A Modified Exponential Model for Predicting the Fatigue Crack Growth Rate in a Pipeline Steel Under Pure Bending

Machine learning (ML) has powerful nonlinear processing and multivariate learning capabilities, so it has been widely utilised in the fatigue field. However, most ML methods are inexplicable black-box models that are difficult to apply in engineering practice. Symbolic regression (SR) is an interpretable machine learning method for determining the optimal fitting equation for datasets. In this study, domain knowledge-guided SR was used to determine a new fatigue crack growth (FCG) rate model. Three terms of the variable subtree of ΔK, R-ratio, and ΔKth were obtained by analysing eight traditional semi-empirical FCG rate models. Based on the FCG rate test data from other literature, the SR model was constructed using Al-7055-T7511. It was subsequently extended to other alloys (Ti-10V-2Fe-3Al, Ti-6Al-4V, Cr-Mo-V, LC9cs, Al-6013-T651, and Al-2324-T3) using multiple linear regression. Compared with the three semi-empirical FCG rate models, the SR model yielded higher prediction accuracy. This result demonstrates the potential of domain knowledge-guided SR for building the FCG rate model.

Acidizing treatments are typically performed intermittently during the life of a well. However, more recently there has been a desire to perform an increased number of acidizing treatments in order to improve production. The acidizing treatments typically involve highly corrosive acids, such as hydrofluoric (HF), hydrochloric (HCl) and acetic acid, which are known to cause significant corrosion, but could also lead to environmentally assisted fatigue and fracture. A study was performed to evaluate the effect of cyclic plastic strains associated with reeling installation on the subsequent fatigue crack growth rate (FCGR) behavior of welded C-Mn line pipe steel in acidizing environments. The influence of the pH of the acidizing environment on the FCGR performance was also investigated as part of this study. This paper compares the results of FCGR tests on as-welded (i.e. unstrained) pipe with those from strained and aged welds, as well as quantifying the effect of the pH of the acidizing treatments. Strained and aged welds were obtained by subjecting the as-welded pipe to 4 cycles of full-scale reeling simulation, with each cycle corresponding to 1% strain. Small-scale compact tension (CT) specimens were then extracted from the strained welds and aged at 250°C for one hour to simulate strain aging. FCGR tests were performed in spent acid with corrosion inhibitor on specimens notched in the parent pipe (PP), heat affected zone (HAZ) and weld centerline (WCL) in both the as-welded and strained and aged condition. The majority of the tests were conducted at room temperature (RT) along with a select few tests at elevated temperature (165°F / 74°C). Overall, the results of frequency scan tests indicated that reeling did not have a significant effect on the FCGR behavior of welded C-Mn line pipe steel in spent acid with inhibitor, regardless of which microstructure was sampled. Frequency scan FCGR tests were also performed on strained and aged samples extracted from the intrados side of the strained welds and notched in the PP, HAZ and WCL to investigate the influence of pH on FCGR behavior. Tests were performed in spent acid with inhibitor at RT, with the pH ranging from 3.7 to 6. The observed FCGRs were higher than in air and all microstructures exhibited a frequency dependence (i.e. the FCGR increased with decreasing frequency). At pH = 3.7, the maximum FCGR was approximately 30 times higher than in air and at pH = 5 the FCGR increased to approximately 80 times higher than in air. However, a further increase in pH to 6 produced a decrease in FCGR. The increase in the maximum FCGR is believed to be due to the decrease in corrosion rate with increasing pH leading to reduced crack closure/blunting. However, as the pH increased to around 6, the corrosion rate decreased substantially, which is likely due to a substantial decrease in the concentration of hydrogen being generated, resulting in a lower FCGR. Paris curve FCGR tests were subsequently conducted on strained and aged samples at 0.1Hz.

A theoretical model for fatigue crack growth rate at low and near threshold stress intensity factor is developed. The crack tip is assumed to be a semicircular notch of radius ρ and incremental crack growth occurs along a distance 4ρ ahead of the crack tip. After analysis of the stress and strain distribution ahead of the crack tip, a relationship between the strain range and the stress intensity range is proposed. It is then assumed that Manson-Coffin cumulative rule can be applied to a region of length 4ρ from the crack tip, where strain reversal occurs. Finally, a theoretical equation giving the fatigue crack growth rate is obtained and applied to several materials (316L stainless steel, 300M alloy steel, 70-30 α brass, 2618A and 7025 aluminum alloys). It is found that the model can be used to correlate fatigue crack growth rates with the mechanical properties of the materials, and to determine the threshold stress intensity factor, once the crack tip radius α is obtained from the previous data.

