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Comparison of Brazed Residual Stress and Thermal Deformation between X-Type and Pyramidal Lattice Truss Sandwich Structure: Neutron Diffraction Measurement and Simulation Study

  • Wenchun Jiang EMAIL logo , Zhiquan Wei , Yun Luo , Weiya Zhang and Wanchuck Woo
Published/Copyright: July 23, 2015
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High Temperature Materials and Processes
From the journal High Temperature Materials and Processes Volume 35 Issue 6

Abstract

This paper uses finite element method and neutron diffraction measurement to study the residual stress in lattice truss sandwich structure. A comparison of residual stress and thermal deformation between X-type and pyramidal lattice truss sandwich structure has been carried out. The residual stresses are concentrated in the middle joint and then decreases gradually to both the ends. The residual stresses in the X-type lattice truss sandwich structure are smaller than those in pyramidal structure. The maximum longitudinal and transverse stresses of pyramidal structure are 220 and 202 MPa, respectively, but they decrease to 190 and 145 MPa for X-type lattice truss sandwich structure, respectively. The thermal deformation for lattice truss sandwich panel structure is of wave shape. The X-type has a better resistance to thermal deformation than pyramidal lattice truss sandwich structure. The maximum wave deformation of pyramidal structure (0.02 mm) is about twice as that of X-type (0.01 mm) at the same brazing condition.

Keywords: lattice truss sandwich structure; brazed residual stress; deformation
PACS: 81.20.Vj Joining; welding; 47.11.Fg Finite element methods

Introduction

Lattice truss sandwich structure is widely used in aerospace because it is a new type of light material with low density and high strength [1]. A lot of attention has been paid on its mechanical strength [2, 3], fatigue [4–6] and creep performance [7, 8]. In recent years, it is used to fabricate the compact heat exchangers because of its high efficiency of heat exchange [9, 10]. The lattice panel heat exchanger is fabricated by brazing the lattice core to solid face sheets [11, 12], which generates a lot of joints. Most sandwich panel structures have been fractured at brazing joints named node failure [13, 14]. One reason is that large residual stresses are generated due to mismatching of thermal expansion coefficient of parts [15, 16], which have a great effect on fracture, creep, fatigue, etc. [17, 18]. Therefore, it is very important to determine the residual stress and deformation to ensure the structure integrity. The joints are surrounded by the face sheets, which brings a lot of difficulties in the measurement. Joseph A. et al. [19] and Khan M.K. et al. [20] measured the residual stress by X-ray diffraction and nanoindentation methods, but they only measure the surface stress. Transmission electron microscopy (TEM) technique [21] is widely used to study the phase transformations in steels, but it is difficult to measure the brazing residual stress. Neutron diffraction [22] is a good method to measure the through-thickness stress, because it has good penetration ability. R.U. Vaidya et al. [23] used neutron diffraction to measure the bulk residual strains in molybdenum disilicide-316L stainless steel brazed joint. Therefore in this paper, neutron diffraction method is used to measure the through-thickness residual stress.

With the development of computer technology, finite element method (FEM) has been widely used to predict the residual stress distribution in the brazing structure [24].

Mansur Akbari et al. [25] developed a thermal-elasto-creep-plastic FEM to study the residual stresses in diamond brazing joint. M. Jacobs et al. [26] predicted the thermal stress in the glass–metal brazing joint of a vacuum vessel in ITER (International Thermonuclear Experimental Reactor) by elastic model and found that the maximum principal stresses in the interlayer exceeded the ultimate tensile strength of the braze alloy. He et al. [27] developed an elastic–plastic FEM model to investigate the residual stress in Si3N4-gradient materials (GM) filler alloy-42CrMo brazing joint, and the effects of GM compositions, layer numbers and thicknesses on the residual stresses have been studied, which provides a guideline to choose an appropriate filler alloy for improving the ceramic–metal joint performance. By using FEM, we [11] studied the residual stresses in a stainless steel X-type lattice truss sandwich structure, and the effects of braze processing parameters including applied load, face sheet thickness, truss thickness and truss length on residual stresses have been investigated, through which the processing parameters were optimized. We also [12] studied the geometrical effect of punching die on residual stress and deformation in a pyramidal lattice truss sandwich structure, which provides a reference for the design of punching die. Several topology, such as pyramidal, X-type, etc., has been developed for lattice truss sandwich structure [4]. But which topology is better is still unclear. Therefore in this paper, a comparison of brazed residual stress and deformation between X-type and pyramidal lattice sandwich structure is performed by FEM, and neutron diffraction measurement is performed to verify the present FEM.

