Semi-elliptical Surface Crack Research Articles

Multi-crack propagation analysis of double-side welded rib-to-deck joint in orthotropic steel decks

Rib-to-deck welded joints are among the most susceptible to fatigue in orthotropic bridge decks (OSDs). Prior research has primarily examined the stress intensity factor (SIF) and propagation morphology of a solitary fracture at these joints, allocating limited attention to the investigation of the propagation of multiple cracks. This paper presents a methodology for simulating and computing the weld toe magnification factor and the SIF of semi-elliptical surface cracks in innovative double-sided welded rib-to-deck (DWRTD) joints. The intention was to simplify the calculation of the SIF for this fatigue detail. The SIF obtained from the calculation model in combination with a multiple crack coalescence approach resulted in a series of fatigue life prediction models of multiple co-planar semi-elliptical cracks. Compared with the results of fatigue tests on the DWRTD joints, the calculated fatigue life and propagation morphology of multiple cracks from the model showed good agreement. Finally, the parameters were analysed to investigate the effects of crack number, bridge deck thickness, residual stress, and penetration rate. Compared to a single crack, multiple cracks reduced the service life of the bridge deck by approximately 30%. When the bridge deck thickness increases from 12 mm to 20 mm, the nominal stress amplitude near the weld ∆σ decreases by 2.2 times, resulting in a 7-fold increase in crack propagation time. Compared to penetration rate and residual stress, ∆σ is the most crucial factor affecting fatigue propagation life. Therefore, it is suggested to increase the thickness of the bridge deck during design.

Dynamic failure assessment analysis of 15MnTi steel supporting structure with a circumferential surface crack under impact loads

Supporting structures, whose strength have great influence on the safe operation of the whole equipment, are widely used in various ship equipment. In this paper, dynamic failure assessment analysis is carried out to discuss the structural integrity of the cracked supporting structure under impact loads. Considering the dynamic response characteristics of structures, the dynamic fracture toughness determined by the loading rate of dynamic J-integrals is used to calculate the failure assessment point (FAP). Due to the widespread uncertainties in practical engineering, such as crack size and mechanical properties of materials, the failure assessment results will also have uncertainty To analyze the structural integrity affected by uncertain variables, the polygonal convex set (PCS) model is introduced to the failure assessment diagram (FAD) to propose a non-probabilistic failure assessment method. The FAP is extended to a failure assessment region, and structural integrity can be analyzed by the non-probabilistic reliability degree. Compared with the traditional interval model, the non-probabilistic reliability degree calculated by PCS model is closer to the probabilistic reliability degree, which avoids premature judgement of structural failure. For the 15MnTi supporting structure with a circumferential semi-elliptical surface crack under impact loads, the critical depth obtained by non-probabilistic methods decrease by 10% compared with deterministic results, and the failure mechanism is summarized as plastic collapse resulting from the excessive net section stress. In the absence of statistical data on crack size or mechanical properties, the non-probabilistic failure assessment method can be used as an effective alternative to the probabilistic method.

Analytical study of CFRP strengthening steel plates with a semi-elliptical surface crack

Flaws and defects are unavoidable in the manufacturing process of steel members. Surface cracks are a common type of defect in steel structures that can introduce fatigue failure under cyclic loading. In this study, stress analysis of carbon fiber reinforced polymer (CFRP) repaired specimens with a semi-elliptical surface crack was conducted by theoretical analysis. The analysis was used to calculate stress intensity factors at crack tips. Finite element analysis was carried out to verify the proposed equations considering CFRP strengthening. Both single-sided and double-sided strengthening methods were considered. Thereafter, a modified Paris Law model was adopted to predict fatigue crack propagation life. Several parameters, which are crack aspect ratio, crack depth ratio, layers of CFRP, CFRP width and stress range are considered to analyze their influence on fatigue life. It was found that the augmentation of crack aspect ratio, layers of CFRP and CFRP width can significantly increase fatigue crack propagation life of repaired specimens. Furthermore, single-sided repairing on cracked side is better than double-sided repairing.

