chinese). [35] Zhang DQ. Basic knowledge of stress determination by X-ray- lecture No.2 basic concept of stress determination by X-ray. Phys Test Chem Anal 2007;43(5):263–5 (in Chinese). [36] Jiang W, Gong J, Tu ST. A new cooling method for vacuum brazing of a stainless steel plate–fin structure. Mater Design 2010;31:648–53.