Numerical modelling and nanoindentation experiment to study the brazed residual stresses in an X-type lattice truss sandwich structure

Materials Science and Engineering A 528 (2011) 4715–4722

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Numerical modelling and nanoindentation experiment to study the brazed residual stresses in an X-type lattice truss sandwich structure Wenchun Jiang a,∗ , H. Chen b , J.M. Gong c , S.T. Tu d a

College of Mechanical and Electronic Engineering, China University of Petroleum, Dongying 257061, PR China Technical Development Department, Ningbo Special Equipment Inspection Institute, Ningbo 315020, PR China School of Mechanical and Power Engineering, Nanjing University of Technology, Nanjing 210009, PR China d 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 c

a r t i c l e

i n f o

Article history: Received 12 January 2011 Received in revised form 22 February 2011 Accepted 22 February 2011 Available online 1 March 2011 Keywords: Lattice truss structure Braze Residual stress FEM Nanoindentation

a b s t r a c t The lattice truss sandwich structures are considered as the most promising advanced lightweight materials used in modern industries and aircrafts. Most sandwich panel structures are fractured at brazed joints named node failure during static and dynamic testing, which is mainly influenced by brazing residual stresses. Finite element method (FEM) was used to study the brazing residual stresses in a stainless steel X-type lattice truss sandwich structure. And the nanoindentation experiment is used to verify the validity of FEM. The effects of braze processing parameters including applied load, face sheet thickness, truss thickness and truss length on residual stresses have been investigated. It is shown than the residual stresses are concentrated on the brazed joint, which has a significant effect on node failure. As the applied load increases, the residual stresses decrease first and then remain unchanged, and the optimal applied load is around 1 MPa. As the face sheet thickness increasing, the residual stresses are increased. Too thin face sheet can cause large residual stresses on the top surface of face sheet. With truss thickness and truss length increase, the residual stresses are decreased first and then increased. The optimized face sheet, truss thickness and truss length are found to be 2 mm, 1 mm and 26 mm. © 2011 Elsevier B.V. All rights reserved.

1. Introduction Ultra-lightweight cellular metallic materials have become the focus of attention in recent years because they exhibit an attractive combination of properties, such as low density, high strength, high specific stiffness, damping capacity, noise absorption, and multifunctional application potential, etc. [1]. Therefore, these materials have been widely used in modern industries and aircrafts [2]. The lattice truss structures are considered as the most promising type of advanced lightweight materials, because they are highly efficient load supporting systems used as the cores of sandwich panels [3]. Tetrahedral [4], pyramidal [5], 3D-Kagome [6], metal textile [7] and woven structures [8] are the main topologies used to construct the lattice truss structures. The tetrahedral truss core panels exhibit particularly good bending performance and feasibility for achieving the minimum weight [9,10]. 3D-Kagome sandwich panels show greater load capacity under compression and shear loading than that of tetrahedral truss core panels and provide isotrophy under shear loading [11,12]. Recently, Lu et al. [13,14] developed an ultralight X-type lattice sandwich structure.

∗ Corresponding author. Tel.: +86 546 8391776; fax: +86 546 8391776. E-mail address: [email protected] (W. Jiang). 0921-5093/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2011.02.073

The open literatures on lattice structure were focused on their mechanical properties [15], fabrication technologies [16–18], failure mechanism [19], etc. Deshpande et al. [20] and Zok et al. [1] developed the micromechanical models for the stiffness and strength of pyramidal lattice truss cores. Fang et al. [21] designed a new Kagome cell and statically indeterminate square cell lattice materials, and investigated their in-plane mechanical properties such as stiffness, yielding, buckling and collapse mechanisms by analytical methods. Alkhader and Vural [22] explored the effect of topology and microstructural irregularity on deformation modes of cellular structures by a simple quantitative technique. Oruganti et al. [23] studied the thermal expansion behavior in fabricated cellular structures. In the fabrication, investment cast [20,24], perforation and folding [25], tri-axial weaving of wires technology [26], extrusion and electrodischarge machining [27] are the main methods used to fabricate the metal lattice truss cores. Water-jet cutting combined with the snap-fitted method [28] and molding hot-press method [18] are also developed to fabricate the carbon fiber composite pyramidal truss structures. Very recently, Moongkhamklang et al. [29] developed a method to fabricate millimeter cell size cellular lattice structures with a square or diamond collinear truss topology. The lattice truss core sandwich panels are fabricated by bonding lattice structures to face sheets [30]. During the brazing, residual stresses and defects would be generated inevitably [31,32], which