Acidizing treatments are typically performed intermittently during the life of a well. However, more recently there has been a desire to perform an increased number of acidizing treatments in order to improve production. The acidizing treatments typically involve highly corrosive acids, such as hydrofluoric (HF), hydrochloric (HCl) and acetic acid, which are known to cause significant corrosion, but could also lead to environmentally assisted fatigue and fracture. A study was performed to evaluate the effect of acidizing treatments on the fatigue behavior of welded C-Mn line pipe steels. This paper describes the results of fatigue crack growth rate (FCGR) tests on as-welded (i.e. unstrained) pipe. FCGR tests were conducted at room temperature (RT) in three different acid conditions: fresh acid with corrosion inhibitor, spent acid with corrosion inhibitor and spent acid without corrosion inhibitor. Frequency scan FCGR tests were performed on compact tension (CT) specimens notched in the parent pipe (PP), heat affected zone (HAZ) and weld centerline (WCL). The FCGRs in all three environments were higher than in air and exhibited a frequency dependence. Tests in fresh acid with inhibitor exhibited plateau FCGR values around 20–30 times higher than in air. Tests in spent acid with inhibitor exhibited a strong frequency dependence with plateau FCGR values approximately 80–100 times higher than in air. In spent acid without inhibitor, the plateau FCGR was around 20 times higher than in air, however at the lowest frequencies the FCGR decreased, most likely due to crack closure/blunting effects. This behavior is consistent with the higher corrosion rate in this uninhibited environment. The role of corrosion products in causing crack closure/blunting was further evidenced in tests performed at elevated temperature (165°F / 74°C), where the FCGR at 1Hz was significantly higher than at RT. The plateau FCGR in fresh acid and spent acid with inhibitor was approximately 40–50 times higher than in air, but the FCGR decreased at lower frequency. This is similarly believed to be due to the higher corrosion rates at elevated temperature causing crack closure/blunting. The FCGR in spent acid without inhibitor at 165°F (74°C) was high initially at 1Hz but then decreased sharply, which is consistent with the highest corrosion rates expected at elevated temperature and in the absence of corrosion inhibitor. Paris curve FCGR tests were subsequently conducted at 0.1Hz. Tests were performed in the worst case combinations of microstructure/environment/temperature identified from the frequency scan tests.

PurposeThe study aims to provide a basis for the effective use of safety-related information data and a quantitative assessment way for the occurrence probability of the safety risk such as the fatigue fracture of the key components.Design/methodology/approachThe fatigue crack growth rate is of dispersion, which is often used to accurately describe with probability density. In view of the external dispersion caused by the load, a simple and applicable probability expression of fatigue crack growth rate is adopted based on the fatigue growth theory. Considering the isolation among the pairs of crack length a and crack formation time t (a∼t data) obtained from same kind of structural parts, a statistical analysis approach of t distribution is proposed, which divides the crack length in several segments. Furthermore, according to the compatibility criterion of crack growth, that is, there is statistical development correspondence among a∼t data, the probability model of crack growth rate is established.FindingsThe results show that the crack growth rate in the stable growth stage can be approximately expressed by the crack growth control curve da/dt = Q•a, and the probability density of the crack growth parameter Q represents the external dispersion; t follows two-parameter Weibull distribution in certain a values.Originality/valueThe probability density f(Q) can be estimated by using the probability model of crack growth rate, and a calculation example shows that the estimation method is effective and practical.

