Pipe Whip Research Articles

Continuum Solution of Simulated Pipe Whip Problem

The pipe whip problem is a highly nonlinear problem which, except for special conditions, is usually solved numerically. When a dynamic load is applied to the base of a pipe (striker) whose end impacts another pipe (target), it is possible for both the striker and the target to experience plastic deformations during impact. A finite element solution considering the nonlinear impact problem with material nonlinearity has been carried out. At the point when the material becomes plastic, high frequency oscillations can set up in the continuum model. Experimental data indicate that these oscillations quickly disappear due to material damping. The effects of plasticity are considered, as are Rayleigh damping and nonlinear damping in the target material.

On the 3-D non-linear analysis of piping

The computer program PAULA for the 3-D non linear analysis of piping is considered with particular reference to the finite elements library (straight pipe, elbow, T-joint, transition, restraint, non-linear superelement). The particular cases of the earthquake and pipe whip analysis are briefly discussed, in the latter case some attention is given to the relative merits of 2-D and 3-D analyses.

An elasto-plastic elbow element—Theory and applications

An original elasto-plastic elbow element has been formulated and developed for inclusion in the library of a finite element code. The main features of the element are based on the following theoretical aspects: Theory 1. (a) Vlasov's thin shell theory 13 is used to correlate generalised strains and mid-thickness displacements. 2. (b) The displacement field is represented by means of a Fourier expansion in the circumferential direction, while a finite difference method is used to compute the derivatives of Fourier coefficients along the azimuthal direction. 3. (c) The flow rule is given in terms of stress resultants and generalised strains; in formulating the stress-strain flow rule, the Iliouchine 14 yield locus theory is used, together with a normality rule. The relative merits of this theory, compared with the more accurate treatments involving Gaussian points through the thickness, are discussed. 4. (d) Local equilibrium equations are waived and a virtual work procedure is used to compute the stiffness matrix of the elbow element. 5. (e) A static condensation procedure is used to reduce the overall stiffness matrix to a ( 12 × 12) matrix, where external generalised forces and displacements are presented so that compatibility with adjacent elements is possible. 6. (f) In order to account for large displacements, the geometry (radius of curvature and central angle) is re-evaluated at each so that the element is compatible with a ‘large displacements’ (updated Lagrangian) approach. Comparisons with published results, in both the elastic and plastic fields, have been obtained experimentally and also by means of other computer codes (MARC, ADINA). A code incorporating this special elbow element has been run for a number of pipe whip cases and the results have been compared with those obtained by means of the ADINA and FRUSTA codes.

An Approximate Method for the Determination of the Response Frequency of Pipe Whip

This paper is concerned with the effect of fluid flow on the static and dynamic characteristics of a simply supported pipe having a hole through the pipe wall to permit a fluid flow. In this approximate analysis based on the virtual work technique, system natural frequencies and mode shapes are determined and compared to the analytical solution of the linear problem given by G. W. Housner [3] and experimental solution of H. L. Dodds, Jr., and H. L. Runyan [2]. An approximate solution satisfying the initial and boundary conditions is presented for free vibrations and for steady-state forced vibrations for the nonlinear problem. In addition, the critical fluid velocity at which the system becomes statically unstable is verified.

Opening and extension of circumferential cracks in a pipe subject to dynamic loads

Nuclear power plants are presently designed to withstand instantaneous pipe severance in combination with the maximum seismic loads. The hypothetical combination of these two unlikely events leads to system designs which are very expensive and require dynamic event devices such as pipe whip restraints which have the potential for deleterious interaction with the piping system during normal operations. These present pipe rupture criteria are based on the a priori hypothesis that the instantaneous guillotine pipe break is possible, rather than from a consideration of the manner in which cracks might open or extend in a real piping system. The objective of this study is to help establish the basis for understanding how cracks which might exist in the primary piping of a pressurized water reactor (PWR) would open and extend so that improved criteria can be developed based on this information. One of the regions where loss of pressure boundary integrity must be postulated is the terminal end of the cold leg at the reactor vessel inlet nozzle. This region (including the effects of the reactor vessel and the primary pump) is modelled for analysis with the MARC general purpose finite element program. A circumferential crack, one-half circumference long, is considered to suddenly occur around the outside of the elbow when the pipe is at normal operating pressure. The most severe part of the safe shutdown earthquake (SSE) loading transient is applied simultaneously with the initiation of the crack. The plastic dynamic analysis of the crack opening effects in the discharge leg pipe is performed using the MARC program until the maximum opening occurs. The J-integral plastic crack extension criterion is computed for all times during the transient. The results indicate that none of the cracks will extend significantly and that the opening areas are small fractions of the flow area of the pipe.