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have a great effect on fracture [33]. Most sandwich panel structures have been fractured at brazed joints named node failure during static and dynamic testing [34,35], which are mainly influenced by the residual stresses and defects resulted from the brazing [36]. But up to now, little attention has been paid to residual stress for the lattice truss structures. As the complexity of the lattice truss structures, it is very difficult to obtain their residual stress distribution by experiments. Finite element method (FEM) has been proved to be a powerful tool to predict the residual stress and deformation in complex structure [37,38]. Therefore in this paper, FEM has been used to simulate the brazing residual stress in an X-type lattice truss sandwich structure, which has been verified by nanoindentation experiment. Some braze processing parameters including the applied load, face sheet thickness, truss thickness and truss length are the key factors because they have great effect on residual stress and strength [39–41]. Therefore the effects of applied load, face sheet thickness, truss thickness and truss length on residual stresses have been discussed here, aiming to provide a reference for design and manufacture of the X-type lattice truss sandwich structure. 2. Brazing of X-type lattice truss structures A slitting, expanding and flattening method is used to form a periodic diamond pattern sheet. Then the diamond sheet is continuously punched with a pair of specially designed punch to form the lattice structure cores. Punching at different locations can form different shape of lattice core. Punching continuously at the node rows of the expanded diamond sheet can form the pyramidal lattice structure, while punching continuously in the middle of two node rows can form the X-type lattice truss structure, as shown in Fig. 1 [13]. The trusses are arranged in triangle shape and X-shaped arrangement in the pyramidal and X-type core, respectively. Lu and co-workers [13,14] found that the mechanical strength of the Xtype lattice sandwich structure is superior to the pyramid lattice structure. In this paper the residual stresses in an X-type lattice sandwich structure are studied by FEM. The lattice structures are brazed to face sheets to form lattice truss core sandwich panels, and the filler metal is pre-located between the face sheet and lattice core. A clamping fixture should

be used to clamp the assembly tightly, which can generate an applied load to ensure the close contact between face sheet and the lattice core. Then the assembly is fixed and brazed in a vacuum furnace. Before brazing, the vacuum-pumping below 10−4 Torr must be first ensured. The stacking is heated to 500 ◦ C at 10 ◦ C/min and the temperature is held for about 60 min to volatilize the binder. Then it is heated to the brazing temperature of 1050 ◦ C and held about 25 min, which makes the carbide of the austenitic stainless steel achieve preferable solid–solution treatment. At last, the assembly is cooled to the ambient temperature in the furnace. 3. FE simulation 3.1. Geometrical model and meshing Fig. 2 shows the sketch of the X-type lattice truss structures [13]. The truss thickness (t), length (l) and width (w) are 1, 22 and 2 mm. The inclination angle ω and ˇ are 41◦ and 40◦ , respectively. The node size b is 3 mm. Finite element code ABAQUS is used to simulate the residual stress. A three dimensional FE model is built as shown in Fig. 3, and its meshing is shown in Fig. 4. In total, 95,218 nodes and 75,461 elements are meshed. 3.2. Residual stress analysis At the high brazing temperature, the assembly is at stress-free state. Therefore, the as-brazed residual stress is simulated during the cooling from 1050 ◦ C to 20 ◦ C. For the present used materials, solid-state phase transformation does not occur. Therefore, the total strain rate can be decomposed into three components as

Fig. 2. Sketching of X-type lattice structure.