It is well known that the welded residual stress has marked influence on fatigue crack growth rate in welding structure. In particular, because the tensile residual stress may accelerate the fatigue crack growth rate, it is important to develope the method of residual stress-relief. We have succeeded in relief of residual stress up to about 80% by using a method of mechanical stress relief which was the slow preloading of welded joint. The effects of residual stress relieved, stress ratio and preloadingg on fatigue crack growth rate in welded joints were investigated in associated with crack closure phenomenon. The results obtained are summarized as follows.(1) For the tensile residual stress fields after preloading, the fatigue crack growth rate was accelerated by the tensile residual stress relieved even if the stress ratio was low. Then, the fatigue crack growth rate accelerated was not changed regardless of the strength of residual stress fields and stress ratio.(2) For the compressive residual stress fields after preloading, the fatigue crack growth rate was considerably lower than that of base metal. After the crack arrested as the stress intensity range approached the threshold for crack growth, the fatigue crack growth rate increased with increasing stress intensity range and stress ratio.(3) The preloading scarecely resulted in the change of crack growth rate in the tensile residual stress field but markedly accelerated the rate in the compressive residual stress field.(4) It became clear that the effects of welding residual stress, stress ratio and preloading on fatigue crack growth rate in welding residual stress fields can be explained by the effective stress intensity range defined from both the welding residual stress- and plastic- induced crack closure.

During the selective laser melting (SLM) process of Ti6Al4V, a special structure can be formed with columnar prior β grains along the building direction and fully martensitic α′ within the β grain. To investigate the influence of such special structure on the fatigue crack growth (FCG) rate, Ti6Al4V specimens fabricated by SLM were heat‐treated at two different temperatures in this study. The columnar grains were retained, and the martensite was decomposed when heat‐treated below the β transus. It is found that all the SLM features were removed when heat‐treated above the β transus. FCG rate tests were subsequently performed at room temperature, and it was found that the prior β grains affected the macroscopic fracture morphology, but there was no discernible influence on the FCG rate. The morphology of the α phase affected the crack growth path and the FCG rate. Changes in the strength‐toughness relationship induced by heat treatment can help understand the decrease in the FCG rate.

A fatigue crack initiated in welded structure propagates through the welded residual stress field. It is a very important problem to clarify the effect of welded residual stress on fatigue crack growth rate. For the butt welded joint of 600MPa grade steel, the effects of tensile and compressive residual stresses were investigated in association with the crack closure phenomenon. The results obtained are summarized as follows.(1) For the welded joint in which the fatigue crack propagated through the tensile residual stress field, the fatigue crack growth rate was accelerated by the tensile residual stress. But, the acceleration of fatigue crack growth rate was independent of the stress ratio and the intensity of residual stress.(2) For the welded joint in which the fatigue crack propagated through the compressive residual stress field, the fatigue crack growth rate decreased with increasing stress intensity range, and the crack arrested as the stress intensity range approached the threshold for crack growth, ΔK0. At the stress intensity range above ΔK0, the fatigue crack growth rate increased with increasing stress intensity range. The increase of stress ratio has given rise to increase in fatigue crack growth rate and decrease in ΔK0 value. Such a stress ratio effect was the same as the results of base metal.(3) It is considered that the welded residual stress has an effect on the fatigue crack growth rate to change the mean stress at the crack tip. This effect may be explained by the equivalent stress ratio, Req, defined by the following equation.Req=R-2Kres/Kmax

The frequency effect on the fatigue crack growth rate of 304 stainless steel

Hydrogen embrittlement phenomenon has been investigated in the current study by performing crack growth rate (CGR) measurements under static and fatigue loading conditions on fracture mechanics-based specimen extracted from X-65 line pipe steel. The source of hydrogen inside the line pipe could be the green/blue hydrogen blending that is being considered in an effort to reduce the carbon footprint of the oil and gas industry. Other environments could be aqueous impurities such as NaCl in presence of the transported CO2 and hydrogen charging conditions created by a possible use of sacrificial metallic coatings. The effect of cyclic loading frequency on fatigue crack growth rate (FCGR) has been investigated in a simplified hydrogen charging environment - 3.5% NaCl solutions containing CO2 at room temperature, with imposed CP. The applied hydrogen charging conditions were electrochemical potentials associated with mixed potential of Zn and/or Al based coatings, being considered for sacrificial metal coatings. FCGR in environment was found to be significantly higher than in-air values and was also found to increase with decrease in frequency of applied fatigue loading, suggesting susceptibility to environmentally assisted cracking. A segmented crevice electrode setup was designed to simulate electrochemical conditions experienced by crack tip for a given bulk chemistry and cathodic polarization (CP) applied to freely exposed surface. It was found that the CP level experienced by electrodes inside the crevice was not the same as that of the freely exposed surface in solution. These experiments supplement the results of the CGR measurement tests.

