| Magnetic flux compression generators rely on the expansion of thin ductile shells to generate magnetic fields. These thin shells are filled with high explosives, which when detonated, cause the shell to expand to over 200% strain at strain-rates on the order of ;A viscoplastic constitutive model is formulated to model the high strain-rate expansion and provide insight into the development of plastic instabilities. This model uses the Johnson-Cook strength model with the Mie-Gruneisen equation of state and a modified Gurson yield surface. The constitutive model includes the modifications proposed by Tvergaard and the plastic strain controlled nucleation introduced by Needleman. The constitutive model is implemented as a user material subroutine into ABAQUS/Explicit, which is a commercially available non-linear explicit dynamic finite element program. A cylindrical shell is modeled using both axisymmetric and plane strain elements.;Two experiments were conducted involving plane wave detonated, explosively filled, copper cylinders. Instability, displacement, and velocity data were recorded using a fast framing camera and a Fabry-Perot interferometer. Good agreement is shown between the numerical results and experimental data. An additional explosively bulged cylinder experiment was also performed and a photomicrograph of an instability is shown to provide a qualitative comparison between the experimental observations and the numerical predictions.;Observations from this research indicate the onset of a quasi-periodic pattern in the through-thickness equivalent plastic strain, which occurs early in the deformation process before the stress waves have attenuated. This quasi-periodic pattern continues to develop, eventually connecting the inner and outer surfaces, at which time quasi-periodic instabilities are observed on the surfaces of the shell. In addition, parameter studies performed as part of this research indicate relationships between the shell thickness, the number of instabilities, and the approximate time to failure. |