Stress intensity factor analysis for mixed-mode fracture behavior of inclined semi-elliptical surface crack in stiffened plate under tension load

This study aims to investigate the mixed-mode fracture behavior of stiffened plates with inclined semi-elliptical surface cracks (ISSCs). For this purpose, a new numerical model is developed for the fracture analysis using FRANC 3D in combination with ABAQUS. Normalized stress intensity factors (SIFs) are used to analyze the fracture behavior at the surface and deepest points of the surface crack. Additionally, an arrest parameter ψ is proposed to quantify the level of crack arrest under mixed-mode conditions. Then, a thorough investigation is conducted to examine the fracture behavior of stiffened plates with ISSCs, focusing on the effects of aspect ratio, relative depth, spacing ratio, stiffness coefficient, crack angle, and loading mode. The findings indicate that the restraint effect of stiffeners on the fracture of large surface cracks is significantly stronger compared to small surface cracks. It is also identified that the restraint effect is more pronounced at the surface point than at the deepest point. Finally, a set of novel formulas is derived to evaluate the mixed-mode SIFs in stiffened plates through statistical analysis of the results.

General point load weight function for semi-elliptical surface cracks in round bars

Offshore mooring chains are continuously subjected to cyclic environmental loadings, resulting in fatigue cracks that always develop at the surface and grow across the circular cross-sections. To analyse the fatigue crack growth in a mooring chain based on a fracture mechanics-based approach, the evaluation of stress intensity factors (SIFs) of surface cracks in the chain segments becomes essential. A general point load weight function of SIFs for semi-elliptical surface cracks in straight and curved round bars was derived in this study. Parametric three-dimensional finite element (FE) models were developed to calculate the SIF solutions for determining the unknown parameters in the weight function. The analysis matrix covered wide ranges of aspect ratios 0.1 ≤ a/c ≤ 2.0, relative crack depths 0.03 ≤ a/D ≤ 0.6 and relative bar curvatures 0.0 ≤ D/Ri ≤ 1.5. The developed weight function was verified against the solutions available in the literature and FE results, indicating good accuracy. The proposed weight function can be used in SIF calculation and remaining fatigue life prediction of surface cracked round bar components under complex stress distributions, such as chain links.

Effect of mixed-mode loading on surface crack propagation in steels

To understand the effect of mixed-mode loading on surface crack propagation in structural alloy steels, fatigue crack growth tests were performed on surface crack tension (SCT) specimens with initial semi-elliptical surface cracks. SCT specimens with cracks normal to the load axis were used for the mode I tests. Experiments with mixed-mode loading were conducted on SCT specimens with inclined surface cracks. A specific feature of the surface crack propagation, in the segmentation of the crack front, the occurrence of «factory roof» patterns, and deviations in the crack front from a planar shape were established under mixed-mode loading. A reverse engineering technique was applied in a numerical study to reproduce a complex fracture surface under mixed-mode loading. The equivalent stress intensity factor (SIF) formulation was used to interpret the fatigue-crack growth rate. A significant reduction in the fatigue crack growth rate was established for mixed-mode loading compared with pure mode I conditions. Several fracture mechanisms were identified along the surface crack front under mixed-mode loading. The areas corresponding to changes in the dominant fracture mechanism were identified using detailed fractography of the fracture surfaces.

Effect of bending stress parallel to the crack plane on J and the limit load of plates with surface cracks

The effect of bending stress parallel to the crack plane on J-integral of plates containing semi-elliptical surface cracks is investigated in this paper. Elastic and elastic–plastic finite element (FE) analyses are used to obtain J values for the surface-cracked plates under membrane stress or through-thickness bending stress normal to the crack plane or under biaxial membrane stresses plus through-thickness bending normal to the crack plane with/without bending stress parallel to the crack plane. The FE results show that, as predicted by linear elastic fracture mechanics, the applied bending stress parallel to the crack plane does not affect the crack tip elastic J. However, it does affect the elastic–plastic J. A limit load (or reference stress) solution for a plate containing a rectangular surface crack under combined biaxial membrane stresses and biaxial bending stresses is developed, which shows good correlation to the elastic–plastic FE J via the reference stress J scheme, for both cases with/without the bending stress parallel to the crack plane. Based on the results of the investigation, a newly-developed local limit load model is updated to include the effects of bending stress parallel to the crack plane for use in structural integrity assessments.

