Linear Elastic Response of Tubes to Internal Detonation Loading

Abstract

This paper deals with the structural response of a tube to an internal gaseous detonation. An internal detonation produces a pressure load that propagates down the tube. Because the speed of the gaseous detonation can be comparable to the flexural wave group speed, excitation of flexural waves in the tube wall must be considered. Flexural waves can result in much higher strains and stresses than static loading with the same loading pressures. Experiments and numerical simulations were used to determine the structural response. In the experiments, a detonation tube was instrumented with a number of strain gages. A series of experiments was carried out under different conditions. Strains were measured that exceeded the equivalent static strain by up to a factor of 3Á9: Special attention was paid to the influence of the detonation speed, reflection and interference of structural waves at flanges and also at the tube end, the linearity of the response, the transient development of the deflection profile, and the influence of detonation cell size. Analytical models and finite element models were used to interpret the observations and to make quantitative predictions of the peak strain. #

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

“…The behavior of tubes near this critical velocity has been studied by numerous authors [4,11,12,20] who have found that a resonance between the traveling load and the speed of flexural waves results in highly amplified displacements, stresses, and strains. This critical velocity is the minimum phase speed of sinusoidal waves in the tube, and hence is located at the minimum of the lowest branch of the dispersion curve (see Fig.…”

“…This deformation is zero at the ends of the tube and reaches a maximum radial displacement of δ at the center. Deformation of this form is motivated by the sinusoidal vibrations that are observed behind a shock or detonation wave [4], which will be considered in more detail in Sec. 5.…”

“…For instance, Beltman et al used a steady-state shell model to analyze peak strains in thin (a/h = 16) tubes subjected to internal shock waves and found reasonably good agreement with finite element models and experimental measurements except in the vicinity of the first critical velocity, where effects of material damping are important and the steady-state approximation is inadequate [3,4]. Likewise Simkins measured hoop strains in a much thicker tube (a/h = 5.2) and found good agreement with the predictions of shell theory [5].…”

“…The structural response of tubes subjected to shock and detonation loads often features a dynamic load amplification [4,11,12] that leads to large stresses and strains near or behind the load front. The magnitude of these stresses and strains cannot be quantified using free-vibration analysis.…”

Response of Piping Tees to Propagating Detonations

“…Ideal detonations propagate at approximately the Chapman-Jouguet (CJ) detonation speed and the detonation pressure axisymmetrically loads the pipe. The structural response of a straight pipe to a detonation propagating at a constant speed was studied in depth by Beltman [5], but industrial piping systems are more complex.…”