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Research Papers: Piper and Riser Technology

# Mechanical Behavior of Dented Steel Pipes Subjected to Bending and Pressure LoadingPUBLIC ACCESS

[+] Author and Article Information
Aglaia E. Pournara

Department of Mechanical Engineering,
University of Thessaly,
Volos 38334, Greece
e-mail: agpourna@uth.gr

Theocharis Papatheocharis

Department of Civil Engineering,
University of Thessaly,
Volos 38334, Greece
e-mail: th_papath@yahoo.gr

Spyros A. Karamanos

Department of Mechanical Engineering,
University of Thessaly,
Volos 38334, Greece;
Institute of Infrastructure and Environment,
School of Engineering,
The University of Edinburgh,
Edinburgh EH9 3FG, UK
e-mail: skara@mie.uth.gr

Philip C. Perdikaris

Department of Civil Engineering,
University of Thessaly,
Volos 38334, Greece
e-mail: filperd@uth.gr

1Corresponding author.

Contributed by the Ocean, Offshore, and Arctic Engineering Division of ASME for publication in the JOURNAL OF OFFSHORE MECHANICS AND ARCTIC ENGINEERING. Manuscript received October 10, 2017; final manuscript received July 6, 2018; published online August 13, 2018. Assoc. Editor: Theodoro Antoun Netto.

J. Offshore Mech. Arct. Eng 141(1), 011702 (Aug 13, 2018) (16 pages) Paper No: OMAE-17-1183; doi: 10.1115/1.4040835 History: Received October 10, 2017; Revised July 06, 2018

## Introduction

Oil and gas pipelines may be significantly damaged due to external interference that causes dents on the pipe wall [13]. In such cases, immediately after the event, the pipeline may appear to fulfill its transportation function, provided that the steel pipe material is ductile enough to resist cracking. Nevertheless, this may be a threat for the long-term structural integrity of the steel pipeline; the dented region is associated with the development of significant strain concentrations and, in the case of repeated loading, fatigue cracks can develop, leading to loss of containment [3].

The remaining life of oil and gas transmission steel pipelines with local wall distortions is a crucial parameter for maintaining an acceptable level of pipeline operation condition. The need for reliable calculation of the remaining life of dented pipes has triggered significant amount of research. Ong [4] calculated local stresses at the area of a long smooth dent on the pipe wall of a pressurized elastic pipe, employing four different two-dimensional shape functions to describe the dent geometry. It was found that the maximum local elastic stress varies between 14 and 21 times the value of the nominal hoop stress due to pressure. In a subsequent work, Ong et al. [5] calculated local elastic stresses at short and smooth dents, in pressurized dented cylinders, using finite element simulation. The peak elastic stress in short dents was found to be significantly less than in long dents. An important conclusion of the work in Ref. [5] was that smooth dents do not affect the bursting capacity of the dented pipeline.

The fatigue resistance of offshore pipelines containing plain (smooth) dents subjected to cyclic pressure has been reported in Ref. [6] based on an experimental program and numerical calculations on 12 in diameter steel pipe specimens. The specimens were dented with the use of a longitudinal wedge-shaped denting tool at various denting depths. The experimental results in Ref. [6] indicated a reduction of pipeline fatigue strength due to plain (smooth) dents with a depth larger than 5% of the pipe diameter. Buitrago and Hsu [7], using a finite element simulation, investigated the fatigue response of nonpressurized tubular steel members containing relatively smooth dents and provided stress concentration factors in the form of parametric equations in terms of geometric parameters for axial and bending loads. Based on available experimental and numerical results, the effect of various defects (e.g., dents, gouges, weld defects, corrosion) on the structural integrity of steel pipelines has been investigated in the course of a joint industry project [3,8] aimed at amending current methodologies toward “fitness-for-purpose” pipeline assessment. This review exercise in Refs. [3] and [8] indicated that very limited data exist for the influence of dents or buckles on the fatigue resistance of pipelines under pressure, while the fatigue capacity of dented or buckled pipes due to bending loads has not been yet investigated.

Full-scale laboratory tests have been performed by Das et al. [9] to investigate the postwrinkling ultimate behavior of steel pipelines. The pipe specimens tested exhibited substantial resistance against fracture under monotonically increasing axisymmetric compressive axial loads and displacements. Fatigue cracks developed, however, at the wrinkled region when a wrinkled pipe specimen was subjected to cyclic strain reversals due to unloading and loading of primary loads. A combined experimental and numerical research has been reported by Dama et al. [10] in an attempt to assess the structural condition of buckled pipes, subjected to both bending and internal pressure. Fatigue failure under repeated loading and pipe burst have investigated, through three full-scale 24 in diameter buckled pipe specimens, supported by nonlinear finite element tools. Considering the maximum strain range from the finite element computations, and a simple and fatigue analysis approach, reasonable predictions for the number of cycles to failure were obtained, in very good agreement with test data. The results of that study demonstrate that under repeated loading, fatigue failure occurs in the buckled area at the location of maximum strain range.

The presence of dents has been recognized as a threat to pipeline integrity, mainly with respect to ultimate pressure capacity [11,12]. A methodology proposed recently in Appendix R of the ASME B31.8 code [13], allows estimation of the maximum strain in a dent assuming the total strain in the dent as the combination of the bending strains in the circumferential and longitudinal direction, and the membrane (stretching) strain in the longitudinal direction. The value of this strain should be less than 6% for dent acceptability.

More recently, the fatigue life of defected X60 steel pipes (residual stresses and microdeformations) has been also investigated by Pinheiro et al. [14] performing small-scale fatigue tests evaluated by the X-ray diffraction method. The three phases of fatigue damage mechanisms have been identified in Ref. [14]: (1) initiation of microcracks, (2) microcracking, and (3) macrocrack propagation. An indicator of the fatigue damage initiation could be based on the duration of the second phase. Furthermore, X-ray diffraction could be a useful means of connecting the macroscopic and microscopic approaches to fatigue studies that have been usually carried out independently until now.

The present paper is part of an extensive research effort at the University of Thessaly on the effects of local pipe wall distortions on the structural integrity of steel pipelines. Preliminary numerical work on the present research has been presented in Ref. [15]. In the present study, the experimental part of this research is presented, supported by numerical simulations, in order to investigate the residual structural integrity of dented steel pipes. Tests on ten 6 in diameter pipe specimens made of steel grade X52 are reported. The steel pipes are initially dented at different depths and, subsequently, they are subjected to further cyclic loading (bending or pressure) in order to estimate their residual strength and remaining life. Finite element simulations are also conducted using finite element models to simulate the experimental procedure for each type of deformation and loading case, calculate local stress and strain distributions at the dented region, estimate fatigue life, and compare it with the experimental results. The results of the present investigation can be used for the reliable assessment of smooth dents in steel pipelines, toward efficient pipeline integrity management.

