Investigating the Effects of Crack Orientation and Defects on Pipeline Fatigue Life Through Finite Element Analysis

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).

Figure 1.

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 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).

Figure 3.

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.

Figure 4.

Figure 5.

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): 1 dadN=C[ (1−f1−R)ΔK ]n(1−ΔKthΔK)p(1−KmaxKcrit)q \[\frac{da}{dN}=C{{\left[ \left( \frac{1-f}{1-R} \right)\Delta K \right]}^{n}}\frac{{{\left( 1-\frac{\Delta {{K}_{th}}}{\Delta K} \right)}^{p}}}{{{\left( 1-\frac{{{K}_{\max }}}{{{K}_{crit}}} \right)}^{q}}}\]

Where K_max is the maximum applied stress intensity factor and K_crit is the critical stress intensity factor at rupture; N is the number of applied fatigue cycles; a is the crack length; R is the stress ratio; ΔK is the amplitude factor of stress intensity factor; C, n, p, and q are empirically derived constants; and (f) is Newman’s closure function (NASA, 2001), introduced to take intoaccount the phenomenon of fracture closure induced by plasticity: 2 f=KopKmax{ max(R,A0+A1R+A2R2+A3R3)→with:R≥0A0+A1R→with:−2≤R≤0A0−2A1→with:R≤−2 \[f=\frac{{{K}_{op}}}{{{K}_{\max }}}\left\{ \begin{array}{*{35}{l}} \max \left( R,{{A}_{0}}+{{A}_{1}}R+{{A}_{2}}{{R}^{2}}+{{A}_{3}}{{R}^{3}} \right)\to \text{with}\,:\,R\ge 0 \\ {{A}_{0}}+{{A}_{1}}R\to \text{with}\,:\,-2\le R\le 0 \\ {{A}_{0}}-2{{A}_{1}}\to \text{with}\,:\,R\le -2 \\ \end{array} \right.\]

Where K_op is the stress intensity factor corresponding to the opening load, A₀, A₁, A₂, and A₃ are coefficients such that: 3 A0=0.825−0.34α+0.05α2[ cos(π2Smax/σ0) ]1α \[{{A}_{0}}=0.825-0.34\alpha +0.05{{\alpha }^{2}}{{\left[ \cos \left( \frac{\pi }{2}{{S}_{\max }}/{{\sigma }_{0}} \right) \right]}^{{}^{1}\!\!\diagup\!\!{}_{\alpha }\;}}\] 4 A1=(0.415−0.071α).Smax/σ0 \[{{A}_{1}}=\left( 0.415-0.071\alpha \right).{{S}_{\max }}/{{\sigma }_{0}}\] 5 A2=1−A0−A1−A1−A \[{{A}_{2}}=1-{{A}_{0}}-{{A}_{1}}-{{A}_{1}}-A\] 6 A3=2A0+A1−1 \[{{A}_{3}}=2{{A}_{0}}+{{A}_{1}}-1\] σ₀ is plane stress factor; S_max/σ₀ is the ratio of the maximum stress applied to the flow stress; α is the constraint parameter which is used to take into account the stress state effect into account. According to theory, when there is plane stress, the value of α is 1, and when there is plane strain, it is 3.

The threshold stress intensity factor amplitude is given by relation (7): 7 ΔKth=ΔK0(aa+a0)1/2(1−f(1−A0)(1−R))(1+CthR) \[\Delta {{K}_{th}}=\Delta {{K}_{0}}\frac{{{\left( \frac{a}{a+{{a}_{0}}} \right)}^{1/2}}}{{{\left( \frac{1-f}{\left( 1-{{A}_{0}} \right)\left( 1-R \right)} \right)}^{\left( 1+{{C}_{th}}R \right)}}}\]

Where ΔK₀ is the threshold stress intensity factor amplitude for R = 0; a is the crack length; a₀ is the initial crack length; C_th is the threshold coefficient; R is load ratio.

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.

Figure 6.

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.

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.