QUASI STATIC AND DYNAMIC AXIAL COMPRESSION BEHAVIOUR OF METALLIC TUBES

Abstract

This study is based on the quasi-static and dynamic axial compression behavior of thin walled mild steel tubes. The energy absorption characteristics and modes of deformation of the mild steel tubes of circular and square cross-sections have been studied under quasi-static, drop impact and projectile impact loadings by performing the finite element computations. The results thus obtained have been validated by carrying out experiments under each loading condition studied numerically. A detailed comparative study has also been performed to describe the axial deformation of equivalent mild steel and 7075-T651 aluminum tubes subjected to 350 kg drop weight impact. The axial crushing behaviour, energy absorption characteristics and the modes of deformations of different geometric sections have been studied, and the response of the two identical sizes with different geometries have been compared. The experiments have been performed to study the axial compression behavior of thin walled mild steel tubes considering circular and square cross-sections. The circular tubes (40, 63, and 75 mm diameter) and square tubes (31.63, 49.69, and 59.12 mm edge length) had equivalent cross-sections, total length (200 mm) and wall thickness (1 mm). These tubes were subjected to drop weight impact of mass 278 kg at incidence velocities in the range 3.11-7.71 m/s and the projectile impact of mass 5 kg at incidence velocities in the range 26-75 m/s maintaining equivalent impact energy. Both circular and the square tubes were also tested under quasi-static loading at a rate of 0.2 mm/sec. Three-dimensional numerical simulations were performed using ABAQUS/Explicit finite element code, and the constitutive and damage behaviour of the mild steel tubes under impact loads as well as under quasi-static loads was incorporated using the Johnson-Cook constitutive and fracture model. All the numerical results were also validated experimentally in order to describe the effectiveness and efficiency of the finite element simulations. The finite element computations have been further carried out on some other geometries of equivalent circular (40, 60 and 80 mm diameter) and square cross-sections (31.63, 47.34, and 63.05 mm edge length) of thin-walled mild steel tubes by a different drop hammer (350 kg) and projectile (5.13 kg) to examine the behavior of various cross-sections of each geometry of tubes keeping wall thickness (1 mm) and length (200 mm) constant. In addition, a comparative study has been conducted numerically to describe the axial deformation behaviour of mild steel and 7075-T651 aluminium tubes against 350 kg drop weight falling from different heights (0.67-4.78 m). Three different cross-sections of the circular (55, 70 and 85 mm diameter) and the square tubes (43.41, 55.19 and 66.97 mm edge length) have been i considered to ascertain the effect of varying cross-sections with respect to the axial compression, deformation mode and energy absorption for the two different materials studied. The validation of the computational and the constitutive models has been carried out under the ballistic impact loading by comparing the total axial compression, under the drop impact loading by comparing the total axial compression, impact force and support reaction and under quasi-static loading by comparing the load displacement behavior. A close correlation between the actual and predicted modes of deformation and the magnitude of the axial compression has been found under quasi-static, drop weight and projectile impact loading. The axial shortening of the circular mild steel tubes decreased while the absorbed energy increased with an increase in the diameter when subjected to the drop weight and the projectile impact loading. For a given impact energy, the axial shortening of the circular tube was higher under the drop weight impact than under projectile impact loading. However, the energy absorption in the tube was almost same under both the loading conditions. For the square mild steel tubes, the axial shortening of the tube decreased with an increase in the edge length whereas the absorbed energy did not show any significant influence of the size of square tube under both drop weight and projectile impact. For a given impact energy, the axial deformation of the square tubes was higher under drop weight impact than under the projectile impact loading. For a given impact energy, the axial compression was higher in the square tubes than that of the circular tubes of equivalent cross-sections while the energy absorption was higher in the circular tube than that of the square tube of equivalent cross-sections. As the size of the tube reduced, the difference of energy absorption between the two geometries increased. The difference between the absorbed energies of the two geometries was higher under drop weight impact than under the projectile impact loading. For all the circular tubes, a concertina mode of deformation occurred during the initial stage, and with the increase in the projectile velocity, the visible diamond mode of formation developed at a later stage. A similar mode of deformation occurred due to drop weight impact but these diamond formations were not clearly visible due to substantial collapse of the tube. The progressive folds under both the impact loadings occurred in a symmetric manner for all the square tubes of varying cross-sections. The crushing of the smaller size tube started at a faster rate leading to collapsing of the folds which resulted in the final crushing of the tube under drop weight impact loading. The collapsing mechanism of the tube under projectile impact was found to be almost same to that of the drop weight impact but the crushing of the tube was not so severe (the final crushed length of the tube is smaller). ii For a given axial compression, the highest energy absorption was found under the projectile impact loading than the drop weight impact loading and the least energy absorption was found under the quasi-static loading describing the influence of loading rate. For both the metallic tubes, the axial compression of 7075-T651 aluminium and mild steel circular tubes decreased with an increase in the diameter of the tube. While the energy absorption increased with an increase in the diameter of the tubes. Thus, the larger diameter tubes described higher crashworthiness than the lower diameter tubes. The axial compression in square tubes has been found to be higher than the circular tubes of equivalent cross-sections. For both the metallic tubes, the axial compression in the square tubes decreased with an increase in the square cross-section edge length (size) of the tubes. While the energy absorption increased with an increase in size of the square tubes. Consequently, the large cross-sectional square tubes described higher crashworthiness than the smaller one. The energy absorption in the circular tube has been found to be higher than the square tubes of equivalent cross-sections, i.e., the circular tube described higher crashworthiness than the square tube. Further, the axial compression in 7075-T651 aluminium tubes has been found to be higher than the mild steel tubes while the energy absorption in mild steel tubes has been found to be higher than 7075-T651 aluminium tubes describing that the mild steel tube is a better energy absorber.