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Effect of thickness of face sheet on the bending fatigue strength of aluminum honeycomb sandwich beams
Engineering Failure Analysis 16 (2009) 1282–1293
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Engineering Failure Analysis journal homepage: www.elsevier.com/locate/engfailanal
Effect of thickness of face sheet on the bending fatigue strength of aluminum honeycomb sandwich beams Yi-Ming Jen *, Li-Yen Chang Department of Mechanical Engineering, Chung Hua University, No. 707, Section 2, Wufu Road, Hsinchu 30012, Taiwan
a r t i c l e
i n f o
Article history: Received 22 May 2008 Accepted 1 August 2008 Available online 12 August 2008 Keywords: Honeycomb sandwich beam Fatigue Debonding Finite element analysis Interfacial stress
a b s t r a c t Three types of aluminum honeycomb sandwich beam specimens with different face sheet thicknesses were employed in the four-point bending fatigue tests to study the effect of face sheet thickness on the fatigue strength. The experimental results show that under the same applied bending loads, no evident relationships exist between the face sheet thickness and the fatigue life of the studied specimens. The main failure mode of the studied specimens is the debonding at the interface between the adhesive and the face sheet based on the observations during the tests. To correlate with the scattering fatigue life data of the studied specimens with different face sheet thicknesses by using the local approaches, three parameters based on the finite element simulated interfacial stresses were proposed herein. The sub-modeling technique was applied in the finite element simulations to determine the local interfacial stresses. The employed local parameters in the study were the interfacial peeling stress, the in-plane interfacial shear stress, and the linear combination of interfacial peeling and shear stress. The comparison of the correlation performance between these employed parameters was made in the study. Furthermore, the nodes with the maximum value of prediction parameters were considered as the potential locations where the debonding failure initiated. The predicted locations of debonding initiation obtained using the three parameters were also compared with the observed ones. The analytical results show that the linearly combined peeling and shear stress parameter yields better fatigue-life correlation and failure-location prediction results than the other two parameters. Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction Sandwich structures are widely employed in aerospace, civil and mechanical industries due to their excellent stiffness/ weight ratio, and heat and acoustic insulation properties. Over the last decade, various improvements have been made in the manufacturing of sandwich structures. For example, sandwich structures with different combinations of core materials and face sheet materials have been developed. Additionally, more assembly techniques, such as screw fasteners, adhesively joints, or blazed bonding, can be applied for bonding the core material and the face sheet than before. These applications and novel manufacturing techniques increase the requirement for the mechanical strengths of the sandwich structures in practical designs. To survey the past studies that investigated the strength of the sandwich structures, many efforts have been made on the topics of static strength. In 1999, Vinson [1] summarized the general analytical concepts of the static strength of the sandwich structures. However, the fatigue behavior of the sandwich structures was seldom been studied.
* Corresponding author. Tel.: +886 3 5186485; fax: +886 3 5186521. E-mail address: [email protected] (Y.-M. Jen). 1350-6307/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.engfailanal.2008.08.004
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The past studies investigating the fatigue behavior of the sandwich structures can be sorted based on the materials employed for the face sheets and the cores. Most sandwich specimens analyzed in the past fatigue studies were made of polymer foam cores with composite face sheets [2–13] or with metal face sheets [14,15]. The applied materials of the composite face sheets included of carbon–fiber and glass–fiber reinforced epoxy/vinylester resins, and the most common polymer foam core materials were polyvinylchloride (PVC), polymethacrylimide (PMI) or polyurethane (PUR). Except for the foam cores, the honeycomb cells have been widely employed as the core materials in the sandwich structures in the last two decades. However, only few studies have investigated the fatigue behavior of bare honeycomb cells or honeycomb sandwich structures. Huang et al. [16,17] analyzed the in-plane and multiaxial fatigue behaviors of bare honeycomb cell materials. The Paris law, Coffin–Manson relation and Basquin’s law were applied to evaluate the fatigue life of honeycomb cells. Furthermore, Schaffner et al. [18] investigated the fatigue damage of randomly distributed and regular hexagonal Voronoi honeycomb cells. The randomly distributed Voronoi honeycomb cells were found to have higher fatigue strength than the regular hexagonal cells. Relatively few studies of the fatigue strength of the sandwich structures with honeycomb cells are available. In 2001, Demelio et al. [19] reported their experimental results for the fatigue behavior of the composite sandwich structures fastened with steel plates using blind fasteners. The sandwich specimens studied were made of nomex honeycomb cores and graphite/Kevlar/glass–epoxy composite face sheets. Furthermore, in 2007, Belingardi et al. [20] investigated the fourpoint bending fatigue behavior of the undamaged and damaged sandwich beams with aluminum honeycomb cores and carbon–fiber composite face sheets. The fatigue failure mode for the undamaged specimens is the collapse of the compressed face sheet, while that of the damaged specimens is the collapse of honeycomb cell walls at the tip of the debonded portion. Also in 2007, Liu and Holmes [21] studied the fatigue crack growth of the Ni-based sandwich structures with Inconel 617 honeycomb cell cores and face sheets. The Paris law was applied to describe the fatigue crack propagation behavior of the studied specimens. The crack growth in the thin face sheets is the primary crack propagation mode. Among the various honeycomb sandwich structures, adhesively bonded aluminum honeycomb sandwich panels are currently popular because of their easy assembly of face sheets and cores. One application of such structures is in the cabin sections of the mass rapid transit systems, such as doors, walls, and floors. Since these sandwich structures are subjected to the dynamic service loading, the progressive fatigue failure are frequently inspected. Fig. 1 displays an actual fatigue failure portion of an adhesively bonded sandwich panel that was applied as a lining plate of a carriage floor in a metropolitan transportation cabin. The fatigue debonding failure between the adhesive and the face sheet is clearly visible. According to the authors’ previous study [22], the pseudo fatigue limit corresponding to 1 million life cycles of the adhesively bonded aluminum honeycomb sandwich panels is only 15% of the ultimate strength, which is markedly less than that of other bonded structures. Accordingly, increasing the fatigue strength is critical to broaden the applications of the adhesively bonded honeycomb sandwich structures. In the practical applications, increasing the face sheet thickness is considered as a valid method for increasing the bending fatigue resistance of the sandwich structures because the thicker face sheet increases the bending stiffness of sandwich structures. The goal of this work is to study the effect of the face sheet thickness on the fatigue strength of aluminum honeycomb sandwich beams. Several local parameters proposed in the authors’ previous study [22] are utilized to correlate with the fatigue life data of the studied specimens with various face sheet thicknesses. These local parameters have been shown to successfully correlate with the fatigue data of the sandwich structures with various honeycomb core densities. These local parameters comprise the interfacial stress states occurring at the interface between the face sheet and the adhesive to reflect the observed debonding failure mechanism. This study extends the application of these interfacial parameters to verify their adequacy in the fatigue-life correlations for the studied specimens with different face sheet thicknesses. Additionally, the prediction performance of the failure initiation locations using these local parameters is also examined to determine the validity of these interfacial parameters for the fatigue design of such adhesively jointed sandwich structures.
Fig. 1. Fatigue debonding failure of an aluminum honeycomb sandwich panel used as the lining plate of a cabin floor.
