On large deformation, damage and failure of ductile plates to blast loading

This paper concerns the irreversible deformation and failure of metal plates to brief, but intense, dynamic (impulsive) load encountered in an air-blast. Hitherto, nearly all of the dynamic structural plasticity models of ‘fully-clamped’ plate only calculates its inelastic (mode I) deformation but have largely ignored damage and failure – exemplified by the partial and/or complete detachment (modes II*, II and III) of a plate from its support through material rupture – that occurs when the blast load is sufficiently intense. An analytical model that captures all three modes of the plate deformation is developed in this paper where emphasis shall be on providing the simplest formulation that contains all the essence of a material and deformation effect needed to quantify the problem. The proposed model adopts an energy density failure criterion of Shen and Jones [19] to delineate the various inelastic failure modes; employs the constitutive framework of limit analysis for simplicity; accounts for the simultaneous influence of bending, membrane stretch and transverse shear through an interaction yield criterion; and, include the effects of strain rate on the material flow stress through the Cowper–Symonds relation. Accuracy of model predictions for square mild-steel plates are assessed through comparison with results from finite element analysis, and experimental data compiled from the literature for a range of impulsive load intensities – they will be shown to be in good general agreement. Design maps delineating the different deformation régimes for different combinations of blast impulse and length versus thickness ratio are constructed for plates of equal mass.