Axial Surface Cracks Research Articles

Burst failure analysis of PVC-UH pipes with axial surface crack based on multiple methodologies

High-performance unplasticized polyvinyl chloride (PVC-UH) offers superior strength and performance compared to PVC, making it a common choice for municipal water supply pipelines. Cracks in PVC-UH pipes are challenging to prevent throughout the entire production and maintenance process. Precise and applicable failure assessment and residual bearing capacity calculation methodology are crucial for ensuring the safe operation and maintenance of PVC-UH municipal water supply pipes. To this end, this paper conducted material uniaxial tensile tests, fracture toughness tests, and pipe burst tests. The study determined the true stress–strain relationship, fracture toughness, burst pressure, and fracture morphology of PVC-UH pipes through testing. Failure pressures of cracked PVC-UH pipes were forecasted using different methodologies, and their accuracy and applicability were evaluated by comparing predicted values with the results of bursting tests. Two calculation methods for determining the failure pressure of pipelines with an axial outer surface crack are proposed based on plastic deformation, damage factor, and fracture mechanics theory. These proposed calculation methods are compared against current methods for determining the failure pressure of pipelines with crack defects, highlighting the higher accuracy of the methods introduced in this paper. The research results can serve as a reference for selecting failure assessment methods for PVC-UH pipelines. Additionally, the proposed calculation methods can accurately and rapidly predict the failure pressure of pipelines with identified axial surface crack sizes, providing technical support for engineering safety assessments of PVC-UH pipelines.

Load-independent creep constraint analysis and solutions for surface cracks in pressurized pipes

Using load-independent creep constraint parameters Q* and Qm*, the variations of crack front stress field and constraint level are analyzed for various crack sizes of pipelines containing internal surface cracks under high temperature conditions. The results show that the trends of stress changes in the axial and circumferential internal surface crack front for different crack sizes are similar. For axial internal surface cracks, when the crack depth to length ratio a/c is the same, the maximum values of crack front Q* and Qm* are shifted from the deepest part of the crack (2Φ/π = 1) to the vicinity of the free surface (2Φ/π = 0.2) as the crack depth a/t increases. As for the circumferential inner surface cracks, when the crack depth a/t exceeds 0.2, the locations where the maximum values of crack fronts Q* and Qm* appear are mainly concentrated in the deepest part of the crack (2Φ/π = 1). Based on the calculation results of the constraint parameters, the empirical formulas for the engineering calculation of the relationship between the average constraint parameters (Qavg* and Qm‐avg*) and the crack size are obtained by fitting.

Fracture analysis of hydrogen-embrittled API X52 pipes at low temperature

This paper quantifies the effect of temperature (ranging from room temperature (RT) to -90 °C) on fracture toughness for hydrogen-embrittled API X52 by combining small punch (SP) test data and finite element (FE) damage analysis. For the FE damage analysis, a multi-axial fracture strain damage model was used, and the parameters were determined by analyzing the tensile and SEN(T) test data in air at RT. The hydrogen-enhanced ductile fracture was considered using the hydrogen-embrittlement constant, which was determined by analyzing the SP test results in hydrogen. Due to the effect of the interaction between strength and hydrogen-induced ductility loss on fracture toughness, the predicted fracture toughness in terms of temperature does not show a monotonic decrease up to -90 °C; rather, it decreases up to -30 °C, then increases slightly before decreasing again. Fracture mechanics analysis of a hydrogen-embrittled pipe with an axial surface crack using the determined fracture toughness values showed that the maximum pressure decreased slightly (less than 9 %) with decreasing temperature up to -90 °C, suggesting that the effect of temperature on the maximum pressure would not be so significant for API X52.

Fatigue crack growth simulation by extended finite element method: A review of case studies

AbstractNumerical simulation of fatigue crack growth (FCG) is presented, based on the application of the extended finite element method (XFEM). Couple of case studies are presented, as a review of recent experience of the Belgrade school of XFEM simulations, established at the Faculty of Mechanical Engineering. Case studies comprised Charpy specimen with initial crack at the notch tip, oil rig pipe with an axial surface crack, pressure vessels with a crack at the welded joint with connecting pipe, turbine shaft with a crack at the transition radius, optimization of a wing spar in respect to FCG, the effect of mesh size on fatigue life estimation of a stringer panel, fatigue life estimation of wing‐to‐fuselage connecting lug, geometry effect on fatigue life of orthopedic plates and fatigue life of hip implant. Based on these case studies, XFEM is discussed in respect to its accuracy and efficiency. It is concluded that XFEM is a versatile tool for simulation of FCG, providing an excellent option for precise and reliable fatigue life of a cracked component.

