- Email: [email protected]
balsa sandwich panels with geometrical triggering features
Composite Structures 92 (2010) 2676–2684
Contents lists available at ScienceDirect
Composite Structures journal homepage: www.elsevier.com/locate/compstruct
Energy absorption of SMC/balsa sandwich panels with geometrical triggering features A. Lindström, S. Hallström * Department of Aeronautical and Vehicle Engineering, Royal Institute of Technology (KTH), SE-100 44 Stockholm, Sweden
a r t i c l e
i n f o
Article history: Available online 31 March 2010 Keywords: Sandwich Energy absorption Edgewise compression Damage triggering
a b s t r a c t The influence of triggering topologies on the peak load and energy absorption of sandwich panels loaded in in-plane compression is investigated. Sandwich panels with different geometrical triggering features are manufactured and tested experimentally. Damage initiation in panels with grooves is investigated using finite element models. As expected the investigated triggering features reduce the extreme load peaks. A less expected result is that the plateau load following peak load tends to be higher for panels with triggering features. Both results are judged favourable for crash performance of panels in vehicle applications. Analysis suggests that there is a transition in failure mode for the studied panels, where the peak load for panels containing no or few grooves seems to be governed by principles of fracture mechanics while for panels with a high number of grooves it appears to be limited by the average stress. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction The use of sandwich panels in vehicle structures is potentially advantageous due to their high bending stiffness and strength, relative to their weight. If they are to be used in crashworthy vehicle structures, their energy absorbing capability must however be comparable with corresponding metal structures and, above all, their energy absorption needs to be predictable. Even though the energy absorbing capability of composite materials can exceed that of metallic structures [1,2] they are rarely used in mass-produced vehicles. One reason for this is the complex damage propagation in composite structures, making it difficult to predict their energy absorption. In this study the behaviour of sandwich panels loaded in in-plane compression is investigated and some means to control their crushing behaviour are presented and evaluated. During quasi-static in-plane loading of sandwich structures the response is typically linear elastic until initiation of damage in the structure. The initial damage can be global buckling, local buckling (wrinkling) or face sheet failure [3]. Damage could also initiate as core failure, but for most structural sandwich panels of practical interest the ultimate strain of the core material exceeds that of the face sheets. When the structure is compressed beyond failure initiation, damage will propagate. Mamalis et al. [4] identified three types of post-initiation collapse modes; global buckling, unstable sandwich disintegration and progressive end-crushing. Face sheet damage could initiate delaminations in the face sheets * Corresponding author. E-mail address: [email protected] (S. Hallström). 0263-8223/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.compstruct.2010.03.018
and debond cracks at the face/core interface. If the fracture toughness of the interface is low such cracks may grow uncontrolled, resulting in rapid and complete separation of the face sheets from the core. If the fracture toughness of the face/core interface is sufficiently high in relation to the bending stiffness and strength of the face sheets, the structure will not be as prone to fail catastrophically [5]. A more stable crushing collapse mode can then be obtained, which generally promotes higher energy absorption. Even if a high compressive load bearing capacity is favourable for the energy absorption of a panel, high peak loads are generally unwanted in vehicle applications due to associated high acceleration pulses for neighbouring structures or passengers in the vehicle. 1.1. Triggering Different kinds of triggering means, in the following referred to as triggers, may be used to initiate damage at lower peak loads and to ensure more repeatable damage propagation in structures. Triggers can also be used to control the location of damage initiation. The triggers can be made in the form of geometrical features or mechanical devices that introduce stress concentrations into the structure, which in turn reduce peak loads and ensure more favourable collapse behaviour. The details of the principles behind the improved collapse behaviour of sandwich structures are not yet entirely understood and one of the goals of this work is to explore such mechanisms further. Structural components designed for efficient energy absorption have been used in vehicle applications for decades. These components are mostly different kinds of beams, tubes, frusta and struts
A. Lindström, S. Hallström / Composite Structures 92 (2010) 2676–2684
[6]. In primary structure such components have almost exclusively been made of steel. In recent years, and predominantly in more extreme cars, composite and even sandwich components have been introduced. The failure mechanisms during compression of metal and composite structures are fundamentally different. Metal structures are relatively ductile and mainly deform plastically, whereas composite materials in general fail in a more brittle manner [7]. Different triggers are used for different material concepts. In metallic tubes, imperfections can be used to ensure stable progressive plastic folding of the structure. Dyes are other commonly used triggers for metal tubes, where the tubes for example can be forced to invert or split [6]. In brittle composite tubes different geometrical features such as chamfered or tulip shaped edges [8,9] are used to trigger progressive crushing. Previous studies on sandwich structures include both metallic triggers and edges of different shapes [10– 12]. Stapleton and Adams [11] investigated the influence of external triggers on the energy absorption of sandwich panels, loaded dynamically in edgewise compression. An internal plug and an external wedge was used to initiate damage in four different sandwich configurations. Some promising results were obtained but it was also concluded that the effect of the initiators depends on the stiffness and strength of the sandwich constituents and the fracture toughness of the face/core interface, in agreement with previous work by the present authors [5]. Velecela et al. [12] investigated the influence of face sheet thickness, length/width aspect ratio and different triggering features on the specific energy absorption of both monolithic laminates and sandwich panels. Three types of triggering features on the plate edges were investigated; chamfered, pyramidal and triangular. A triangular triggering shape gave the best results, promoting stable progressive end-crushing. 2. Approach In the present study two conceptually different triggering features were investigated. One was chamfering of the face sheets and the other was introduction of transverse grooves, both along the loaded edges of sandwich panels, as illustrated in Fig. 1. Chamfering of the face sheets is likely to reduce the initial failure load. The effective stiffness of the structure is also expected to decrease. Grooves reduce the effective load carrying area and thereby the effective stiffness and initial failure load, in a similar way as chamfering. Failure is expected to initiate in or at the remaining material between the grooves. In addition, grooves may initially prohibit damage growth in-plane, perpendicular to the direction of the applied load as such damage propagation can be interrupted by the grooves.
The material concept was the same as in previous work by Lindström and Hallström [13], but from another manufacturing batch. The compressive properties of the SMC face sheets and the balsa core are presented in Table 1. Details of the experiments for determination of properties are found in [13]. Panels with nominal dimensions of 100 100 15.5 mm were manufactured. The loaded edges were milled in order to ascertain that they were plane and mutually parallel. Samples with chamfered face sheets or 4, 9, 14 or 19 sawed grooves were manufactured. The grooves were sawed to a width wg of approximately 1.7 mm and the depth hg was similar to the face sheet thickness tf of 1.5 mm, see Fig. 1. Corresponding panels without triggering features were also prepared for reference testing. The sandwich panels were compressed between two flat metal plates in an Instron 4505 universal testing machine without additional boundary support. A 100 kN load cell was used for the load measurements. The deformation rate in the experiments was set to 5 mm/min and the tests were run to at least 20 mm deformation, during which the load and deformation was recorded continuously. A Redlake MotionPro X-3 Plus high-speed camera was used to record the failure progression in some of the sandwich panels. The pictures were recorded at a rate of 50 fps during 120 s. Thus, images from the first 10 mm compression of the panels were recorded, which was sufficient to capture the initiation of failure and a significant part of the subsequent damage progression. During the experiments different load and energy measures were examined. These measures are defined below and illustrated for the reference panel in Fig. 2. The load vs. displacement response was linb was reached and subsequent continued ear until the peak load P compression resulted in a fairly constant plateau load Pp. The average plateau load is defined as the average load in the region illustrated in Fig. 2, truncated at a maximum displacement of 20 mm. The peak load per unit width can be calculated as
b r ¼ 2tf r ^f ; P
ð1Þ
^ f is the compression where tf is the face sheet thickness and r strength of the face sheet. The contribution from the core is small for the studied materials, and thus neglected. For the case of a panel with grooves the peak load per unit width can be estimated to
b r ¼ 2 w wg ng t f r ^f ; P w
ð2Þ
where w is the width of the panel and ng is the number of grooves. The total work W of the force P acting on the sandwich panel during a compression event is
W¼
3. Experiments
2677
Z
d
P dd;
ð3Þ
0
The investigated sandwich panels consisted of sheet molding compound (SMC) glass fibre face sheets and a balsa wood core.