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Table 1 Global dimensions of the honeycomb sandwich specimens Specimen type
Thickness of the face sheet, hf (mm)
Height of the core, hc (mm)
Length of the inclined wall, H (mm)
Length of the central wall, L (mm)
Thickness of the inclined wall, T (mm)
Cell wall angle, h (°)
Width of the specimen, W (mm)
Relative density, q*/qs
A B C
1.0 1.2 1.5
30 30 30
6.16 6.16 6.16
9.89 9.89 9.89
0.07 0.07 0.07
45 45 45
90 90 90
0.012 0.012 0.012
2. Experimental program To reduce the residual stress, the studied specimens were cut by a water jet to the required dimensions from the 1200 mm 1200 mm sandwich panels, which were manufactured by mounting the aluminum face sheets onto the aluminum honeycomb cores using the epoxy adhesive. The materials for the face sheets and the honeycomb cells are aluminum 5052-H32 and 3104-H19, respectively. The employed adhesive is epoxy resin mixed with a modified polyamines hardener. The mechanical properties of the employed materials are described in [22]. Table 1. presents the global dimensions of the studied specimens, and the dimensional symbols used in Table 1 can be referred to Fig. 2. Three types of specimens with different face sheet thicknesses were utilized in the experimental program to study the effect of face sheet thickness on the fatigue properties of adhesively bonded sandwich specimens. The specimens with 0.8, 1.0, and 1.2 mm face sheet thicknesses were designated the type A, B and C specimens, respectively. Notably, the type B specimens employed herein are identical to the type A specimens used in the authors’ previous work [22]; therefore, the experimental and analytical data for this type of specimens reported in [22] are employed herein for comparisons. In Table 1, the relative density, which is defined as the ratio of honeycomb density q* to that of the cell wall material qs, can be expressed as
q t=lðh=l þ 1Þ ¼ qs ðh=l þ sin hÞ cos h
ð1Þ
These symbols used in Eq. (1) are also shown in Fig. 2. The shape of the honeycomb cell is hexagonal. Because the honeycomb core was constructed by expanding the periodically strip-glued aluminum sheets, the thickness of the central wall is double that of the inclined wall. Additionally, the longitudinal axis of the specimen was set perpendicular to the central wall of the honeycomb cell.
F Fmax Fmin
F
F
Time
60 mm
Z X
Face Sheet Core Face Sheet
hf hc Y hf 200 mm
F
F
Strain Gauge Measurement X Z
Y
Position 1
£c
Position 2
2t l h t
Fig. 2. Setup for the four-point bending fatigue test on aluminum honeycomb sandwich beams.
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Global Coarse-Mesh Model Local Fine-Mesh Model Outer Span Inner Span
X
Z
26 mm
19 mm
Y
9 mm
Fig. 3. Locations of the global coarse-mesh model and the local fine-mesh model relative to the studied specimen.
All of the bending fatigue tests were performed at room temperature using an Instron 8872 servo-hydraulic testing system with a four-point bending jig. Fig. 2 presents a schematic diagram of the four-point bending tests. Two upper rollers with a 60 mm inner span were used to apply the loading, and two lower rollers with a 200 mm outer span were employed for supports. The loading ratio, defined as the minimum applied load to the maximum applied load in the fatigue cycle, was set at 0.1 for all fatigue tests. The waveform was sinusoidal with a frequency of 3 Hz. The maximum applied loads Fmax in the fatigue tests were selected as 40%, 35%, 30%, 25%, 20%, and 15% of the ultimate applied loads in the static bending tests, Fult. The ultimate applied loads in the bending tests for the type A, B and C specimens are 2030, 1826, and 1806 N, respectively. The variation in the static strength for the three specimen types is slight, demonstrating that the effect of face sheet thickness on the static strength is minor. The fatigue life is defined as the number of cycles corresponding to a 10% decrease
a Core Wall h t = Height of Fillet Leg R = Fillet Redius
Adhesive
R ht ht
Face Sheet
b
Fig. 4. (a) Schematic illustration of the local dimensions for the shape of the adhesive, and (b) an enlarged view of the adhesive leg for the type B specimen.
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in flexural stiffness of the specimen compared with the stable value. When the testing cycles reaches the defined cycle numbers of fatigue failure, the visible debonding failure can be observed and the specimen stiffness begins to decline rapidly. 3. Finite element analysis According to the observations made during the fatigue tests, the debonding failure along the interface between the adhesive and the face sheet is the primary failure mode. Hence, the stress states at the interface are critical in fatigue design of the adhesively bonded sandwich beams. The FE code ANSYS [23] was employed to obtain the interfacial stress behavior. The submodeling technique was utilized to overcome the difficulties associated with the complex configuration of specimens and the high computational cost in the numerical simulations. In applying the sub-modeling technique, the global coarse mesh model was established and solved first. The simulated results for the global model were then applied as the boundary conditions for the local fine-mesh model. In this study, only one quarter specimen was considered as the global model due to the geometrical symmetry. Fig. 3 shows the relative location of the global model with respect to the whole specimen. Only the face sheets and the honeycomb cells were considered in the global model. The rollers and the specimen were considered as the contact pairs in the FE simulations to reflect the actual situations of the applied loads and the supports. One portion of the studied specimen beneath the upper roller was selected as the local model because the debonding failure was observed to initiate at the adhesive-face sheet interface beneath the upper roller. Fig. 3 shows the location of the local model with respect to the specimen. In the local fine-mesh model, in addition to the face sheet and the honeycomb cells, the adhesive was also considered in the meshing. The shape and dimensions of the adhesive were determined using a microscope and two characteristic dimensions—the height of the fillet leg ht and the fillet radius R—were employed to describe the adhesive shape. Fig. 4a presents the schematic definitions of these two characteristic dimensions. Fig. 4b shows an enlarged photograph of the adhesive shape of a type B specimen as an example. In the present study, the average height of the fillet leg
Fig. 5. (a) Global coarse-mesh FE model, (b) local fine-mesh model, and (c) enlarged view of the local meshes near the portion of the adhesive for the type C specimen.
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and the fillet radius for the studied specimens are 0.3 and 0.35 mm, respectively. These local dimensions of the adhesive are employed to establish the meshes of the local fine-mesh model. Eight-node solid elements were used for most meshes in the global and local FE models except for the portion of the adhesive in the local models. Four-node tetrahedral elements were applied as the adhesive meshes due to the complex geometrical shape of the adhesives. Figs. 5a and b show the meshes of the global and local FE models of the type C specimen, respectively. Fig. 5c presents an enlarged view of meshes near the interfaces between the adhesive and the face sheet for the same specimen. The material properties of the face sheet and cell material in the FE simulations were assumed to be elastic–plastic. The von Mises yield criterion and kinematic hardening rule were employed in the nonlinear analyses. Furthermore, the property of the adhesive was assumed to be elastic–perfectly plastic because the stress–strain curve for the bulk specimen of adhesive is flat when the applied load exceeds the yield point. For each fatigue testing case, the stress behavior was simulated for three loading cycles to obtain the stable stress/strain response. The stress states at the potential locations of failure initiation were employed in the local parameters to evaluate the fatigue life of the studied specimens. To examine the validity of the FE simulations for the global models, two biaxial strain gauges were mounted on the bottom face sheet to measure the local strains. Fig. 2 shows the two locations for strain measurement—positions 1 and 2. Position 1 is located at the geometrically central point of the bottom face sheet, and position 2 is located at the midpoint between the projective lines of the upper roller and lower roller on the bottom face sheet. Figs. 6a and b present the comparisons of the FE simulated strains exx and eyy at positions 1 and 2 for the type B specimen with the measured results under the loading
Applied Load; F (N)
2000
1500
1000
Type B Specimen Position 1
ε x x Exper.
500
ε y y Exper. ε x x F.E.M ε y y F.E.M
0 -400
-200
0
200
400
600
Strain; ε xx ε yy (μ mm/ mm)
Applied Load; F (N)
2000
1500
1000
Type B Specimen Position 2 ε xx Exper.
500
ε yy Exper. ε xx F.E.M ε yy F.E.M
0 -400
-200
0
200
400
600
Strain; ε xx ε yy (μ mm/ mm) Fig. 6. Comparison between the FE simulated strains and the strain gauge measured data at (a) position 1 and (b) position 2 for the type B specimen.