## Experimental Setup and Pipe Specimens

The experimental program consists of ten tests on 1 m long steel X52 6 in diameter seamless pipe specimens. Denting of the specimens is performed with a wedge indenter at zero pressure, and subsequently the specimens are subjected to cyclic loading as follows:

• Six dented specimens are subjected to cyclic bending until pipe wall fractures due to low-cycle fatigue,

• Four dented specimens are subjected to cyclic pressure loading for a significant number of cycles and, subsequently, the pressure is raised monotonically until burst.

Six of the specimens have nominal thickness equal to 4.78 mm (∅168.3/4.78), which corresponds to a diameter-to-thickness ratio (D/t) equal to 35. The other four specimens have a nominal thickness value equal to 3 mm (∅165/3), with D/t equal to 55, which have been machined from the original geometry (∅168.3/4.78), so that the specimen thickness was reduced to a mean value of a 2.8 mm for a 500 mm long central pipe region. A 100 mm long transition zone (tapered section) on both sides of the 500 mm long central region has also been manufactured, where pipe thickness is gradually decreased from the pipe ends, producing a smooth slope of less than 2 deg, so that thickness discontinuity is avoided. Furthermore, two 1.5 in diameter holes have been drilled on the wall of all specimens, each hole at a distance of 150 mm from the end plate, to construct nozzles for the application of pressure. Pipe specimens ∅168.3/4.78 ($D/t=$ 35) and ∅165/3 ($D/t=$ 55) are shown in Fig. 1.

After the formation of denting, the specimens are further subjected to cyclic loading, to estimate their residual strength and the remaining life. Two loading patterns have been considered: (a) cyclic bending loading is applied through a four-point bending loading configuration until fatigue cracking occurs in the low-cycle fatigue range and (b) cyclic pressure is applied for a significant number of cycles (5000 cycles) followed by monotonic increase of pressure until burst. The specimen ends are capped with thick plates, to enable the application of internal pressure and the connection with adjacent pipe parts for the experimental setup.

In the following paragraphs, the application of denting, cyclic bending, and pressure loading on the specimens is presented in detail. Denting and cyclic bending have been conducted at the RC Structures laboratory facilities of the Department of Civil Engineering, University of Thessaly, whereas the pressure tests (both monotonic and cyclic) have been performed at EBETAM S.A., Volos, Greece.

###### Denting Procedure.

Denting is performed on each of the ten pipe specimens through the application of a rounded wedge indenter, shown in Fig. 2, oriented perpendicular to the pipe axis, so that a smooth dent is formed on the pipe wall (Fig. 2(b)). The total wedge height is 80 mm, the horizontal length is 85 mm, and the radius of the rounded wedge is equal to 5 mm. The horizontal steel plate on top of the denting wedge device is bolted at the bottom of the hydraulic actuator, as shown in Fig. 2(a).

During denting, the specimen is supported on a wooden base (280 mm × 280 mm × 200 mm) shown in Fig. 2(a). The wooden base was constructed longitudinally by connecting 50 mm long wooden parts. The top surface of each wooden part was properly curved so that, after connecting these parts, the top surface of the entire base could prevent movement of the tubular specimen. Moreover, to avoid the development of any stress concentration in the pipe at the edge of the wooden base, the radius of base curve was made greater than the nominal radius of the pipe. Furthermore, as shown in Fig. 2(a), the wooden base was stiffened along both directions (length and height) with the use of steel rods in order to avoid excessive deformations of the wood material during the application of the denting load.

Uniaxial strain gages have been installed at several critical locations along the outer surface of the pipe specimens in the vicinity of the dent, in order to monitor the evolution of local strains during the denting process (Fig. 3). These locations are as close as possible to the critical areas, determined by preliminary finite element analyses, in a way that they are not damaged by the denting tool during the denting process. Additionally, two wire LVDT sensors, attached to the specimen, recorded the indenter downward movement during denting; one end of each LVDT is fixed on the steel frame, while the moving end is hinged on the horizontal steel plate of the denting tool. Furthermore, DCDT transducers measured the relative displacement of the top surface of the wooden base with respect to its base during denting as shown in Fig. 2(b).

###### Cyclic Bending Setup.

Cyclic bending is applied on the dented specimens, as depicted in Fig. 4. The 1 m long specimens are connected using a bolted connection on either side to two heavy-walled 7 in diameter 650 mm long tubes (∅193.7/10) made of high-strength steel referred to as “stiff-pipe” in Fig. 4(a). The entire 2615 mm long system is supported using a double-hinge “roller” system with ball-joint hinges at the two ends.

Bending load is applied using a 500 kN hydraulic actuator through a stiffened horizontal steel beam with a system of two special ball-joint hinges and appropriate wooden grips (clamps) shown in Fig. 4(c). The wooden grips consist of properly curved wooden slices, which were glued and clamped together, as shown in Fig. 4(c), and are connected to a horizontal steel beam through appropriate hinges, which allow rotation in the bending plane. The hinges of this four-point bending configuration also minimize the axial load introduced by the transverse bending loads of the pipe due to the constraints imposed by the wooden grips and the supports.

During the test, using appropriately located strain gages, the value of the axial load at the maximum applied bending load was estimated as less than 8% of the axial yield strength and, therefore, it is considered negligible for the purposes of the present investigation. Furthermore, a low level of internal pressure equal to 0.1 bar is applied to the specimens during the test. As shown in Fig. 5, a manometer is placed at one nozzle, while the other nozzle is used as the “gate valve.” During the cyclic bending tests, the level of internal pressure is kept constant and monitored. Failure of a specimen is defined at the stage where through-thickness crack is detected, associated with a sudden internal pressure decrease.

###### Pressure Test Procedure.

Each of the four specimens subjected to pressure loading has been connected with a 450 bar capacity water pump (Fig. 6), instrumented with several manometers of various pressure ranges. Cyclic pressure has been applied to the ∅168.3/4.78 specimens with a pressure range (Δp) equal to 135 bar, while the ∅165/3 specimens were subjected to Δp equal to 83 bar. In both cases, the pressure loading ratio R is equal to 0.1, and the pressure is applied at a frequency of about 0.1 Hz. Following cyclic pressure loading, the specimens are pressurized monotonically until burst.

