Modeling of the Effect of Plasticity on the Response of Pipe Systems to Internal Explosions

Abstract

Pipe systems that are used in the process industry may occasionally be subjected to internal deflagration and detonation waves. In those cases the design of the pipe system should be explosion resistant or even explosion proof. The usual design rule for the analysis of the mechanical response is based on the hoop stress calculated with an equivalent static pressure load, which depends on the magnitude of the detonation pressure. However, it has been found that the response of a pipe to a traveling detonation wave shows a number of effects that lead to much higher stresses. See [1] and [2]. One of these effects is mode coupling, i.e., the excitation of circumferential bending modes, coupled to the initial hoop stress or breathing mode, which may lead to an increase of the local maximum stress by a factor 2.6. Mode coupling has been investigated theoretically for rings and it has been demonstrated also experimentally, among others by Li c.s. [5]. Using finite element modeling we have investigated under what conditions mode coupling can occur in pipes in which a detonation wave propagates. It appears that a condition for mode coupling in a 3D configuration is that the detonation velocity is larger than the first critical velocity Vc0. For a pipe section of limited length mode coupling will be enhanced by the flanges at both boundaries which reflect flexural waves that propagate in axial direction. Furthermore, the effect of limited plasticity has been investigated. The results show that mode coupling is being reduced by plasticity. The conclusion is that with plasticity the detonation load can be larger without bursting of the pipe. However, mode coupling will still occur in spite of plastic deformation. In the paper the modeling of 2D mode coupling is presented and compared with the theoretical analysis. Moreover, the extension of the model to a pipe with a finite length and an “infinite pipe” is discussed and the effect of plasticity is analyzed. The analysis incorporates the influence of the material strain rate sensitivity and it considers the response for regular structural pipe steel as well as high strength steel.