Crash behavior of obliquely loaded aluminum extrusions

Transcription

1 Crash behavior of obliquely loaded aluminum extrusions A. Reyes, M. Lartgseth and O. S. Hopperstad Structural Impact Luboratoly (SIMLQ.b), Department of Structural Engineeringj Norwegian Universip oj Science and Technology, Norway Abstract The energy absorbing capability of obliquely loaded aluminum extrusions was studied through quasi-static experiments. Square aluminum columns in alloy AA6060 were clamped at one end and oblique load conditions were realized by applying a force with different angles to the centerline of the column. The primary variables were load angle, wall thickness and heat treatment of alloy. In addition, numerical simulations were performed and comparisons with the experimental results were satisfactory. Numerical simulations with other load angles than in the experiments were also carried out to supplement the experimental results. Introduction Energy absorbers are often used in vehicles to protect passengers and the structure itself during impact. A typical energy absorber is the crash box, designed to control the initial kinetic energy of the car during impact, while the force levels are kept sufficiently low to avoid permanent deformations in the rest of the car body. Studies of energy absorption through axial crushing and bending of columns have been completed over many years [1, 2]. However, during an actual crash event, the energy absorber will seldom be subjected to either pure axial or bending collapse, but rather a combination of the two modes. In an oblique impact, the crash boxes will be subjected to both axial forces and moments, which may lead to global bending of the crash box. This lowers the energy absorption and both moments and axial forces will be transferred to the rest of the structure.

2 Q5(-J 2002 WIT Press, Ashurst Lodge, Southampton, SO40 7AA, UK. All rights reserved.. iil llcrloljs1 11A,! shock </111[Illlpc[ct I [1 Introductory studies [3] on columns with the width to thickness ratio (M) ranging from 32 to 42 showed that the energy absorption was considerably lowered when introducing a load angle of only 5. It was therefore desirable to increase the thickness to get higher energy absorption. Consequently, in the present study, the energy absorbing capability of square aluminum columns subjected to oblique loading was investigated. Wall thickness, heat treatment of alloy (temper) and load angle have been the primary variables, while the mean load has been the main response parameter. A total of 72 quasi-static tests have been carried out. In addition, numerical analyses of all the experiments were carried out, as well as numerical analyses with other load angles than in the experimental program. Test program and experimental set-up Oblique loading was realized as shown in Table 1. The column was clamped at the lower end, and free at the top. The force was applied through a rigid body placed at the upper end of the column. A test-rig constructed for this purpose was used in the experiments [3], and the applied load angle was assumed almost conservative, i.e. with constant load angle, 6? Table 1 also shows the test specimen s geometry and the test program. The length and width of the test specimens were constant, 199 mm and 80 mm respectively. The square tubes were made of aluminum alloy AA6060. The effect of heat treatment of the aluminum alloy was investigated by testing two tempers, T4 and T6, which have different hardening behavior. Figure 1 shows typical engineering stress-strain curves for both tempers, obtained from standard tensile tests. T4 has a much lower yield stress than T6, but exhibits more strain hardening and is much more ductile. The wall thickness was varied between 1.9 mm and 4.5 mm, while the load angle varied between 5 and 30. The following identification system was used: T- dh-)1, where T stands for temper, 6 is the load angle, h is the wall thickness and )1 is the repetition number. The mean crush load was used as the response parameter to evaluate the columns energy absorbing capability. Table 1: Test program w mm IL--I

3 eng [N/mm2] , ~ \ 50 o Eeng~/o;5 Figure 1: Engineering stress-strain curves of tempers T4 and T6 Numerical analyses Numerical analyses were performed using the FE-code LS-DYNA [4]. The main objective was to show that the response of the test specimens could be predicted with sufficient accuracy. Due to symmetry, one half of the column was modeled using the Belytschko-Tsay shell element. The load was applied at the upper end of the specimen, through a rigid body modeled with shell elements. The free length of the specimens was 199 mm as in the experiments, and the rigid body 70 mm. All the degrees of tleedom were fixed at the lower end, while the upper end was fixed to the rigid body. Axial crushing of columns with the same geometry has been studied by Langseth et al [5], so the number of elements needed was based on these studies, and a total of 5280 elements were used. A proper description of the strain hardening properties of aluminum is necessary for a good correlation between the experimental and predicted responses of the obliquely loaded aluminum extrusions. The uniaxial true stressstrain behavior was fitted to a five-parameter model [3]. The rigid body was given a prescribed velocity field, which ensured that the loading took place gradually and that unnecessary dynamics in the numerical solution were avoided. Initial geometrical imperfections may have an influence on the peak load as well as on the energy absorption, so initial imperfections were prescribed both along the length and width of the model in the analyses. Based on the studies of Opheim [6], one half-sine wave across the width, and five half-sine waves along the length, with an amplitude of 0.1 mm, were applied in the numerical simulations. Analyses of all the experiments were carried out. Additionally, analyses with load angle 10, 2.5 and 90 were also performed to supplement the experimental results.