a
where d is the deformation in the direction of the applied load. When comparing the results from different panels it may be more
b
Fig. 1. Triggering topologies. (a) Panel with chamfered face sheets and (b) panel with grooves.
2678
A. Lindström, S. Hallström / Composite Structures 92 (2010) 2676–2684
Table 1 Compressive mechanical properties from experiments (average and standard deviation). Property
Result
SMC Young’s modulus in 1-direction Ef1 (GPa) SMC Young’s modulus in 2-direction Ef2 (GPa) ^ f 1 (MPa) SMC compressive strength in 1-direction r ^ f 2 (MPa) SMC compressive strength in 2-direction r Balsa Young’s modulus in transverse direction Ec,t (MPa) ^ c;t (MPa) Balsa compressive strength in transverse direction r
13.1 ± 0.7 10.9 ± 1.0 161 ± 13 137 ± 10 69.2 ± 36 1.20 ± 0.5
bond and delamination cracks were clearly visible in both face sheets, as shown in Fig. 4c. During the following compression, the face sheets delaminated and split further, generating damage with broom-like features. The panels with grooves showed no damage in the face sheets prior to their peak load. During the following compression, delaminations and/or debonds were formed. The drop from peak load to plateau load was more prolonged for the chamfered panels than for all other panels. Unfortunately, the scatter in peak load was significant for panels with 4 grooves. For all other panels it was more moderate. It may be explained by extreme variation of properties in the constituent materials for the panels with 4 grooves but it was not possible to confirm during the experiments. Regardless of the scatter the plateau level clearly decreased with increasing deformation for panels with 19 grooves while it increased for panels with 4 and 9 grooves. For panels with 14 grooves the plateau level was virtually constant. 5. Numerical analysis
Fig. 2. Load definitions.
relevant to express the work per unit weight deformed material, often referred to as specific energy absorption. A more appropriate term may be specific energy transition, avoiding indications about to what extent the measured energy is really absorbed, dissipated, accumulated or transformed. The total specific energy transition Ws is here defined as
Ws ¼
W ; Aqd
ð4Þ
where A is the gross cross section area and q is the density of the panels. As the energy before failure initiation only is a small share of the total energy during extensive crushing of structures, it is interesting to compare the resulting specific energy transition Wps during the plateau load defined as
W ps ¼
Pp w ; Aq
ð5Þ
where Pp is the plateau load per unit width. As the term energy absorption is well established it will be used in parallel with the term energy transition throughout this paper. 4. Results from experiments The results from the experiments are illustrated in Fig. 3 and in Table 2, where the load values are presented together with standard deviations. All presented load values are expressed per unit b r was calculated width. The analytical peak load per unit width P using average values of the two directional properties presented in Table 1. Typical damage progression events in panels with different triggering features are presented in Figs. 4–6. For sandwich panels with chamfered face sheets debond and/or delamination cracks initiated at relatively small displacements. After the peak load was reached (at 1.926 mm deformation for the panel in Fig. 4) de-
From the experimental results presented in Table 2 it can be concluded that triggers in the form of grooves have a high potential for both reducing the peak load and increasing the energy absorption of sandwich panels. It can also be seen that the analytical peak b r , which is based on measurements of the face sheet load P strength, does not satisfactory explain the differences in experimental peak load for panels with varying number of groves. The load levels differ for some cases, which could be due to scatter in material properties, but the overall trend among the results seems to differ as well. This nurtured the hypothesis that the peak load of panels with grooves may be governed by principles of fracture mechanics rather than mean stress. To further explore the influence of grooves on the failure initiation in sandwich panels a finite element (FE) analysis was made, using the software ABAQUS [14]. The contribution to the strength from the core material was assumed negligible for the studied load case. Thus, only a single face sheet was modelled, with different numbers of square notches. The notches are in the following still referred to as grooves, for consistency with their sandwich counterparts. The studied cases were one reference face sheet without triggers and face sheets with 4, 9, 14 and 19 grooves. The models were built using plane strain elements of the types CPE8R and CPE6, which are eight noded elements with reduced integration, and six noded elements, respectively [14]. The material was considered isotropic and linear elastic with average properties from the two directions given in Table 1. The Poisson’s ratio was assumed to be 0.3. Each model was loaded in compression by applying a prescribed displacement. The loaded edges were modelled as pinned implying that all displacements perpendicular to the direction of the applied displacement were prevented on the loaded edges, representing conditions of zero slip between the panels and the supports and thus presence of singular stresses at boundaries of the loaded edges. To determine the influence of the grooves on the peak load a linear elastic fracture mechanics approach was used. All sites where singular stresses were expected to occur were similar in shape, being re-entrant or salient right angle corners. The stress around such corners can be described by
rij ¼
X
Q p rkp 1 fijp ðuÞ;
ð6Þ
p
where the corner constitutes the origin of a cylindrical coordinate system (r, u). Qp are generalised stress intensity factors associated in pairs with the stress intensity exponents kp, and fijp are nondimensional angular functions describing how the contribution from each term to a certain Cartesian stress component (ij) varies
2679
A. Lindström, S. Hallström / Composite Structures 92 (2010) 2676–2684
b
a
400
Load [kN/m]
Load [kN/m]
400 300 200 100 0
300 200 100
0
5
10
15
0
20
0
5
400
20
400
Load [kN/m]
Load [kN/m]
15
d
c 300 200 100 0
300 200 100
0
5
10
15
0
20
0
5
10
15
20
Displacement [mm]
Displacement [mm]
f
e
400
Load [kN/m]
400
Load [kN/m]
10
Displacement [mm]
Displacement [mm]
300 200
200 100
100 0
300
0
5
10
15
0
20
0
5
10
15
20
Displacement [mm]
Displacement [mm]
Fig. 3. Load–displacement curves from experiments. (a) Reference panels, (b) chamfered panels, (c) panels with 4 grooves, (d) panels with 9 grooves, (e) panels with 14 grooves, (f) panels with 19 grooves.
Table 2 Predicted peak load and experimental results.
