Mechanism Of Strain Growth Phenomenon In Spherical Containment Vessel Subjected To Internal Blast Loading

Strain growth,which is a phenomenon often observed in the response of explosion containment vessels subjected to internal blast loading,threats the safety of the vessels.The resonance due to the periodic blast loading and the superposition of different vibration modes are the two causes of the strain growth.The mechanism of the strain growth is not fully investigated and few studies are on the strain growth in the plastic response.Aiming at these problems,the mechanism of the strain growth in spherical containment vessel is investigated through the experiments,numerical simulation and theoretical analysis in this paper.Experiments of the spherical containment vessels under blast loading are carried out.It is found that in the range of the scaled distance 0.36⁰.87m/kg^1/3 and equivalent density?explosion equivalent divided by vessel volume?0.36⁴.94kgTNT/m³,the periodic blast loading at the inner wall of the shell consists of three pulses and quasi-static pressure phase,and each pulse includes shock section and quasi-steady pressure section.The strain growth in elastic response and plastic response of the spherical shell is observed.For the strain growth in elastic response,it is found that the strain growth mainly results from the superposition of different vibration modes,the phenomenon at the pole opposite to the opening of the shell is the most serious along the shell,and the phenomenon causes the plastic response from the elastic reponse.For the strain growth in plastic response,it is found that the phenomenon mainly results from the resonance due to the periodic blast loading,the maximum strain peak appears during the second period of shell virabtion,and the phenomenon is mainly attributed to the first two pulses.Based on the experimental results,the simplified model of the periodic blast loading is proposed and the empirical diagrams or formulas of the time,scaled impulse of shock section,peak and quasi-static pressure of each pulse and the quasi-static pressure are obtained.It is found that the time of each pulse decreases and then increases with the scaled distance decreasing,dimensionless parameters of the peak and scaled impulse of shock section of the first pulse keep linear relations with the scaled distance in the logarithmic coordinates,the peak and scaled impulse of shock section of the second pulse are 0.27times and 0.5 times the size of those of the first pulse respectively,and the peak of the third pulse is 0.18 times the size of that of the first pulse.It is also found that the quasi-steady pressure of each pulse and quasi-static pressure keep linear relations with the equivalent density,the quasi-steady pressure of the first pulse is slightly smaller than the quasi-static pressure,and the quasi-steady pressures of the second and third pulses are approximately equal to the quasi-static pressure.The responses of the spherical shell under a single pulse and several pulses are investigated through theory analysis.And then,only based on the explosion equivalent and the size of the shell,the analysis method is proposed to resolve the key issues,containing the emergence of the strain growth and the maximum strain growth factor,which provides a quick and easy way to analyze the strain growth induced by the resonance due to the periodic blast loading.It is found that the strain growth phenomena in the shells of different thicknesses are the same in the elastic reponse with the explosion equivalent and spherical shell diameter unchanging,but not the same in the plastic response.It is also found that the maximum growth strain factor is 1.5 in the elastic reponse,1.25 in the large plastic reponse,and between 1.25 and 1.5 in the small plastic reponse.The mechanism of the strain growth induced by the superposition of the different vibration modes in the elastic response is systematically and deeply investigated by the sub-strains induced by bending modes and membrane modes,which provides a new method to study the strain growth.The theories on shell vibration and bending wave are used to explain the mechanism.Results are found as follows:?1?Bending waves are caused by differences between the movements of the perturbation and spherical shell,and the diffusion phenomenon occurs when bending waves propagate along.?2?The strain growth mainly results from the superposition of the breathing mode and the bending mode with close frequency.?3?The interaction between bending waves and membrane vibration influences the aptitudes and periods of bending strain and membrane strain curves.?4?The strain growth factor along the shell with the perturbation is spatially cyclic.?5?The strain growth factor at the pole is the largest in the whole shell.?6?New measures are proposed to restrain the growth strain,including avoiding perturbation completely constrained,reducing the size and weight of the perturbation,symmetrically arranging perturbations,etc.The plastic response caused by the strain growth is investigated through numerical simulation.It is observed that the strain growth causes the plastic response from the elastic response,and causes the plastic response from the former plastic response.The offset of mean line of the strain curve represents the plastic strain for the the strain growth induced the resonance due to the blast loading,but not for the the strain growth induced the superposition of different vibration modes because of the cyclic alternating compression and plastic reponse,and the offset maybe zero when the plastic response is caused by the latter strain growth.