Fig. 1. Fabrication process of pyramidal (a) and X-type truss structures (b).

Fig. 3. Geometrical model.

W. Jiang et al. / Materials Science and Engineering A 528 (2011) 4715–4722

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Fig. 4. FE meshing of total structure (a) and the local in brazed joint (b).

follows:

3.3. Material properties

ε = εe + εp + εts

(1)

where, εe , εp and εts stands for elastic strain, plastic strain and thermal strain, respectively. 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 CTE. For the plastic strain, a rateindependent plastic model is employed with Von Mises yield surface, temperature-dependent mechanical properties and linear kinematic hardening model. This analysis was simplified according to the following considerations: (1) the capillarity of filler metal at brazing temperature is out of view; (2) the solutionizing and the diffusion of the filler components to base metal are not included; (3) the creep behavior during the brazing process is not considered.

The materials of face sheet and truss are 304 stainless steel, and the filler metal is BNi2. For the residual stress analysis, temperature-dependent mechanical properties of materials are incorporated. The material properties relevant to residual stress are elastic modulus, yield stress, Poisson’s ratio, and the coefficient of thermal expansion (CTE), which is listed in Table 1 [42]. 3.4. Boundary conditions During the vacuum braze, 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 the Ydirection. Thus the rigid body motion was avoided. A pressure load with 1 MPa was applied on the top of face sheet to simulate the clamping pressure.

Table 1 Mechanical material properties of 304 and BNi2. Material

Temperature (◦ C)

CTE (1/◦ C)

Young’s modulus (GPa)

Poisson’s ratio

Yield strength (MPa)

304

20 400 900 20 400 900

16.0 × 10−6 18.1 × 10−6 19.7 × 10−6 13.5 × 10−6 16.8 × 10−6 21.3 × 10−6

199 166 111 205.1 183.2 127.6

0.28 0.26 0.24 0.296 0.306 0.328

206 108 62 424 368 255

BNi2

W. Jiang et al. / Materials Science and Engineering A 528 (2011) 4715–4722

1600

In order to verify the validity of the present FE method, a Tbutt brazed joint is built as shown in Fig. 5. Two stainless steel plates were brazed together with filler metal BNi-2 according to the brazing process in Section 2. The generated residual stresses are predicted and measured by FEM and nanoindentation method, respectively. The FE meshing of the butt joint is shown in Fig. 6. Due to the advantages of point positioning with micrometer scale, independency of material microstructure and low restriction on the surface condition, the residual stress characterization method for micro joint based on nanoindentation technique [43] has been initially developed and used in characterizing the microregion stress. Nanoindentation is based on the load-sensing or depth-sensing measurement technology under the scale level of micro-newton loading and the nano-depth. Researches reveal [44] that indentation load–depth curve shape is different for cases with/without the residual stress. The change in indentation deformation caused by the residual stress was identified in the indentation loading–displacement curve (L–h curve) in Fig. 7. Noting that the solid curve in Fig. 7 represents the behavior of an essentially unstressed (i.e. stress-free) material, it is apparent that the applied load for the material with tensile stressed is lower than that with compressive stress for the same maximum indentation depth, and the load for unstressed case is just in the middle state. The schematic diagram for the detailed changes in contact morphology is presented in Fig. 8. Apparently, the indentation impression is changed for different stress state: tensile stress can cause the sink-in of contact surface around the indenter and com-

1400

Indentation Load L/mN

4. Experimental verification of the FE method

Stress-free Tensile stress Compresive-stress

1200 L C

Lres,C

1000

A

800 L0 600

C

Loading part

200 0

Lres,T

LT

400

B

Unloading part

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ht 0

1000

2000

3000

4000

5000

6000

Indentation Displacement h/nm Fig. 7. Effect of residual stress on the load–displacement curve.

Fig. 5. The brazed butt joint.

Fig. 6. FE meshing of the brazed butt joint.