Development of pressure-temperature limit curves considering unified constraint for reactor pressure vessel

In this work, the pressure-temperature (P-T) limit curves considering unified constraint for a typical large-sized reactor pressure vessel (RPV) with axial surface cracks have been investigated and developed based on the KJ-Ad* two-parameter and the Master Curve (MC) method. The ASME fracture toughness KIc curve and the MC with and without considering unified constraint for irradiated RPV steel were used in the constructions of the P-T limit curves. The effects of crack sizes (constraint levels) and fracture toughness curves on the P-T limit curves have been analyzed for the RPV under heatup and cooldown conditions. The results further show that the P-T limit curves based on traditional ASME KIc curve has the highest degree of conservatism and the use of the MC method can significantly increase the safety margin of P-T limit curves. With increasing crack sizes (increasing constraint levels), the safety region in P-T limit curves reduces, which may lead to the decrease of operating flexibility for nuclear power plants. The accuracy of the P-T limit curves can be improved by considering unified constraint. For smaller size cracks with lower constraint in the RPV, the consideration of constraint can reduce conservatism of the P-T limit curves, and for larger size cracks with higher constraint, it can avoid the non-conservatism. It is recommended to obtain more accurate P-T limit curves based on the MC with considering unified constraint and finite element analysis for RPVs under various operating conditions.

Integrity assessment considering unified constraint for reactor pressure vessel under pressurized thermal shock

The integrity assessment methodology based on a new unified constraint parameter Ad* and the Master Curve has been investigated for a typical Chinese reactor pressure vessel (RPV) containing axial surface cracks subjected to pressurized thermal shock (PTS). The thermal–mechanical analysis was carried out under two different PTS transients using finite element method. The integrity assessment has been conducted by comparing the KJ-T curve and KJc-T curve (KJ is elastic–plastic stress integrity, KJc is fracture toughness and T is the crack-tip temperature), and the safety margin was quantitatively analyzed. The results show that the Ad* value does not change with temperature and loads (thermal load and internal pressure load) during PTS due to its load and material independences, and which facilitates the constraint analysis for a RPV under PTS. For smaller size surface cracks usually occurring in the RPV, the integrity assessment considering unified constraint under PTS can reduce excessive conservatism of traditional assessment method. The safety margin of integrity assessment is mainly influenced by constraint levels, PTS transients and fracture toughness of irradiation materials, and methods for increasing safety margin are discussed.

Magnetic field and thermal environment effects on sound transmission loss of double-walled cracked piezoelectric cylindrical nanoshells

Based on a non-local strain gradient theory (NSGT), this article analytically studies the sound transmission loss (STL) performance of a special type of double-walled partially cracked piezoelectric nanoshell structures of cylindrical shape undergoing initial electric potential and longitudinal magnetic field. The structure, which includes a specific number of axial and circumferential surface cracks, is struck by a plane wave in a thermal setting. Such cracks have minimal size compared to the nano-shell structure as a whole, minimizing the effects of curvature for this problem. The first-order shear deformation theory (FSDT) is utilized to explain the displacement components, and Hamilton’s concept is applied to obtain the coupled vibroacoustic equations that are used to generate the governing equations of the system for the two crack types, giving us an idea of the resulting structural stiffness in the presence of cracks using coefficients of crack compliance that are derived from the line spring model (LSM). The mechanical and acoustic properties are then checked to see their effect on the system response followed by a series of validation case studies. This evaluation also allows one to optimize a similar structure by selecting appropriate external parameters such as electric voltage, magnetic field intensity, different crack types, nonlocal and strain gradient parameters, variations of temperature, and incident angle of sound waves.