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condition, respectively. The simulated strain values are in agreement with the experimental ones, indicating that the FE simulated results for the global model are reliable. Furthermore, a convergence study was conducted to examine the correctness of simulated results for the local model. In the convergence study, a series of FE analyses of the local models were performed by reducing the mesh size by a factor of 2. That is, the mesh size near the adhesive fillet leg in the current FE analysis is half of that in the former FE analysis. When the difference in the simulated von Mises stress between the two successive analyses is less than 5%, the final mesh size for the FE analyses of the local fine-mesh models is determined as the mesh size applied in the last analysis. According to the results of the convergence study, the final mesh size near the fillet leg of the adhesive applied in this work is 0.044 mm. Notably, this mesh sizes in the local models were kept constant for all types of specimens. 4. Fatigue life prediction parameters To interpret the fatigue failure mechanism of the adhesively bonded sandwich beams, three local interfacial parameters were applied to correlate with the fatigue life data of specimens with different face sheet thicknesses. These local parameters were obtained form the FE simulated stress states at the potential failure locations. Based on the observations made in the fatigue tests, the main failure mode is the interfacial debonding between the adhesive and the face sheets. Therefore, the interfacial peeling and shear stresses are considered the primary causes of the debonding failure. These driving forces of debonding failure were integrated into the local prediction parameter to assess the fatigue life of the adhesively bonded sandwich specimens. Furthermore, since the local parameters are based on the physical failure mechanism of the studied specimens, an appropriate parameter should be able to predict accurately the potential locations of failure initiation. The first employed local parameter is the maximum peeling stress at the interface between the adhesive and the face sheet rp,max. According to the reference coordinate system, the maximum peeling stress rp,max, is the maximum value of rzz at the interfacial plane. The second employed local parameter is the maximum interfacial shear stress sr,max, which can be obtained using the following equation:
sr;max ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s2xz;max þ s2yz;max
ð2Þ
where sxz,max and syz,max are the maximum in-plane shear stress components acting on the interface, respectively. The third considered local parameter is the linear combination of the maximum interfacial peeling and shear stresses. For a specific fatigue life, the application of the combined parameter can be expressed as
sr;max þ krp;max ¼ constant
ð3Þ
where k is a material constant that should be determined experimentally, and is 0.5 herein. The concept of the combined parameter is based on the critical plane approach, which has been widely applied in the multiaxial fatigue design for metal materials. Clearly, the critical plane in this study is the interfacial plane between the adhesive and the face sheets since the debonding failure is initiated at the interface during the fatigue tests. In this study, the local parameters based on the FE simulated stress components for the nodes located on the interfacial plane between the adhesive and the face sheet are analyzed and compared. When using a specific local parameter, the node
Table 2 Experimental results in the fatigue tests for the aluminum honeycomb sandwich beam specimens with various face sheet thicknesses Type A specimen
Type B specimen [22]
Type C specimen
Loading level Fmax/Fult (%)
Maximum applied loading, Fmax (N)
Fatigue life, Nf (cycles)
Loading level Fmax/Fult (%)
Maximum applied loading, Fmax (N)
Fatigue life, Nf (cycles)
Loading level Fmax/Fult (%)
Max. applied loading, Fmax (N)
Fatigue life, Nf (cycles)
40
812.0
40
730.4
722.4
710.5
35
639.1
35
632.1
30
609.0
30
547.8
30
541.8
25
507.5
25
456.5
25
451.5
20
406.0
20
365.2
20
361.2
15
304.5
–
–
10,730 8170 5230 6980 12,170 20,060 21,620 44,530 23,550 62,400 77,150 42,360 657,400 615,450 328,450 – – –
40
35
3710 4450 3350 5320 9890 12,740 13,830 11,390 28,820 44,090 55,970 102,690 85,080 61,625 102,630 472,850 154,220 284,920
15
270.9
14,880 14,030 11,650 31,880 17,550 23,850 35,610 28,000 66,020 41,560 67,300 75,570 >1,000,000 280,380 105,880 459,880 195,420 >1,000,000
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corresponding to the maximum value of the local parameter is considered the potential location of debonding failure initiation. Moreover, the maximum parameter value is used to evaluate the fatigue-life of the studied specimens. 5. Results and discussion Table 2 lists the experimental results of the four-point bending fatigue tests for the studied sandwich specimens with different face sheet thicknesses. Fig. 7 shows the relationship between the maximum applied loads Fmax, and the experimental fatigue lives of the studied specimens Nf. The scattering of data points demonstrates that under the same applied bending loads, no empirical relationship exists between the face sheet thickness and fatigue life. Furthermore, the applied load is not an adequate parameter in evaluating the fatigue life because this parameter fails to correlate with all fatigue life data of the studied specimens with different face sheet thicknesses. Fig. 8 presents a photograph of the type C specimen taken when the number of loading cycles reached the defined cycle number of fatigue failure. The debonding at the interface between the adhesive and the face sheets exists beneath the upper roller. This debonding propagates along the interface into the portion between the inner and outer rollers. Clearly, the stress states acting on the interface are the main driving forces of debonding and thus, the fatigue failure. Hence, the interfacial stresses should be considered in the local parameters to evaluate the fatigue life of the studied adhesively bonded sandwich beam specimens. Fig. 9 shows the correlation performance of the normalized load parameter Fn with the experimental data for the studied specimens with different face sheet thicknesses. The normalized applied load was defined as the ratio of maximum applied load Fmax to the ultimate load of the specimen in the static bending test Fult. In Fig. 9, the relationship between the normal-
Maximum Applied Load; F max (N)
2000
1000
Type A Specimen; hf = 1.0 mm Type B Specimen; hf = 1.2 mm [22] Type C Specimen; hf = 1. 5 mm
100 2 1x10
3
1x10
4
1x10
5
1x10
6
1x10
1x10
7
Fatigue Life; Nf (Cycles) Fig. 7. Relationship between the applied loads and the fatigue life of the studied specimens.
Fig. 8. Fatigue failure mode for the type C specimen.
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0.9
Maximum Normalized Load; Fn
Type A Specimen; hf = 1.0 mm Type B Specimen; hf = 1.2 mm [22] Type C Specimen; hf = 1.5 mm
Factor of two Factor of three Best fit of all data points
0.1 1x102
1x103
1x104
1x105
1x106
1x107
Fatigue Life; Nf (Cycles)
0.8
0.20 F = 500 N
0.7
0.19
Interfacial Peeling Stress, σp Interfacial Shear Stress, τr
0.6
0.18 0.17
0.5
0.16
0.4
0.15 0.14
0.3
0.13 0.2 0.12 0.1 0 0.8
0.11 1.0
1.2
1.4
1.6
0.10 1.8
Simulated Interfacial Shear Stress, τr (MPa)
Simulated Interfacial Peeling Stress, σp (MPa)
Fig. 9. Correlation results with the fatigue life data of the studied specimens obtained using the normalized applied loads.