Introduction to the fabrication of the lattice truss sandwich structure

The diamond pattern sheet is fabricated by a slitting, expanding and flattening method [28]. Punching at the diamond node and side can form the pyramidal and X-type lattice truss structure, respectively, as shown in Figure 1. The core materials are annealed to relax the residual stress induced by cutting and punching. The lattice truss structures are brazed to face sheets to form the sandwich panel structures. Filler metal BNi-2 is pre-located between the face sheet and lattice core. A clamping fixture is used to clamp the assembly tightly to ensure the close contact between face sheet and the lattice core. Then the assembly is put in a vacuum furnace. Before brazing, the vacuum pumping below 10−4 torr must be first ensured. The stacking is heated to 400°C at 10°C/min and the temperature is held for about 1 h. Then it is heated to the brazing temperature of 1,050°C and held for about 30 min. At last, the assembly is cooled to the ambient temperature in the furnace. For 316L stainless steel there is a sensitization problem which could decrease the corrosion resistance. Therefore, in order to avoid the sensitization around 620°C, a quick cooling is carried out between 1,050 and 620°C and then followed by a slow cooling from 620°C to room temperature (20°C/min).

Figure 1: Sketching of pyramidal (a) and X-type lattice truss structure (b). ω and β: inclination angle; b: node size; t: truss thickness; l: truss length; w: truss width.
Figure 1:

Sketching of pyramidal (a) and X-type lattice truss structure (b). ω and β: inclination angle; b: node size; t: truss thickness; l: truss length; w: truss width.

Finite element model

Geometrical model and meshing

Figure 1 shows the sketch of the pyramidal and X-type lattice truss sandwich structure. The truss thickness (t), length (l) and width (w) are 1, 22 and 2 mm. The thickness of face sheet is 2 mm. The inclination angle ω and β are 41° and 40°, respectively. The node size b is 3 mm. Finite element code ABAQUS is used to simulate the brazing temperature and residual stress. The time integration in FEM is explicit integration because it can save computation time. Figure 2 shows the finite element model for pyramidal and X-type lattice truss sandwich structures, which contains 9 unit cells. Three-dimensional finite element model is built and the meshing is shown in Figure 3. The effect of mesh sensitivity on calculation results have been performed, and finally, 101,995 nodes, 76,056 elements and 79,037 nodes, 59,832 elements are meshed in X-type and pyramidal lattice truss sandwich structure, respectively. It has a fine meshing around the brazing joint while it is coarse far away. The element type for temperature and stress calculation is DC3D8 and C3D8, respectively, which are three-dimensional solid eight integration element for thermal and stress analysis, respectively. A sequential coupling FEM is developed to calculate the brazing temperature and residual stress, which is described in detail as follows.

Figure 2: Geometrical model of pyramidal (a) and X-type (b) lattice truss sandwich structure.
Figure 2:

Geometrical model of pyramidal (a) and X-type (b) lattice truss sandwich structure.

Figure 3: Finite element meshing of pyramidal (a) and X-type (b) lattice truss sandwich structure.
Figure 3:

Finite element meshing of pyramidal (a) and X-type (b) lattice truss sandwich structure.

