Pressure equipment is widely used in contemporary industry, for example, in the transport and storage of fluids (petroleum, gas, water, and oil). Pipeline transport is the cheapest and safest way to transport large amounts of energy over long distances (Zhang, Sun, et al., 2018). The steady rise in the world’s demand for energy resources, such as gas and oil,is propelling the development of new pipelines with optimal profitability, requiring increases in pressures and diameters(Cristoffanini et al., 2014).
Further increasing the resistance of pipelines is becoming a necessity, as is improving their mechanical and chemical characteristics. In certain strategic sectors, such as aeronautics, the automotive industry, or oil infrastructure, fatigue accounts for more than half of the sources of failures observed in real-world systems. The integrity of structures in service crucially depends on their resistance to such fatigue. Under real service conditions, these structures are often subjected to complex and non-proportional cyclic loadings and are not immune to mechanical attacks, giving rise to surface defects that represent favorable sites for the initiation and propagation of cracks (Ballantyne, 2008; Irfan & Omar, 2017).
Pipelines, in particular, are susceptible to various types of defects, such as fatigue cracking, corrosion, etc. (Mohitpour et al, 2010; Zarea et al, 2012). Stress concentrations have been found to account for about 70% of crack initiation and subsequent ruptures in service (European Gas Pipeline Incident Data Group, 2020; Alberta Energy Regulator, 2020). The presence of such defects can be very harmful, and their fatigue behavior becomes dangerously unpredictable, hence the importance of quantifying fatigue damage for the prevention of failures in the oil and gas pipeline industry.
When there is a risk of catastrophic failure, such as bursting at the location of a crack, the concept of damage tolerance becomes a key tool. Broek (1989) defined damage tolerance as the capacity of a structure to withstand damage in the form of cracks without consequences until the damaged component can be repaired. Evaluation of crack propagation rates and prediction of the residual fatigue life are important for the design of structures and their maintenance under the effect of cyclic loading (the fatigue phenomenon). A number of published studies have proposed propagation models for cyclic loadings under constant amplitude and/or variable amplitudes (the phenomenon of overload or underload) (Kocańda & Torzewski, 2009; Jasztal et al., 2010). For aircraft structures, Moussouni et al. (2022) have developed an empirical model based on the Gamma function under applied constant amplitude loading. This model has used experimental data for aluminum alloy 2024 T351 published by Benachour et al. (2017), where best correlation is given comparatively to experimental data and Paris’ law.
There are two types of models. Empirical models (Paris & Erdogan, 1963; Elber, 1970), which only constitute an analytical description of results obtained in the laboratory by empirically incorporating the influence of various factors, are therefore limited to the framework that was used to establish them, unlike theoretical models (Forman et al., 1967; Weertman, 1973; Bibly et al., 1963) – the latter, in turn, have the disadvantage of rarely taking into account the role of the various factors. Currently, numerical models are finding application in simulating the behavior of crack propagation across all kinds of investigated materials (Fuiorea et al., 2009; Augustin, 2009; Witek, 2011). Several models have been proposed to predict the growth kinetics of defects, depending not only on the amplitude of the applied load, but also on all the factors affecting their propagation (Kebir et al, 2017; Kebir et al., 2021). The lifetime of these structures has been estimated using several methods.
Moreover, it has also been noted that many metal structures are affected by fatigue corrosion (Kudari & Sharanaprabhu, 2017; Kamińska et al., 2020; Czaban, 2017). Other studies (Sun & Cheng, 2019; Soares et al., 2019; Chen et al., 2015; Hredil et al., 2020) haveinvestigated pipelines with interacting corrosion defects. Fatigue behavior of two interacting 3D cracks in an offshore pipeline has been studied by Low (2021) using FEM. A simulation model to study fatigue behavior was developed by Zhang, Xiao, et al. (2018).