Thickness of Face Sheet; hf (mm) Fig. 10. Relationship between the FE simulated interfacial peeling/shear stresses and the face sheet thickness of the studied specimens with an applied load of F = 500 N.
ized applied load and the experimental fatigue life is fitted using a power law, which is a straight line in the log–log scale diagram. The solid line in this figure represents the best fitting line of all fatigue data points. The deviation bands from the best fitting line with factors 2 and 3 are also provided in this figure to examine the scattering degree of the data points. The regression study was performed to examine the correlation performance of the normalized applied loads. The coefficient of determination—R squared is 0.818, indicating that the good correlation results are obtained when the normalized load parameter is used to evaluate the fatigue life. However, the application of this global parameter in fatigue design is difficult as the ultimate bending strength of the studied specimens should be first obtained analytically or experimentally. Accordingly, for the fatigue design in practice, the local parameters based on the actual failure mechanism are more adequate to correlate with the fatigue life of the studied specimens with different face sheet thicknesses than the global loading parameters. Fig. 10 shows the relationship between the FE simulated results of the maximum interfacial stress state and the face sheet thickness of the studied specimens under a fixed applied load of F = 500 N. Both the interfacial peeling and shear stress decrease as the face sheet thickness increases, demonstrating that increasing the face sheet thickness can reduce the interfacial stresses effectively and the fatigue resistance can be improved significantly. Figs. 11–13 show the correlation results of the three local parameters—the interfacial peeling stress, the interfacial shear stress, and the linear combination of peeling and
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Maximum Interfacial Peeling Stress; σp,max (MPa)
3 Type A Specimen; hf = 1.0 mm Type B Specimen; hf = 1.2 mm [22] Type C Specimen; hf = 1.5 mm
1
Factor of two Factor of three Best fit of all data points
0.1 2 1x10
1x10
3
4
1x10
5
1x10
6
1x10
Fatigue Life; Nf (Cycles) Fig. 11. Correlation results with the fatigue-life data of the studied specimens obtained using the maximum interfacial peeling stress parameter.
Maximum Interfacial Shear Stress; τ r,max (MPa)
0.6 Type A Specimen; hf = 1.0 mm Type B Specimen; hf = 1.2 mm [22] Type C Specimen; hf = 1.5 mm
0.1
0.05 2 1x10
Factor of two Factor of three Best fit of all data points
1x10
3
4
1x10
5
1x10
1x10
6
Fatigue Life; Nf (Cycles) Fig. 12. Correlation results with the fatigue-life data of the studied specimens obtained using the maximum interfacial shear stress parameter.
shear stresses—with the fatigue data. The coefficients of determination-R squared for the three correlation results shown in Figs. 11–13 using interfacial peeling, shear and combined parameters are 0.697, 0.881 and 0.778, respectively. The regression study demonstrates that of the three local parameters, the interfacial shear stress parameter and the combined parameter yield more acceptable correlation results than the interfacial peeling stress parameter. Moreover, the difference in correlation performance between the interfacial shear stress parameter and the combined parameter is slight. Fig. 14 shows the comparison between the predicted locations of debonding failure initiation using the three local parameters and the experimental ones observed in the fatigue tests. The combined parameter and the maximum interfacial peeling stress parameter predict the locations of debonding failure initiation accurately, whereas the failure locations predicted using the interfacial shear stress parameter are far from the observed ones. When examining the correlation results with the fatigue life data and the prediction performance of the debonding locations together, the linear combination of interfacial peeling and shear stresses is considered as the most accurate parameter in the fatigue design of the adhesively bonded sandwich beam structures than the other two parameters. The successful fatigue-life correlations and failure-location predictions via using the combined parameter elucidates that both the interfacial peeling stress and the interfacial shear stress contribute to the debonding failure in the fatigue tests. A parameter considering either the interfacial shear stress or the interfacial peeling stress only fails to accurately predict the fatigue life and failure location simultaneously because the parameter can-
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Linearly Combined Interfacial Stress Parameter; τr,max + kσp,max (MPa)
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2 Type A Specimen; hf = 1.0 mm Type B Specimen; hf = 1.2 mm [22] Type C Specimen; hf = 1.5 mm
1
Best fit of all data points Factor of two Factor of three
0.1 2 1x10
3
1x10
4
1x10
5
1x10
1x10
6
1x10
7
Fatigue Life; Nf (Cycles) Fig. 13. Correlation results with the fatigue-life data of the studied specimens obtained using the linearly combined interfacial peeling and shear stress parameter.
: Symmetric Line of specimen : Applied line of Inner Roller : Observed Failure Location Predicted Failure Location : Interfacial Peeling Stress Parameter : Interfacial Shear Stress Parameter : Linearly Combined Interfacial Stress Parameter
TYPE A
fine-mesh model
TYPE B [22]
TYPE C
fine-mesh model
fine-mesh model
Fig. 14. Comparison between the observed debonding locations and the predicted ones using the local parameters.
not correctly interpret the failure mechanism of debonding failure. Furthermore, the successful experiences in applying the combined parameter in the fatigue assessment of the studied sandwich specimens with different face sheet thicknesses herein and those with different core densities [22] suggests that the linear combination of interfacial peeling and shear stresses is an effective parameter in the fatigue strength design of the adhesively bonded honeycomb sandwich structures with various geometrical variables. 6. Conclusions Three types of adhesively bonded sandwich beam specimens with different face sheet thicknesses were used in this study to investigate the effect of the face sheet thickness on the fatigue strength of the studied specimens. The FE simulated interfacial stresses were incorporated into the local parameters to correlate with the fatigue life data of the studied sandwich specimens. Several conclusions can be drawn from the experimental and analytical results.
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1. Under the same applied bending loads, no apparent relationship exists between the face sheet thickness and the fatigue life of the studied specimens. Furthermore, the applied load fails to correlate with the experimental fatigue data points. 2. The main fatigue failure mode for the adhesive bonded honeycomb sandwich beams is the debonding at the interface between the adhesive and the face sheet. 3. The normalized applied load parameter provides good life evaluation performance. However, the parameter is not suitable for usage in the fatigue design because the ultimate bending strength should be obtained experimentally or analytically first. 4. The interfacial shear stress parameter and the combined parameter yield better correlation results with the experimental data than the interfacial peeling parameter. However, the difference in correlation performance between the interfacial shear parameter and the combined parameter is slight. 5. Of the three local parameters, only the combined interfacial shear and peeling stress parameter provides good evaluation results in both fatigue-life correlations and failure-location prediction. These analytical results reveal that both the interfacial peeling stress and the interfacial shear stress contribute to the debonding failure.
Acknowledgements The authors would like to thank the National Science Council of the Republic of China, Taiwan, for financially supporting this research under Contract No. NSC-95-2262-E-216-015-CC3. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23]
Vinson JR. The behavior of sandwich structures of isotropic and composite materials. Technomic Publ. Co. 1999. Burman M, Zenkert D. Fatigue of foam core sandwich beams – 1: Undamaged specimens. Int J Fatigue 1997;19(7):551–61. Burman M, Zenkert D. Fatigue of foam core sandwich beams – 2: Effect of initial damage. Int J Fatigue 1997;19(7):563–78. Burchardt C. Fatigue in sandwich structures loaded in transverse shear. Compos Struct 1997;40(1):73–9. Burchardt C. Fatigue of sandwich structures with inserts. Compos Struct 1997;40(3–4):201–11. Clark SD, Shenoi RA, Allen HG. Modelling the fatigue behaviour of sandwich beams under monotonic, 2-step and block-loading regimes. Compos Sci Technol 1999;59(4):471–86. Kulkarni N, Mahfuz H, Jeelani S, Carlsson LA. Fatigue crack growth and life prediction of foam core sandwich composites under flexural loading. Compos Struct 2003;59(4):499–505. El Mahi A, Khawar Farooq M, Sahraoui S, Bezazi A. Modelling the flexural behaviour of sandwich composite materials under cyclic fatigue. Mater Des 2004;25(3):199–208. Kanny K, Mahfuz H. Flexural fatigue characteristics of sandwich structures at different loading frequencies. Compos Struct 2005;67(4):403–10. Freeman B, Schwingler E, Mahinfalah M, Kellogg K. The effect of low-velocity impact on the fatigue life of Sandwich composites. Compos Struct 2005;70(3):374–81. Shafiq B, Quispitupa A. Fatigue characteristics of foam core sandwich composites. Int J Fatigue 2006;28(2):96–102. Bezazi A, Pierce SG, Worden K, Harkati EH. Fatigue life prediction of sandwich composite materials under flexural tests using a Bayesian trained artificial neural network. Int J Fatigue 2007;29(4):738–47. Soni SM, Gibson RF, Ayorinde EO. The influence of subzero temperatures on fatigue behavior of composite sandwich structures. Compos Sci Technol 2008. Harte AM, Fleck NA, Ashby MF. The fatigue strength of sandwich beams with an aluminum alloy foam core. Int J Fatigue 2001;23(6):499–507. Bozhevolnaya E, Thomsen OT. Structurally graded core junctions in sandwich beams: fatigue loading conditions. Compos Struct 2005;70(1):12–23. Huang JS, Lin JY. Fatigue of cellular materials. Acta Mater 1996;44(1):289–96. Huang JS, Liu SY. Fatigue of honeycombs under in-plane multiaxial loads. Mater Sci Eng A – Struct 2001;308(1–2):45–52. Schaffner G, Guo XE, Silva MJ, Gibson LJ. Modeling fatigue damage accumulation in two-dimensional Voronoi honeycombs. Int J Mech Sci 2000;42(4):645–56. Demelio G, Genovese K, Pappalettere C. An experimental investigation of static and fatigue behaviour of sandwich composite panels joined by fasteners. Composites Part B: Eng 2001;32(4):299–308. Belingardi G, Martella P, Peroni L. Fatigue analysis of honeycomb-composite sandwich beams. Composites Part A: Appl Sci Manuf 2007;38(4):1183–91. Liu L, Holmes JW. Experimental investigation of fatigue crack growth in thin-foil Ni-base sandwich structures. Int J Fatigue 2007;29(8):1452–64. Jen YM, Chang LY. Evaluating bending fatigue strength of aluminum honeycomb sandwich beams using local parameters. Int J Fatigue 2008;30(6):1036–46. ANSYS User’s Manual, Release 8.1. Swanson Analysis System Inc., 2003.