Fatigue fracture is one of the main failure modes of Ti-6Al-4V alloy, fracture toughness and crack closure have strong effects on the fatigue crack growth(FCG) rate of Ti-6Al-4V alloy. The FCG rate of Ti-6Al-4V is investigated by using experimental and analytical methods. The effects of stress ratio, crack closure and fracture toughness on the FCG rate are studied and discussed. A modified prediction model of the FCG rate is proposed, and the relationship between the fracture toughness and the stress intensity factor(SIF) range is redefined by introducing a correcting coefficient. Notched plate fatigue tests (including the fracture toughness test and the FCG rate test) are conducted to investigate the influence of affecting factors on the FCG rate. Comparisons between the predicted results of the proposed model, the Paris model, the Walker model, the Sadananda model, and the experimental data show that the proposed model gives the best agreement with the test data particularly in the near-threshold region and the Paris region, and the corresponding calculated fatigue life is also accurate in the same regions. By considering the effects of fracture toughness and crack closure, the novel FCG rate prediction model not only improves the estimating accuracy, but also extends the adaptability of the FCG rate prediction model in engineering.

Steel catenary risers (SCRs) are increasingly used in deepwater oil and gas developments. SCRs can be subject to low-stress high-cycle fatigue loading (e.g. VIV) and corrosive environments (internal and external). When the production fluids are sour, higher fatigue crack growth rates (FCGRs) are expected and shorter overall life compared to performance in air. Published data from tests carried out on C-Mn pipeline steel have shown that sour FCGRs can be 100 times faster than in air. Shallow cracks have been shown to grow up to an order of magnitude faster than deep cracks in a sour environment at the same (low) value of applied stress intensity factor range (?K). In many cases it is material behaviour in this low ?K regime that dominates fatigue life. The possible influence of crack depth on material behaviour should be considered when conducting tests to determine FCGRs for use in fracture mechanics calculations. Low ?K data are usually determined under decreasing ?K conditions, by which time the crack is deep. In reality a flaw is likely to grow under increasing ?K conditions, such that the flaw is shallow at the beginning of life (when ?K is low). At low values of ?K (i.e. approaching threshold) FCGRs in C-Mn pipeline steel determined from decreasing ?K tests have been shown to be substantially lower than those determined from increasing ?K tests. This demonstrates a potential non-conservatism if the low ?K data generated under decreasing ?K conditions are used to predict the behaviour of a much shallower flaw. This paper presents the results of recent sour FCGR tests on C-Mn pipeline steel. Increasing ?K tests were performed on specimens containing shallow initial flaws at very high stress ratios, to obtain data at lower ?K. This paper provides valuable insight into current best practice methods for generating sour FCGR data when qualifying girth welds for sour service. Introduction and Background Steel catenary risers (SCRs) are increasingly used in deepwater oil and gas developments to transfer production fluids from the seabed to surface facilities. SCRs can be subject to both fatigue loading, for example from wave and tidal motion, vortex induced vibration (VIV) and operating loads, and corrosive environments (internal and external). When the production fluids are sour (i.e. contain water and H2S) higher fatigue crack growth rates (FCGRs) are expected and therefore shorter overall life compared to performance in air, as a result of the interaction between fatigue crack growth and sulphide stress cracking (SSC). Successful design is critically dependent on the availability of appropriate experimental data to quantify the extent to which fatigue lives are reduced and rates of fatigue crack growth are increased. C-Mn steel is generally the most economic material for the construction of offshore pipelines and risers and there is an industry need to understand better and to quantify its fatigue crack growth behaviour in sour service environments. If carbon steel can provide adequate performance under (mildly) sour conditions then the use of more expensive corrosion resistant alloys (CRAs) and clad materials might be avoided.

The increase in fatigue crack growth rates observed for Zircaloy-4 in a PWR environment

Effects of stress ratio and temperature on fatigue crack growth in a Ti–6Al–4V alloy

Predicting fatigue crack growth rates and thresholds at low temperatures