## Material Properties and Wall Thickness Measurements

###### Material Testing.

Monotonic tests and low-cycle fatigue tests have also been performed on the X52 steel pipe material to determine material properties. Strip specimens have been extracted from the seamless 6 in pipes, in the longitudinal direction and machined in accordance with the ASTM E606 standard [16]. The stress–strain relationship has been obtained from tensile coupon tests and the corresponding curve is shown in Fig. 7, indicating yield stress ($σY$) equal to 364 MPa, and ultimate stress ($σUTS$) equal to 525.8 MPa at a 18% uniform elongation. In addition to tensile testing, information for the cyclic loading response of the steel material has also been available based on a total of 30 cyclic tests performed by FEUP, Porto [17] on strip specimens with loading ratio $R$ equal to −1 and 0. In those tests, the low-cycle fatigue ($Δε−N$) curve for the X52 steel material was developed, which can be expressed by the Coffin–Manson–Basquin equation as follows: Display Formula

(1)$Δε=0.0104(2N)−0.1133+0.333(2N)−0.4807$

###### Thickness Measurements.

Prior to testing, thickness measurements were obtained at specific points around several cross sections along the specimen's length using an ultrasonic device, as shown in Fig. 8. A mean thickness value was measured equal to 5.03 mm for the ∅168.3/4.78 specimens, which is greater than the nominal value, while for specimens ∅165/3, a mean value equal to 2.79 mm was recorded.

## Experimental Results

Two sizes of the dent depth, $d$, have been considered, namely $d/D=$ 6% and 12% (Table 1) and the experimental results are shown in Tables 24. During denting, the specimen is placed on the wooden base while its ends are totally unrestrained. First, cyclic bending tests on six dented specimens (SP1d, SP3d, SPd5, SP6d, SP9d, and SP10d) have been performed. The second part of the experimental work consists of pressure loading on four dented specimens (SP2d, SP4d, SP7d, and SP8d).

###### Denting Results.

The denting process is performed through the hydraulic actuator at very low speed until a prescribed value of dent depth is reached. Following a short parametric numerical study, this value is set at about 16 mm for SP1d, SP4d, SP6d, SP7d, and SP9d, and 27 mm for SP2d, SP3d, SP5d, SP8d, and SP10d. Subsequently, the load is removed, and the permanent dent depth is approximately equal to either 10 or 20 mm, corresponding to $d/D=$ 6% and $d/D=$ 12%, respectively. The dent results are summarized in Table 1, whereas Fig. 9 shows the denting load–displacement curves for specimens SP1d, SP3d, SP5d, SP6d, SP9d, and SP10d, where the displacement is equal to the stroke of the hydraulic actuator. These “load-stroke” curves are compared, also, with the load versus displacement curves obtained from the LVDT measurements, as presented in Fig. 10 for specimen SP10d. The latter displacement value has been calculated as the average value of the two LVDT transducers during the denting procedure. The maximum recorded stroke is only about 0.5 mm larger than the average value recorded from the transducers implemented on the denting tool.

The evolution of axial and hoop local strains at the dented region of specimens SP5d and SP10d is shown in Fig. 11. It should be noticed that a relatively small elastic movement of the upper surface of the wooden base is also recorded from the DCDTs during denting, as shown in Fig. 12. This elastic vertical displacement reaches a maximum value of 0.85 mm and 0.05 mm in the case of ∅ 168.3/4.78 and ∅ 165/3 pipe specimens, respectively.

###### Cyclic Bending Test Results.

Following the denting procedure described in the previous paragraph, the dented pipe specimens are subjected to cyclic bending using the four-point bending setup shown in Fig. 4, through a displacement-controlled pattern, and the results are summarized in Table 4. The bending moment M is equal to $Fa/2$, where F is the total vertical force applied by the hydraulic cylinder, and a is the distance between the point where the transverse load is applied to the specimen and the nearest end support. The bending moment values for each bent specimen are reported in terms of the corresponding bending curvature values, calculated from the expression $k=2φ/L$, where $φ$ is the end-section rotation of the specimen during stroke application and L is the specimen length. The rotations of the end sections were calculated using the corresponding wire position measurements. Using these measurements, the slope of the stiff parts of the specimens was calculated, assuming that they are rigid. Uplift of the ball-joint hinges was also measured and was found to be negligible. In the above calculation, the resulting curvature value should be considered as a “global curvature value” for the entire specimen. Furthermore, the moment and curvature values are reported in a normalized form; moment values are normalized with the “plastic bending moment” value $M0=σyDm2t$ and the curvature values with the “curvature-like” parameter $k0=t/Dm2$, where $σy$ is the yield stress of the material (equal to 364 MPa), $Dm$ is the mean pipe diameter, and t is the nominal pipe thickness.

The loading sequence followed for the dented specimens SP5d and SP6d is shown in Fig. 13 in terms of the corresponding moment–curvature curves. The two specimens are first bent beyond the limit load and, subsequently, are subjected to cyclic loading in two stages. During this procedure, the dent was at the compressive side of the specimen with a load ratio R equal to 0.1. Following a number of loading cycles, each specimen failed because of fatigue cracking at the dent “ridge,” as depicted in Fig. 14. Failure is defined as the stage where the fatigue crack develops through the entire pipe wall thickness, and this is referred to as “through-thickness” crack. The number of cycles to this failure stage is equal to 950 and 1100 for specimen SP5d and SP6d, respectively, and the through-thickness fatigue crack of specimen SP5d is shown in Fig. 14.

Specimens SP1d and SP3d have been subjected to a different cyclic bending pattern, shown in Figs. 15 and 16. Initially, both specimens are bent beyond the maximum bending load, with the dent in compression. Subsequently, reverse bending has been applied so that the dented region is under tension, whereas the opposite region of the pipe is in compression. This loading situation resulted in local buckling at the opposite side of the dent due to excessive compressive strain (Fig. 17). Under cyclic loading, fatigue cracks were developed at the buckle “ridge.” The crack pattern is quite similar to the one shown in Fig. 14.

Specimens SP9d and SP10d (∅ 165/3) are subjected to bending until the maximum bending load is reached, with the dent located at the compression side of the pipes. Subsequently, cyclic bending is applied with a loading ratio R equal to 0.1. In this case, monotonic bending beyond the maximum bending load is first applied, as shown in the corresponding moment–curvature diagrams in Fig. 18 for SP9d and SP10d specimens. The failed pattern of specimen SP9d under cyclic bending is shown in Fig. 19. Specimens SP9d and SP10d failed after the application of 2300 and 125 bending cycles, respectively, as shown in Table 2.