Contents lists available at ScienceDirect
Engineering Failure Analysis journal homepage: www.elsevier.com/locate/engfailanal
Effect of thickness of face sheet on the bending fatigue strength of aluminum honeycomb sandwich beams Yi-Ming Jen *, Li-Yen Chang Department of Mechanical Engineering, Chung Hua University, No. 707, Section 2, Wufu Road, Hsinchu 30012, Taiwan
a r t i c l e
i n f o
Article history: Received 22 May 2008 Accepted 1 August 2008 Available online 12 August 2008 Keywords: Honeycomb sandwich beam Fatigue Debonding Finite element analysis Interfacial stress
a b s t r a c t Three types of aluminum honeycomb sandwich beam specimens with different face sheet thicknesses were employed in the four-point bending fatigue tests to study the effect of face sheet thickness on the fatigue strength. The experimental results show that under the same applied bending loads, no evident relationships exist between the face sheet thickness and the fatigue life of the studied specimens. The main failure mode of the studied specimens is the debonding at the interface between the adhesive and the face sheet based on the observations during the tests. To correlate with the scattering fatigue life data of the studied specimens with different face sheet thicknesses by using the local approaches, three parameters based on the finite element simulated interfacial stresses were proposed herein. The sub-modeling technique was applied in the finite element simulations to determine the local interfacial stresses. The employed local parameters in the study were the interfacial peeling stress, the in-plane interfacial shear stress, and the linear combination of interfacial peeling and shear stress. The comparison of the correlation performance between these employed parameters was made in the study. Furthermore, the nodes with the maximum value of prediction parameters were considered as the potential locations where the debonding failure initiated. The predicted locations of debonding initiation obtained using the three parameters were also compared with the observed ones. The analytical results show that the linearly combined peeling and shear stress parameter yields better fatigue-life correlation and failure-location prediction results than the other two parameters. Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction Sandwich structures are widely employed in aerospace, civil and mechanical industries due to their excellent stiffness/ weight ratio, and heat and acoustic insulation properties. Over the last decade, various improvements have been made in the manufacturing of sandwich structures. For example, sandwich structures with different combinations of core materials and face sheet materials have been developed. Additionally, more assembly techniques, such as screw fasteners, adhesively joints, or blazed bonding, can be applied for bonding the core material and the face sheet than before. These applications and novel manufacturing techniques increase the requirement for the mechanical strengths of the sandwich structures in practical designs. To survey the past studies that investigated the strength of the sandwich structures, many efforts have been made on the topics of static strength. In 1999, Vinson [1] summarized the general analytical concepts of the static strength of the sandwich structures. However, the fatigue behavior of the sandwich structures was seldom been studied.
* Corresponding author. Tel.: +886 3 5186485; fax: +886 3 5186521. E-mail address: [email protected] (Y.-M. Jen). 1350-6307/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.engfailanal.2008.08.004
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The past studies investigating the fatigue behavior of the sandwich structures can be sorted based on the materials employed for the face sheets and the cores. Most sandwich specimens analyzed in the past fatigue studies were made of polymer foam cores with composite face sheets [2–13] or with metal face sheets [14,15]. The applied materials of the composite face sheets included of carbon–fiber and glass–fiber reinforced epoxy/vinylester resins, and the most common polymer foam core materials were polyvinylchloride (PVC), polymethacrylimide (PMI) or polyurethane (PUR). Except for the foam cores, the honeycomb cells have been widely employed as the core materials in the sandwich structures in the last two decades. However, only few studies have investigated the fatigue behavior of bare honeycomb cells or honeycomb sandwich structures. Huang et al. [16,17] analyzed the in-plane and multiaxial fatigue behaviors of bare honeycomb cell materials. The Paris law, Coffin–Manson relation and Basquin’s law were applied to evaluate the fatigue life of honeycomb cells. Furthermore, Schaffner et al. [18] investigated the fatigue damage of randomly distributed and regular hexagonal Voronoi honeycomb cells. The randomly distributed Voronoi honeycomb cells were found to have higher fatigue strength than the regular hexagonal cells. Relatively few studies of the fatigue strength of the sandwich structures with honeycomb cells are available. In 2001, Demelio et al. [19] reported their experimental results for the fatigue behavior of the composite sandwich structures fastened with steel plates using blind fasteners. The sandwich specimens studied were made of nomex honeycomb cores and graphite/Kevlar/glass–epoxy composite face sheets. Furthermore, in 2007, Belingardi et al. [20] investigated the fourpoint bending fatigue behavior of the undamaged and damaged sandwich beams with aluminum honeycomb cores and carbon–fiber composite face sheets. The fatigue failure mode for the undamaged specimens is the collapse of the compressed face sheet, while that of the damaged specimens is the collapse of honeycomb cell walls at the tip of the debonded portion. Also in 2007, Liu and Holmes [21] studied the fatigue crack growth of the Ni-based sandwich structures with Inconel 617 honeycomb cell cores and face sheets. The Paris law was applied to describe the fatigue crack propagation behavior of the studied specimens. The crack growth in the thin face sheets is the primary crack propagation mode. Among the various honeycomb sandwich structures, adhesively bonded aluminum honeycomb sandwich panels are currently popular because of their easy assembly of face sheets and cores. One application of such structures is in the cabin sections of the mass rapid transit systems, such as doors, walls, and floors. Since these sandwich structures are subjected to the dynamic service loading, the progressive fatigue failure are frequently inspected. Fig. 1 displays an actual fatigue failure portion of an adhesively bonded sandwich panel that was applied as a lining plate of a carriage floor in a metropolitan transportation cabin. The fatigue debonding failure between the adhesive and the face sheet is clearly visible. According to the authors’ previous study [22], the pseudo fatigue limit corresponding to 1 million life cycles of the adhesively bonded aluminum honeycomb sandwich panels is only 15% of the ultimate strength, which is markedly less than that of other bonded structures. Accordingly, increasing the fatigue strength is critical to broaden the applications of the adhesively bonded honeycomb sandwich structures. In the practical applications, increasing the face sheet thickness is considered as a valid method for increasing the bending fatigue resistance of the sandwich structures because the thicker face sheet increases the bending stiffness of sandwich structures. The goal of this work is to study the effect of the face sheet thickness on the fatigue strength of aluminum honeycomb sandwich beams. Several local parameters proposed in the authors’ previous study [22] are utilized to correlate with the fatigue life data of the studied specimens with various face sheet thicknesses. These local parameters have been shown to successfully correlate with the fatigue data of the sandwich structures with various honeycomb core densities. These local parameters comprise the interfacial stress states occurring at the interface between the face sheet and the adhesive to reflect the observed debonding failure mechanism. This study extends the application of these interfacial parameters to verify their adequacy in the fatigue-life correlations for the studied specimens with different face sheet thicknesses. Additionally, the prediction performance of the failure initiation locations using these local parameters is also examined to determine the validity of these interfacial parameters for the fatigue design of such adhesively jointed sandwich structures.