Application of plastic analysis to the pipe whip problem

The problem of design against pipe whip is briefly reviewed and some methods of calculation applicable to the problem are considered. Emphasis is given to two methods of analysis. The first makes use of the ‘FRUSTA’ programme; this method only considers the moment deflections so that it can only be regarded as a simplified approach leading to approximate results. As an alternative, a fully 3-D plastic element method is considered (the PAPS element), the basic hypotheses being briefly reviewed. Comparisons between the two approaches are provided. Finally, a model including restraint aspects is discussed which allows the consideration of V bars, plastic elements, dampers and friction type restraints. Typical examples are given and discussed.

680. パイプホイップ現象に及ぼす各種パラメータの影響

A pipe whip test is one of the main subjects of the pipe rupture tests performed in Japan Atomic Energy Research Institute. In 1979, the pipe whip test of 4B, sch-80 pipe will be done under the BWR condition. As the preliminary analysis of this test, the pipe whip analysis of 4B, sch-80 pipe was implemented in order to make clear of the influences of the physical parameters on the pipe whip behavior. The pipe whip analysis was treated as nonlinear dynamic analysis of pipe-restraint system by using the general purpose finite element program ADINA. Overhang length, clearance between pipe and restraint, restraint length and cross section area of restraint were taken as physical parameters. It was clarified through this analysis how restraint displacement, restraint strain and distribution of energy between pipe and restraint were influenced by these parameters.

Modelling techniques for pipe whip analysis

The dynamic model used to describe the pipe and the restraint to predict their behaviour during the accident transient is described. The pipe is simulated by means of a series of finite elements, having a complex elasto-plastic behaviour. Each element can be subdivided in to a number of subelements whose flexibilities are computed and internally condensed at the element level. The strain energy is the main parameter in describing the stiffness characteristics of each subelement; the material is assumed to behave elastically provided that the strain energy is less than a given amount; afterwards a plastic flow of the type σ = Aϵ m is assumed ( σ = stress , ϵ = strain ). Elastic unloading is assumed. For each subelement the complete behaviour can be derived from its energy. Ovalization of the pipe is assumed when the maximum strain is larger than a given amount; a relationship ϵ = const. × thickness/diameter is used to determine the critical strain. The instability of the pipe is simulated by means of unloading followed by the formation of a hinge. Crushing of the pipe as a consequence of its impact on a hard surface can be considered and the consequent absorption of energy in the pipe is simulated by means of a fictitious restraint. The restraining action can be simulated by either a restraint or a damper. For the first, a bilinear characteristic after a no load phase is assumed, elastic unloading is provided. For the damper a restraining force proportional to the velocity is assumed. A step-by-step integration procedure is used, a plastic stepwise elastic approach is followed and the constant average acceleration scheme is used. At each step in which a change in the characteristics (from elastic to plastic or vice versa) takes place a check is made to make sure that no excessive difference between the theoretical and actual value of the moment results as a consequence of the integration procedure. The maximum value of this ratio is recorded. Typical examples are studied and are reported.

Pipe whip analysis for nuclear reactor applications

The main problems encountered in pipe whip analysis are discussed and the way the authors tried to solve them is described. Such problems are: 1. (a) Breakage locations: AEC criteria are presented and discussed. 2. (b) Force computations: The jet force intensities during the accident are computed following Moody's theory. A computer program makes such an analysis automatically. Forces consequent to a longitudinal and a circumferential break are calculated; The forces consequent to the longitudinal break are computed as a sum of the forces consequent to two circumferential breaks, a mitigation coefficient is assumed. 3. (c) Preliminary analysis: Provided that a ‘restraint solution’ is necessary (and the related criteria are briefly discussed), a tentative distribution of the restraints is computed by means of a simple energy balance between the work done by the jet forces and the work absorbed both in the pipe and the restraint. A computer program makes such an analysis automatically. 4. (d) Final solution appraisal: The tentative solution obtained in the initial step is re-evaluated by means of a detailed dynamic elastoplastic code (FRUSTA, which is described in the companion paper). A typical example is given, the jet forces and a tentative restraint distribution are computed; the various models used in the final appraisal solution are described and the results are evaluated mainly in order to check the validity of the preliminary criterion.