Reference Chamfered 4 Grooves 9 Grooves 14 Grooves 19 Grooves
0
0
rðaub Þ ¼ Q ð1abu Þ rk1 1 ;
b r (kN/m) P
b (kN/m) P
Pp (kN/m)
Ws (kJ/kg)
Wps (kJ/kg)
447 – 417 379 341 303
398 ± 17 185 ± 7.0 396 ± 87 382 ± 19 364 ± 25 289 ± 23
80.9 ± 12 98.4 ± 9.8 121 ± 12 135 ± 23 137 ± 13 114 ± 2.1
13.5 ± 1.7 15.0 ± 1.3 19.0 ± 1.3 20.1 ± 3.6 19.4 ± 2.0 17.1 ± 0.4
11.8 14.7 17.9 19.5 19.1 16.9
± 1.7 ± 1.4 ± 1.8 ± 3.8 ± 2.2 ± 0.3
circumferentially around the corner. It should be noted that the dimension of the stress intensity factors Qp differs with kp. The k values can be derived as roots to an eigenvalue problem from relations given by Williams [15], and existence of kp < 1 obviously enables singular stress terms. Assuming such existence and sorting the terms in Eq. (6) by ascending values of k the stress field in the vicinity of the corner will be dominated by the first term (p = 1) (provided that k1 is a single-root and Q1 and fij1 are nonzero). Assuming that conditions of linear elasticity prevail there exists a critical stress intensity factor Q1c for the corner, similar to the fracture toughness KIc for a crack. A specific stress component (ab), in 0 the vicinity of, and in a specific angular direction u to the corner can be expressed as
ð7Þ
and a failure criterion for the corner could be posed also in terms of ðabu0 Þ Q 1c . Theoretical k values for the two corner types were calculated and the lowest value (k1) for each corner was used to back-calcuðabu0 Þ from FE stress data. late associated stress intensity factors Q 1 A prescribed compressive displacement was applied to the FE models and the corresponding load per unit width PFE was derived by summation of the nodal reaction forces at the opposite side of ðabu0 Þ the model. Q 1;FE was then determined by extracting stress data 0 at various radial distances r in a certain direction u from the corners, and performing a least square fit to Eq. (7). More specifically, stresses parallel to the direction of the applied displacement were extracted in the direction perpendicular to the applied displacement. This value was used to calculate the critical load due to corner stress singularity for pinned panels as ðabu0 Þ
b Q ¼ Q 1c 0 PFE : P ðabu Þ Q 1;FE
ð8Þ
Assuming that the reference panels failed due to fracture at the boundaries of their loaded edges, the reference case was used to ðabu0 Þ as determine Q 1c
2680
A. Lindström, S. Hallström / Composite Structures 92 (2010) 2676–2684
d
c
b
a
e
f
g Load [kN/m]
150
100
50
0
0
5
10
15
20
Displacement [mm] Fig. 4. Failure progression in panel with chamfered face sheets. (a) d = 0.7 mm, (b) d = 1.1 mm, (c) d = 2.0 mm, (d) d = 3.6 mm, (e) d = 6.2 mm, (f) d = 9.5 mm, (g) load– displacement curve, with a–f marking the corresponding photo of damage progression.
ðabu0 Þ
Q 1c
¼
b exp ðabu0 Þ P Q ; PFE 1;FE
ð9Þ
b exp is the where all values are taken from the reference panels and P critical load per unit width from the corresponding experiments. The reference panels without triggers only contained four corners, i.e. the four corners of the panel itself. It was learned from the analysis that these corners were also the locations with the strongest stress fields for the panels containing grooves. Therefore the stress intensities at the corners denoted a in Fig. 1b were evaluated for all panel cases. For the upper groove corners (i.e. corners a and b in Fig. 1b) k1 = 0.711, for the present boundary conditions. For the lower groove corners (corners c and d in Fig. 1b) k1 has a lower value (about 0.54) than at the upper corners, indicating areas of stronger singular stress fields there. However the lower value corresponds to mode I (symmetric opening) deformation of the corner regions and such deformation was found to be suppressed at the lower cor-
ners for the studied load case. The second (k2) value for the lower corner is about 0.91, corresponding to mode II (antisymmetric shearing) deformation and a weaker stress field than at the upper pinned corners. (In the experiments the lower corners of the test specimens were also blunt rather than perfectly square, which further reduced the stress concentrations there.) Consequently, since the only difference between the investigated models was the number of grooves, the same fracture mechanics criterion could be used for all cases. The upper groove corners were identified as the critical ones and, since the stress levels at the corners are mesh dependent, specific concern was made to use similar mesh refinement at all studied sites with singular stresses. 6. Results from numerical analysis The stress distributions parallel and perpendicular to the direction of the applied displacement in a panel with 4 grooves are illus-
A. Lindström, S. Hallström / Composite Structures 92 (2010) 2676–2684
a
c
b
e
2681
d
f
g
300
Load [kN/m]
250 200 150 100 50 0
0
5
10
15
20
Displacement [mm] Fig. 5. Failure progression in panel with 4 grooves. (a) d = 1.4 mm, (b) d = 1.7 mm, (c) d = 2.4 mm, (d) d = 4.9 mm, (e) d = 7.8 mm (f) d = 9.9 mm, (g) load–displacement curve, with a–f marking the corresponding photo of damage progression.
trated in Fig. 7. Fig. 8 illustrates the stress in the parallel direction on the loaded edges of panels with 4 and 19 grooves. It is clearly seen that the grooves introduce stress concentrations at the salient corners on the loaded edge for the panels. The lower re-entrant corners of the grooves are obviously sites of singular stresses as well. However, the studied configurations and load cases are such that the re-entrant corners are exposed to very limited deformations. The stress distribution on the loaded edges is therefore not only dependent on the area reduction, but also on the stress singularities caused at the corners. The salient corners of a panel with pinned boundary conditions have as already mentioned a theoretical k value of 0.711, whereas the results from the FE analysis was 0.708 ± 0.003. It should be noted that the k value decreased slightly with an increasing number of grooves. A plausible explanation is that the stress fields of neighbouring corners start to interfere when the distance between grooves becomes small. The influence of the area reduction and the stress singularities on the peak load is illustrated in Fig. 9, where the failure load from experiments is plotted together with results from the FE fracture mechanics anal-
ysis and strength predictions according to a simple mean stress criterion. 7. Discussion All panels with triggers exhibited lower peak load than the reference panels. The reduction was however moderate for panels with 4, 9 and 14 grooves while it was more significant for panels with 19 grooves and panels with chamfered face sheets. For the latter the peak load reduction was more than 50% and the drop from peak to plateau load levels was also gradual. For all other panels the load dropped instantly from peak to plateau level. It should be noted that the scatter in peak load of the panels with 4 grooves was relatively high. Two panels failed at peak loads higher than the reference panels, whereas the peak loads of the other two panels were lower than expected. One of the stronger panels failed at the edge without grooves, which indicated that 4 grooves were insufficient to ensure triggering of the studied cases. The other configurations showed surprisingly low scatter.
