Fracture prediction of thin plates under localized impulsive loading. Part I: dishing

A comprehensive analysis of deformation and fracture of thin plates subjected to localized impulsive loading is presented. The paper addresses many aspects of the problem including calibration for plasticity and fracture, and detailed description of three stages of dynamic response, i.e. dishing, discing and petalling. Because of a rather broad coverage, the paper is divided into two parts with a clearly defined focus of each part. In Part I, the transient response of the plates under a localized pulse loading was investigated analytically and numerically. A precise determination of the transient and permanent deformation of plates in the so-called dishing stage is important for the prediction of the onset of fracture, which will be dealt with in Part II. The final deflected shapes of the plates obtained numerically were shown to agree well with the wave type solution developed earlier by one of the present authors and the experimental results available in the literature. Several new aspects of the transient response of plates, not previously reported were identified and discussed. A comprehensive parametric study on the dynamically loaded plates with various spatial and temporal distributions of dynamic pressure was then conducted. It was observed that the permanent shape of the plate is strongly dependent on the spatial distribution of pressure loading. Furthermore, a comparison between the response of circular and square plates was also presented. In Part II, the onset of circumferential cracking and subsequent propagation of radial cracks were predicted analytically and numerically. The accumulated equivalent plastic strain with the stress triaxiality as a weighting function was introduced as a ductile fracture criterion. An accurate representation of the true stress–strain curve and the critical damage/fracture function for AH36 steel material were calibrated from tensile tests on round specimen and parallel numerical simulations. By calculating distributions and histories of stress and strain, the initiation site and extent of fracture were predicted by the present fracture criterion. It was clearly shown that the fracture pattern of thin circular plates consisting of discing followed by petalling can be predicted with great realism provided the fracture criterion is properly formulated.