# EXPERIMENTAL AND NUMERICAL STUDY OF THE ENERGY ABSORPTION CAPACITY OF PULTRUDED COMPOSITE TUBES

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3 Figure 2: a, b. circular tube with triggering type 1 of 45 o and type 2 of 60 o. c, d. square tube with triggering type 1 of 45 o and type 2 of 20 o. For the experiments a 100KN INSTRON 4505 was used. The velocity of the compression test was 200mm/min. Force versus displacement was measured and the specific energy absorption was calculated from the formula: E S = Ed ρl S = LS FdL ρl S 0 J kg Where Ed is the dissipated energy, Ls is the deformation length, F is the force and ρ is the linear density of the tube. The specific energy was calculated for 50 mm crushing. 3. NUMERICAL MODELLING The LS-DYNA [10] code was used in conducting all the simulations. For all the models shell elements were used, simulating the different types of triggering. The Belyschko Tsay quadrilateral element was used to model the tubes. The meshed shell elements were located at the mid-plane of each tube and in case of triggering 1 for all the models the top edge of the tube had an angle of 45 o in order to simulate the initiation of the damage Material Model The material model 54 of LS-DYNA was selected to model both the tubes. Material model 54 has the option of using either the Tsai Wu failure or the Chang Chang failure criterion for assessing lamina failure. The Chang Chang criterion is the modification of the Hashin s failure criterion [7].The post-failure conditions in the Material 54 model simulates four types of failure (i.e., tensile fiber mode, compressive fiber mode, tensile matrix mode and compressive matrix mode). If fiber breakage and/or fiber matrix shear failure occurs in a lamina, both the lamina s transverse modulus and minor Poisson s ratio are reduced to zero, the change in the longitudinal modulus and shear modulus follows the Weibull distribution. If matrix failure occurs either in tension or (1)

4 compression, then the transverse modulus and minor Poisson s ratio are reduced to zero, while the longitudinal modulus and shear modulus remain unchanged [7]. The mechanical properties of the tubes are given in Table 2. The properties were measured after conducting tests on specimens made by the same material of the tubes. Table 2. Material model parameters Density (kg/m 3 ) ρ 1900 Longitudinal modulus (Pa) Ea 33.5e+09 Transverse modulus (Pa) Eb 8e+09 In-plane shear modulus (Pa) Gab 5.5e+09 Out of plane shear modulus (Pa) Gbc 5.5e+09 Minor Poisson s ratio vab 0.29 Longitudinal tensile strength (Pa) X T 400e+06 Longitudinal compressive strength (Pa) X C 200e+06 In-plane shear strength (Pa) S C 25e Boundary Conditions The bottom of the tube was constrained by the *RIGIDWALL_GEOMETRIC_FLAT command in order to simulate the plane where the tube is standing on while the modeled upper end was free and subjected to compression by a moving plate. The loading plate was modeled as *MAT_RIGID. The density of both loading plate and tube were scaled up by factor 1000 for the purpose of computation efficiency, while still maintaining a quasi-static condition [7, 11]. It was observed that the ratio of the total kinetic energy to the total internal energy was less than 4% during the crushing process. The loading plate was displaced using the *BOUNDARY_ PRESCRIBED_ MOTION_ RIGID command at a constant rate of 200mm/min. The contact algorithm *CONTACT_ CONSTRAINT_ NODES_ TO_ SURFACE was used to simulate the boundary conditions between the plate and the tube. 4. RESULTS In the Figures 3 to 8 the comparison can be seen between numerical and experimental results. Visually the deformation of the circular tubes matches with the deformation in the experiments. In the square tubes there is no initiation of failure in the corners of the geometry as it was observed in the experiments and it is one of the reasons that the numerical curve differs from the experimental (Figures 7-8). Comparison of the force vs. displacement curves shows relatively good agreement between the numerical and the experimental results. In all numerical models the peak force was more or less the same with the peak force in the experiments. On the other hand the prediction of the absorbed energy for a crushing distance of 0.05m is not very accurate as it can be seen in Table 3, one of the main reasons is that no friction mechanism was taken into account and also the use of shell elements in combination with the material model do not simulate accurately the mechanisms of fracture and delamination. The effect of triggering can be seen on Table 3 and Figure 9. The tubes that absorb the most energy are the square with triggering 2 and the 38mm circular with triggering 1. In order to choose energy absorber for high velocity impact from quasistatic testing the most effective tubes are the two circular tubes(38mm and 50mm) with triggering 2