Brazing temperature simulation

The brazing temperature simulation is carried out by considering thermal conduction, heat convection and radiation. The heat conduction was calculated by

(1)s=−ρC∂T∂t+∇K∇T

where s is the volume of the heat source in unit, ρ is the density of the materials, C is the specific heat, T is the temperature, t is time and K is conductivity.

The heat convection was calculated by

(2)Φ=hAtw−tf

where Φ is the heat transfer in unit time, h is convective heat transfer coefficient (10 W/m2K−1), A is contacting area, tw is the temperature of solid surface and tf is the temperature of fluid surface.

The radiation was calculated by [25]

(3)q=εAσ(Ts4−Tfurn4)

where q is the irradiance, ε is the emissivity, Ts is the temperature of brazed parts and Tfurn is the temperature of high vacuum furnace. σ is Stefan–Boltzmann constant (5.67 × 10-8W m−2K−4).

Residual stress analysis

The residual stress is calculated by thermal-elasto-plastic model, using the temperature distribution obtained from the thermal analysis as input data. The total strain is decomposed into elastic strain, plastic strain and thermal strain. Elastic strain is modeled using the isotropic Hooke’s law with temperature-dependent Young’s modulus and Poisson’s ratio. The thermal strain is calculated using the temperature-dependent coefficient of thermal expansion (CTE). For the plastic strain, a rate-independent plastic model is employed with von Mises yield surface, temperature-dependent mechanical properties and isotropic hardening model. In the cooling stage, the time at creep temperature is very short, but it has effect on residual stress. Mansur Akbari et al. studied the brazed residual stress considering the creep effect by Norton’s steady-state power law [25]. But here, due to that the filler metal is very thin and the material properties after brazing are different from the as-cast filler metal, it is very difficult to get the creep parameters. Therefore, the creep behavior is not considered in the simulation [26], which should be studied in the future.

Material properties and boundary conditions

The materials of face sheet and truss are 316L stainless steel, and the filler metal is BNi-2. The temperature-dependent material properties are incorporated, which are listed in Tables 1 and 2 [18, 29].

Table 1:

Thermal properties of 316L and BNi-2 [11, 29].

MaterialTemperature (°C)Conductivity (W/(m °C) )Density (kg/m3)Specific heat (J/(°C · kg) )
316L2013.317,966492
40019.477,966538
90026.337,966659
BNi-22025.597,850469.51
40029.187,850577.73
90033.587,8501,161.34
Table 2:

Mechanical properties of 316L and BNi-2 [11, 29].

MaterialTemperature (°C)Young’s modulus (GPa)Poisson’s ratioCTE (1/°C)Yield strength (MPa)
316L20196.50.291.46 × 10−5243
400172.60.291.74 × 10−5163
900116.80.291.90 × 10−599
BNi-220205.10.2961.35 × 10−5300
400183.20.3061.68 × 10−5220
8001610.32819.9 × 10−5160

During the vacuum brazing, the face sheet, truss and filler metal should be assembled and fixed tightly to prevent mismatching. The symmetric boundary conditions were applied on the left and front face of the model, and the bottom face was constrained in Y-direction. Thus the rigid motion was avoided. A pressure load with 1 MPa was applied on the top of face sheet to simulate the clamping pressure [11].

Neutron diffraction measurement

In this paper, in order to verify the present FEM, a butt joint is prepared as shown in Figure 4, and the residual stress is measured through thickness by neutron diffraction. Two 4–mm-thick 316L stainless steel plates were brazed together according to the brazing procedure in section “Introduction to the fabrication of the lattice truss sandwich structure”. And the residual stress is calculated according to the FEM described in section “Finite element model”. During the brazing, a load was applied on the top surface to prevent the moving of the parts, and the bottom surface was not allowed to move. Therefore, during the simulation the nodes on the bottom surface were constrained.

Figure 4: Simplified model to verify the FEM results.
Figure 4:

Simplified model to verify the FEM results.