Stress intensity factor and fatigue life evaluation for important points of semi-elliptical cracks in welded pipeline by Bezier extraction based XIGA and new correlation model

NURBS-based Bezier extraction in extended isogeometric analysis (XIGA) using thermo elastic-plastic equation has been proposed for evaluating the stress intensity factor (SIF) in the various relative crack depths, aspect ratios, and important points (surface points and deepest point) of the semi-elliptical surface crack in weld line of pipelines under cyclic internal pressure. In this approach, the level set technique is used for identifying the grid points around the crack front and the crack surface. Crack in the specified domain is modeled by Heaviside and crack front enrichment functions and remeshing due to crack growth does not require. Also, new correlation models are proposed to predict SIF in these points of the crack front. Based on the proposed correlations, fatigue crack propagation, and fatigue life are investigated. Modified walker equation used for predicting fatigue crack propagation rate and fatigue life in the welded pipeline. The finite element method (FEM) analysis with a similar condition was performed and compared with XIGA and correlation models to validate the presented method. The results demonstrate good agreement. Thus, the proposed approach successfully studies the 3D crack problem with acceptable accuracy.

Experimental studies of the influence of biaxial bending on the crack resistance of reactor pressure vessel steel

Background: to assess the residual life of nuclear reactor hulls in Ukraine, normative temperature dependences of the crack resistance of hull steels obtained on standard samples with a deep through crack under plane strain conditions are used. However, it is known that the thickness of the wall of the reactor body is subject to biaxial loading, which affects the value of the crack resistance characteristics. Therefore, in order to substantiate the possibility of lengthening beyond the design resource of VVER-1000 reactor hulls, an experimental study of the effect of biaxial load on the crack resistance characteristics of hull reactor steel 15X2NMFAA is relevant. Objective: development of an experimental technique and investigation of crack resistance under biaxial loading on small-sized samples in the the brittle-ductile transition temperature range of reactor steels. Methods: on the basis of numerical and engineering calculations, a specimen was developed, the corresponding additional equipment for its tests under biaxial loading on a uniaxial servo-hydraulic machine. The influence of biaxial bending on the fracture toughness of reactor steel 15X2NMFAA was experimentally investigated. Results: the results obtained on cruciform specimen are calculated according to the ASTM 1921 standard and plotted on the Master curve (temperature dependence of fracture toughness). The analysis showed that the data on crack resistance obtained on samples with "short" (a/W=0.1...0.2) linear and surface semi-elliptical cracks exceed the upper limit of the confidence interval of the Master curve, and biaxial loading of cruciform specimen reduces crack resistance compared to uniaxial loading.

Constraint characterization and fracture initiation analysis for semi-elliptical surface cracks in reactor pressure vessel

The constraint and fracture initiation for semi-elliptical surface cracks in an actual large scale reactor pressure vessel (RPV) have been investigated by finite element analysis. The results show that the overall constraint level of the cracks increases when the crack depth a/t increases and crack aspect ratio a/c decreases. For most cracks with a/t = 0.25–0.8 and a/c = 0.2–2, the constraint level is higher than the standard plane strain specimen, and the conventional fracture assessment may possibly yield non-conservatism. The aspect ratio a/c has obvious effects on the distributions of the new unified constraint parameters Ad* and the elastic-plastic stress intensity factor KJ and the fracture initiation position along the crack fronts. For low aspect ratio cracks with a/c < 1.0, fracture initiation probably appears in the deepest region of the crack. For high aspect ratio cracks with a/c ≥ 1.0, fracture initiation is likely to occur in the near-surface region. To improve the accuracy of fracture assessment for cracks in the RPV, the constraint effect requires to be incorporated. The engineering estimation methods of the parameters Ad* and KJ at the crack initiation positions have been provided and verified.