###### Pressure Tests Results.

Four dented specimens (SP2d, SP4d, SP7d, and SP8d) are tested under pressure loading and the results are summarized in Table 3. The following loading protocol is followed: pipes are subjected first to 5000 cycles of pressure loading with $pmin=$ 1.5 MPa and $pmax=$ 15 MPa for the ∅168.3/4.78 specimens and $pmin=$ 0.92 MPa to $pmax=$ 9.20 MPa for the ∅165/3 specimens. The value of the maximum pressure $pmax$ corresponds to 72% of the nominal yield pressure ($pY=2σYt/D$), which is calculated equal to 20.55 MPa and 13.2 MPa for the ∅168.3/4.78 and ∅165/3 pipe specimens, respectively. Subsequently, the specimens are subjected to monotonically increasing pressure up to burst. No failure or damage is detected due to cyclic pressure loading for the SP2d, SP4d, and SP7d specimens. The pressure level at which burst rupture occurs for the dented specimens SP2d and SP4d is 32 MPa and 31.6 MPa, respectively, whereas for the case of SP7d specimen, the burst pressure is equal to 16.7 MPa. It is interesting to notice that these values are close to the theoretical value of burst pressure $pb$ calculated from the simplified formula: $pb=2σUTSt/D$, where $σUTS$ is the ultimate tensile stress of the steel X52 material, herein equal to 525 MPa, according to material testing (Fig. 7). One may readily calculate the value of $pb$ equal to 30 MPa and 19.12 MPa for ∅168.3/4.78 and ∅165/3 specimens, respectively. This indicates that the presence of a smooth dent on the pipe wall has a negligible effect on the burst capacity of the dented pipe. It is interesting to note that rupture of the pipe wall has occurred away from the dented area, as shown in Fig. 20. This observation is consistent with the large-scale test on a locally buckled 24 in diameter pipe reported by Dama et al. [10]. Furthermore, the application of internal pressure resulted in a reduction of the dent size and a “smoothening” of the dented area, before pipe wall rupture occurred.

On the other hand, SP8d specimen failed during the cyclic pressure loading stage and cracked at the ridge of the dent region at about 2500 cycles, as shown in Fig. 21. A review of thickness measurements, described in Sec. 3.2, showed that the local thickness recorded in the region of the dent was equal to 1.8 mm only, which is substantially lower than the mean pipe thickness (equal to 3 mm). This small thickness value is due to machining process, and explains the rapid development of a fatigue crack at the dented region of SP8d.

## Finite Element Simulation

###### Numerical Model.

Nonlinear finite element tools have been employed to simulate the development of denting and the mechanical behavior of the dented pipes under cyclic bending and pressure loading, using finite element program abaqus. The developed numerical models are capable of describing large displacements and strains, as well as inelastic behavior of materials in a rigorous manner. The pipe is simulated with four-node reduced-integration shell elements (S4R), which have shown to perform very well in nonlinear analysis problems involving large inelastic deformations and buckling of steel cylinders with similar $D/t$ ratio [18]. A general view of the finite element model is shown in Fig. 22.

To describe inelastic material behavior of the pipe specimens, a J2 (von Mises) flow plasticity model is employed. The model is calibrated through appropriate uniaxial tensile tests on steel coupon specimen extracted from the X52 6 in pipes (yield stress equal to 364 MPa and ultimate stress equal to 521 MPa).

The finite element model consists of five parts: the denting tool, the pipe specimen, the wooden base that supports the pipe movement during indentation, and the two “stiff” pipe segments (see Fig. 22) on either end of the specimen. The stiff pipe segments are simulated with beam elements of appropriate cross-sectional and material properties with simply supported conditions at the two ends. The thick end plates were modeled through a “kinematic coupling” constraint at the end nodes. During cyclic bending, loading is applied at two specific points of the beam elements, corresponding to the locations of the wooden grips used in the experiments.

The wedge-type denting tool is oriented in a direction perpendicular to the pipe axis, shown in Fig. 22. The radius of the rounded wedge is equal to 5 mm, similar to the one used in the experiments. The denting tool is designed as a nondeformable “analytical rigid” part. Contact interaction is imposed between the wedge surface and the outer surface of the pipe wall.

The geometry of the wooden base considered in the model is the one used in the experiments during the denting process (Fig. 2(b)) with dimensions 280 mm × 280 mm, whereas the upper surface is curved to support the pipe model. Contact conditions are imposed between this curved surface and the pipe outer surface so that penetration of the pipe within the base is prevented, but pipe uplifting is allowed.

###### Simulation of Pipe Denting.

In the numerical simulation of denting, the pipe is simply supported by the support plate, whereas the two pipe ends are unrestrained, resulting in a small uplifting and bending of the pipe specimen. Following the experimental procedure, two values for dent depth are considered in this numerical study, namely 6% and 12% of the pipe diameter, corresponding to the values of the residual dent size. The dent profile and the von Mises stress distribution around the dent region after elastic rebounding are shown in Fig. 23. Additionally, as shown in Fig. 24, the force versus denting displacement curves for specimens SP3d and SP6d compare well with the experimental diagrams during denting and unloading. The finite element model indicates a stiffer response during unloading, due to the fact that the wooden base and the indenter are modeled as nondeformable bodies. Nevertheless, the shape of the dent geometry in Fig. 23, as well as the comparison of axial and hoop strain values at the ridges of the dent profile, shown in Fig. 25, as obtained from numerical values and test results (specimen SP5d) is considered quite satisfactory.

###### Cyclic Bending of Dented Pipes.

Following denting, cyclic bending loading is applied to the dented pipe as described in Sec. 4.2 for the experimental procedure. The finite element model is shown in Fig. 26. At each loading stage, a total of ten bending cycles are applied. Figures 27 and 28 show the load–displacement curves for the analyses of SP3d and SP5d, which compare fairly well with the experimental results. The deformed shapes of specimen SP5d and SP3d (subjected to reverse loading) are shown in Figs. 29 and 30, respectively. In the latter case, the dented area at the top of the specimen is under tension and due to reverse bending, local buckling is developed at the opposite side of the pipe wall due to excessive compression. In this case, the maximum local strain range occurs at the buckled area due to local pipe wall folding so that fatigue crack eventually develops.

The “geometrical local strain” values on the inner and outer pipe surfaces, denoted as $εi$ and $εo$, respectively, are calculated for the dented models using the following expressions from the ASME B31.8 standard [13], and the results are shown in Table 4Display Formula

(2)$εi=ε12−ε1(ε2+ε3)+(ε2+ε3)2$
Display Formula
(3)$εo=ε12+ε1(−ε2+ε3)+(−ε2+ε3)2$

where $ε1$ refers to the bending strain in the circumferential direction, while $ε2$ and $ε3$ refer to the bending and membrane strain in the longitudinal direction. Strains $ε1$, $ε2$, and $ε3$ are calculated as follows [13]: Display Formula

(4)$ε1=t2(1R0−1R1)$
Display Formula
(5)$ε2=−12R2t$
Display Formula
(6)$ε3=12(dL)2$

In Eqs. (4)(6), $R0$ is the radius of curvature of the undeformed pipe surface (equal to pipe radius $R$ = $D$/2), whereas $t, d, L$ denote pipe wall thickness, dent depth, and dent length in the longitudinal direction, respectively. The external surface radii of curvature $R1$ and $R2$ (see Fig. 31) are measured in the transverse and longitudinal planes passing through the dent. The value of $R1$ is positive when the dent partially flattens the pipe, i.e., when the curvature of the pipe surface in the transverse plane is in the same direction as the original surface radius of curvature $R0$. Otherwise, if the dent is “re-entrant,” corresponding to wall inversion, the value of $R2$ is negative. The dent length $L$ is defined as the distance between the dent shoulders along the longitudinal direction, where an abrupt change of pipe-wall local curvature is detected at both sides of the dent.