Rigid Plastic Beam Model for Pipe Whip Analysis

A method is developed for the analysis of a rigid-plastic propped cantilever beam with a gap at the support for use in the study of pipe whip. The blowdown thrust is assumed to be a suddenly applied constant force and the restraint is assumed to act as a rigid-plastic spring. The type of response is shown to depend on the lengths of the cantilever and the segment overhanging the restraint as well as the ratio of the blowdown thrust to the restraint reaction. In long cantilevers, the first hinge to form moves to the support after contact is made with the restraint. A second hinge will form at the restraint if the reaction is large enough. It is shown that if the cantilever is long enough and the restraint reaction above a certain critical value, the displacements at the tip and the restraint are independent of length. It is shown that neglecting the fact the hinge moves introduces large errors.

On finite element analysis of pipe whip problems

The nonlinear dynamic finite element solution of pipe whip problems is presented. The finite element modelling used, the step-by-step incremental solution of the nonlinear equations of motion and design considerations are discussed. The influence of various physical parameters on the response of the pipe and the restraint, and the effects of using different finite element models are considered. Specific emphasis is directed to the verification of the accuracy of the solutions obtained using energy balance checks.

Elastic-Plastic Analysis of Curved Structures Subjected to Static and Dynamic Loads

A method is presented for the finite-element analysis of curved planar structures consisting of a combination of thin straight and curved beam elements. In the analysis both static and dynamic loads, elastic-plastic deformations, strain-hardening and hysteresis effects are taken into consideration. The properties of the curved beam element are derived based on the exact solutions of previously developed Euler differential equations for a circular ring accounting for the effect of extensional deformations. The elements of the stiffness and consistent mass matrices of the planar curved beam element are derived in closed-form, thus eliminating the loss of computer time and round-off errors associated with extensive matrix operations in the computational algorithm. The effect of rotary inertia is also considered in the derivation of the consistent mass matrix. The applicability of the analytical method presented herein is demonstrated by the solution of some typical structures subjected to static and dynamic loads, in particular, pipe whip restraints.

Dynamic analysis of nonlinear pipe whip restraints

Abstract A pipe whip restraint utilizing the dissipative capacity of a plastically deforming element has been developed. The transient dynamic behavior of the pipe and the restraint is studied using a discrete mathematical model consisting of nonlinear spring, mass, and damper elements. The forcing function is a fluid dynamic transient resulting from a break in a main steam line which is part of a Westinghouse pressurized water reactor (PWR) nuclear plant. An extensive parametric study shows the relative influence of gap, restraint support rigidity, the elastic and plastic behavior of pipe, break opening time, and finally the change in restraint mass on the behavior of the pipe restraint system.

Application of fracture mechanics to nuclear piping systems

With the introduction of Nuclear Energy into the power industry, rigid requirements for the design of piping have been set up to prevent accidents that may cause dangers to the health and safety of the public. Of particular concern is the rupture of a pipe. In this paper, nuclear piping systems are examined from a fracture mechanics viewpoint considering present day ASME code standards. Included are calculations of the critical crack length for a typical piping system. A brief discussion of the pipe whip phenomenon is also given.

High chromium steels

Structural integrity of components containing fluids is critical for economic, environmental and safety issues. Any risk of catastrophic failure, in the form of either brittle or ductile manner, is not acceptable across the industries. Consequently, many efforts have been invested in the structural integrity aspect to improve the assessment methodologies. One of the ways to aid the decision whether or not to live with the defect is through the demonstration of Leak-Before-Break (LBB). LBB which is a well-established practice in the nuclear industry, albeit as a defence-in-depth argument or to justify the elimination of pipe whip restraints, also finds its applicability in other industries. A review of the available procedures, their associated limitations and the research carried out in the last thirty years is presented in this paper. Application of this concept within non-nuclear industries is also discussed.