Evaluation and optimization of meshless methods to estimation of the 3D-stress intensity factors in mode I–III for fatigue life prediction cracked shaft under uni and multi-axial cyclic loading

In this research, in order to estimate 3D-Stress Intensity Factors in mode I–III, fatigue crack growth and fatigue life prediction of a cracked shaft under various cyclic loading, meshless methods are evaluated and the most appropriate method is selected. For better results, the Base Functions (BFs) are first identified and their performance and efficiency are compared with each other. In addition, while enriching the BFs in all methods and study the effect of increasing the number of sentences of Polynomial-BFs (m = 4, 7,10) and their Linearity or Quadraticity in the accuracy of calculations, two sets of Extend-Enriched-RBFs including the Multi-Quadrics and Gaussian RBFs are used in MQ-RPIM and EXP-RPIM methods. To optimize the shape parameters in the RPIM method and determine the Penalty Factor in the MLPG method, Uni and Multi-objective PSO algorithm was used. Then, a shaft with an initial semi-elliptic surface crack as a 3D-meshless domain for discretizing the weak differential equations was selected and modeled under a fixed latitude tensile, bending, and torsional cyclic loads. Changing the standard values of the shape parameters and estimating their optimal values by the PSO algorithm and comparison of findings with the results of Experimental, MLPG, PIM, FEM, and XFEM methods, has led to the best answer from the applied methods for calculation of; displacement, strain and stress fields, and the SIFs in Mode I–III. Finally, based on the results of uniaxial cyclic load analysis and selection of the MQ-RPIM method, the Multi-axial Cyclic load analysis has been performed on 3D-domain. During this analysis, the Paris Parametric equation along with the Elliptic equation and Liu’s Virtual Strain Energy (VSE) model was used to estimate the fatigue crack growth and fatigue life prediction of a submersible cracked shaft of a pump used in water pumping stations.

Stress intensity factors and weight functions for semi-elliptical cracks at weld toes in U-rib-to-deck joints

The weight function (WF) has unique advantages when calculating the stress intensity factor (SIF) and evaluating the fatigue performance of cracked components. However, exiting WFs are common for simple geometries, but cannot accurately calculate the SIFs for surface cracks in U-rib-to-deck joints. Here, WFs are derived for semi-elliptical surface cracks in U-rib-to-deck joints. Firstly, the finite element method (FEM) is used to calculate the SIF for semi-elliptical surface cracks at weld toes in U-rib-to-deck joints. The effect of different crack configurations, such as the weld angle (θ), aspect ratio (a/c), crack depth ratio (a/T), and deck-to-rib thickness ratio (T/t), on SIFs is discussed. Then new WFs are developed and validated based on different stress distributions, and the effects of different crack geometric characteristics are considered. Finally, using the derived WFs, the SIFs for surface crack in a U-rib-to-deck joint are calculated accounting for the welding residual stresses. Comparisons were made with predictions from the existing WFs for T-plate joints, and the FEM. The proposed WFs comprehensively account for the effects of the crack geometry characteristics of U-rib-to-deck joints and accurately calculate the SIFs for surface cracks at weld toes.

Fatigue Crack Propagation Prediction of Corroded Steel Plate Strengthened with Carbon Fiber Reinforced Polymer (CFRP) Plates.

The purpose of this study is to investigate the mechanism of improving fatigue performance and the estimation model of fatigue life for corroded steel plate strengthened with CFRP plates. A new two-stage fatigue crack propagation prediction model for the corroded steel plate strengthened with CFRP plates was proposed; moreover, the identification of critical rust pits and the equivalent method of initial cracks, and the calculation method of stress intensity factor (SIF) values at the crack tip were established. The accuracy of the proposed model was verified by comparing the predicted and tested fatigue life of the corroded steel plate strengthened with CFRP plates. Finally, the proposed two-stage crack propagation model was applied to carry out a parameter analysis to investigate the effect of weight loss rate, equivalent initial crack size, adhesive thickness, CFRP stiffness and CFRP prestress level on the fatigue crack propagation of the corroded steel plate strengthened with CFRP plates. Results showed that the maximum depth and the average width of the rust pits were suggested to be taken as the equivalent dimensions of the initial semi-elliptical surface crack for the fatigue crack propagation prediction of corroded steel plate strengthened with CFRP plates. Increasing the weight loss rate of the corroded steel plate, the initial crack size or the adhesive thickness would accelerate the crack growth and reduce the fatigue life, whereas increasing the stiffness or prestress level of the CFRP plate would significantly reduce the crack growth rate and increase the fatigue life. The smaller the initial crack size, the more sensitive the crack propagation life was to the variation of equivalent initial crack size. The influence of adhesive thickness on the fatigue life was limited and convergent, and the application of prestressing could significantly improve the utilization rate of CFRP materials and the fatigue strengthening effect of the corroded steel plate.