The dent is considered acceptable when both values of $εi$ and $εo$ are lower than 6% for the case of smooth dents [13]. Based on the results presented in Table 4, using the above methodology, all dents fell far beyond the strain acceptability limit of 6%. However, it is worth noticing that dented pipes with these specific local dents sustained numerous bending and pressure cycles before failure as reported in the test results in Tables 2 and 3. From the above observations, this strain criterion could be considered rather conservative. The maximum value of local strain variation ($Δεmax$), calculated at the critical dent location during the application of cyclic bending or cyclic pressure, is depicted in the third column of Table 5.

Internal pressure is applied incrementally on the dented specimen models. The results show that the dented profile “smoothens” with increasing pressure (Fig. 32) and the dent size decreases with a tendency of gradual dent flattening, an observation also reported in Ref. [10]. The range of cyclic pressure applied ($Δp=$ 13.5 MPa, with $pmax$ = 15 MPa), and the value of the corresponding strain concentration factor (SNCF) is small, which justifies the experimental observations that dented pipes are capable of sustaining 5000 pressure cycles without failure or other damage, provided that local thinning does not exist at the critical location of the dented area.

The diagrams of Fig. 33 present the response of the dented pipe SP2d under monotonically increasing internal pressure; in terms of dent profile, increase of internal pressure results in a decrease of dent depth. The maximum internal pressure $pmax$ obtained from the finite element analysis is equal to about 33 MPa for specimens SP2d and SP4d and 17 MPa for specimens SP7d and SP8d. Beyond those pressure levels, convergence of numerical solution is not possible due to excessive plastification of the pipe wall. These pressure levels compare quite well with the burst pressure values measured in the experiments for both D/t values and are close to the approximate analytical expression $pb=2σUTSt/D$ for the burst pressure of nondented pipes. This verifies that the burst pressure may not be affected by the presence of smooth dents. The coordinates in the vertical axis of Fig. 33, normalized by the pipe radius $R$, refer to the position of the top outer wall generator for various pressure levels.

Cyclic internal pressure is applied on the dented pipe models (SP2d, SP4d, SP7d, and SP8d) according to the test procedure followed for these specimens. In particular, the models for specimens SP2d and SP4d are subjected to ten pressure cycles with a pressure range of $Δp$ = 13.5 MPa, followed by a monotonic increase of pressure, while the models for specimens SP7d and SP8d are subjected to ten pressure cycles with a pressure range of $Δp$ = 8.28 MPa, also followed by monotonic pressure. The maximum strain range $Δεmax$ calculated at critical locations of the dented area is depicted in Table 6.

## Fatigue Analysis

Using the finite element model presented and the material fatigue curve of the X52 steel material, a simple and efficient strain-based fatigue assessment approach is proposed for the specimens under consideration. This approach refers to a fatigue-life prediction method, also employed in a previous work by Dama et al. [10]. In the present paper, this approach is enhanced and validated for the purposes of the present research. A similar methodology on fatigue assessment has also been proposed by API-579/ASME FFS-2007 standard [11], described in Annex B1, Section B1.5.4. For the case of cyclic bending, the dented pipes with D/t = 35 have been analyzed, whereas for the case of cyclic pressure, fatigue analysis for both cases of D/t = 35 and 55 is presented.

The maximum value of local strain range $Δεimax$ for each loading case (i) is obtained from the numerical simulations of dented specimens and is depicted in Table 5. The $Δεimax$ values are used as input to an appropriate $Δε−N$ fatigue curve of the pipe material to obtain the number of bending or pressure cycles to failure $Ni$ corresponding to $Δεi$. Combining the values of $Ni$ for each loading case (i) with the actual load cycles applied, $ni$, a damage factor $Df$ is calculated, which quantifies material damage due to low-cycle fatigue, using Miner's rule for variable amplitude loading, expressed as follows [19]: Display Formula

(7)$Df=∑iniNi$

In Eq. (7), $Ni$ is the number of cycles corresponding to $Δεi$ obtained from the $Δε−N$ fatigue curve, and $ni$ is the number of real cycles applied. The results of this analysis are depicted in Table 5 for the pipe specimens under consideration.

The values of $Δεmax$ refer to the maximum local strain ranges at the dented critical region, and are employed to calculate the so-called SNCF using the nominal strain range $Δεnom$ due to the applied loading. The latter is calculated through elementary Mechanics of Materials, considering the initial (intact) circular geometry of the pipe cross section. In the case of four-point bending, $Δεnom$ is calculated as follows: Display Formula

(8)$Δεnom=2αΔFEπD2t$

where $ΔF$ is the range of total transverse load applied to the specimen, $α$ is the distance between the hinge support and the point of load application, D is the outer diameter of the pipe, whereas E and ν are Young's modulus and Poisson's ratio of the pipe material. For the cyclic bending loading conditions under consideration, the SNCF value is computed through the maximum strain variation, and it is shown in Table 5.

The results depicted in Table 5 indicate that the values of the calculated damage factor Df are quite close to 1, showing a good correlation between test results and numerical analysis. Furthermore, Table 5 indicates that the last stage of the bending curve, corresponding to severe pipe deformation, is associated with quite high SNCF values because of severe folding of the pipe wall. The calculated SNCF values are consistent with those reported by Dama et al. [10] for locally buckled pipes.

In the case of cyclic internal pressure loading $Δp$, the value of SNCF is computed as the ratio of the maximum local strain range in the hoop direction, $Δεmax$, obtained numerically, over the corresponding nominal strain $Δεmax$, computed from elementary mechanics of materials as follows: Display Formula

(9)$Δεnom=D2t(1−v2)EΔp$

In Eq. (9), E and ν are Young's modulus and Poisson's ratio of pipe material, respectively, while $Δp$ is the range of the applied pressure.

Dented specimens SP2d and SP4d were subjected to cyclic pressure Δp = 13.5 MPa, with a maximum value of 15 MPa, and the corresponding strain concentration factor computed numerically is equal to 3.11 and 3.03, respectively, corresponding to a local strain variation $Δεmax$ equal to 0.259% and 0.252%. Using this value and the fatigue curve of Eq. (1), the fatigue life of SP2d specimen can be estimated as equal to 500,000 cycles. This result verifies the fact that SP2d and SP4d specimens are capable of sustaining 5000 pressure cycles without failure or other damage, as observed experimentally. Furthermore, the results indicate that the existence of a dent may not affect the fatigue life of these two specimens, due to pressure cycles.

