Effect of internal pressure and dent depth on strain distribution of

pressurized pipe subjected to indentation

Maziar Ramezani and Thomas Neitzert

Centre of Advanced Manufacturing Technologies (CAMTEC), Auckland University of Technology, New Zealand.

Email: maziar.ramezani@aut.ac.nz , thomas.neitzert@aut.ac.nz

Keywords: Finite element simulation; Indentation; Internal pressure; Pipe.

Abstract: A dent in a pipeline is a permanent plastic deformation of the circular cross section of the

pipe. This paper discusses numerical results obtained from finite element (FE) simulation of

pressurized pipe subjected to radial denting by a rigid indenter. Dent produced by rectangular shape

indenter is assessed and the strain distribution of the pipe is investigated. The effect of internal

pressure and dent depth on the distribution of strain is also studied. The results show that the

circumferential and longitudinal strains increase with increasing the internal pressure and the depth of

the dent. Numerical results are compared with an empirical theoretical model in order to demonstrate

the accuracy of the analysis.

Introduction

Accurate prediction of the lifetime of damaged pipelines due to outside force is very important. In

order to accurately predict the remaining life it is essential to accurately determine the stress and strain

in the damaged region. Mechanical damage is normally divided into two categories, dents and gouges,

which are deformations in the wall of a pipe that serve as crack initiation sites. Dents typically result

from a purely radial deformation whereas a gouge has a component of deformation along the surface

of the pipe. Dents not only affect the structural integrity of pipelines but they cause a local decrease in

the pipe’s cross-section, which in turn affects the flow through the pipe (Cosham and Hopkins, 2004).

A dent is a gross distortion of the pipe cross-section. Dent depth is defined as the maximum reduction

in the diameter of the pipe compared to the original diameter. Pipe denting is a complex phenomenon

that significant plastic strain occurs when the dent first forms. The pipe tends to re-round upon

pressure cycling, such that the observed deformation understates the true damage that has

accumulated in the pipe (Jiao and Shuai, 2011). The size, shape, and location of the original dent

affect the remaining life, as do external factors such as the constraint provided by the surrounding soil.

Few papers have been published previously to investigate the effect of dents on pipeline integrity

(see e.g. Lancaster and Palmer, 1994; Orynyak and Shlapak, 2001; Liu and Francis, 2004; Iflefel et al.,

2005). Hyde et al. (2005, 2007) determined the elastic-plastic behavior of unpressurised pipes with

long offset indentations and unsymmetrical support conditions by experimental tests, FE analyses and

analytical methods. Błachut and Iflefel (2008) presented detailed experimental work on damaged

laboratory scale mild steel pipes collapsed by bending moment.

Błachut and Iflefel (2011) studied the indentation of pipes subjected to transverse denting by a

rigid indenter. Dents produced by different shapes of indenters are assessed for the amount of

cross-sectional distortion of the pipe and for propagation of this distortion along the length of the pipe.

Baek et al. (2012) investigate the effect of the dent magnitude on the collapse behavior of a dented

pipe subjected to a combined internal pressure and in-plane bending. Most of these papers

investigated the dent on unpressurized pipes and only few works has been done on dented pipes in

which the pipe is pressurized prior to denting. The current paper aims at providing additional insight

into the structural behavior and strain distribution of pressurized dented pipes.

Applied Mechanics and Materials Vol. 376 (2013) pp 135-139© (2013) Trans Tech Publications, Switzerlanddoi:10.4028/www.scientific.net/AMM.376.135

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In order to handle the complexities associated with dents, an elastic-plastic finite element

simulation of a pressurized dented pipe is conducted and the formation of the dent and strain

distribution around the dent location is investigated. A parametric study is performed to investigate

the influence of internal pressure and dent depth on strain distribution.

Finite Element Simulation

The ABAQUS FE code has been adopted as the analysis tool. This is an implicit analysis code

suitable for modelling both material and geometric nonlinearities, and has good contact modelling.

The main objective is to reproduce the indentation load vs. displacement curves by simulating an

indented pipe and then investigating the strain distribution in the dented region of the pipe. Due to the

symmetry of the geometry and loading, it is only necessary to model half of the pipe and appropriate

constraints are imposed on the symmetry plan. The FE mesh is uniform and the tube is modelled using

C3D8R element which is an 8-node linear brick with reduced integration and hourglass control. The

pipe specimen has 762 mm outer diameter; 8.5 mm wall thickness and 2000 mm length. Therefore,

the outer diameter to wall thickness ratio is 90 and the length to diameter ratio is 2.6. The pipe

material is steel and the true stress–true strain curves were obtained from tensile experiments and

plastic material properties are included, with nonlinear isotropic strain hardening. The internal

pressure is applied as a function of yield pressure, yp . Yield pressure causes the stress in the hoop

direction to reach material's yield stress level, y . The following equation can be used to relate yp

and y .

i

y

yr

tp

(1)

where t is the pipe wall thickness and ri is the inner radius of the pipe. In the FE modeling, the internal

pressure is applied to the inner surface of the pipe to simulate the field condition. The level of internal

pressure and the indentation depth are varied in the FE simulations to investigate their effects on the

load-displacement curves and the strain distributions in the dented region of the pipe.