Fig. 8. Surface morphologies around the indenter contact for different residual stress states: (a) tensile stress induced sink-in; (b) stress-free nanoindentation; (c) compressive stress induced pile-up.

W. Jiang et al. / Materials Science and Engineering A 528 (2011) 4715–4722

L1 − L2 2

tan2

˛h2res

(2)

where the surface residual stress  res can be evaluated by studying important parameters from the load–displacement curve including the contact pressure Pave , the ratio m of contact areas with/without the residual stress, the difference Lres of the maximum indention load, the effective cone semi-angle ˛, angle ˇ = /2 − ˛, the residual depth hres after unloading and the actual contact area Ac . It must be noted here that the indentation experiments provide an in-plane “average stress” (average of transverse and longitude components). Current nanoindentation experiments were completed in the mechanical testing platform of MTS® NANO-INDENTER-XP. The Berkovich indenter was used. The typical depth-controlled indentation cycle was as following: (1) Load at the rate 10 nm/s to a maximum depth of 5000 nm; (2) Hold the maximum load for 10 s to reduce the adverse effect of material creep; (3) Unload to 70 percent of the maximum depth, hold for 100 s to obtain the equipment drift rate and then unload completely; (4) 304 type stainless steel, the same as the joint substrate, was used as the reference to obtain the zero residual stress indentation response. To avoid the effect of work hardening on the measurement results, surface treatment is forbidden before nanoindentation. Therefore, the indentation points must be positioned close to the joint interface as much as possible and away from the coated region due to overflowing of the liquid filler alloy at the brazing temperature, as shown in Fig. 9. All the indentation points are connected into two testing paths parallel to the joint interface which are plotted in Fig. 5. Fig. 10 shows the residual stress distribution along reference paths 1 and 2 shown in Fig. 5. It can be seen that the residual stress along the two paths show a good distribution trend, which proved that the present FE method is right and can be used to predict the residual stress in the complex X-type lattice structure.

Fig. 9. Testing point positioning near the region of joint interface.

Average residual stress σ avg/MPa

res = ±

(a) 120 1#

100

_______

Experiment FEM

10#

80 60 40 20

3#

7#

5#

4#

8#

0 -20 -40

2#

0

9#

2000

4000

6000

8000

10000

Distance along path 1 (y u=65μm) x/μm

(b) 40 Average residual stress σ avg /MPa

pressive stress can result into the pile-up of contact surface. hn and hp are the depth, which are difficult to be measured experimentally. The actual contact depth hc varies under the effect of hn or hp , and the contact radius a and the actual contact area Ac change accordingly, as shown in Fig. 8. Ac and the load difference Lres , which is obtained from the L–h curves for stressed and stressfree state in Fig. 7, are two important parameters used in residual stress measurement by nanoindentation. The “Energy method Model” based on energy conversation before/after indentation [45] is used to built in surface stress measurement:

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Experiment FEM

30 20 10

11#

13#

0

14#

16# 19#

22# 20#

-10 -20 -30

12# 21#

-40 -50

0

2000

4000

6000

8000 10000 12000

Distance along path 2 (yd=85μm) x/μm Fig. 10. Results comparison of experiment and FEM: (a) Path1; (b) Path 2.

5. Results and discussion Residual stress components from FE analysis are obtained in the following direction: (1) longitudinal stress S33, represents the stress in Z-axis direction; (2) transverse stress S11, refers the stress in X-axis direction; (3) thickness stress S22, is the stress in Y-axis direction. 5.1. Residual stress distribution Fig. 11 shows the contours of S11, S22 and S33 distribution. It can be seen that their peak values are 231, 47.8, and 224 MPa, respectively. The peaks of S11 and S33 are located at the fillet. S22 is very small and the discussion in the following is focused on S11 and S33. The stress concentration at the fillet is one of the reasons why the failure is located on the brazed joint. The material mismatching between base metal and filler metal has a great effect on the stress concentration in the braze joint. The face sheet and X-type truss lattice core have a constraint on the braze joint, which can also lead to large residual stress. The X-type truss and filler metal with high strength also have a constraint on the face sheet against the braze joint, which brings large residual stresses on the top surface of face sheet, as shown in Fig. 12. The maximum residual stresses of S11 and S33 on the top surface sheet are about 153 and 114 MPa, respectively. The residual stresses are influenced by braze processing parameters, such as applied load, face sheet thickness, truss thickness,

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Fig. 12. Residual stress contours of S11 (a) and S33 (b) on the top surface of face sheet.