4 ~5~ Sllllcllfivs 1 tllkr <shock (1/7,/ It)lpact 1 11 Results and discussion When a tube is loaded axially, it can absorb energy by progressive buckling. As opposed to axial crushing, the obliquely loaded columns collapse globally after the creation of the first lobe. This leads to much lower energy absorption for thin-walled columns when introducing a load angle. One way to increase the energy absorption is clearly to increase the thickness. Therefore, the wall thickness in the experiments was varied from 1.9 mm to 4.5 mm and the effect of different tempers was also studied. Visual observations All the columns collapsed globally after the first lobe was developed. The development of the first lobe varied somewhat in the experiments: the compression flange would buckle either outward or inward. Although the buckle always was developed at the lower end of the column, there was a variation in the distance from the bottom of the column to the lobe. Figure 2 shows two specimens where the compression flange buckled outward, while the two sidewalls buckled inward. This was typical for specimens with thickness 3.5 and 4.5 mm in temper T6. The columns with wall thickness 3.5 and 4.5 mm in temper T4, however, typically experienced that the compression flange buckled inward. For thickness 2.0 and 2.5 mm, there was some variation in the deformation mode. Although the specimens in Figure 2 have the same deformation mode, in the sense that the compression wall buckled outward, one can see that there is quite a difference in the extent of the buckle, which can be considered as a plastic hinge. The lobe in the coiumn with temper T6 is much more localized than for the column with temper T4. This can be explained by the fact that T4 exhibits much more strain hardening than T6. Figure 2: Deformation modes for 15, h = 2.0 mm, tempers T6 (left) and T4 (right)

5 Incipient fracture was T No such behavior Energy absorption.yfrl/(rf(/lj,y I jder s/70(k([)ld /m,p(wf 1 // ~5-3 observed in the corners of all the repetitions of was found for temper T4. Typical force-displacement curves for a column with wall thickness 2.0 mm, and three different load angles are shown in Figure 3. The very high peak force corresponds to the buckling of the compression flange and then the force for a load angle of 5 drops drastically. The peak force decreases for larger angles. After a certain displacement, the curves with the same thickness and temper approach the same value. This behavior is the same for all the columns. Figure 4 a) shows the force-plastic displacement curves for a column with wall thickness, h = 2 mm and load angle, 19= 30 for tempers T4 and T6. There is clearly a difference in behavior of the two tempers, as temper T6 gets a much higher peak force and the force level falls more rapidly. Figure 4 b) is the same case, except that the wall thickness is 4.5 mm. The curves get a totally different shape when the wall thickness is increased. The force does not fall that quickly for T6. For temper T4, however, the force level remains higher than the initial force (when dp= O) for the whole displacement. The mean crushing force of axially loaded columns proposed by Abramowicz and Jones [7] for a rigid plastic material was calculated for the columns in the experiments. Here, a. is taken as the average value of the yield and ultimate stresses, Oozand ~, to account for the hardening of the material [8], here called co,.v~. Figure 5 and Figure 6 show the mean load for the experiments and the analyses, The mean load, which is defined as the energy divided by the displacement, is determined for a plastic displacement d,, =30 mm, see figure in Table 1. (1) 50 w 30 20<, o--, I, ~- r4 o d, [mm] Figure 3: Force-plastic displacement curves, h = 2.0 mm, T6

6 254.s1/1/, 1///, s I Ildel.Sho( k,lll[i lmpacl I t I 0 --A, I I I o a) d, :?] I 01 - T -.,. I. T -i b) d. /&] Figure 4: Force-plastic displacement curves. The calculated mean crushing forces for axially loaded columns, using eqn ( 1), are also included in the figure as the values for 6 = OO. The energy absorption ability drops by YO depending on wall thickness and temper, by introducing a load angle of 5. The drop in the mean load from (1 to 5 is decreasing with increasing wall thickness and is overall lower for T4 than for T6. As Figure 5 and Figure 6 also show, the mean load decreases with increasing load angle, i.e. when introducing more bending into the column. The mean loads from the LS-DYNA analyses are plotted in the figures as well. It is obvious that the mean loads predicted by LS-DYNA were lower than the experimental values. Analyses without initial imperfections have also been carried out for some of the cases. The results from these were either closer to the experiments, or were not affected by this change. The initial imperfections also have an effect on the peak forces. The peak forces for the analyses with the initial imperfections are in agreement with the experiments, while the analyses without initial imperfections overestimate the peak forces. Dimensional analysis gives four dimensionless parameters, i.e. n terms, for the present problem where, b is the width, h the wall thickness, L the load angle and Fme<l!l the mean force. 114 is proportional to the ratio between the mean force and a term which is related to the plastic moment pr. unit length of a plate element. H4 was calculated for all the experiments with both ~) = o&,~ and C% defined as [7] (2) (3) where & is the strain at the maximum stress level. Hd was then plotted vs. the load angle in Figure 7. This parameter exhibits limited variation for a constant