Modern aircraft use different types of pipes to transport fuel, hydraulic fluids, compressed air and other fluids essential to their proper operation. Defects in pipes due to corrosion effects can have significant consequences on aircraft leading to a reduction in their structural strength. This can lead to leaks or even rupture of the pipes, which compromises the safety of the aircraft.
In the present study, the AFGROW calculation code and the NASGROW model describing the crack growth rate are used to predict the fatigue life of pipelines with defects subjected to internal pressure. The influence of several parameters (pipe thickness, defect size, pipe radius and internal pressure) on the lifetime is examined.
This section examines the behavior of an external crack in the wall of a tube subjected to internal pressure. We are only interested in longitudinal and circumferential tube cracks, as these are important causes of leaks of transported fluid. We also studied the influence of the length of the crack on its propagation using the stress intensity factor; this work is part of the linear mechanics of fracture. In all this we used the Abaqus software, which allowed us to quantify the fracture in materials by the stress intensity factor.
The process simulation includes the geometric configuration of the tube (L = 1000 mm, D = 350 mm) followed by the tube under boundary conditions of internal pressure (P = 10 bars) and the mechanical properties of XC52 steel (Table 1). Also, we chose a finite quadratic type of mesh as appropriate for our case study (Figure 1).
Mechanical properties of X52 steel. (Harter, 2002; NASA, 2001)
Young’s modulus |
200 |
Poisson’s ratio |
0.30 |
Yield stress σY (MPa) | 410 |
Ultimate tensile stress σUTS (MPa) | 498 |
Elongation |
35 |
Toughness fracture (Mpa.mm1/2) | 95 |
Threshold (MPa.mm1/2) | 7 |
Firstly, the simulation consists in seeing the stress distribution Syy at the crack tip for the two cases studied: longitudinal and circumferential cracks in the tube wall. Given the concentration of stresses at the crack tip creating local plastification, the size of this zone must remain small compared to the length of the crack, so as to disrupt the structure of the pipeline, which leads to a fracture (Figure 2).
Figure 3 shows the evolution of the integral J as a function of crack length for a longitudinal (axial) crack and circumferential (transversal) crack, respectively. Comparison of the J integral values in Fig. 3 shows that the circumferential crack is more dangerous than the longitudinal crack with respect the cracks size. This change in variable behavior may be explained in terms of changes in the mode of loading. One can deduce that the type loading is responsible for the failure mode of API 5L X52 pipe in the presence of a defect. The same result has been observed by Benhamena et al. (2011), where the J integral values are found to be more important for a longitudinal crack as compared to a circumferential crack. In other studies, however, the opposite case is reported, with integral J values for a longitudinal pipe crack being significantly greater as compared to those for a circumferential crack (Kaddouri et al., 2004; Mechab et al., 2020).
Figures 4 and 5, respectively, present the stress intensity factor (SIF) for mode I and II (KI and KII) as function of the crack length for both crack orientations (longitudinal and circumferential). The resulting curves indicate that the SIF is large for a circumferential crack as compared to a longitudinal crack. The difference is important for crack length greater than 3.5 mm in mode I. On the other hand, the SIF for mode II (KII) is largely greater for the circumferential crack.
Fatigue life was predicted by a numerical simulation in the AFGROW software (Harter, 2002) using the NASGRO crack growth rate equation (NASA, 2001), given by the relation (1):
Where
Where
The threshold stress intensity factor amplitude is given by relation (7):
Where Δ
The algorithm for simulation by the AFGROW calculation code and the model NASGROW to predict fatigue life of a pipeline subjected to internal pressure is shown in Figure 6.
The material used in this study was API 5L Grade B, X52 steel, produced by AMPTA (Arcelor Mittal pipe and Algeria tube). Mechanical properties for the NASGROW model are presented in Table 2. Given the importance of pipeline distances and for good profitability, gas and oil companies use around ten grades of steel in different shades (Grade A, Grade B, X42, X46, X52, X56, X60, X65, X70, X80, etc.) (Harter, 2002; NASA, 2001).