450 S11 S33

Residual stress (MPa)

400 350 300 250 200

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 Applied load (MPa) Fig. 13. Effect of applied load on residual stresses. Fig. 11. Residual stress contours of S11 (a), (b) S22 and (c) S33.

peak residual stresses decrease first and then keep unchanged. The optimized applied load is around 1 MPa. truss length, etc. In order to decrease the residual stress and increase the strength, it is very important to explore the relationship between residual stress and processing parameters, which can provide a reference for optimizing the braze processing. Here the effects of applied load, face sheet thickness, truss thickness and truss length on residual stresses are discussed in the following. 5.2. Effect of applied load During the brazing, a pressure load should be applied to ensure a close contact between face sheet and core. The applied load has many additional functions such as: (1) ensure the capillary force and prevent mismatching between base metal and filler metal; (2) generate compressive stress to counteract tensile residual stress; (3) promote the diffusion of filler metal elements and increase the bonding ratio, etc. Keeping the rest parameters unchanged, the applied load is changed to discuss its effect on residual stress. Fig. 13 shows the effect of applied load on the maximum residual stresses in the brazed joint. As the applied load increases, the

5.3. Effect of face sheet thickness Keeping the rest parameters constant, the face sheet thickness was changed to discuss its effect. Four FE models with a face sheet thickness of 1.5, 2.0, 2.5 and 3 mm were developed and calculated. It was found that the peak stresses are increased as the face sheet thickness increases, as shown in Fig. 14. The face sheet has a constraint on the brazing joint, and this constraint increases with an increase in face sheet thickness, which leads to the residual stresses increase. The residual stresses on the top surface of face sheet have been decreased as the face sheet thickness increase, as shown in Fig. 9. When the face sheet is 1.5 mm, S33 on its top surface sheet is 229 MPa, which has exceeded the yield strength. This means that too thin face sheet can cause large residual stress on the top surface of face sheet. From Figs. 14 and 15, it can be concluded that the optimized face sheet thickness is 2 mm. Theoretically, increasing the face sheet thickness can increase the bending fatigue resistance of the sandwich structures because

W. Jiang et al. / Materials Science and Engineering A 528 (2011) 4715–4722

320

300 S11 S33

S11 S33

300

260

Residual stress (MPa)

Residual stress (MPa)

280

240 220 200 180

280 260 240 220

160 140 1.4

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0.4

1.6

1.8 2.0 2.2 2.4 2.6 2.8 Face sheet thickness (mm)

3.0

0.6

3.2

0.8

1.0

1.2

1.4

1.6

Truss thickness (mm) Fig. 16. Effect of truss thickness on residual stress.

Fig. 14. Effect of face sheet thickness on residual stress in the brazing joint.

320 S11 S33

240

200

Residual stress (MPa)

S11 S33

220 Residual stress (MPa)

300

180 160 140 120 100

280 260 240 220

80 16

60 1.4

1.6

1.8 2.0 2.2 2.4 2.6 2.8 Face sheet thickness (mm)

3.0

24

5.4. Effect of truss thickness Five FE models with a truss thickness of 0.5, 0.75, 1.0, 1.25 and 1.5 mm were developed to discuss its effect on residual stresses, keeping the rest parameters unchanged. With the truss thickness increase, the maximum residual stresses decrease first and then increase, and the optimized truss thickness is about 1 mm, as shown in Fig. 16. The strength mismatching between filler metal and the lattice core plays an important role on the residual stress. For X-type lattice