The residual stress is measured by neutron diffraction measurement using the residual stress instrument at HANARO reactor of Korea Atomic Energy Research Institute [30]. The neutron diffraction measurement is based on Bragg’s law: nλ=2dsinθ, where n is an integer, d is lattice spacing and 2θ is the diffraction angle. The strain (ε) can be determined by measuring the scattering angle (θ) of a material under stress and the scattering angle (θ0) of the same material free of stress, which is given by ε=Δd/d=−(θ−θ0)cotθ. The lattice spacing d is measured in the direction bisecting the incoming and diffracted neutron beams. The strains in three mutually orthogonal directions x, y and z are measured, and the principal stress can be calculated using the generalized Hook’s law:

(4)σi=Ehkl1+νhklεii+νhkl1−2νhklεxx+εyy+εzz

where Ehkl and νhkl are elastic modulus and Poisson’s ratio. The “stress-free” reference samples were cut by electrodischarge machine to measure the do (θ0) values. The Si (111) bent perfect crystal was chosen for the monochromator and produced neutrons with the wavelength of 1.46 Å at the take-off angles (2θM) of 45o. The gauge volume is 1×1×1 mm3. Six points are measured and the location is shown in Figure 4.

Results and discussion

Comparison between FEM and neutron diffraction measurement

Figure 5 shows the residual stress distribution by neutron diffraction measurement and FEM. The residual stresses are concentrated around the brazing joint and then decrease to the surface. Due to that the thickness is very thin and the normal stress is very small; therefore, the normal stress is not shown here and only longitudinal (LD) and transverse (TD) stresses are presented. It shows that there is a slight deviation between measurement and FEM, but the total distribution trend is good. In the simulation, the material properties, microstructure and plastic performance, etc. have a great effect on residual stress, which may be different from the actual data and brings the deviation in some points between FEM and measurement. The stresses are not symmetric because of the constraint on the bottom surface, which is similar to that found by Hamilton N.R. et al. [24]. The result proves that the present FEM is right and can be used to predict the residual stress in the complex lattice truss sandwich structure.

Figure 5: Residual stress through the thickness by FEM and neutron diffraction measurement.
Figure 5:

Residual stress through the thickness by FEM and neutron diffraction measurement.

Comparison of residual stress between X-type and pyramidal truss structure

Two reference paths P1 and P2, as shown in Figure 3, are picked to fully discuss the results. P1 is along the center of the brazing joint, and P2 is through the center of face sheet and truss. The residual stresses are concentrated on the brazing joints, which is affected by the material mismatching between base metal and filler metal as listed in Table 2. The face sheet and lattice core have a constraint on the braze joint, which can also lead to large residual stress.

Figure 6 shows the residual stress distribution along P1. Both models have the similar distribution trend: the residual stresses are concentrated in the middle and then decrease rapidly to both the ends. This is because at the edges the material is unsupported in the longitudinal direction and therefore no stress can be sustained in this direction at the edges. The maximum LD and TD stresses of pyramidal lattice truss sandwich structure are 220 and 202 MPa, respectively, while they decrease to 190 and 145 MPa for X-type lattice truss sandwich structure, respectively. In total, the residual stresses in X-type lattice truss sandwich structure are smaller than those in pyramidal lattice truss sandwich structure.

Figure 6: Comparison of residual stress along P1.
Figure 6:

Comparison of residual stress along P1.

Figure 7 shows the residual stress distribution along P2. P2 contains face sheet, filler metal and truss. In total, tensile stresses are shown in the face sheet, while compressive stresses are presented in the truss. This is because the thickness of face sheet is higher than truss, and it has a larger mechanical strength than the core. Therefore, the truss is compressed and shows the compressive stress. The residual stresses increase gradually through face sheet and then increase rapidly in the filler metal, finally they decrease rapidly in the truss. It obviously shows that the residual stress along P2 in X-type is smaller than the pyramidal lattice truss sandwich structure.

Figure 7: Comparison of residual stress along P2.
Figure 7:

Comparison of residual stress along P2.