Mechanical properties of X52 steel for NASGROW model. (Harter, 2002; NASA, 2001)
Young’s modulus |
200 |
Poisson’s ratio |
0.30 |
Yield stress σY(MPa) | 410 |
Ultimate tensile stress σUTS(MPa) | 498 |
Elongation |
35 |
Toughness fracture |
95 |
Threshold |
200 |
0.65 | |
0.001 | |
1.15e-10 | |
2.41 |
In this study we considered, we consider a longitudinal semi-elliptical crack present in the internal wall of the pipe. The geometry of the pipe is shown schematically in Figure 7.
The dimensions of the pipe are as follows:
Semi-elliptical flaws are characterized by the two ratios
In this section of this study, four different thicknesses were considered (
Test simulation conditions with different values of relative depth
Test | ||||
---|---|---|---|---|
1 | 350 | 344 | 3 | 0.30 |
2 | 350 | 342 | 4 | 0.25 |
3 | 350 | 340 | 5 | 0.20 |
4 | 350 | 339 | 6 | 0.16 |
Figures 8 to 11 present the evolution of the crack depth and length crack (
Figures 12 and 13, respectively, show the evolution of the crack depth and crack with respect to number cycles for different relative crack depth
Figure 13 shows the evolution of the relative crack depth
In this section of the study, we considered the influence of defect size on fatigue lifetime. Seven aspect ratios (
Tests simulation conditions with different values of aspect ratio
Test | Depth | Length | Aspect ratio |
---|---|---|---|
1 | 1 | 1 | 1 |
2 | 1 | 1.2 | 0.83 |
3 | 1 | 1.4 | 0.71 |
4 | 1 | 1.6 | 0.62 |
5 | 1 | 1.8 | 0.55 |
6 | 1 | 2 | 0.50 |
The evolution of the aspect ratio (
The dimensions of the structure are important parameters; for this purpose, we have simulated several tests by varying the radius of the pipeline. Table 5 presents the dimensions of the pipe and the crack.
Tests simulation conditions with different values of outer diameter
Test | ||||
---|---|---|---|---|
1 | 350 | 340 | 5 | 0.2 |
2 | 345 | 335 | 5 | 0.2 |
3 | 340 | 330 | 5 | 0.2 |
4 | 335 | 325 | 5 | 0.2 |
Figures 15 to 18 present the evolution of the transversal and longitudinal crack lengths (
Figure 19 shows the evolution of the outside diameter of the pipe according to the number of cycles. An increase in the outside diameter of the pipe leads to an increase in fatigue life.
Four pressure values (
Figure 20 shows the evolution of the depth of transversal crack and length of longitudinal crack respect to number cycles for different values of internal pressure. Note that an increase in internal pressure leads to an increase in the crack propagation rate and, consequently, to a reduction in the fatigue life.
The evolution of internal pressure with respect to number cycles is presented in Figure 21. As this figure shows, high internal pressure leads to short fatigue life and when the pressure decreases, the fatigue life increases.
This comprehensive numerical study has produced several critical findings regarding the fatigue life of pipelines in the face of defects and crack orientations. Most notably, it establishes that circumferential (transversal) cracks pose a higher risk than their longitudinal (axial) counterparts, due to differences in loading modes. Additionally, it was discovered that cracks oriented perpendicular to the pipe’s length tend to propagate more rapidly. The study also highlights the greater danger presented by semi-circular cracks over circular ones, emphasizes the beneficial impact of increasing pipe section on resistance to loading, and reveals that a larger conduit radius enhances the service life. A crucial observation is the inverse relationship between applied pressure and service life, underlining the need for careful pressure management to prevent premature pipeline failure.
Overall, the findings of this research may help improve the maintenance and monitoring strategies used for fluid transport systems, particularly in the aviation sector, by providing a deeper understanding of crack evolution in pipelines. Through the application of finite element analysis, this work not only aids in predicting the fatigue life of pipelines more accurately but also facilitates informed decision-making regarding their integrity and maintenance.