LARGE DEFORMATIONS ON METALLIC SHELL STRUCTURES

Abstract

Shell structures made up of different materials are widely used in automotive, aerospace, heavy engineering, armoured and also in construction industry due to their better structural performance. Study of their large deformation behaviour is important for their use in critical design applications like nose cone of aircraft, launch vehicles and ballistic missiles, as these provide efficient energy absorption. In case of vehicles, shell structure takes major components of impact load during collision and undergoes plastic deformation, as a result the load transmitted to the inside electronic components is minimized. Shell structures response is very complex to different types of loadings. The participating parameters to responses are thickness, shape, diameter, diameter to thickness ratio and the physical state of the shell. Highly transient like impact and quasi-static loading makes the shell structure response more * complex. In light of their wide application in different areas, the researchers were attracted to carry out investigations in which the shell structures can be used in different application. In this dissertation different studies on metallic (aluminum) shells having different geometries are undertaken to examine the different deformation characteristics and associated Force-Displacement variation. The following cases of study have been carried out in the present research programme and results are presented herein. Study of contraction of tubes of different thicknesses, through die of varying entry semi apical angle to see the effect of tube and die parameters on large deformation characteristics. Study of inversion mode of deformation for shell structures having different geometrical features and different sections to explore the effect of these parameters on inversion process. Shells which are complex in manufacturing are also investigated. Axial compressions of shells having discontinuity and complexity in geometry are studied. The effects of shapes, material strength and contact friction on deformation characteristics are studied. Complex geometries which are difficult in manufacturing are studied analytically. On the basis of result obtained in above studies, a combination of mode of deformation of shells has been designed to improve the performance of crush can for its energy absorption characteristics. Study of different modes and mechanisms of deformations of tubes and comparison of their deformation characteristics. Studies on large deformation problems with highly transient in nature like bullet 40 speed attenuation to different shapes of dome and blast diffusion to different shapes of vehicle hull. In present study the experimental and numerical simulations are carried out for different studies as mentioned above. The samples were compressed in quasi static loading case and their load displacement graphs were recorded. The experiments were also simulated numerically using Finite Element (FE) code LS-Dyna. Some studies were carried out only using numerical simulation. The samples were made with spinning, machining and manufacturing process. All samples were made up of aluminium. The fixtures were made of steel and their purpose was to hold the samples in place and apply the specified loading. The machines used for experiments were INSTRON make universal testing machine of 4, 10 and 25 T capacities. To feed actual material properties of aluminium in simulations, the material test pieces of the samples were made as per ASTM E8 and tested to obtain respective stress strain curves. The different studies reported in this dissertation conclude the following; • The tube contraction through conical die is an interesting large deformation phenomenon. The contraction phenomena ctm affected by tube's as well on die's characteristics. It is observed that the die having entry semi apical angle with 5 degree offers more frictional resistance on tube and requires almost continuous rising force to continue the contraction process. With increasing entry semi angle, the force displacement graph rises sharply till the tube maneuvers the conical portion and then it stabilizes. • Inversion of different shells was studied in detail by studying the effect of geometrical features, cross sections and complex shapes. It is found that the geometrical features play an important role in deciding the shape characteristics of force displacement graph. It is found that the sections except circular and frusta, try to reshape themselves into a section having more edges than the parent section during inversion process. Moreover, it also found that the energy requirement increases with decrease in number of edges. Friction IV IV plays significant role in inversion during the self contact and contact between disjointed parts. The axial compression of the combined shells having two shapes (cylinder at top and conical at bottom) shows interesting deformation characteristics. The specimens having semi apical angle of bottom half less than 9 degree deformed by development of concertina folds in top cylinder portion. Specimens having 15 degree semi apical angle deformed by development of instability at neck (junction of top cylinder and flared bottom). With increased semi apical angle, (at 20 degree) inward inversion takes place. For 25 degree and higher value semi apical angle, curl out phenomenon was noticed. It is observed that the friction offered by base plate, affect the characteristics of deformation process. At higher friction at base, curl out process is changed to inversion. Introduction of geometrical features like step, depression, holes and step at the neck of 15 degree I semi apical shell, could lead the deformation with inversion. For sample with hump, the top cylindrical portion deforms while bottom portion deforms for samples having step, depression and holes. • The large deformation phenomend rim studied by combining more than two basic shapes. The top geometry is combination of cylinder at top and frusta at bottom. The bottom geometry is inverted crater/inverted spherical shell. The quasi static compression experiments are performed on these two separately as well by combining these two by weld. It is observed that top halve undergoes inversion starting from its neck while bottom halve undergoes inward dimpling when they are tested individually. Once they are joined, the behaviour changed to upward curl at bottom junction associated with b dimpling. When the shells having two steps and different semi apical angles are compressed, it is observed that with higher semi apical angle say 10 degree, inversion start at bottom step. The rolling hinge formed moves upward. The upward movement of rolling hinge has lower volume of hinge in upside, as the shape is conical. Due to reduction in hinge volume, the downward trend of graph is obtained. The semi apical angle of 5 degree leads inversion at top step and rolling hinge moves downward. The rolling hinge volume is more in downward direction and hence the upward trend of graph is noticed. Compression studies on geometrical metallic frusta by finite element simulation shows that the features and shapes play an important role in deciding characteristics of force displacement graph. It is observed that for the most of the 9' features the Force-Displacement graphs are not smooth except in case of few features lv like step. • Conventional crush can configuration is changed by plugging deformation mechanism of shells into it for improved performance. The mechanisms tried are 40 inversion and contraction of shells. The best worked out mechanism is tube contraction. • Comparison of deformation modes of tube having same specifications (outer diameter, inner diameter, length and material) shows lot of interesting characteristics of large deformations. Different deformation modes studied are bending, expansion, contraction, curl in/out, tearing, flattening and indenting. It is observed that the few deformation process like expansion and contraction starts with lot of perturbation on other hand process like bending and indenting have smooth Force-Displacement (F-H) graph. • The numerical study of bullet speed attenuation with different domes shows that the shallow dome could attenuate the maximum speed, while circular dome could attenuate minimum. The blast simulation on different vehicle hull shows that the triangular, parabolic and pentagonal shape hulls are effective in energy dissipation. The flat and wavy hull shapes are worst in performance. This knowledge could be deployed for better selection of shell structures, their better design and optimized way of utilization to develop a more efficient and economical energy absorbing device. The numerical simulation methodology could be used successfully to simulate large deformation phenomenc2 and can be deployed on those phenomena with confidence, for which experimentation is difficult.