Discussion

Compared with the pyramidal lattice truss sandwich structure, the maximum LD and TD stresses in the joint of X-type have decreased about 15% and 40%, respectively, which is helpful to decrease the risk of node failure found in the lattice truss structure. Zhang et al. [31] have found that the compressive and shear peak strengths of the X-type lattice structure are about 30% higher than those of the pyramidal lattice truss having the same relative density. The theoretical and numerical study supports the argument that the X-type structure is superior to the pyramidal lattice structure in terms of mechanical strength [32]. That is to say, the mechanical strength of X-type is larger than pyramidal structure, which can limit the deformation of filler metal and decrease the residual stress in X-type structure.

We found that the panel structure has a thickness reduction deformation by simulating the unit cell [12], but it is different for a large lattice structure with a lot of units. Therefore, in this paper, the finite element models contain nine units. Figure 8 shows the deformation along the middle line of upper face sheet. The upper face sheet has a wave-shaped deformation, because the trusses have support on the node joint and brings a non-uniform deformation and stresses. For pyramidal type, its wave amplitude (~0.011 mm) is much larger than that of X-type lattice truss sandwich structure (0.001 mm). The maximum wave deformation of pyramidal structure is about ~0.02 mm, which is about twice as that of X-type (only 0.01 mm), because the staggered joints in X-type limit the truss moving along longitudinal direction. The X-type lattice truss sandwich structure has a relative uniform deformation than that of pyramidal, because the X-type has a larger strength than that of pyramidal structure. It concludes that the X-type structure has a good resistance to thermal deformation than pyramidal structure.

Figure 8: The deformation along the middle line of upper face sheet.
Figure 8:

The deformation along the middle line of upper face sheet.

In recent years, the lattice truss sandwich panel structure is used to fabricate the heat exchangers. It has a good creep and fatigue strength and has a good application in high temperature with thermal cycles. Decreasing the as-brazed residual stress and thermal deformation is very important to ensure its structure integrity. Here we compared the residual stress and deformation between X-type and pyramidal lattice truss structure and found that the X-type is more suitable for lattice truss sandwich structure heat exchanger.

Conclusions

This study carried out a comparison of residual stress and thermal deformation between X-type and pyramidal lattice truss sandwich structure during the brazing fabrication by FEM. The FEM results have been verified by neutron diffraction measurement and the following conclusions are achieved.

  1. Large residual stresses are generated in the braze joints due to the mismatching of mechanical properties among the face sheet, filler metal and truss core. The residual stresses are concentrated in the middle joint and then decrease gradually to both the ends. The residual stresses in X-type lattice truss sandwich structure are smaller than the pyramidal lattice truss sandwich structure. The maximum longitudinal and transverse stresses in X-type lattice truss sandwich structure have been decreased about 15% and 40%, respectively, compared to those in pyramidal structure.

  2. The lattice truss sandwich structure has a wave-shaped thermal deformation. The maximum wave deformation of pyramidal structure is about twice as that of X-type. The X-type has a better resistance to thermal deformation than pyramidal truss sandwich structure.

Funding statement: Funding: The authors gratefully acknowledge the support provided by the Shandong Natural Science Foundation for Distinguished Young Scholars (JQ201417), National Natural Science Foundation of China (11372359) and Fundamental Research Funds for the Central Universities (10CX04030A, 14CX05036A and 15CX08006A).

