Saturated Impulse For Ship Plates Under Blast Loading

In general,the explosive loadings imposed on the ship plates are represented only by the maximum load and total impulse of the loading pulse.However,the research on saturated impulse shows that the total impulse design based on the loading pulse is inaccurate.Only the part of the impulse less than the value of saturated impulse has an influence on the permanent deformation.Hence,the prediction of the large deformation of ship plates is more reasonable and accurate when taking the effect of the saturated impulse into account.In this paper,detailed parametric studies of saturated impulse for square plates under rectangular pressure pulse are conducted;the saturated impulse for stiffened square plates under rectangular pressure pulse are also investigated;finally the air blast tests for square steel plates are performed.The obtained results are outlined as following:?1?Based on the finite element numerical simulations by excluding the effects of strain rate sensitivity,it can be concluded that the saturated impulses of square plates and stiffened square plates under rectangular pressure pulse obey scaling laws.The empirical formulae for the permanent deflection of three sets of geometrically similar plate structures are proposed.?2?A rigid-plastic analysis is proposed to quantify the stiffening effects on saturated impulse caused by the strain rate sensitivity and strain hardening.Two stiffening factors n₁ and ₂n,which characterizes the stiffening effect of strain rate sensitivity and strain hardening are suggested respectively.An integrated stiffening factor n retaining both strain rate sensitivity and strain hardening is also presented.A quantitative relationship is found that the saturated displacement is inversely proportional to n and the saturated impulse is inversely proportional to n.Finally,the problem of non-scalability of saturated impulse of square plates under rectangular pulse caused by strain rate effect is solved by properly correcting the plate thickness.This plate thickness,when applied to the model,makes it able to assure the satisfaction of the scaling laws.?3?For square plates with same dimension,which are made of different yield-stress steels,under a pressure amplitude,the ratio of their saturated permanent deflection approximately equals the reciprocal of the ratio of their yield stresses;the ratio of their saturated loading duration for the maximum deflection approximately equals the reciprocal of the square root of the ratio of their yield stresses.For square plates which are made of the same steel and with the same side length while different plate thicknesses,under a pressure amplitude,the ratio of their saturated permanent deflection approximately equals the reciprocal of the square of the ratio of their thicknesses;the saturated loading duration is independent on plate thickness.A simple estimation of the dimensionless pressure amplitude is made for the onset of failure Mode 2 identified by Menkes and Opat^[90]for a square plate by using a rigid-plastic procedure.The relationships of dimensionless parameters related to saturated impulse between two square plates made of elastic-plastic materials,such as mild steel and aluminum,are similar.The rigid-plastic analysis is proved to be efficient to reveal the quantitative relationships related to saturated impulse.?4?The relationship of saturated impulse between different stiffener configurations is investigated.The ranking of their resistance to deformation is obtained.?5?The air blast tests of square plates are conducted and the results of pressure in free field and the final displacement of plates are obtained.Numerical simulations are performed and its comparison with the experimental results is satisfactory.Therefore,the finite element model is validated.