2682
A. Lindström, S. Hallström / Composite Structures 92 (2010) 2676–2684
a
c
b
e
d
f
g
400
Load [kN/m]
350 300 250 200 150 100 50 0
0
5
10
15
20
Displacement [mm] Fig. 6. Failure progression in panel with 9 grooves. (a) d = 1.5 mm, (b) d = 1.6 mm, (c) d = 3.3 mm, (d) d = 5.0 mm, (e) d = 8.3 mm, (f) d = 9.9 mm, (g) load–displacement curve, with a–f marking the corresponding photo of damage progression.
Fig. 7. Stress distributions on panel with 4 grooves; (a) perpendicular to and (b) parallel to the direction of the applied displacement.
Somewhat unexpected, all triggered panels also showed higher plateau load levels than the reference panels. The energy absorption up to 20 mm compression was also higher for all panels with triggers, in spite of their lower peak loads. The increase of plateau load for the panels with chamfered face sheets was however lower than for the panels with grooves. It can fur-
ther be noted from Fig. 3 that the plateau load increased with increasing deformation for panels with 4 and 9 grooves, but dropped for panels with 19 grooves. For the reference panels and panels with 14 grooves the plateau levels were virtually constant. The plateau level for panels with chamfered edges initially decreased but then increased towards the end of the com-
2683
A. Lindström, S. Hallström / Composite Structures 92 (2010) 2676–2684
upper edge lower edge
1500
1000
500
0
b Stress [MPa]
Stress [MPa]
a
upper edge lower edge
1500 1000 500
0
0.02
0.04
0.06
0.08
0.1
0
0
x−coordinate [m]
0.02
0.04
0.06
0.08
0.1
x−coordinate [m]
Fig. 8. Stress parallel to the direction of the applied load along loaded edges for panels with (a) 4 and (b) 19 grooves.
Critical load [kN/m]
500 450 400 350 300 250
0
5
10
15
20
Number of grooves b Q and area reduction P b r , and Fig. 9. Predicted peak load due to corner singularity P b exp . experimental value P
pression phase. The reasons behind these differences were not elucidated by the presented study. The chamfered face sheets buckled away from the core, as seen in Fig. 4, since the chamfering caused skew loading of the face sheet edges. The relatively low plateau load for these panels was likely correlated with the large face sheet deflections. The face sheets on the panels with grooves remained more straight, leading to more localised crushing and likely also to the observed higher plateau load levels. However, after prolonged compression some of the panels with chamfered face edges reached plateau levels more similar to the panels with grooves. In general, one would expect the plateau load for all panels to approach similar levels after certain compression, since the effects caused by triggering are unlikely to remain long after the damage has progressed beyond the triggered regions. Tendencies towards similar plateau levels at large deformations are visible in Fig. 3 for panels with 4, 9 and 14 grooves, two of the chamfered panels and two reference panels. However, the panels with 19 grooves showed no such tendencies but rather displayed a monotonically decaying plateau load. The responses from all four specimens were strikingly consistent and no explanation for this decay was found in the study. The peak loads of the panels with grooves were not reduced in proportion to the area reduction. The area reduction of the panels with 4, 9, 14 and 19 grooves were approximately 7%, 15%, 24% and 32%, respectively. The peak load reduction, however, was only 0.5%, 4%, 8% and 27%, respectively. Fig. 9 indicates that the peak load is governed by the stress intensity at the corners for panels with few grooves, but by the average stress for panels with many grooves, and that some failure mechanism transition occurs in between. As shown in the figure the critical load due to corner stress singularities is calibrated with results from the reference panel. However the trend of the results came out similarly when the panels with 4 grooves were used for calibration of the criterion. The influence of the grooves on the local stress is clearly shown in Figs. 7 and 8. During compression the material between the
grooves tend to expand transversely with respect to the applied displacement, due to Poisson’s effects. Since such deformation is restricted at the loaded boundaries the stress fields around the groove corners become singular, clearly seen in Fig. 8a. The boundary effects are more pronounced for panels with more grooves. The stress levels at the opposite edge without triggers is naturally independent of the number of grooves, whereas the stress levels increase at the upper edge with increasing number of grooves. It should be noted that the peak stress levels in the models are mesh dependent due to their singular nature. All corner areas were however modelled with similar mesh refinement at the corners, which justified comparisons. 8. Conclusions The peak load for SMC/balsa sandwich panels loaded in in-plane compression was clearly reduced when triggering features were introduced. In addition the specific energy absorption of sandwich panels with triggers was increased in comparison to that of reference panels without triggers. Chamfered edges reduced the peak load more than grooves. Grooves, on the other hand, increased the subsequent plateau load levels and, consequently, the energy absorption more. As few as 4 grooves did not ensure damage initiation where intended in the studied panels. Panels with 9 grooves showed the highest average specific energy absorption in the study. The difference between the panels with 9 and 14 grooves, however, was relatively small and not statistically certain. A transition of failure mechanisms was found in the analysis, suggesting that the peak load was governed by the stress concentrations on the loaded edges for panels with no or few grooves but governed by the average stress for panels with many grooves. The overall trend from the experiments correlates well with the analysis, considering the scatter among the experimental results. Acknowledgement The authors gratefully acknowledge Rieter Automotive Management AG for supporting the presented work. References [1] Farley GL. Energy absorption of composite materials. J Compos Mater 1983;17:267–79. [2] Mamalis AG, Robinson M, Manolakos DE, Demosthenous GA, Ioannidis MB, Carruthers J. Review crashworthy capability of composite material structures. Compos Struct 1997;37(2):109–34. [3] Fleck NA, Sridhar I. End compression of sandwich columns. Composites: Part A 2002;33:353–9. [4] Mamalis AG, Manolakos DE, Ioannidis MB, Papapostolou DP. On the crushing response of composite sandwich panels subjected to edgewise compression: experimental. Compos Struct 2005;71:246–57. [5] Lindström A, Hallström S. In-plane compression of sandwich panels with debonds. Compos Struct 2010;92(2):532–40.
2684
A. Lindström, S. Hallström / Composite Structures 92 (2010) 2676–2684
[6] Alghamdi AAA. Collapsible impact energy absorbers: an overview. Thin-Walled Struct 2001;39:189–213. [7] Carruthers JJ, Kettle AP, Robinson AM. Energy absorption capability and crashworthiness of composite material structures: a review. Appl Mech Rev 1998;51(10):635–49. [8] Hull D. A unified approach to progressive crushing of fibre-reinforced composite tubes. Compos Sci Technol 1991;40:377–421. [9] Thornton PH, Jeryan RA. Crash energy management in composite automotive structures. Int J Impact Eng 1988;7(2):167–80. [10] Pitarresi G, Carruthers JJ, Robinson AM, Torre G, Kenny JM, Ingleton S, et al. A comparative evaluation of crashworthy composite sandwich structures. Compos Struct 2007;78:34–44.
[11] Stapleton SE, Adams DO. Crush initiators for increased energy absorption in composite sandwich structures. J Sandwich Struct Mater 2008;10(4):331–54. [12] Velecela O, Found MS, Soutis C. Crushing energy absorption of GFRP sandwich panels and corresponding monolithic laminates. Composites: Part A 2007;38:1149–58. [13] Lindström A, Hallström S. Energy absorption of sandwich panels subjected to in-plane loads. In: 8th Biennial ASME conference on engineering systems design and analysis. ASME; 2006. [14] ABAQUS. Online users manual, version 6.7; 2007. . [15] Williams ML. Stress singularities resulting from various boundary conditions in angular corners of plates in extension. J Appl Mech 1952;19:526–8.