References

[1] G.W. Kooistra and H.N.G. Wadley, Mater. Sci. Eng. A, 28 (2007) 507–514.10.1016/j.matdes.2005.08.013Search in Google Scholar

[2] X. Wang, J. Gong, Y. Zhao and Y. Wang, High Temp. Mater. Process. (2014), DOI: 10.1515/htmp-2014-0039.Search in Google Scholar

[3] J.S. Moita, A.L. Araújo, C.M. Mota Soares and C.A. Mota Soares, Adv. Eng. Softw., 66 (2013) 34–39.10.1016/j.advengsoft.2012.10.002Search in Google Scholar

[4] D.T. Queheillalt, Y. Murty and H.N.G. Wadley, Scripta Mater., 58 (2008) 76–79.10.1016/j.scriptamat.2007.08.041Search in Google Scholar

[5] F. Côté, V.S. Deshpande and N.A. Fleck, Scripta Mater., 56 (2007) 585–588.10.1016/j.scriptamat.2006.12.035Search in Google Scholar

[6] F. Côté, N.A. Fleck and V.S. Deshpande, Int. J. Fatigue, 29 (2007) 1402–1412.10.1016/j.ijfatigue.2006.11.013Search in Google Scholar

[7] S.M. Oppenheimer and D.C. Dunand, Acta Mater., 55 (2007) 3825–3834.10.1016/j.actamat.2007.02.033Search in Google Scholar

[8] Z.G. Fan, C.Q. Chen and T.J. Lu, Mater. Sci. Eng. A, 540 (2012) 83–88.10.1016/j.msea.2012.01.086Search in Google Scholar

[9] T. Kim, H.P. Hodson and T.J. Lu, Int. J. Heat Mass Transfer, 48 (2005) 4243–4264.10.1016/j.ijheatmasstransfer.2005.04.026Search in Google Scholar

[10] T.J. Lu, L. Valdevit and A.G. Evans, Prog. Mater. Sci., 50 (2005) 789–815.10.1016/j.pmatsci.2005.03.001Search in Google Scholar

[11] W.-C. Jiang, H. Chen, J.M. Gong and S.T. Tu, Mater. Sci. Eng. A, 528 (2011) 4715–4722.10.1016/j.msea.2011.02.073Search in Google Scholar

[12] W.-chun Jiang, B. Yang, B.Y. Wang, H. Chen and J.M. Gong, Mater. Des., 49 (2013) 1048–1055.10.1016/j.matdes.2013.01.059Search in Google Scholar

[13] G. Zhang, B. Wang, Li. Ma, J. Xiong and L. Wu, Comp. Struct., 100 (2013) 451–463.10.1016/j.compstruct.2013.01.012Search in Google Scholar

[14] D.T. Queheillalt and H.N.G. Wadley, Mater. Des., 30(2009) (1975) 1966–.10.1016/j.matdes.2008.09.015Search in Google Scholar

[15] C.T. Chang and R.K. Shiue, Int. J. Refractory Metals Hard Mater., 23 (2005) 161–170.10.1016/j.ijrmhm.2005.01.002Search in Google Scholar

[16] R. Monti, F. Coppola, P. Gasbarri and U. Lecci, Acta Astronaut., 66 (2010) 897–913.10.1016/j.actaastro.2009.09.009Search in Google Scholar

[17] J.E. LaRue and S.R. Daniewicz, Int. J. Fatigue, 29 (2007) 508–515.10.1016/j.ijfatigue.2006.05.008Search in Google Scholar

[18] L.Y. Chen, G.Z. Wang, J.P. Tan, F.Z. Xuan and S.T. Tu, Eng. Fract. Mech., 97 (2013) 80–91.10.1016/j.engfracmech.2012.10.020Search in Google Scholar

[19] A. Joseph, S.K. Rai, T. Jayakumar and N. Murugan, Int. J. PVP, 82 (2005) 700–705.10.1016/j.ijpvp.2005.03.006Search in Google Scholar

[20] M.K. Khan, M.E. Fitzpatrick, S.V. Hainsworth, A.D. Evans and L. Edwards, Acta Mater., 59 (2011) 7508–7520.10.1016/j.actamat.2011.08.034Search in Google Scholar

[21] R. Delville, B. Malard, J. Pilch, P. Sittner and D. Schryvers, Acta Mater., 58 (2010) 4503–4515.10.1016/j.actamat.2010.04.046Search in Google Scholar