7 .Slmcillws [ 11(L 1,Yhock 1!11(/ltllp(lc t I 1[ 255 load angle especially when Q, is taken as defined in eqn (3). This implies that ~l(oo = eqn (3)) depends only on the load angle. H4(@ = c&), however, seem to depend on both the load angle and the temper. The figure also includes the theoretical values for axial crushing (0= 0 ) (from eqn (1)), and as expected the scaled mean force (114) is here a function of the bflz ratio (IIl). This indicates that a change in behavior takes place with respect to the effect of the plate slenderness when increasing the load angle. 80 J T4 - ~+---- Experiment, h=l.9 mm 60-- L Analysis, h=l.9mm ~ Experiment, h.2.5 mm ~ Jf h, -- a -- Analysis, h=2.5mm 8 j, ~ Experiment, h=3.5 mm ~ 40 +, Analysis, h=3,5mm. ~ Experimentr h=4.5 mm 4Q Analysis, h=4.5mm Theoretical model, h=l.9 ~,.1< : ;; : Theoretical model, h=2.5 I ~ A->-.:! Theorti@lmodel, h=3.5 % Theoretical model, h= o o~. ~- -, o Angle, 0 PI Figure 5: Mean force vs. load angle, temper T4 4) T6 ~ Experiment, h=l,9 mm Analysis, h=l.9mm L Experimentr h=2.5 mm 5 --A Analysis, h=2.5mm u ~ Experiment, h=3,5 mm E * Analysis, h=3.5mm +. ~ Experiment, h=4.5 mm s Analysisr h=4,5mm 5 : \ * Theoretical model, h=l.9 k 40: ~~:::::::-:;:-;:;::;: : ; E::*!;:: -.,. 0 +-~ --r- ~ Angle, 0 [01 Figure 6: Mean force vs. load angle, temper T6

8 ~5(j 2002 WIT Press, Ashurst Lodge, Southampton, SO40 7AA, UK. All rights reserved..\f/ ll<t/ll e.\ [ Ild, r.si1ocl (1?1([ [I?]pmr I I I. z T4 + T6 A T4 Theoretical model T6 Theoretical model o F 122mn Goh2 do r l LL...L r Angle, $ [01 T4 T6 A J L. T4 Theoretical model T6 Theoretical model 1 30 J I o+ o Ii ~ Angle, (3 [ ] Figure 7: Dimensionless mean force vs load angle Conclusions The crushing behavior of square aluminum columns subjected to oblique loads has been studied experimentally and numerically, and the following conclusions can be drawn:

9 The energy absorption drops drastically by introducing a load angle of5 and decreases further with increasing load angle. The shape of the force-plastic displacement curves changes when the wall thickness is increased. The large drop from the initial peak force disappears, and for temper T4, the force level remains higher than the initial force for the whole displacement. The deformation mode depends on temper and thickness. The dimensionless mean force, TI~, depends mainly on the load angle, when q is defined as in eqn (3). LS-DYNA predicted conservative values of the mean loads. Acknowledgements The authors would like to thank Hydro Automotive Structures for their generous support of the research project that forms the basis for the present work. Thanks are also given to Mr. T. Meltzer and Mr. J.T. Sundal who have provided technical assistance in the laboratory. References [1] Kecman, D, Bending collapse of rectangular and square section tubes, 1)71. Journal A4ech.Sci., Vol. 25, No. 9-10, pp , 1983 [2] Jones, N, Structural lnzpact, Cambridge University Press: Cambridge, 1989 [3] Reyes, A, Langseth, M. & Hopperstad, 0.S, Crashworthiness of aluminum extrusions subjected to oblique loading: Experiments and numerical analyses, 2001, prepared for publication [4] Hallquist, J.0, LS-DYNA Theoretical Manual, Livermore Software Technology Corporation, California, 1998 [5] Langseth, M, Hopperstad, 0.S. & Berstad, T, Crashworthiness of aluminuium extrusions: validation of numerical simulation, effect of mass ratio and impact velocity, Infemational Journal of Impact Engineering, 22, , 1999 [6] Opheim, B.S, Bending of Thin-Walled Alunzinunl Extrusions, Doctoral thesis, Department of Structural Engineering, Norwegian University of Science and Technology, Trondheim, 1996 [7] Abramowicz, W. & Jones, N, Dynamic progressive buckling of circular and square tubes, International Journal of Inlpact Engineering, 4(4):243-70, 1986 [8] Langseth, M. & Hopperstad, 0,S, Static and dynamic axial crushing of square thin-walled aluminium extrusions, ]ntemational Journal of impact Engineering, 18, , 1996