Analysis of the deformation and failure of blast loaded unstiffened and striffened plates
Creators: name: Rudrapatna, Nagaraja
Publisher: name: University of British Columbia
Year: 2009

description: A numerical investigation into the deformation and failure of clamped unstiffened and stiffened mild steel plates is carried out. Studies indicate that with increasing load intensity, simple plate structures under blast loading exhibit the three general modes of failure: mode I (large inelastic deformation), mode II (tensile tearing and deformation) and mode III (shear rupture). The failure analysis of plate structures subjected to blast loading is still considered a difficult task. These problems are highly nonlinear due to the combined effect of large deformation, material plasticity and high strain-rates. The present work develops a semi-numerical model for failure prediction which is aimed at providing a simple tool for preliminary design/analysis of such structures. Analytical failure models have been incorporated in an existing finite element code which handles the large deformation, elastic-plastic transient behaviour of unstiffened and stiffened plate structures. The finite element formulation employs existing super finite plate and beam elements. An interactive failure model is proposed to predict the tearing and rupture of thin steel plates and stiffened plate structures under blast loading. The model accounts for the membrane and bending strains as well as the transverse shear stress experienced by the structure under the applied load. The interaction between the tensile tearing and shearing mode of failure is considered via an interaction relation between the strain and stress ratios. Two interactive failure criteria are considered, either Linear (LIC) or Quadratic (QIC) based on the way the ratios are added. The bending strain is estimated by assuming that a plastic hinge line develops at the boundary, while the membrane strain is calculated using the finite element prediction of the deformed profile. The total strain, composed of membrane and bending components, is then divided by a specified rupture strain for the material, to obtain the strain ratio. Since the finite element formulation is based on Kirchhoff plate bending theory, there is no direct prediction of shear strains (stresses). In order to achieve a continuous estimation of the shear force and stress along the plate boundary, a series of very stiff springs are introduced there. The use of high stiffness values effectively simulates the clamped boundary condition of the problem. The estimated shear stress is then compared to the ultimate shear strength of the material to form a stress ratio. A node release algorithm is developed to simulate the progression of rupture. The analysis is continued in the post-failure phase to account for the deformation which continues during the free flight of the torn plate. The predicted failure modes using the above model for blast loaded plate structures are presented and compared with previously published experimental data. The Quadratic Interaction Criterion predicts consistently better results than the Linear Interaction Criterion as compared to the experimental results. The results clearly indicate the influence of shear on the failure mechanism not only for mode III, but also for mode II. The results confirm the importance of the interaction effects of tensile and bending strain on tearing and shear failure.