[22] D.W. Brown, T.M. Holden, B. Clausen, M.B. Prime, T.A. Sisneros, H. Swenson and J. Vaja, Acta Mater., 59 (2011) 864–873.10.1016/j.actamat.2010.09.022Search in Google Scholar

[23] R.U. Vaidya, P. Rangaswamy, M.A.M. Bourke and D.P. Butt, Acta Mater., 46 (1998) 2047–2061.10.1016/S1359-6454(97)00429-1Search in Google Scholar

[24] N.R. Hamilton, M.O. Robbie, J. Wood, A. Galloway, I. Katramados and J. Milnes, Fus. Eng. Des., 86 (2011) 1642–1645.10.1016/j.fusengdes.2011.04.027Search in Google Scholar

[25] M. Akbari, S. Buhl, C. Leinenbach, R. Spolenak and K. Wegener, Mech. Mater., 52 (2012) 69–77.10.1016/j.mechmat.2012.04.010Search in Google Scholar

[26] M. Jacobs, G. Van Oost, J. Degrieck, I. De Baere, A. Gusarov and V. Massaut, Fus. Eng. Des., 86 (2011) 2831–2838.10.1016/j.fusengdes.2011.05.003Search in Google Scholar

[27] Y. He, J. Zhang, F. Pan, C. Liu and X. Li, Ceram. Int., 39 (2013) 709–718.10.1016/j.ceramint.2012.06.082Search in Google Scholar

[29] O. Muránsky, C.J. Hamelin, M.C. Smith, P.J. Bendeich and L. Edwards, Comput Mater Sci., 54 (2012) 125–134.10.1016/j.commatsci.2011.10.026Search in Google Scholar

[30] W. Woo, G.B. An, E.J. Kingston, A.T. DeWald, D.J. Smith and M.R. Hill, Acta Mater., 61 (2013) 3564–3574.10.1016/j.actamat.2013.02.034Search in Google Scholar

[31] Q. Zhang, Y. Han, C. Chen and T. Lu, Sci. China Ser. E Technol. Sci., 52 (2009) 2147–2154.10.1007/s11431-009-0219-9Search in Google Scholar

[32] Q. Zhang, A. Chen, C. Chen and T. Lu, Sci. China Series E: Technol. Sci., 52 (2009) 2670–2680.10.1007/s11431-009-0228-8Search in Google Scholar

Received: 2015-2-23
Accepted: 2015-5-25
Published Online: 2015-7-23
Published in Print: 2016-6-1

©2016 by De Gruyter

This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

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https://doi.org/10.1515/htmp-2015-0046
Keywords for this article
lattice truss sandwich structure; brazed residual stress; deformation
Creative Commons
BY-NC-ND 3.0

Articles in the same Issue

  1. Frontmatter
  2. Research Articles
  3. Effect of Activating Agent on the Preparation of Bamboo-Based High Surface Area Activated Carbon by Microwave Heating
  4. Research on the Microstructure and Mechanical Property of Ti-7Cu Alloy after Semi-Solid Forging
  5. Synthesis and Characterization of BiFeO3 Ceramic by Simple and Novel Methods
  6. Synthesis and Characterization of Lead Sulfide Nanostructures with Different Morphologies via Simple Hydrothermal Method
  7. Comparison of Brazed Residual Stress and Thermal Deformation between X-Type and Pyramidal Lattice Truss Sandwich Structure: Neutron Diffraction Measurement and Simulation Study
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  11. Constitutive Equation for 3104 Alloy at High Temperatures in Consideration of Strain
  12. Microstructural Properties and Four-Point Bend Fatigue Behavior of Ti-6.5Al-2Zr-1Mo-1V Welded Joints by Electron Beam Welding
  13. Oxidizing Roasting Performances of Coke Fines Bearing Brazilian Specularite Pellets
  14. Purification of Niobium by Electron Beam Melting
  15. Void Formation during Diffusion – Two-Dimensional Approach
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