48

56

64

Fig. 17. Effect of truss length on residual stresses.

truss core, the plastic buckling stress  c is given by [13]: c =

the thicker face sheet can increase the bending stiffness of sandwich structures. But in fact, this is not the case. Jen and Chang [36] studied the effect of face sheet thickness on the fatigue strength of honeycomb sandwich beams by four-point bending fatigue tests. Their experimental results show that no evident relationships exist between the face sheet thickness and the fatigue life. The reason has not been explained in detail by them, and which can be explained by our present work. As the face sheet thickness increases, the bending stiffness of sandwich structures is increased, but the corresponding increased residual stresses can decrease the fatigue strength at the same time. The interaction of the two factors make the face sheet has little effect on increasing the fatigue life.

40

Truss length (mm)

3.2

Fig. 15. Effect of face sheet thickness on residual stress on the top surface of face sheet.

32

2 kx2 Et 12

 t 2 0.5 l

(3)

where t and l are the truss thickness and length, Et is the Shanley–Engesser tangent modulus obtained from the stress vs. strain response of the parent alloy, and 1 < kx < 2. From Eq. (3), it can be seen that the core strength is increased with truss thickness increase. As the truss thickness increasing, the strength difference between filler metal and the core becomes smaller and the residual stresses are decreased. When the truss thickness is further increased, the strength difference between filler metal and the core becomes larger again, which in turn increase the residual stresses. In addition, the constraint on the braze joint is increased with an increase in truss thickness, which also results in an increase of residual stress. This can be used to explain why the residual stresses decrease first and then increase as the truss thickness increase. 5.5. Effect of truss length Keeping the rest parameters unchanged, ten FE models with a truss length of 14, 18, 22, 26, 30, 38, 42, 50, 58 and 64 mm were developed to discuss its effect on residual stresses. With the truss length increase, the maximum residual stresses decrease first and then increase, as shown in Fig. 17. The minimum residual stresses can be achieved when the truss length is around 26 mm. The core

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strength is decreased with truss length increase as shown in Eq. (3), which leads to residual stress decrease first. But when the truss length is further increased, the constraint of truss core on the braze joint is also increased, resulting in an increase of residual stresses. 6. Conclusions This study performs a finite element analysis of brazed residual stress in a stainless steel X-type lattice truss sandwich structure. And the FEM was also verified by nanoindentation method. The effects of braze processing parameters including applied load, face sheet thickness, truss thickness and truss length on residual stresses have been investigated. Based on this study the following conclusions could be achieved. (1) Due to the mechanical properties mismatching among the face sheet, filler metal and truss core, large residual stresses are generated in the brazed joint and the stresses are concentrated in the fillet. (2) With the applied load increase, the residual stresses are decreased first and then remain unchanged, and the optimal applied load is around 1 MPa. (3) With the face sheet thickness increasing, the residual stresses in brazing joint are increased. Too thin face sheet thickness can cause large residual stress on the top surface of face sheet. The optimized face sheet is 2 mm. (4) With an increase in truss thickness and truss length, the residual stresses are decreased first and then increased, and the optimized truss thickness and truss length are found to be 1 mm and 26 mm, respectively. Acknowledgments The authors gratefully acknowledge the support from the National Natural Science Foundation of China (no. 50835003), Natural Science Foundation of Shandong Province of China (No. ZR2010AQ002) and Key Laboratory of Pressure System and Safety (MOE), East China University of Science and Technology References [1] F.W. Zok, S.A. Waltner, Z. Wei, H.J. Rathbun, R.M. McMeeking, A.G. Evans, Int. J. Solid Struct. 41 (22–23) (2004) 6249–6271. [2] D.T. Queheillalt, H.N.G. Wadley, Mater. Des. 30 (6) (2009) 1966–1975. [3] D.T. Queheillalt, G. Carbajal, G.P. Peterson, H.N.G. Wadley, Int. J. Heat Mass Transfer 51 (1–2) (2008) 312–326.

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