Fig. 1. Fatigue debonding failure of an aluminum honeycomb sandwich panel used as the lining plate of a cabin floor.
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Table 1 Global dimensions of the honeycomb sandwich specimens Specimen type
Thickness of the face sheet, hf (mm)
Height of the core, hc (mm)
Length of the inclined wall, H (mm)
Length of the central wall, L (mm)
Thickness of the inclined wall, T (mm)
Cell wall angle, h (°)
Width of the specimen, W (mm)
Relative density, q*/qs
A B C
1.0 1.2 1.5
30 30 30
6.16 6.16 6.16
9.89 9.89 9.89
0.07 0.07 0.07
45 45 45
90 90 90
0.012 0.012 0.012
2. Experimental program To reduce the residual stress, the studied specimens were cut by a water jet to the required dimensions from the 1200 mm 1200 mm sandwich panels, which were manufactured by mounting the aluminum face sheets onto the aluminum honeycomb cores using the epoxy adhesive. The materials for the face sheets and the honeycomb cells are aluminum 5052-H32 and 3104-H19, respectively. The employed adhesive is epoxy resin mixed with a modified polyamines hardener. The mechanical properties of the employed materials are described in [22]. Table 1. presents the global dimensions of the studied specimens, and the dimensional symbols used in Table 1 can be referred to Fig. 2. Three types of specimens with different face sheet thicknesses were utilized in the experimental program to study the effect of face sheet thickness on the fatigue properties of adhesively bonded sandwich specimens. The specimens with 0.8, 1.0, and 1.2 mm face sheet thicknesses were designated the type A, B and C specimens, respectively. Notably, the type B specimens employed herein are identical to the type A specimens used in the authors’ previous work [22]; therefore, the experimental and analytical data for this type of specimens reported in [22] are employed herein for comparisons. In Table 1, the relative density, which is defined as the ratio of honeycomb density q* to that of the cell wall material qs, can be expressed as
q t=lðh=l þ 1Þ ¼ qs ðh=l þ sin hÞ cos h
ð1Þ
These symbols used in Eq. (1) are also shown in Fig. 2. The shape of the honeycomb cell is hexagonal. Because the honeycomb core was constructed by expanding the periodically strip-glued aluminum sheets, the thickness of the central wall is double that of the inclined wall. Additionally, the longitudinal axis of the specimen was set perpendicular to the central wall of the honeycomb cell.
F Fmax Fmin
F
F
Time
60 mm
Z X
Face Sheet Core Face Sheet
hf hc Y hf 200 mm
F
F
Strain Gauge Measurement X Z
Y
Position 1
£c
Position 2
2t l h t
Fig. 2. Setup for the four-point bending fatigue test on aluminum honeycomb sandwich beams.
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Global Coarse-Mesh Model Local Fine-Mesh Model Outer Span Inner Span
X
Z
26 mm
19 mm
Y
9 mm
Fig. 3. Locations of the global coarse-mesh model and the local fine-mesh model relative to the studied specimen.
All of the bending fatigue tests were performed at room temperature using an Instron 8872 servo-hydraulic testing system with a four-point bending jig. Fig. 2 presents a schematic diagram of the four-point bending tests. Two upper rollers with a 60 mm inner span were used to apply the loading, and two lower rollers with a 200 mm outer span were employed for supports. The loading ratio, defined as the minimum applied load to the maximum applied load in the fatigue cycle, was set at 0.1 for all fatigue tests. The waveform was sinusoidal with a frequency of 3 Hz. The maximum applied loads Fmax in the fatigue tests were selected as 40%, 35%, 30%, 25%, 20%, and 15% of the ultimate applied loads in the static bending tests, Fult. The ultimate applied loads in the bending tests for the type A, B and C specimens are 2030, 1826, and 1806 N, respectively. The variation in the static strength for the three specimen types is slight, demonstrating that the effect of face sheet thickness on the static strength is minor. The fatigue life is defined as the number of cycles corresponding to a 10% decrease
a Core Wall h t = Height of Fillet Leg R = Fillet Redius
Adhesive
R ht ht
Face Sheet
b
Fig. 4. (a) Schematic illustration of the local dimensions for the shape of the adhesive, and (b) an enlarged view of the adhesive leg for the type B specimen.
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in flexural stiffness of the specimen compared with the stable value. When the testing cycles reaches the defined cycle numbers of fatigue failure, the visible debonding failure can be observed and the specimen stiffness begins to decline rapidly. 3. Finite element analysis According to the observations made during the fatigue tests, the debonding failure along the interface between the adhesive and the face sheet is the primary failure mode. Hence, the stress states at the interface are critical in fatigue design of the adhesively bonded sandwich beams. The FE code ANSYS [23] was employed to obtain the interfacial stress behavior. The submodeling technique was utilized to overcome the difficulties associated with the complex configuration of specimens and the high computational cost in the numerical simulations. In applying the sub-modeling technique, the global coarse mesh model was established and solved first. The simulated results for the global model were then applied as the boundary conditions for the local fine-mesh model. In this study, only one quarter specimen was considered as the global model due to the geometrical symmetry. Fig. 3 shows the relative location of the global model with respect to the whole specimen. Only the face sheets and the honeycomb cells were considered in the global model. The rollers and the specimen were considered as the contact pairs in the FE simulations to reflect the actual situations of the applied loads and the supports. One portion of the studied specimen beneath the upper roller was selected as the local model because the debonding failure was observed to initiate at the adhesive-face sheet interface beneath the upper roller. Fig. 3 shows the location of the local model with respect to the specimen. In the local fine-mesh model, in addition to the face sheet and the honeycomb cells, the adhesive was also considered in the meshing. The shape and dimensions of the adhesive were determined using a microscope and two characteristic dimensions—the height of the fillet leg ht and the fillet radius R—were employed to describe the adhesive shape. Fig. 4a presents the schematic definitions of these two characteristic dimensions. Fig. 4b shows an enlarged photograph of the adhesive shape of a type B specimen as an example. In the present study, the average height of the fillet leg
Fig. 5. (a) Global coarse-mesh FE model, (b) local fine-mesh model, and (c) enlarged view of the local meshes near the portion of the adhesive for the type C specimen.