A Creep Constitutive Model, Based on Deformation Mechanisms and Its Application to Creep Crack Growth

In this paper, a constitutive model, based on the creep deformation mechanism in P91 steel, under a wide range of stress levels, was established and embedded into finite element software. The accuracy and reliability of the model was verified by comparing the simulation of uniaxial creep tensile test results and the experimental data under different stress levels for P91 steel at 600 °C. The creep crack growth behavior of P91 steel, under a wide range of stress levels was simulated using a ductility-exhaustion-based damage model, combined with the stress-dependent creep ductility model, and the predicted creep crack growth (CCG) rates were compared with the experimental data. Finally, the established model was used to predict the CCG behavior for the pressurized pipes with axial surface cracks. The results show that the constitutive model, established on the basis of the creep deformation mechanism, agrees better with the experimental data than other constitutive models. The CCG rate varies at different direction angles θ for the axial surface cracks. The direction angle θ corresponding to the maximum creep crack length is about 33°, when the internal pressure exceeds 10 MPa. The initial crack shape (a0/c0) = 1, and it does not change with different initial crack depth ratios (a0/t). The established constitutive model can be well used in CCG life analyses and designs of high-temperature structures.

Application of unified constraint-dependent Master Curve in fracture assessment of cracked pressure vessels

In this work, the application of the unified constraint-dependent Master Curve (UCMC) in fracture assessment based on the newly developed T0-Ad* correlation equation (T0 is the MC reference temperature, and Ad* is a new unified constraint parameter) has been investigated for cracked pressure vessels. A large number of three-dimensional (3D) finite element analyses have been conducted to calculate the parameter Ad* and the crack driving force parameter KJ for various axial semi-elliptical surface cracks. Based on the KJ-Ad* two-parameter, the locations of crack initiation along the crack fronts were predicted. The fracture prediction results of the UCMC method have been comparatively analyzed with those of the conventional standard MC (SMC) method. It has been shown that for most shallow cracks with lower constraint, the application of the UCMC method can reduce the conservatism of the SMC method. For some deeper and longer cracks with higher constraint, the UCMC method may eliminate slight non-conservative fracture assessment of the SMC method. The UCMC method can incorporate both in-plane and out-of-plane constraints in cracked structures, and it may be possibly applicable to wide ranges of structural geometries, crack sizes, materials, temperatures and loading levels.

Closed-Form Stress Intensity Factor Solutions for Circumferential and Axial Surface Cracks With Large Aspect Ratios in Pipes

Abstract The ASME Boiler and Pressure Vessel Code Section XI prescribes the stress intensity factor solutions at the surface and deepest points for a semi-elliptical crack. The ASME Code Section XI, however, provides no solutions for a crack with a large aspect ratio, that is a crack in which the crack depth a is larger than the half-length c. The difficulty in treating the crack with a large aspect ratio relates to the position of the maximum stress intensity factor, which appears at neither the surface point nor the deepest point. In this paper, we investigate the influence of the stress intensity factor at the maximum point for circumferential and axial inside surface cracks with a large aspect ratio in a cylinder. First, we obtain the influence coefficients Gi for the stress intensity factor at the surface point, the deepest point, and the maximum point by finite element analysis, and developed a series of closed-form Gi solutions. Three geometrical factors are considered as parameters affecting the influence coefficients Gi: aspect ratio (a/ℓ = 0.5, 1.0, 2.0, and 4.0), crack depth ratio (a/t = 0.01, 0.1, 0.2, 0.2, 0.4, 0.6, and 0.8), and radius to thickness ratio (Ri/t = 2, 5, 10, 20, 40, and 80). Finally, we propose methods for evaluating the stress intensity factor for a crack with a large aspect ratio in a manner that characterizes the influence of the solutions at the maximum point.

Reference stress J estimation for cylinders with axial surface cracks under combined pressure and global bending moment

Several available limit load solutions for cylinders containing axial surface cracks, including the R6 global limit pressure solutions and newly published global/local solutions for combined pressure and global bending moment, are validated for J predictions via the reference stress J scheme using 336 finite element (FE) elastic-plastic J cases. The results for pure pressure loading show that the R6 global Tresca limit pressure solution for internal cracks is reasonably conservative but that for external cracks needs to apply a factor of 0.95. The results for combined loading show that the R6 global limit pressure solutions are non-conservative when the bending moment is significant and the newly published global/local limit load solutions can lead to good J predictions but the predictions may be non-conservative for some cases. Modifications to the newly published global/local limit load solutions are proposed and further validation using the FE J results shows that both the modified new global/local limit load solutions can lead to reasonable conservative J predictions when used with the reference stress J scheme.