Contents lists available at ScienceDirect
Composite Structures journal homepage: www.elsevier.com/locate/compstruct
Energy absorption of SMC/balsa sandwich panels with geometrical triggering features A. Lindström, S. Hallström * Department of Aeronautical and Vehicle Engineering, Royal Institute of Technology (KTH), SE-100 44 Stockholm, Sweden
a r t i c l e
i n f o
Article history: Available online 31 March 2010 Keywords: Sandwich Energy absorption Edgewise compression Damage triggering
a b s t r a c t The influence of triggering topologies on the peak load and energy absorption of sandwich panels loaded in in-plane compression is investigated. Sandwich panels with different geometrical triggering features are manufactured and tested experimentally. Damage initiation in panels with grooves is investigated using finite element models. As expected the investigated triggering features reduce the extreme load peaks. A less expected result is that the plateau load following peak load tends to be higher for panels with triggering features. Both results are judged favourable for crash performance of panels in vehicle applications. Analysis suggests that there is a transition in failure mode for the studied panels, where the peak load for panels containing no or few grooves seems to be governed by principles of fracture mechanics while for panels with a high number of grooves it appears to be limited by the average stress. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction The use of sandwich panels in vehicle structures is potentially advantageous due to their high bending stiffness and strength, relative to their weight. If they are to be used in crashworthy vehicle structures, their energy absorbing capability must however be comparable with corresponding metal structures and, above all, their energy absorption needs to be predictable. Even though the energy absorbing capability of composite materials can exceed that of metallic structures [1,2] they are rarely used in mass-produced vehicles. One reason for this is the complex damage propagation in composite structures, making it difficult to predict their energy absorption. In this study the behaviour of sandwich panels loaded in in-plane compression is investigated and some means to control their crushing behaviour are presented and evaluated. During quasi-static in-plane loading of sandwich structures the response is typically linear elastic until initiation of damage in the structure. The initial damage can be global buckling, local buckling (wrinkling) or face sheet failure [3]. Damage could also initiate as core failure, but for most structural sandwich panels of practical interest the ultimate strain of the core material exceeds that of the face sheets. When the structure is compressed beyond failure initiation, damage will propagate. Mamalis et al. [4] identified three types of post-initiation collapse modes; global buckling, unstable sandwich disintegration and progressive end-crushing. Face sheet damage could initiate delaminations in the face sheets * Corresponding author. E-mail address: [email protected] (S. Hallström). 0263-8223/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.compstruct.2010.03.018
and debond cracks at the face/core interface. If the fracture toughness of the interface is low such cracks may grow uncontrolled, resulting in rapid and complete separation of the face sheets from the core. If the fracture toughness of the face/core interface is sufficiently high in relation to the bending stiffness and strength of the face sheets, the structure will not be as prone to fail catastrophically [5]. A more stable crushing collapse mode can then be obtained, which generally promotes higher energy absorption. Even if a high compressive load bearing capacity is favourable for the energy absorption of a panel, high peak loads are generally unwanted in vehicle applications due to associated high acceleration pulses for neighbouring structures or passengers in the vehicle. 1.1. Triggering Different kinds of triggering means, in the following referred to as triggers, may be used to initiate damage at lower peak loads and to ensure more repeatable damage propagation in structures. Triggers can also be used to control the location of damage initiation. The triggers can be made in the form of geometrical features or mechanical devices that introduce stress concentrations into the structure, which in turn reduce peak loads and ensure more favourable collapse behaviour. The details of the principles behind the improved collapse behaviour of sandwich structures are not yet entirely understood and one of the goals of this work is to explore such mechanisms further. Structural components designed for efficient energy absorption have been used in vehicle applications for decades. These components are mostly different kinds of beams, tubes, frusta and struts
A. Lindström, S. Hallström / Composite Structures 92 (2010) 2676–2684
[6]. In primary structure such components have almost exclusively been made of steel. In recent years, and predominantly in more extreme cars, composite and even sandwich components have been introduced. The failure mechanisms during compression of metal and composite structures are fundamentally different. Metal structures are relatively ductile and mainly deform plastically, whereas composite materials in general fail in a more brittle manner [7]. Different triggers are used for different material concepts. In metallic tubes, imperfections can be used to ensure stable progressive plastic folding of the structure. Dyes are other commonly used triggers for metal tubes, where the tubes for example can be forced to invert or split [6]. In brittle composite tubes different geometrical features such as chamfered or tulip shaped edges [8,9] are used to trigger progressive crushing. Previous studies on sandwich structures include both metallic triggers and edges of different shapes [10– 12]. Stapleton and Adams [11] investigated the influence of external triggers on the energy absorption of sandwich panels, loaded dynamically in edgewise compression. An internal plug and an external wedge was used to initiate damage in four different sandwich configurations. Some promising results were obtained but it was also concluded that the effect of the initiators depends on the stiffness and strength of the sandwich constituents and the fracture toughness of the face/core interface, in agreement with previous work by the present authors [5]. Velecela et al. [12] investigated the influence of face sheet thickness, length/width aspect ratio and different triggering features on the specific energy absorption of both monolithic laminates and sandwich panels. Three types of triggering features on the plate edges were investigated; chamfered, pyramidal and triangular. A triangular triggering shape gave the best results, promoting stable progressive end-crushing. 2. Approach In the present study two conceptually different triggering features were investigated. One was chamfering of the face sheets and the other was introduction of transverse grooves, both along the loaded edges of sandwich panels, as illustrated in Fig. 1. Chamfering of the face sheets is likely to reduce the initial failure load. The effective stiffness of the structure is also expected to decrease. Grooves reduce the effective load carrying area and thereby the effective stiffness and initial failure load, in a similar way as chamfering. Failure is expected to initiate in or at the remaining material between the grooves. In addition, grooves may initially prohibit damage growth in-plane, perpendicular to the direction of the applied load as such damage propagation can be interrupted by the grooves.
The material concept was the same as in previous work by Lindström and Hallström [13], but from another manufacturing batch. The compressive properties of the SMC face sheets and the balsa core are presented in Table 1. Details of the experiments for determination of properties are found in [13]. Panels with nominal dimensions of 100 100 15.5 mm were manufactured. The loaded edges were milled in order to ascertain that they were plane and mutually parallel. Samples with chamfered face sheets or 4, 9, 14 or 19 sawed grooves were manufactured. The grooves were sawed to a width wg of approximately 1.7 mm and the depth hg was similar to the face sheet thickness tf of 1.5 mm, see Fig. 1. Corresponding panels without triggering features were also prepared for reference testing. The sandwich panels were compressed between two flat metal plates in an Instron 4505 universal testing machine without additional boundary support. A 100 kN load cell was used for the load measurements. The deformation rate in the experiments was set to 5 mm/min and the tests were run to at least 20 mm deformation, during which the load and deformation was recorded continuously. A Redlake MotionPro X-3 Plus high-speed camera was used to record the failure progression in some of the sandwich panels. The pictures were recorded at a rate of 50 fps during 120 s. Thus, images from the first 10 mm compression of the panels were recorded, which was sufficient to capture the initiation of failure and a significant part of the subsequent damage progression. During the experiments different load and energy measures were examined. These measures are defined below and illustrated for the reference panel in Fig. 2. The load vs. displacement response was linb was reached and subsequent continued ear until the peak load P compression resulted in a fairly constant plateau load Pp. The average plateau load is defined as the average load in the region illustrated in Fig. 2, truncated at a maximum displacement of 20 mm. The peak load per unit width can be calculated as
b r ¼ 2tf r ^f ; P
ð1Þ
^ f is the compression where tf is the face sheet thickness and r strength of the face sheet. The contribution from the core is small for the studied materials, and thus neglected. For the case of a panel with grooves the peak load per unit width can be estimated to
b r ¼ 2 w wg ng t f r ^f ; P w
ð2Þ
where w is the width of the panel and ng is the number of grooves. The total work W of the force P acting on the sandwich panel during a compression event is
W¼
3. Experiments
2677
Z
d
P dd;
ð3Þ
0
The investigated sandwich panels consisted of sheet molding compound (SMC) glass fibre face sheets and a balsa wood core.
