On the Adequacy of Shell Models for Predicting Stresses and Strains in Thick-walled Tubes Subjected to Detonation Loading

This paper analyzes the adequacy of shell models for predicting stresses and strains in thick-walled tubes subjected to detonation loads. Of particular interest are the large axial strains which are produced at the inner and outer surfaces of the tube due to bending along the tube axis. First, comparisons between simple shell theory and a static finite element model are used to show that the axial strain varies proportionally with wall thickness and inversely with the square of the axial wavelength. For small wavelengths, this comparison demonstrates nonlinear behavior and a breakdown of the shell model. Second, a dynamic finite element model is used to evaluate the performance of transient shell equations. This comparison is used to quantify the error of the shell model with increasing wall thickness and show that shell models can be inaccurate near the load front where the axial curvature is high. Finally, the results of these analyses are used to show that the large axial strains which are sometimes observed in experiments cannot be attributed to throughwall bending and appear to be caused instead by non-ideal conditions present in the experiments. NOMENCLATURE a Mean tube radius h Wall thickness E Elastic modulus G Shear modulus E/2(1+ν) L Tube length u Axial displacement υd Dilatational Wave speed √ E/ρ(1−ν2) υs Shear wave speed √ κG/ρ υco First critical wave speed w Radial displacement wb Component of radial displacement due to axial bending ws Component of radial displacement due to transverse shear z Radial distance from middle surface of tube β Shell thickness parameter h/ √ 12a εθ Hoop strain εx Axial strain κ Shear correction factor, taken to be 5/6 ν Poisson’s ratio ρ Density of tube ψx Angular deformation of tube