Leak before break fracture assessment of pressurized unplasticized PVC pipes with axial surface crack: Experimental and analytical analysis

This paper compares Failure Assessment Diagram-based and Stress Intensity Factor-based analytical approaches with experimental results for assessing leak before break in axial finite semi-elliptical cracked Polyvinyl Chloride pipes subjected to internal pressure. Surface crack length of 25, 40 and 60 mm and depth to thickness ratio of 0.25, 0.5 and 0.75 were investigated. Burst pressures are experimentally evaluated for all cracked and uncracked samples. Results illustrated that the Failure Assessment Diagram approach is more reliable than Stress Intensity Factor approach for fracture assessment of unplasticized PVC pipes.

Constraint-corrected fracture mechanics analysis of nozzle crotch corners in pressurized water reactors

This paper presents fracture mechanics analysis results for various cracks located at pressurized water reactor pressure vessel nozzle crotch corners taking into consideration constraint effect. Technical documents such as the ASME B&PV Code, Sec.XI were reviewed and then a fracture mechanics analysis procedure was proposed for structural integrity assessment of various nozzle crotch corner cracks under normal operation conditions considering the constraint effect. Linear elastic fracture mechanics analysis was performed by conducting finite element analysis with the proposed analysis procedure. Based on the evaluation results, elastic-plastic fracture mechanics analysis taking into account the constraint effect was performed only for the axial surface crack of the reactor pressure vessel outlet nozzle with cladding. The fracture mechanics analysis result shows that only the axial surface crack in the reactor pressure vessel outlet nozzle has the stress intensity factor exceeding the low bound of upper-shelf fracture toughness irrespectively of considering the constraint effect. It is confirmed that the J-integral for the axial crack of the outlet nozzle does not exceed the ductile crack initiation toughness. Hence, it can be ensured that the structural integrity of all the cracks is maintained during the normal operation.

Stress Analysis in Damaged Pipeline with Composite Coating

This paper studied the distribution of stresses near damage in the form of axial surface cracks in a pipeline reinforced with a spiral-wound composite coating. The authors applied the homogenization method to determine the effective elastic characteristics of a structurally anisotropic layered package. By means of the classical momentless theory of shells, it was established that the stress state of the coated intact pipe under the pressure of the pumped product depends on the parameters of the geometry of the capacity strip, as well as on the component composition of the heterogeneous coating. The finite element method was applied to solve the problem of plane deformation of a piecewise homogeneous ring with an internal crack perpendicular to the interface. This problem assumes the linearity of the materials and the ideal mechanical contact with the layers. The effect of the composite coating and the size of the damage on the magnitudes of the energy flow into the crack tip, and on the stress intensity factor, was studied in detail. Various variants of the coating were considered, namely, winding of the coating on an unloaded pipe and reinforcement of the pipe under repair pressure.

Limit load for cylinders with axial internal surface cracks under combined internal pressure and global bending moment

The global and local limit loads for cylinders with axial internal surface cracks under combined internal pressure and global bending moment are investigated using the elastic-perfectly plastic finite element (FE) method. An ellipse function is recommended to describe the relationship between the normalised global limit pressure and normalised global limit bending moment. The predictions using the ellipse function are conservative compared with the global FE results except for the cases with bending moment dominance, where the predictions may be slightly non-conservative. The investigation shows that the local limit load FE results can be well described by the local limit load model recommended by Lei and the predictions are all reasonably conservative except for cases with very long and deep cracks. Further work is required to validate the recommended global and local limit load solutions for J predictions when they are used in the reference stress J scheme.

Statistical inference and performance evaluation for failure assessment models of pipeline with external axial surface cracks

It is important to investigate the uncertainty of failure assessment models for safety management and reliability calculations of pipelines containing cracks. In this paper, firstly, we predict the burst pressure of 250 experiments with 9 different failure assessment models and obtain the prediction accuracy (PA) based on the measured test data. Secondly, the PA of different models is analyzed according to the new model prediction performance evaluation system, which includes distributional location characteristics (rough accuracy, risk, robustness and conservativeness) and stability (dispersion, correlation and multi-peakedness). Finally, the critical safety factors are determined for different models to control reliability based on the best-fit distribution. The results show that for distribution location characteristics, CorLAS is the most accurate; the R6-2A-I (R6-Option 2A, global solution based on the Tresca criteria, 2016), API-Ⅱ (API RP 579-Level 2, 2016), R6-2A-III (R6-Option2A, local solution, 2016) and SINTAP-I (SINTAP-Level 1, 1999) are robust; CorLAS and R6-2A-II (R6-Option 2A, global solution based on the von Mises criteria, 2016) are risky, and GB-Ⅱ (GB/T-Conventional Assessment, 2019) and BS7910-Ⅰ (BS 7910-Option 1, 2019) are very conservative. The order of their stability is: ① R6-2A-III; ② R6-2A-I, R6-2A-II, API-Ⅱ and SINTAP-I; ③ GB-Ⅱ and BS7910-Ⅰ; ④ Battelle; ⑤ CorLAS. GB-Ⅱ, BS7910-Ⅰ, Battelle and CorLAS are dispersed. The correlation between PA and pc is weak and negligible for all models. The best-fit distributions are lognormal for R6 and SINTAP and GMM for the others. Finally, the use of all models is recommended by considering the critical safety factors.