Similarly, the SNCF value computed numerically for specimen SP7d is equal to 2.26, as shown in Table 6. Using the fatigue methodology presented herein and using the $Δε−N$ fatigue curve of Eq. (1), the fatigue life for specimen SP7d is estimated as over 1,000,000 pressure cycles. This explains the fact that the specimen survived 5000 cycles without any visible damage.

Based on the above results of cyclic pressure on the dented pipe specimens SP2d, SP4d, and SP7d, one may conclude that the presence of smooth dents may not affect the fatigue life of pipes subjected to internal pressure. Furthermore, the burst pressure may not be affected by the prior application of cyclic pressure.

On the other hand, specimen SP8d failed because of fatigue cracking the after only 2500 pressure cycles. The reason for this premature failure of specimen SP8d is due to the substantially reduced local thickness at the dented region, which resulted in the early development of a fatigue crack.

Finally, the maximum allowable number of pressure cycles for the pressure loading under consideration has been calculated for specimens SP2d, SP4d, SP7d, and SP8d, according to API 579/FFS-1 provisions [11] as described in Chapter 12 for level 2 assessment. These numbers of cycles are shown in Table 6, and are significantly lower than the actual number of cycles at failure recorded experimentally. Moreover, one should note that the dents developed on the SP2d and SP8d specimens are considered not acceptable for level 1 assessment, as the dent depth on the pressurized specimens, d, is found greater than 7% of the nominal diameter of the specimens. Figure 34 compares the fatigue curve specified by API 579/FFS-1 with the material fatigue curve of X52 of Eq. (1), obtained experimentally. This comparison explains the discrepancy in the prediction of loading cycles to failure. Using the API fatigue curve, the assessment methodology in API 579/FFS-1 becomes quite conservative in terms of predicting the number of pressure cycles that a smooth (nongauged) dent could withstand. This conservativeness is attributed to the fact that the API 579/FFS-1 fatigue curve accounts indirectly for degradation (aging) of the pipe material due to service conditions throughout the operational life of the pipe component, an issue that has not been considered in the present study.

## Parametric Analysis on the Strain Concentration Factor Value

A parametric numerical analysis has also been conducted in order to obtain the strain concentration factor for dented pipes ∅168.3/4.78 ($D/t=$ 35) subjected to cyclic bending, considering various dent depths ranging from 1.2% to 14.3% of the nominal pipe diameter $D$. The geometry and material properties of the pipe models under consideration are those used for the simulation of the experimental procedure, described in Sec. 5.

The pipes are dented first up to various dent depths and, subsequently, they are subjected to cyclic bending. For the specific analysis, the loading pattern applied in the numerical models is shown in Fig. 35 for the dented pipes with dent depths d/D equal to 1.2% and 14.3%. The dented pipes are bent monotonically up to a specific curvature value, $kmax$. After unloading, cyclic bending is applied with a load ratio R equal to zero. The curvature $k$ is normalized by the curvature-like parameter $kc=t/D2$; for the pipes under consideration $kc$ is equal to 1.69 × 10−4 mm−1. The values of $kmax/kc$ examined in the present study vary from 0.1 to 1, as depicted in Fig. 35 for the case of $kmax/kc=$ 1. In Fig. 35, the moment values are normalized by $Mc=σyDm2 t$, which corresponds to the fully plastic bending moment of the pipe cross section, calculated equal to 46.52 kNm. During cyclic loading, the maximum local axial strain ranges have been readily obtained and the SNCF values have been calculated at the critical region of each dent size ($d/D=$ 1.2–14.3%). The increase of SNCF value with respect to the normalized dent depths ($d/D$) is depicted in Fig. 36 for various $kmax/kc$ ratios. Furthermore, the SNCF value increases with the increase of $kmax/kc$ ratio for the dent depths under consideration, as presented in Fig. 37. The strain concentration associated with the SNCF value may have a very important influence on the fatigue life of the dented pipe subjected to cyclic bending.

## Conclusions

Combining experimental testing and numerical simulations, the mechanical behavior of dented pipes under pressure and bending loading has been examined. The experimental investigation consisted of ten X52 steel pipe specimens; five ∅168.3/4.78 ($D/t=$ 35) pipes and five ∅165/3 ($D/t=$ 55) pipes. The specimens have been initially dented at depths equal to 6% and 12% of their diameter. Subsequently, the specimens have been tested under various loading conditions (bending and pressure). It is found that the cyclic bending loading applied to four dented specimens, has caused fatigue cracking, located at the ridge of the dented area, at a number of loading cycles ranging from 125 to 2300.

Furthermore, a detailed finite element simulation of the experimental procedure (both denting and cyclic loading) has been conducted. This finite element analysis, together with the use of an appropriate fatigue curve for the pipe material, is considered as a sufficient tool for the prediction of pipeline fatigue life.

In addition to bending, pressure loading has been considered. Four pipes were subjected to a combination of cyclic (5000 cycles) and monotonic pressure. Three specimens performed very well, whereas the forth specimen could not sustain only a part pressure cycles and failed under fatigue due to local wall thinning. The results indicate that the dented pipes under consideration, even with a substantial size of dent, in the absence of local wall thinning, are capable of sustaining a significant number of pressure cycles, whereas their resistance to burst pressure and the corresponding location of rupture are not affected by the presence of smooth dents.

## Acknowledgements

The research present in this paper has been co-financed by the European Union (European Social Fund—ESF) and Greek national funds through the Operational Program “Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF) - Research Funding Program: Heracleitus II investing in knowledge society through the European Social Fund.

Partial funding has also been provided by the ULCF project, sponsored by the European Commission [17] in the Research Fund for Coal and Steel program. The authors would like to thank EBETAM S. A., Volos, Greece, for providing the facilities for pressure testing, as well as Dr. Abilio M. P. de Jesus, FEUP, Porto, Portugal, for providing the cyclic test data for the X52 steel pipe material.