a
where d is the deformation in the direction of the applied load. When comparing the results from different panels it may be more
b
Fig. 1. Triggering topologies. (a) Panel with chamfered face sheets and (b) panel with grooves.
2678
A. Lindström, S. Hallström / Composite Structures 92 (2010) 2676–2684
Table 1 Compressive mechanical properties from experiments (average and standard deviation). Property
Result
SMC Young’s modulus in 1-direction Ef1 (GPa) SMC Young’s modulus in 2-direction Ef2 (GPa) ^ f 1 (MPa) SMC compressive strength in 1-direction r ^ f 2 (MPa) SMC compressive strength in 2-direction r Balsa Young’s modulus in transverse direction Ec,t (MPa) ^ c;t (MPa) Balsa compressive strength in transverse direction r
13.1 ± 0.7 10.9 ± 1.0 161 ± 13 137 ± 10 69.2 ± 36 1.20 ± 0.5
bond and delamination cracks were clearly visible in both face sheets, as shown in Fig. 4c. During the following compression, the face sheets delaminated and split further, generating damage with broom-like features. The panels with grooves showed no damage in the face sheets prior to their peak load. During the following compression, delaminations and/or debonds were formed. The drop from peak load to plateau load was more prolonged for the chamfered panels than for all other panels. Unfortunately, the scatter in peak load was significant for panels with 4 grooves. For all other panels it was more moderate. It may be explained by extreme variation of properties in the constituent materials for the panels with 4 grooves but it was not possible to confirm during the experiments. Regardless of the scatter the plateau level clearly decreased with increasing deformation for panels with 19 grooves while it increased for panels with 4 and 9 grooves. For panels with 14 grooves the plateau level was virtually constant. 5. Numerical analysis
Fig. 2. Load definitions.
relevant to express the work per unit weight deformed material, often referred to as specific energy absorption. A more appropriate term may be specific energy transition, avoiding indications about to what extent the measured energy is really absorbed, dissipated, accumulated or transformed. The total specific energy transition Ws is here defined as
Ws ¼
W ; Aqd
ð4Þ
where A is the gross cross section area and q is the density of the panels. As the energy before failure initiation only is a small share of the total energy during extensive crushing of structures, it is interesting to compare the resulting specific energy transition Wps during the plateau load defined as
W ps ¼
Pp w ; Aq
ð5Þ
where Pp is the plateau load per unit width. As the term energy absorption is well established it will be used in parallel with the term energy transition throughout this paper. 4. Results from experiments The results from the experiments are illustrated in Fig. 3 and in Table 2, where the load values are presented together with standard deviations. All presented load values are expressed per unit b r was calculated width. The analytical peak load per unit width P using average values of the two directional properties presented in Table 1. Typical damage progression events in panels with different triggering features are presented in Figs. 4–6. For sandwich panels with chamfered face sheets debond and/or delamination cracks initiated at relatively small displacements. After the peak load was reached (at 1.926 mm deformation for the panel in Fig. 4) de-
From the experimental results presented in Table 2 it can be concluded that triggers in the form of grooves have a high potential for both reducing the peak load and increasing the energy absorption of sandwich panels. It can also be seen that the analytical peak b r , which is based on measurements of the face sheet load P strength, does not satisfactory explain the differences in experimental peak load for panels with varying number of groves. The load levels differ for some cases, which could be due to scatter in material properties, but the overall trend among the results seems to differ as well. This nurtured the hypothesis that the peak load of panels with grooves may be governed by principles of fracture mechanics rather than mean stress. To further explore the influence of grooves on the failure initiation in sandwich panels a finite element (FE) analysis was made, using the software ABAQUS [14]. The contribution to the strength from the core material was assumed negligible for the studied load case. Thus, only a single face sheet was modelled, with different numbers of square notches. The notches are in the following still referred to as grooves, for consistency with their sandwich counterparts. The studied cases were one reference face sheet without triggers and face sheets with 4, 9, 14 and 19 grooves. The models were built using plane strain elements of the types CPE8R and CPE6, which are eight noded elements with reduced integration, and six noded elements, respectively [14]. The material was considered isotropic and linear elastic with average properties from the two directions given in Table 1. The Poisson’s ratio was assumed to be 0.3. Each model was loaded in compression by applying a prescribed displacement. The loaded edges were modelled as pinned implying that all displacements perpendicular to the direction of the applied displacement were prevented on the loaded edges, representing conditions of zero slip between the panels and the supports and thus presence of singular stresses at boundaries of the loaded edges. To determine the influence of the grooves on the peak load a linear elastic fracture mechanics approach was used. All sites where singular stresses were expected to occur were similar in shape, being re-entrant or salient right angle corners. The stress around such corners can be described by
rij ¼
X
Q p rkp 1 fijp ðuÞ;
ð6Þ
p
where the corner constitutes the origin of a cylindrical coordinate system (r, u). Qp are generalised stress intensity factors associated in pairs with the stress intensity exponents kp, and fijp are nondimensional angular functions describing how the contribution from each term to a certain Cartesian stress component (ij) varies
2679
A. Lindström, S. Hallström / Composite Structures 92 (2010) 2676–2684
b
a
400
Load [kN/m]
Load [kN/m]
400 300 200 100 0
300 200 100
0
5
10
15
0
20
0
5
400
20
400
Load [kN/m]
Load [kN/m]
15
d
c 300 200 100 0
300 200 100
0
5
10
15
0
20
0
5
10
15
20
Displacement [mm]
Displacement [mm]
f
e
400
Load [kN/m]
400
Load [kN/m]
10
Displacement [mm]
Displacement [mm]
300 200
200 100
100 0
300
0
5
10
15
0
20
0
5
10
15
20
Displacement [mm]
Displacement [mm]
Fig. 3. Load–displacement curves from experiments. (a) Reference panels, (b) chamfered panels, (c) panels with 4 grooves, (d) panels with 9 grooves, (e) panels with 14 grooves, (f) panels with 19 grooves.
Table 2 Predicted peak load and experimental results.