Creep fracture parameter C* solutions for circumferential surface cracks in pressurized cylinders

The creep fracture mechanics parameter C* is an important input parameter in creep life assessment of cracked components, and it should be accurately calculated. In the author's previous work, the C* solutions for axial surface cracks in pressurized cylinders have been investigated and given. In present work, the C* solutions for circumferential surface cracks have further been investigated and developed. Based on extensive finite element analyses, the creep influence function Hc values for calculating C* have been calculated, tabulated and fitted into equations for circumferential internal and external surface cracks in pressurized cylinders. The equations for estimating C* for materials with different creep exponent n are also investigated and given. The accuracy of all equations has been verified by finite element analyses. The effects of the crack sizes, orientation (axial and circumferential), location (internal and external) and cylinder geometries on the C* distributions along the crack fronts have been analyzed.

Reference stress based J estimation equations applicable to cracked cylinders with a Wide range of radius-to thickness ratios: Part I- axial surface cracks

This paper compares systematic finite element results with reference stress based J estimation equations for pressurised axial surface and through-wall cracked cylinders with the radius-to-thickness ratio ranging from five up to seventy. It is found that, for the reference stress, the use of the Tresca limit pressure given in R6 provides satisfactory results for all cases considered; for both inner and external axial surface cracks; for both semi-elliptical and constant-depth axial surface cracks. These results are obtained for high strain hardening materials such as Type 304 stainless steel.

Analysis of the constraint levels and the creep crack initiation times for pressurized pipes with long surface cracks

Abstract The constraint levels and the creep crack initiation (CCI) times for pressurized pipes with four types of long surface cracks and different geometrical sizes were investigated by using 3D finite element (FE) method. The C*–Q* two-parameter approach was also applied to estimate the CCI times for different conditions. For each type of long surface cracks, it could be found that the larger crack depth (a/t) was associated with the larger constraint and shorter the CCI time. Furthermore, for the same crack depth (a/t) and pressure, the order of constraint levels was axial internal crack > circumferential internal crack > axial external crack > circumferential external crack, while the CCI times were in contrary sequence. Generally, long external surface cracks were less dangerous than long internal surface cracks no matter they were axial or circumferential surface cracks. Additionally, the fitting formulae between CCI times and crack depth ratio a/t and pressure (or stress intensity factor) were developed and verified to be effective. The power law relation between the CCI times and constraint parameter Q* was also established and validated. Finally, the suitability of the transient prediction models in C*–Q* two-parameter approach was verified by comparing results of the two-parameter theoretical analysis and simulation. What's more, it was known that for long internal surface cracks (axial or circumferential), the K-RR solutions were more accurate than the HRR-RR solutions when pressure is below 10 MPa, while the HRR-RR solutions would be better for higher pressure. As to the long external surface cracks, the critical pressure between these two solutions was about 12 MPa.

Creep fracture parameter C* solutions for axial internal and external surface cracks in pressurized cylinders

Accurate calculations of creep fracture mechanics parameter C* is very important for life prediction and assessment of high-temperature cracked components. The current two engineering estimation approaches (EPRI and reference stress approaches) for C* can seriously overestimate or sometimes underestimate C* of cracked components, thus it is desirable to develop accurate C* solutions. In this work, based on extensive three-dimensional (3D) finite element analyses, the C* solutions for axial internal and external surface cracks with a wide range of sizes in pressurized cylinders with different geometry sizes are investigated and developed. The creep influence function Hc for calculating C* along the crack fronts has been obtained and fitted into equations, and the accuracy of the equations has been verified. The correlation equations between C* and creep hardening exponent n are firstly developed which can be conveniently used to estimate C* for materials with different n values. The effects of crack sizes and cylinder geometries on the C* distributions along the crack fronts also are analyzed.