The surface to surface contact between the indenter and the tube is modelled through the

master-slave algorithm implemented in ABAQUS. The simulation has two steps, i.e. loading and

unloading, and the non-linear geometry NLGEOM option in ABAQUS has been used throughout the

analysis. For all of the non-linear elastic–plastic analyses, large deformation and large strain effects

are incorporated in order to obtain the strain distribution within the indented pipes. Figure 1 shows the

deformed pipe under indentation and the magnitude of spatial displacements at nodes is illustrated in

Figure 2.

Results and Discussions

The indentation load-displacement curves of the steel pipe at different internal pressures are shown in

Figure 3. The process of introducing a dent into a pipeline involves both elastic and plastic

deformation and when the indenter is removed the dent will spring back to some degree. The depth of

a dent in a pipeline changes as the internal pressure changes and the dent rerounds under increasing

internal pressure. Rerounding can be elastic (no permanent change in the dent depth), or plastic (a

permanent reduction in the dent depth). Under cyclic internal pressure loading, the dent can exhibit

incremental rerounding behaviour, until it shakes down to an elastic response. The spring back and

rerounding behavior of a dent depends upon the pipe geometry, the material properties, whether the

pipeline is pressurized or unpressurized, and the shape of the dent. The FE analysis was repeated at

each internal pressure to achieve the same final dent depth of (d/Do)=0.04, where d is the dent depth

and Do is the outside diameter of the pipe. The pipe remains pressurised during the loading and

unloading stages. It can be seen that a permanent indentation depth of 30mm is obtained after

complete unloading when the indenter separates from the pipe. The general shape of the

136 Materials and Diverse Technologies in Industry and Manufacture

force-deflection curve depends on the magnitude of the internal pressure. In general, the load carrying

capacity increases with increasing pressure and the deformation caused by a given load reduces with

increasing internal pressure.

The distribution of the circumferential and the longitudinal strains at different internal pressures

and (d/Do)=0.04 are depicted in Figures 4 and 5. It can be seen that the level of strain increases by

increasing the internal pressure and the location of the maximum strain moves outward by increasing

the pressure. Additional simulations were carried out for two other values of prescribed dent depth,

i.e. for (d/Do)=0.06 and (d/Do)=0.08 and with the internal pressure of (p/py)=0.15. The results are

illustrated in Figures 6 and 7 and show an increase in the circumferential and the longitudinal strains,

with increasing the dent depth. The combined effects of internal pressure and dent depth on the

maximum circumferential and longitudinal strains are shown in Figures 8 and 9. According to the

figures, the maximum strains increases constantly by increasing the internal pressure and the dent

depth and all the curves show the same trend.

In another study, pipes of the same dimension were dented with zero internal pressure and then

pressurized. Maxey (1986) presented the following empirical equation for the variation of the central

dent displacement with internal pressure.

)1(213.1d

w

p

p

y

(2)

where w is the inward radial displacement at the centre of the dent, measured from the original

cylindrical pipe surface. It can be seen from Figure 10 that the dent depth is reduced significantly upon

pressurization which indicates an immediate permanent plastic deformation from the earliest dent

movement. Although Eq. (2) was initially developed for aluminum pipes, a good agreement can be

seen between the theoretical and FE simulation results.

Conclusions

Finite element analyses are carried out to model the denting process and to determine the strains

distributions within the pressurized dented pipe. A number of observations can be made as a result of

this study of a single geometry pipe, (Do/t)=90, subjected to denting. Within the studied range of

internal pressures, the magnitude of the denting force increases nearly linearly with denting depth. For

a pressurized pipe, the magnitude of the denting force increases significantly with increasing the

internal pressure. It was also observed that the maximum circumferential and longitudinal strains

increase by increasing the internal pressure and the dent depth.

Fig. 1 FE simulation of the pressurized pipe under

indentation.

Fig. 2 Spatial displacements at nodes.

Applied Mechanics and Materials Vol. 376 137

Fig. 3 Indentation load vs dent depth at different

pressures for (d/Do)=0.04.

Fig. 4 Circumferential strain at different pressures

for (d/Do)=0.04.

Fig. 5 Longitudinal strain at different pressures for

(d/Do)=0.04.

Fig. 6 Effect of dent depth on circumferential strain

at (p/py)=0.15.

Fig. 7 Effect of dent depth on longitudinal strain at

(p/py)=0.15.

Fig. 8 Effect of internal pressure and dent depth on

maximum circumferential strain.

Fig. 9 Effect of internal pressure and dent depth on

maximum longitudinal strain.

Fig. 10 Comparison of FE simulation and empirical

theoretical model.

138 Materials and Diverse Technologies in Industry and Manufacture

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