Reference Chamfered 4 Grooves 9 Grooves 14 Grooves 19 Grooves
0
0
rðaub Þ ¼ Q ð1abu Þ rk1 1 ;
b r (kN/m) P
b (kN/m) P
Pp (kN/m)
Ws (kJ/kg)
Wps (kJ/kg)
447 – 417 379 341 303
398 ± 17 185 ± 7.0 396 ± 87 382 ± 19 364 ± 25 289 ± 23
80.9 ± 12 98.4 ± 9.8 121 ± 12 135 ± 23 137 ± 13 114 ± 2.1
13.5 ± 1.7 15.0 ± 1.3 19.0 ± 1.3 20.1 ± 3.6 19.4 ± 2.0 17.1 ± 0.4
11.8 14.7 17.9 19.5 19.1 16.9
± 1.7 ± 1.4 ± 1.8 ± 3.8 ± 2.2 ± 0.3
circumferentially around the corner. It should be noted that the dimension of the stress intensity factors Qp differs with kp. The k values can be derived as roots to an eigenvalue problem from relations given by Williams [15], and existence of kp < 1 obviously enables singular stress terms. Assuming such existence and sorting the terms in Eq. (6) by ascending values of k the stress field in the vicinity of the corner will be dominated by the first term (p = 1) (provided that k1 is a single-root and Q1 and fij1 are nonzero). Assuming that conditions of linear elasticity prevail there exists a critical stress intensity factor Q1c for the corner, similar to the fracture toughness KIc for a crack. A specific stress component (ab), in 0 the vicinity of, and in a specific angular direction u to the corner can be expressed as
ð7Þ
and a failure criterion for the corner could be posed also in terms of ðabu0 Þ Q 1c . Theoretical k values for the two corner types were calculated and the lowest value (k1) for each corner was used to back-calcuðabu0 Þ from FE stress data. late associated stress intensity factors Q 1 A prescribed compressive displacement was applied to the FE models and the corresponding load per unit width PFE was derived by summation of the nodal reaction forces at the opposite side of ðabu0 Þ the model. Q 1;FE was then determined by extracting stress data 0 at various radial distances r in a certain direction u from the corners, and performing a least square fit to Eq. (7). More specifically, stresses parallel to the direction of the applied displacement were extracted in the direction perpendicular to the applied displacement. This value was used to calculate the critical load due to corner stress singularity for pinned panels as ðabu0 Þ
b Q ¼ Q 1c 0 PFE : P ðabu Þ Q 1;FE
ð8Þ
Assuming that the reference panels failed due to fracture at the boundaries of their loaded edges, the reference case was used to ðabu0 Þ as determine Q 1c
2680
A. Lindström, S. Hallström / Composite Structures 92 (2010) 2676–2684
d
c
b
a
e
f
g Load [kN/m]
150
100
50
0
0
5
10
15
20
Displacement [mm] Fig. 4. Failure progression in panel with chamfered face sheets. (a) d = 0.7 mm, (b) d = 1.1 mm, (c) d = 2.0 mm, (d) d = 3.6 mm, (e) d = 6.2 mm, (f) d = 9.5 mm, (g) load– displacement curve, with a–f marking the corresponding photo of damage progression.
ðabu0 Þ
Q 1c
¼
b exp ðabu0 Þ P Q ; PFE 1;FE
ð9Þ
b exp is the where all values are taken from the reference panels and P critical load per unit width from the corresponding experiments. The reference panels without triggers only contained four corners, i.e. the four corners of the panel itself. It was learned from the analysis that these corners were also the locations with the strongest stress fields for the panels containing grooves. Therefore the stress intensities at the corners denoted a in Fig. 1b were evaluated for all panel cases. For the upper groove corners (i.e. corners a and b in Fig. 1b) k1 = 0.711, for the present boundary conditions. For the lower groove corners (corners c and d in Fig. 1b) k1 has a lower value (about 0.54) than at the upper corners, indicating areas of stronger singular stress fields there. However the lower value corresponds to mode I (symmetric opening) deformation of the corner regions and such deformation was found to be suppressed at the lower cor-
ners for the studied load case. The second (k2) value for the lower corner is about 0.91, corresponding to mode II (antisymmetric shearing) deformation and a weaker stress field than at the upper pinned corners. (In the experiments the lower corners of the test specimens were also blunt rather than perfectly square, which further reduced the stress concentrations there.) Consequently, since the only difference between the investigated models was the number of grooves, the same fracture mechanics criterion could be used for all cases. The upper groove corners were identified as the critical ones and, since the stress levels at the corners are mesh dependent, specific concern was made to use similar mesh refinement at all studied sites with singular stresses. 6. Results from numerical analysis The stress distributions parallel and perpendicular to the direction of the applied displacement in a panel with 4 grooves are illus-
A. Lindström, S. Hallström / Composite Structures 92 (2010) 2676–2684
a
c
b
e
2681
d
f
g
300
Load [kN/m]
250 200 150 100 50 0
0
5
10
15
20
Displacement [mm] Fig. 5. Failure progression in panel with 4 grooves. (a) d = 1.4 mm, (b) d = 1.7 mm, (c) d = 2.4 mm, (d) d = 4.9 mm, (e) d = 7.8 mm (f) d = 9.9 mm, (g) load–displacement curve, with a–f marking the corresponding photo of damage progression.
trated in Fig. 7. Fig. 8 illustrates the stress in the parallel direction on the loaded edges of panels with 4 and 19 grooves. It is clearly seen that the grooves introduce stress concentrations at the salient corners on the loaded edge for the panels. The lower re-entrant corners of the grooves are obviously sites of singular stresses as well. However, the studied configurations and load cases are such that the re-entrant corners are exposed to very limited deformations. The stress distribution on the loaded edges is therefore not only dependent on the area reduction, but also on the stress singularities caused at the corners. The salient corners of a panel with pinned boundary conditions have as already mentioned a theoretical k value of 0.711, whereas the results from the FE analysis was 0.708 ± 0.003. It should be noted that the k value decreased slightly with an increasing number of grooves. A plausible explanation is that the stress fields of neighbouring corners start to interfere when the distance between grooves becomes small. The influence of the area reduction and the stress singularities on the peak load is illustrated in Fig. 9, where the failure load from experiments is plotted together with results from the FE fracture mechanics anal-
ysis and strength predictions according to a simple mean stress criterion. 7. Discussion All panels with triggers exhibited lower peak load than the reference panels. The reduction was however moderate for panels with 4, 9 and 14 grooves while it was more significant for panels with 19 grooves and panels with chamfered face sheets. For the latter the peak load reduction was more than 50% and the drop from peak to plateau load levels was also gradual. For all other panels the load dropped instantly from peak to plateau level. It should be noted that the scatter in peak load of the panels with 4 grooves was relatively high. Two panels failed at peak loads higher than the reference panels, whereas the peak loads of the other two panels were lower than expected. One of the stronger panels failed at the edge without grooves, which indicated that 4 grooves were insufficient to ensure triggering of the studied cases. The other configurations showed surprisingly low scatter.