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and the fillet radius for the studied specimens are 0.3 and 0.35 mm, respectively. These local dimensions of the adhesive are employed to establish the meshes of the local fine-mesh model. Eight-node solid elements were used for most meshes in the global and local FE models except for the portion of the adhesive in the local models. Four-node tetrahedral elements were applied as the adhesive meshes due to the complex geometrical shape of the adhesives. Figs. 5a and b show the meshes of the global and local FE models of the type C specimen, respectively. Fig. 5c presents an enlarged view of meshes near the interfaces between the adhesive and the face sheet for the same specimen. The material properties of the face sheet and cell material in the FE simulations were assumed to be elastic–plastic. The von Mises yield criterion and kinematic hardening rule were employed in the nonlinear analyses. Furthermore, the property of the adhesive was assumed to be elastic–perfectly plastic because the stress–strain curve for the bulk specimen of adhesive is flat when the applied load exceeds the yield point. For each fatigue testing case, the stress behavior was simulated for three loading cycles to obtain the stable stress/strain response. The stress states at the potential locations of failure initiation were employed in the local parameters to evaluate the fatigue life of the studied specimens. To examine the validity of the FE simulations for the global models, two biaxial strain gauges were mounted on the bottom face sheet to measure the local strains. Fig. 2 shows the two locations for strain measurement—positions 1 and 2. Position 1 is located at the geometrically central point of the bottom face sheet, and position 2 is located at the midpoint between the projective lines of the upper roller and lower roller on the bottom face sheet. Figs. 6a and b present the comparisons of the FE simulated strains exx and eyy at positions 1 and 2 for the type B specimen with the measured results under the loading
Applied Load; F (N)
2000
1500
1000
Type B Specimen Position 1
ε x x Exper.
500
ε y y Exper. ε x x F.E.M ε y y F.E.M
0 -400
-200
0
200
400
600
Strain; ε xx ε yy (μ mm/ mm)
Applied Load; F (N)
2000
1500
1000
Type B Specimen Position 2 ε xx Exper.
500
ε yy Exper. ε xx F.E.M ε yy F.E.M
0 -400
-200
0
200
400
600
Strain; ε xx ε yy (μ mm/ mm) Fig. 6. Comparison between the FE simulated strains and the strain gauge measured data at (a) position 1 and (b) position 2 for the type B specimen.
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condition, respectively. The simulated strain values are in agreement with the experimental ones, indicating that the FE simulated results for the global model are reliable. Furthermore, a convergence study was conducted to examine the correctness of simulated results for the local model. In the convergence study, a series of FE analyses of the local models were performed by reducing the mesh size by a factor of 2. That is, the mesh size near the adhesive fillet leg in the current FE analysis is half of that in the former FE analysis. When the difference in the simulated von Mises stress between the two successive analyses is less than 5%, the final mesh size for the FE analyses of the local fine-mesh models is determined as the mesh size applied in the last analysis. According to the results of the convergence study, the final mesh size near the fillet leg of the adhesive applied in this work is 0.044 mm. Notably, this mesh sizes in the local models were kept constant for all types of specimens. 4. Fatigue life prediction parameters To interpret the fatigue failure mechanism of the adhesively bonded sandwich beams, three local interfacial parameters were applied to correlate with the fatigue life data of specimens with different face sheet thicknesses. These local parameters were obtained form the FE simulated stress states at the potential failure locations. Based on the observations made in the fatigue tests, the main failure mode is the interfacial debonding between the adhesive and the face sheets. Therefore, the interfacial peeling and shear stresses are considered the primary causes of the debonding failure. These driving forces of debonding failure were integrated into the local prediction parameter to assess the fatigue life of the adhesively bonded sandwich specimens. Furthermore, since the local parameters are based on the physical failure mechanism of the studied specimens, an appropriate parameter should be able to predict accurately the potential locations of failure initiation. The first employed local parameter is the maximum peeling stress at the interface between the adhesive and the face sheet rp,max. According to the reference coordinate system, the maximum peeling stress rp,max, is the maximum value of rzz at the interfacial plane. The second employed local parameter is the maximum interfacial shear stress sr,max, which can be obtained using the following equation:
sr;max ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s2xz;max þ s2yz;max
ð2Þ
where sxz,max and syz,max are the maximum in-plane shear stress components acting on the interface, respectively. The third considered local parameter is the linear combination of the maximum interfacial peeling and shear stresses. For a specific fatigue life, the application of the combined parameter can be expressed as
sr;max þ krp;max ¼ constant
ð3Þ
where k is a material constant that should be determined experimentally, and is 0.5 herein. The concept of the combined parameter is based on the critical plane approach, which has been widely applied in the multiaxial fatigue design for metal materials. Clearly, the critical plane in this study is the interfacial plane between the adhesive and the face sheets since the debonding failure is initiated at the interface during the fatigue tests. In this study, the local parameters based on the FE simulated stress components for the nodes located on the interfacial plane between the adhesive and the face sheet are analyzed and compared. When using a specific local parameter, the node
Table 2 Experimental results in the fatigue tests for the aluminum honeycomb sandwich beam specimens with various face sheet thicknesses Type A specimen
Type B specimen [22]
Type C specimen
Loading level Fmax/Fult (%)
Maximum applied loading, Fmax (N)
Fatigue life, Nf (cycles)
Loading level Fmax/Fult (%)
Maximum applied loading, Fmax (N)
Fatigue life, Nf (cycles)
Loading level Fmax/Fult (%)
Max. applied loading, Fmax (N)
Fatigue life, Nf (cycles)
40
812.0
40
730.4
722.4
710.5
35
639.1
35
632.1
30
609.0
30
547.8
30
541.8
25
507.5
25
456.5
25
451.5
20
406.0
20
365.2
20
361.2
15
304.5
–
–
10,730 8170 5230 6980 12,170 20,060 21,620 44,530 23,550 62,400 77,150 42,360 657,400 615,450 328,450 – – –
40
35
3710 4450 3350 5320 9890 12,740 13,830 11,390 28,820 44,090 55,970 102,690 85,080 61,625 102,630 472,850 154,220 284,920
15
270.9
14,880 14,030 11,650 31,880 17,550 23,850 35,610 28,000 66,020 41,560 67,300 75,570 >1,000,000 280,380 105,880 459,880 195,420 >1,000,000
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corresponding to the maximum value of the local parameter is considered the potential location of debonding failure initiation. Moreover, the maximum parameter value is used to evaluate the fatigue-life of the studied specimens. 5. Results and discussion Table 2 lists the experimental results of the four-point bending fatigue tests for the studied sandwich specimens with different face sheet thicknesses. Fig. 7 shows the relationship between the maximum applied loads Fmax, and the experimental fatigue lives of the studied specimens Nf. The scattering of data points demonstrates that under the same applied bending loads, no empirical relationship exists between the face sheet thickness and fatigue life. Furthermore, the applied load is not an adequate parameter in evaluating the fatigue life because this parameter fails to correlate with all fatigue life data of the studied specimens with different face sheet thicknesses. Fig. 8 presents a photograph of the type C specimen taken when the number of loading cycles reached the defined cycle number of fatigue failure. The debonding at the interface between the adhesive and the face sheets exists beneath the upper roller. This debonding propagates along the interface into the portion between the inner and outer rollers. Clearly, the stress states acting on the interface are the main driving forces of debonding and thus, the fatigue failure. Hence, the interfacial stresses should be considered in the local parameters to evaluate the fatigue life of the studied adhesively bonded sandwich beam specimens. Fig. 9 shows the correlation performance of the normalized load parameter Fn with the experimental data for the studied specimens with different face sheet thicknesses. The normalized applied load was defined as the ratio of maximum applied load Fmax to the ultimate load of the specimen in the static bending test Fult. In Fig. 9, the relationship between the normal-
Maximum Applied Load; F max (N)
2000
1000
Type A Specimen; hf = 1.0 mm Type B Specimen; hf = 1.2 mm [22] Type C Specimen; hf = 1. 5 mm
100 2 1x10
3
1x10
4
1x10
5
1x10
6
1x10
1x10
7
Fatigue Life; Nf (Cycles) Fig. 7. Relationship between the applied loads and the fatigue life of the studied specimens.