## References

Doglione, R. , and Firrao, D. , 1998, “Structural Collapse Calculations of Old Pipelines,” Int. J. Fatigue, 20(2), pp. 161–168.
Netto, T. A. , Ferraz, U. S. , and Estefen, S. F. , 2005, “The Effect of Corrosion Defects on the Burst Pressure of Pipelines,” J. Constr. Steel Res., 61(8), pp. 1185–1204.
Cosham, A. , and Hopkins, P. , 2004, “The Effect of Dents in Pipelines—Guidance in the Pipeline Defect Assessment Manual,” Int. J. Pressure Vessels Piping, 81(2), pp. 127–139.
Ong, L. S. , 1991, “Derivation of Stress Associated With a Long Axial Dent in a Pressurized Cylinder,” Int. J. Mech. Sci., 33(2), pp. 115–123.
Ong, L. S. , Soh, A. K. , and On, J. L. , 1992, “Experimental and Finite Element Investigation of a Local Dent on a Pressurized Pipe,” J. Strain Anal., 27(3), pp. 177–185.
Fowler, J. R. , 1993, “Criteria for Dent Acceptability in Offshore Pipelines,” Offshore Technology Conference (OTC 7311), Houston, TX, May 3–6, pp. 481–493.
Buitrago, J. , and Hsu, T. M. , 1996, “Stress Concentration Factors for Dented Tubular Members,” Offshore Mechanics and Artic Engineering Conference (OMAE), Florence, Italy, June 16–20, pp. 291–296.
Macdonald, K. A. , and Cosham, A. , 2005, “Best Practice for the Assessment of Defects in Pipelines—Gouges and Dents,” Eng. Failure Anal., 12(5), pp. 720–745.
Das, S. , Cheng, J. J. R. , and Murray, D. W. , 2007, “Prediction of the Fracture Life of a Wrinkled Steel Pipe Subject to Low Cycle Fatigue Load,” Can. J. Civ. Eng., 34(9), pp. 1131–1139.
Dama, E. , Karamanos, S. A. , and Gresnigt, A. M. , 2007, “Failure of Locally Buckled Pipelines,” ASME J. Pressure Vessel Technol., 129(2), pp. 272–279.
API, 2007, “Fitness-for-Service,” American Petroleum Institute, Washington, DC, No. API 579/ASME FFS-1.
CSA, 2007, “Oil and Gas Pipeline Systems,” Canadian Standard Association, Mississauga, ON, Canada, No. CSA-Z662.
ASME, 2007, “Gas Transmission and Distribution Piping Systems,” American Society of Mechanical Engineers, New York, ASME Standard No. B31.8.
Pinheiro, B. , Lesage, J. , Pasqualino, I. , Benseddiq, N. , and Bemporad, E. , 2015, “Toward a Fatigue Life Assessment of Steel Pipes Based on X-Ray Diffraction Measurements,” ASME Paper No. OMAE2015-42277.
Pournara, A. E. , and Karamanos, S. A. , 2012, “Structural Integrity of Steel Hydrocarbon Pipelines With Local Wall Distortions,” ASME Paper No. PVP2012-78131.
ASTM, 2012, “Standard Test Method for Strain-Controlled Fatigue Testing,” American Society for Testing and Materials, West Conshohocken, PA, ASTM No. E606/E606M-12.
Fernandes, A. A. , de Jesus, A. A. , Jorge, R. N. , Coppola, T. , Demofonti, G. , Thibaux, P. , Van Wittenberghe, J. , Van Poucke, M. , Martinez, X. , Barbu, L. , Oller, S. , Barbat, A. , Karamanos, S. A. , Pournara, A. , Chatzopoulou, G. , Varelis, G. E. , Salvatore, W. , Banushi, G. , Morelli, F. , Erdelen-Peppler, M. , and Knauf, G. , 2013, “Ultra Low Cycle Fatigue of Steel Under High-Strain Loading Conditions,” RFCS Program, Brussels, Belgium, Contract No. RFSR-CT-2011-00034, Final Report of ULCF Project, accessed July 25, 2018,
Vasilikis, D. , Karamanos, S. A. , Van Es, S. H. J. , and Gresnigt, A. M. , 2016, “Ultimate Bending Capacity of Spiral-Welded Steel Tubes—Part II: Predictions,” Thin-Walled Struct., 102, pp. 305–319.
Dowling, N. E. , 2013, Mechanical Behavior of Materials, 4th ed., Pearson, Essex, UK.
Topics: Pressure , Pipes , Steel , Stress
View article in PDF format.

## References

Doglione, R. , and Firrao, D. , 1998, “Structural Collapse Calculations of Old Pipelines,” Int. J. Fatigue, 20(2), pp. 161–168.
Netto, T. A. , Ferraz, U. S. , and Estefen, S. F. , 2005, “The Effect of Corrosion Defects on the Burst Pressure of Pipelines,” J. Constr. Steel Res., 61(8), pp. 1185–1204.
Cosham, A. , and Hopkins, P. , 2004, “The Effect of Dents in Pipelines—Guidance in the Pipeline Defect Assessment Manual,” Int. J. Pressure Vessels Piping, 81(2), pp. 127–139.
Ong, L. S. , 1991, “Derivation of Stress Associated With a Long Axial Dent in a Pressurized Cylinder,” Int. J. Mech. Sci., 33(2), pp. 115–123.
Ong, L. S. , Soh, A. K. , and On, J. L. , 1992, “Experimental and Finite Element Investigation of a Local Dent on a Pressurized Pipe,” J. Strain Anal., 27(3), pp. 177–185.
Fowler, J. R. , 1993, “Criteria for Dent Acceptability in Offshore Pipelines,” Offshore Technology Conference (OTC 7311), Houston, TX, May 3–6, pp. 481–493.
Buitrago, J. , and Hsu, T. M. , 1996, “Stress Concentration Factors for Dented Tubular Members,” Offshore Mechanics and Artic Engineering Conference (OMAE), Florence, Italy, June 16–20, pp. 291–296.
Macdonald, K. A. , and Cosham, A. , 2005, “Best Practice for the Assessment of Defects in Pipelines—Gouges and Dents,” Eng. Failure Anal., 12(5), pp. 720–745.
Das, S. , Cheng, J. J. R. , and Murray, D. W. , 2007, “Prediction of the Fracture Life of a Wrinkled Steel Pipe Subject to Low Cycle Fatigue Load,” Can. J. Civ. Eng., 34(9), pp. 1131–1139.
Dama, E. , Karamanos, S. A. , and Gresnigt, A. M. , 2007, “Failure of Locally Buckled Pipelines,” ASME J. Pressure Vessel Technol., 129(2), pp. 272–279.
API, 2007, “Fitness-for-Service,” American Petroleum Institute, Washington, DC, No. API 579/ASME FFS-1.
CSA, 2007, “Oil and Gas Pipeline Systems,” Canadian Standard Association, Mississauga, ON, Canada, No. CSA-Z662.
ASME, 2007, “Gas Transmission and Distribution Piping Systems,” American Society of Mechanical Engineers, New York, ASME Standard No. B31.8.
Pinheiro, B. , Lesage, J. , Pasqualino, I. , Benseddiq, N. , and Bemporad, E. , 2015, “Toward a Fatigue Life Assessment of Steel Pipes Based on X-Ray Diffraction Measurements,” ASME Paper No. OMAE2015-42277.
Pournara, A. E. , and Karamanos, S. A. , 2012, “Structural Integrity of Steel Hydrocarbon Pipelines With Local Wall Distortions,” ASME Paper No. PVP2012-78131.
ASTM, 2012, “Standard Test Method for Strain-Controlled Fatigue Testing,” American Society for Testing and Materials, West Conshohocken, PA, ASTM No. E606/E606M-12.
Fernandes, A. A. , de Jesus, A. A. , Jorge, R. N. , Coppola, T. , Demofonti, G. , Thibaux, P. , Van Wittenberghe, J. , Van Poucke, M. , Martinez, X. , Barbu, L. , Oller, S. , Barbat, A. , Karamanos, S. A. , Pournara, A. , Chatzopoulou, G. , Varelis, G. E. , Salvatore, W. , Banushi, G. , Morelli, F. , Erdelen-Peppler, M. , and Knauf, G. , 2013, “Ultra Low Cycle Fatigue of Steel Under High-Strain Loading Conditions,” RFCS Program, Brussels, Belgium, Contract No. RFSR-CT-2011-00034, Final Report of ULCF Project, accessed July 25, 2018,
Vasilikis, D. , Karamanos, S. A. , Van Es, S. H. J. , and Gresnigt, A. M. , 2016, “Ultimate Bending Capacity of Spiral-Welded Steel Tubes—Part II: Predictions,” Thin-Walled Struct., 102, pp. 305–319.
Dowling, N. E. , 2013, Mechanical Behavior of Materials, 4th ed., Pearson, Essex, UK.