2682
A. Lindström, S. Hallström / Composite Structures 92 (2010) 2676–2684
a
c
b
e
d
f
g
400
Load [kN/m]
350 300 250 200 150 100 50 0
0
5
10
15
20
Displacement [mm] Fig. 6. Failure progression in panel with 9 grooves. (a) d = 1.5 mm, (b) d = 1.6 mm, (c) d = 3.3 mm, (d) d = 5.0 mm, (e) d = 8.3 mm, (f) d = 9.9 mm, (g) load–displacement curve, with a–f marking the corresponding photo of damage progression.
Fig. 7. Stress distributions on panel with 4 grooves; (a) perpendicular to and (b) parallel to the direction of the applied displacement.
Somewhat unexpected, all triggered panels also showed higher plateau load levels than the reference panels. The energy absorption up to 20 mm compression was also higher for all panels with triggers, in spite of their lower peak loads. The increase of plateau load for the panels with chamfered face sheets was however lower than for the panels with grooves. It can fur-
ther be noted from Fig. 3 that the plateau load increased with increasing deformation for panels with 4 and 9 grooves, but dropped for panels with 19 grooves. For the reference panels and panels with 14 grooves the plateau levels were virtually constant. The plateau level for panels with chamfered edges initially decreased but then increased towards the end of the com-
2683
A. Lindström, S. Hallström / Composite Structures 92 (2010) 2676–2684
upper edge lower edge
1500
1000
500
0
b Stress [MPa]
Stress [MPa]
a
upper edge lower edge
1500 1000 500
0
0.02
0.04
0.06
0.08
0.1
0
0
x−coordinate [m]
0.02
0.04
0.06
0.08
0.1
x−coordinate [m]
Fig. 8. Stress parallel to the direction of the applied load along loaded edges for panels with (a) 4 and (b) 19 grooves.
Critical load [kN/m]
500 450 400 350 300 250
0
5
10
15
20
Number of grooves b Q and area reduction P b r , and Fig. 9. Predicted peak load due to corner singularity P b exp . experimental value P
pression phase. The reasons behind these differences were not elucidated by the presented study. The chamfered face sheets buckled away from the core, as seen in Fig. 4, since the chamfering caused skew loading of the face sheet edges. The relatively low plateau load for these panels was likely correlated with the large face sheet deflections. The face sheets on the panels with grooves remained more straight, leading to more localised crushing and likely also to the observed higher plateau load levels. However, after prolonged compression some of the panels with chamfered face edges reached plateau levels more similar to the panels with grooves. In general, one would expect the plateau load for all panels to approach similar levels after certain compression, since the effects caused by triggering are unlikely to remain long after the damage has progressed beyond the triggered regions. Tendencies towards similar plateau levels at large deformations are visible in Fig. 3 for panels with 4, 9 and 14 grooves, two of the chamfered panels and two reference panels. However, the panels with 19 grooves showed no such tendencies but rather displayed a monotonically decaying plateau load. The responses from all four specimens were strikingly consistent and no explanation for this decay was found in the study. The peak loads of the panels with grooves were not reduced in proportion to the area reduction. The area reduction of the panels with 4, 9, 14 and 19 grooves were approximately 7%, 15%, 24% and 32%, respectively. The peak load reduction, however, was only 0.5%, 4%, 8% and 27%, respectively. Fig. 9 indicates that the peak load is governed by the stress intensity at the corners for panels with few grooves, but by the average stress for panels with many grooves, and that some failure mechanism transition occurs in between. As shown in the figure the critical load due to corner stress singularities is calibrated with results from the reference panel. However the trend of the results came out similarly when the panels with 4 grooves were used for calibration of the criterion. The influence of the grooves on the local stress is clearly shown in Figs. 7 and 8. During compression the material between the
grooves tend to expand transversely with respect to the applied displacement, due to Poisson’s effects. Since such deformation is restricted at the loaded boundaries the stress fields around the groove corners become singular, clearly seen in Fig. 8a. The boundary effects are more pronounced for panels with more grooves. The stress levels at the opposite edge without triggers is naturally independent of the number of grooves, whereas the stress levels increase at the upper edge with increasing number of grooves. It should be noted that the peak stress levels in the models are mesh dependent due to their singular nature. All corner areas were however modelled with similar mesh refinement at the corners, which justified comparisons. 8. Conclusions The peak load for SMC/balsa sandwich panels loaded in in-plane compression was clearly reduced when triggering features were introduced. In addition the specific energy absorption of sandwich panels with triggers was increased in comparison to that of reference panels without triggers. Chamfered edges reduced the peak load more than grooves. Grooves, on the other hand, increased the subsequent plateau load levels and, consequently, the energy absorption more. As few as 4 grooves did not ensure damage initiation where intended in the studied panels. Panels with 9 grooves showed the highest average specific energy absorption in the study. The difference between the panels with 9 and 14 grooves, however, was relatively small and not statistically certain. A transition of failure mechanisms was found in the analysis, suggesting that the peak load was governed by the stress concentrations on the loaded edges for panels with no or few grooves but governed by the average stress for panels with many grooves. The overall trend from the experiments correlates well with the analysis, considering the scatter among the experimental results. Acknowledgement The authors gratefully acknowledge Rieter Automotive Management AG for supporting the presented work. References [1] Farley GL. Energy absorption of composite materials. J Compos Mater 1983;17:267–79. [2] Mamalis AG, Robinson M, Manolakos DE, Demosthenous GA, Ioannidis MB, Carruthers J. Review crashworthy capability of composite material structures. Compos Struct 1997;37(2):109–34. [3] Fleck NA, Sridhar I. End compression of sandwich columns. Composites: Part A 2002;33:353–9. [4] Mamalis AG, Manolakos DE, Ioannidis MB, Papapostolou DP. On the crushing response of composite sandwich panels subjected to edgewise compression: experimental. Compos Struct 2005;71:246–57. [5] Lindström A, Hallström S. In-plane compression of sandwich panels with debonds. Compos Struct 2010;92(2):532–40.
2684
A. Lindström, S. Hallström / Composite Structures 92 (2010) 2676–2684
[6] Alghamdi AAA. Collapsible impact energy absorbers: an overview. Thin-Walled Struct 2001;39:189–213. [7] Carruthers JJ, Kettle AP, Robinson AM. Energy absorption capability and crashworthiness of composite material structures: a review. Appl Mech Rev 1998;51(10):635–49. [8] Hull D. A unified approach to progressive crushing of fibre-reinforced composite tubes. Compos Sci Technol 1991;40:377–421. [9] Thornton PH, Jeryan RA. Crash energy management in composite automotive structures. Int J Impact Eng 1988;7(2):167–80. [10] Pitarresi G, Carruthers JJ, Robinson AM, Torre G, Kenny JM, Ingleton S, et al. A comparative evaluation of crashworthy composite sandwich structures. Compos Struct 2007;78:34–44.
[11] Stapleton SE, Adams DO. Crush initiators for increased energy absorption in composite sandwich structures. J Sandwich Struct Mater 2008;10(4):331–54. [12] Velecela O, Found MS, Soutis C. Crushing energy absorption of GFRP sandwich panels and corresponding monolithic laminates. Composites: Part A 2007;38:1149–58. [13] Lindström A, Hallström S. Energy absorption of sandwich panels subjected to in-plane loads. In: 8th Biennial ASME conference on engineering systems design and analysis. ASME; 2006. [14] ABAQUS. Online users manual, version 6.7; 2007.