Fig. 8. Fatigue failure mode for the type C specimen.
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0.9
Maximum Normalized Load; Fn
Type A Specimen; hf = 1.0 mm Type B Specimen; hf = 1.2 mm [22] Type C Specimen; hf = 1.5 mm
Factor of two Factor of three Best fit of all data points
0.1 1x102
1x103
1x104
1x105
1x106
1x107
Fatigue Life; Nf (Cycles)
0.8
0.20 F = 500 N
0.7
0.19
Interfacial Peeling Stress, σp Interfacial Shear Stress, τr
0.6
0.18 0.17
0.5
0.16
0.4
0.15 0.14
0.3
0.13 0.2 0.12 0.1 0 0.8
0.11 1.0
1.2
1.4
1.6
0.10 1.8
Simulated Interfacial Shear Stress, τr (MPa)
Simulated Interfacial Peeling Stress, σp (MPa)
Fig. 9. Correlation results with the fatigue life data of the studied specimens obtained using the normalized applied loads.
Thickness of Face Sheet; hf (mm) Fig. 10. Relationship between the FE simulated interfacial peeling/shear stresses and the face sheet thickness of the studied specimens with an applied load of F = 500 N.
ized applied load and the experimental fatigue life is fitted using a power law, which is a straight line in the log–log scale diagram. The solid line in this figure represents the best fitting line of all fatigue data points. The deviation bands from the best fitting line with factors 2 and 3 are also provided in this figure to examine the scattering degree of the data points. The regression study was performed to examine the correlation performance of the normalized applied loads. The coefficient of determination—R squared is 0.818, indicating that the good correlation results are obtained when the normalized load parameter is used to evaluate the fatigue life. However, the application of this global parameter in fatigue design is difficult as the ultimate bending strength of the studied specimens should be first obtained analytically or experimentally. Accordingly, for the fatigue design in practice, the local parameters based on the actual failure mechanism are more adequate to correlate with the fatigue life of the studied specimens with different face sheet thicknesses than the global loading parameters. Fig. 10 shows the relationship between the FE simulated results of the maximum interfacial stress state and the face sheet thickness of the studied specimens under a fixed applied load of F = 500 N. Both the interfacial peeling and shear stress decrease as the face sheet thickness increases, demonstrating that increasing the face sheet thickness can reduce the interfacial stresses effectively and the fatigue resistance can be improved significantly. Figs. 11–13 show the correlation results of the three local parameters—the interfacial peeling stress, the interfacial shear stress, and the linear combination of peeling and
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Maximum Interfacial Peeling Stress; σp,max (MPa)
3 Type A Specimen; hf = 1.0 mm Type B Specimen; hf = 1.2 mm [22] Type C Specimen; hf = 1.5 mm
1
Factor of two Factor of three Best fit of all data points
0.1 2 1x10
1x10
3
4
1x10
5
1x10
6
1x10
Fatigue Life; Nf (Cycles) Fig. 11. Correlation results with the fatigue-life data of the studied specimens obtained using the maximum interfacial peeling stress parameter.
Maximum Interfacial Shear Stress; τ r,max (MPa)
0.6 Type A Specimen; hf = 1.0 mm Type B Specimen; hf = 1.2 mm [22] Type C Specimen; hf = 1.5 mm
0.1
0.05 2 1x10
Factor of two Factor of three Best fit of all data points
1x10
3
4
1x10
5
1x10
1x10
6
Fatigue Life; Nf (Cycles) Fig. 12. Correlation results with the fatigue-life data of the studied specimens obtained using the maximum interfacial shear stress parameter.
shear stresses—with the fatigue data. The coefficients of determination-R squared for the three correlation results shown in Figs. 11–13 using interfacial peeling, shear and combined parameters are 0.697, 0.881 and 0.778, respectively. The regression study demonstrates that of the three local parameters, the interfacial shear stress parameter and the combined parameter yield more acceptable correlation results than the interfacial peeling stress parameter. Moreover, the difference in correlation performance between the interfacial shear stress parameter and the combined parameter is slight. Fig. 14 shows the comparison between the predicted locations of debonding failure initiation using the three local parameters and the experimental ones observed in the fatigue tests. The combined parameter and the maximum interfacial peeling stress parameter predict the locations of debonding failure initiation accurately, whereas the failure locations predicted using the interfacial shear stress parameter are far from the observed ones. When examining the correlation results with the fatigue life data and the prediction performance of the debonding locations together, the linear combination of interfacial peeling and shear stresses is considered as the most accurate parameter in the fatigue design of the adhesively bonded sandwich beam structures than the other two parameters. The successful fatigue-life correlations and failure-location predictions via using the combined parameter elucidates that both the interfacial peeling stress and the interfacial shear stress contribute to the debonding failure in the fatigue tests. A parameter considering either the interfacial shear stress or the interfacial peeling stress only fails to accurately predict the fatigue life and failure location simultaneously because the parameter can-
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Linearly Combined Interfacial Stress Parameter; τr,max + kσp,max (MPa)
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2 Type A Specimen; hf = 1.0 mm Type B Specimen; hf = 1.2 mm [22] Type C Specimen; hf = 1.5 mm
1
Best fit of all data points Factor of two Factor of three
0.1 2 1x10
3
1x10
4
1x10
5
1x10
1x10
6
1x10
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Fatigue Life; Nf (Cycles) Fig. 13. Correlation results with the fatigue-life data of the studied specimens obtained using the linearly combined interfacial peeling and shear stress parameter.
: Symmetric Line of specimen : Applied line of Inner Roller : Observed Failure Location Predicted Failure Location : Interfacial Peeling Stress Parameter : Interfacial Shear Stress Parameter : Linearly Combined Interfacial Stress Parameter
TYPE A
fine-mesh model
TYPE B [22]
TYPE C
fine-mesh model
fine-mesh model
Fig. 14. Comparison between the observed debonding locations and the predicted ones using the local parameters.
not correctly interpret the failure mechanism of debonding failure. Furthermore, the successful experiences in applying the combined parameter in the fatigue assessment of the studied sandwich specimens with different face sheet thicknesses herein and those with different core densities [22] suggests that the linear combination of interfacial peeling and shear stresses is an effective parameter in the fatigue strength design of the adhesively bonded honeycomb sandwich structures with various geometrical variables. 6. Conclusions Three types of adhesively bonded sandwich beam specimens with different face sheet thicknesses were used in this study to investigate the effect of the face sheet thickness on the fatigue strength of the studied specimens. The FE simulated interfacial stresses were incorporated into the local parameters to correlate with the fatigue life data of the studied sandwich specimens. Several conclusions can be drawn from the experimental and analytical results.
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1. Under the same applied bending loads, no apparent relationship exists between the face sheet thickness and the fatigue life of the studied specimens. Furthermore, the applied load fails to correlate with the experimental fatigue data points. 2. The main fatigue failure mode for the adhesive bonded honeycomb sandwich beams is the debonding at the interface between the adhesive and the face sheet. 3. The normalized applied load parameter provides good life evaluation performance. However, the parameter is not suitable for usage in the fatigue design because the ultimate bending strength should be obtained experimentally or analytically first. 4. The interfacial shear stress parameter and the combined parameter yield better correlation results with the experimental data than the interfacial peeling parameter. However, the difference in correlation performance between the interfacial shear parameter and the combined parameter is slight. 5. Of the three local parameters, only the combined interfacial shear and peeling stress parameter provides good evaluation results in both fatigue-life correlations and failure-location prediction. These analytical results reveal that both the interfacial peeling stress and the interfacial shear stress contribute to the debonding failure.
Acknowledgements The authors would like to thank the National Science Council of the Republic of China, Taiwan, for financially supporting this research under Contract No. NSC-95-2262-E-216-015-CC3. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23]
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