The Plastic Response of Rectangular Membrane Plates to Mild Explosive Loading Functions.

This report presents the results of an effort to determine the failure of flat plates under mild impulsive loads typically found in fuel air explosions. Such failure may occur according to the criteria associated with stress wave propagation or due to an excessive deflection associated with the dynamic response of the plate. Using an energy method and a membrane model, a set of equations describing dynamic plate response are presented. Experimental observations and results of plate failure, along with pressure-time histories of controlled gas bag tests, are reported. In the case of ductile metals, such aluminum, mild steel, and some stainless steels used in aircraft, radar vans, etc., the elastic portion of the stress-strain curve is quite small, and the assumption of a rigid-strain-hardening constitutive relation appears to be quite realistic. A potential function representing the plastic work and based on an initial membrane stress and strain-hardening was developed for an assumed deflection curve. Using a generalized forcing function, based on actual pressure time histories for fuel air explosions, and this potential function, equations of motion were formulated using lagrangian methods. Assumed deflection curves which satisfied given boundary conditions were used, and the resulting non-linear differential equation was solved using an analog simulation program. The equation yields center point deflections, which is associated with a plate criterion based on maximum elongation of the material. Center point deflection predictions using this model are in good agreement with experimental results. Plate failure is initiated at the edge of the plate and is predictable using the ultimate strain of the material and the membrane model.