5 because the force is not increasing rapidly and it is easier to initiate the failure. In general triggering 2 is most effective in initiating damage. Table 3. Absorbed energy for 0.05m crushing distance Experimental Numerical Difference 38mm_triggering_ Joule Joule 24.08% 38mm_triggering_ Joule Joule 0.47% 50mm_triggering_ Joule Joule 20.25% 50mm_triggering_ Joule Joule 24.99% Square_triggering_ Joule Joule 12.02% Square_triggering_ Joule Joule 21.85% Figure 3: The force vs. displacement for the tube of 38mm with triggering 1. Figure 4: The force vs. displacement for the tube of 38mm with triggering 2.

6 Figure 5: The force vs. displacement for the tube of 50mm with triggering 1. Figure 6: The force vs. displacement for the tube of 50mm with triggering 2. Figure 7: The force vs. displacement for the square tube with triggering 1.

7 Figure 8: The force vs. displacement for the square tube with triggering 2. Figure 9. Experimental load-displacement curves. 5. CONCLUSIONS Summarizing the results of this study it was found that finite element analysis can be used as a design tool and is able to give relatively accurate results considering that the finite element models are simply designed and are mainly based on the mechanisms of material model that was used. The results from this study can be used for further research on impact and blast load in order to choose an effective energy absorber. It was observed that the two circular tubes with triggering 2 seem to be the most effective ones because the peak force is low and not reached rapidly as a result the energy absorber will be deformed easier. The experimental results give also an estimation of the force that is required to achieve failure and initiate the damage.

8 REFERENCES 1- S. R. Guillow, G. Lu, R. H. Grzebieta, Quasi-static axial compression of thin-walled circular aluminum tubes, International Journal of Mechanical Sciences 43 (2001) M. Langseth, O. S. Hopperstad, T. Berstad, Crashworthiness of aluminum extrusions: validation of numerical simulation, effect of mass ratio and impact velocity, International Journal of Impact Engineering 22 (1999) 829} A.M. Elgalai, E. Mahdi, A. M. S. Hamouda, B. S. Sahari, Crushing response of composite corrugated tubes to quasi-static axial loading, Composite Structures 66 (2004) A. G. Mamalis, D. E. Manolakos, M. B. Ioannidis, D. P. Papapostolou, Crashworthy characteristics of axially statically compressed thin-walled square CFRP composite tubes: experimental, Composite Structures 63 (2004) A. G. Mamalis, D. E. Manolakos, M. B. Ioannidis, D. P. Papapostolou, The static and dynamic axial collapse of CFRP square tubes: Finite element modeling, Composite Structures 74 (2006) H. G. S. J. Thuis & V. H. Metz, The influence of trigger configurations and laminate lay-up on the failure mode of composite crush cylinders, Composite Structures 25 (1993) Haipeng Han, Farid Taheri, Neil Pegg, You Lu, A numerical study on the axial crushing response of hybrid pultruded and ±45 braided tubes, Composite Structures 80 (2007) Hong-Wei Song, Zhi-Min Wan, Zhi-Min Xie, Xing-Wen Du, Axial impact behavior and energy absorption efficiency of composite wrapped metal tubes, International Journal of Impact Engineering 24 (2000) 385} M. Guden*, S. Yu ksel, A. Tas_demirci, M. Tanog lu, Effect of aluminum closedcell foam filling on the quasi-static axial crush performance of glass fiber reinforced polyester composite and aluminum/composite hybrid tubes, Composite Structures 81 (2007) LS-DYNA keyword user s manual, V971, LSTC, Livermore, CA, Feixia Pan, Jiansen Zhu, Antti O. Helminen, Ramin Vatanparast, NOKIA Inc., Three Point Bending Analysis of a Mobile Phone Using LS-DYNA Explicit Integration Method, 9th International LS-DYNA Users Conference.

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