## Figures

Fig. 1

6 in diameter 1 m long X52 pipe specimens: (a) pipe with 4.78 mm thickness and (b) machined pipe at 2.8 mm thickness

Fig. 2

(a) Wedge-shaped denting tool and wooden base to support pipe specimens during denting and (b) pipe denting process configuration

Fig. 3

Schematic view of the strain gages implemented at the denting region: (a) SP5d specimen, (b) SP6d specimen, and (c) strain gages attached to the dent ridges of SP5d pipe specimen after denting

Fig. 4

Four-point bending test setup: (a) schematic overall experimental configuration, (b) side view of bent specimen and the cross-beam, and (c) hinged end support of specimen and wooden clamp for load application

Fig. 5

Pressure valve and manometer for low-level internal pressure measurement during cyclic bending

Fig. 6

Application of internal pressure on pipe specimen SP2d

Fig. 7

Pipe material stress–strain curve (X52 steel grade)

Fig. 8

(a) Thickness measurements on ∅168.3/4.78 pipe specimens using an ultrasonic device and (b) marked ∅165/3 specimens

Fig. 9

Load–displacement (stroke) diagrams during the denting procedure, for specimens: (a) SP1d and SP3d, (b) SP5d and SP6d, and (c) SP9d and SP10d

Fig. 10

Load–displacement diagrams during the denting procedure of the SP10d specimen and comparison of the displacement values from the LVDTs and the applied stroke of the hydraulic actuator

Fig. 11

Evolution of longitudinal and hoop strains during denting for specimens (d/D = 12%): (a) SP5d and (b) SP10d

Fig. 12

Load versus displacement diagrams of the wooden base top surface during denting of the SP3d and SP1d pipe specimens

Fig. 13

Normalized experimental moment–curvature diagrams for specimens SP5d and SP6d under monotonic and cyclic bending

Fig. 14

Dented specimen SP5d subjected to cyclic four-point bending: (a) general configuration of dented specimen and (b) pipe wall rupture at dent ridge

Fig. 15

Moment–curvature diagram for specimen SP1d subjected to reverse and cyclic bending

Fig. 16

Moment–curvature diagram for specimen SP3d subjected to reverse and cyclic bending

Fig. 17

(a) Dented specimen SP1d and (b) detail of buckle development at the opposite side of the dent during reverse and cyclic four-point bending

Fig. 18

Moment–curvature diagrams for specimens: (a) SP9d and (b) SP10d

Fig. 19

Pipe wall rupture of specimen SP9d due to cyclic bending loading at the dent “ridge”

Fig. 20

(a) Rupture of specimen SP2d (∅168.3/4.78), (b) detail of crack opening in specimen SP2d, and (c) ruptured (burst) pipe specimen SP7d (∅165/3) due to increased internal pressure

Fig. 21

Pipe wall rupture of SP8d pipe specimen (∅165/3) due to fatigue loading (cyclic internal pressure); wall rupture occurred at the “ridge” of the dented region

Fig. 22

Finite element model: (a) different parts of the model and (b) shell finite element mesh of the dented specimen

Fig. 23

Deformed geometry and distribution of Von Mises stress in MPa obtained from finite element simulations after the removal of denting load: (a) specimen SP1d (d/D= 6%) and (b) specimen SP5d (d/D= 12%)

Fig. 24

Load–displacement curves for (a) SP6d and (b) SP3d models during denting in comparison with the corresponding experimental curves

Fig. 25

Strain evolution in terms of (a) denting load and (b) denting tool displacement, during the denting process of SP5d specimen (for strain gages refer to Fig. 3)

Fig. 26

Schematic representation of the loading pattern in the finite element model employed for cyclic bending on dented pipes

Fig. 27

Moment–curvature bending diagram for specimen SP3d (reverse and cyclic bending) obtained from finite element analysis and comparison with the corresponding experimental results

Fig. 28

Moment–curvature diagrams from experimental and finite element results for specimen SP5d

Fig. 29

Deformed shapes of specimen SP5d: (a) finite element model and (b) deformed shape from experiment

Fig. 30

Deformed shapes of SP3d specimen subjected to reverse and cyclic bending: (a) finite element model and (b) experiment

Fig. 31

Local curvatures of pipe wall surface for estimating strains in smooth dents, as specified in Ref. [11]

Fig. 32

Dent geometry for d/D= 6%: (a) before the application of internal pressure and (b) after the application of internal pressure

Fig. 33

“Smoothening” of the dent profile with the increase of internal pressure (in MPa) for pipe specimen SP2d

Fig. 34

Comparison of API 579 fatigue curve [11] with X52 fatigue curve of pipe material [17]

Fig. 35

Normalized moment–curvature diagrams for dented pipes with d/D= 1.2% and 14.3% subjected to bending (maximum curvature kmax/kc= 1)

Fig. 36

Strain concentration factor values in terms of the normalized dent depth (d/D) for kmax/kc ratios ranging from 0.1 to 1

Fig. 37

Strain concentration factor values in terms of kmax/kc ratio for four levels of dent depth ratio values (d/D ranging from 1.2% to 14.3%)

## Tables

Table 1 Geometrical characteristics of pipe specimens ∅168.3/4.78 and ∅165/3
Table 2 Cyclic-bending fatigue results in dented pipe specimens
Table 4 Geometric strain calculations for dented pipes subjected to cyclic bending obtained from FE analysis
Table 5 Fatigue analysis of dented specimens under cyclic bending
Table 6 Fatigue analysis for dented specimens under cyclic pressure

## Errata

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