Determination of allowable axial flaw sizes in stainless steel pipes based on probabilistic fracture mechanics

The flaw evaluation is required if a flaw is detected in the pipe during the service life. The critical flaw size is the limit size of flaw that will cause the pipe to fail under service conditions, while the allowable flaw size is defined as the limit flaw size determined by evaluation procedures based on the standards. Therefore, the evaluation procedures will be simplified by comparing the detected flaw size with the allowable flaw size. Existing standards and studies have provided the allowable circumferential surface flaw size for pipes under combined various loading conditions and the allowable axial surface flaw size for pipes under pure internal pressure. Consequently, the pipes with axial surface semi-elliptical cracks under combined loading are considered in this paper. Normalized critical flaw sizes (ratio of the flaw depth to flaw half-length, a/t) are obtained by using the deterministic failure assessment diagram (FAD) method, and normalized allowable flaw sizes (ratio of the flaw depth to flaw half-length, a/t) are evaluated by probabilistic analysis. The methods were applied to calculate the numerical results for DN150 304 stainless steel pipes with axial flaws under various loading conditions. The smaller value of the allowable internal flaw size and external flaw size is determined as the final allowable flaw size. For considering the failure probabilities, the results of the allowable flaw size based on the probabilistic analysis are more conservative than the allowable end-of-evaluation-period flaw depth based on the limit load criteria by using the safety factor as provided in the Acceptance Standards of Section XI of the ASME Code (ASME XI).

Predicting Fatigue Crack Growth Behavior of Coalesced Cracks Using the Global-Local Superimposed Technique

The S-version Finite Element Method (FEM) is known as a global-local superimposed approach that consists of two separate meshes referred to as global and local cracks. The relationship between the energy release rate and the Stress Intensity Factor (SIF) is evaluated to characterize the growth behavior of the fatigue cracks. The SIF is determined using the Virtual Crack Closure Method (VCCM). The cracks propagated in the direction of the loading before coalescing into a single crack. Each crack begins with a length of 10mm and a depth of 3mm. After the crack coalesces, the diameter of the surface crack before it breaks is 28mm, whereas the depth of the crack is 5.3mm. The V-shaped surface crack forms quickly after coalescence occurs and continues to propagate into a massive semi-elliptical surface crack before finally breaking. The result was validated and compared between S-version FEM and the analytical solution. The behavior of the fatigue crack growth shows a good agreement between both methods with small errors. The result indicates that the Root Mean Square Error (RMSE) values before coalescing are 0.1496 with 0.6, and after coalescing is 0.4, the RMSE value is 0.1665. Therefore, it can be stated that the S-version FEM approach can predict the growth of fatigue cracks.

Two-dimensional weight function for the determination of stress intensity factors for semi-elliptical surface cracks in finite-thickness and finite-width plates

In this study, a new two-dimensional (2D) weight function of stress intensity factors (SIFs) for semi-elliptical surface cracks in finite-thickness and finite-width plates subjected to arbitrary stress distributions was proposed. To determine the unknown coefficients in the weight function, parametric three-dimensional finite element (FE) models were developed to obtain the solutions of SIFs. The analysis matrix covers wide ranges of relative crack-length ratios 0.1 ≤ c/W ≤ 0.9, to consider the finite width effect, as well as aspect ratios 0.2 ≤ a/c ≤ 1.0 and relative crack-depth ratios 0.025 ≤ a/T ≤ 0.8. The present weight function was verified against the FE results and the solutions available in the literature. The maximum differences were within 6% for both the surface and deepest points. The proposed 2D weight function can be applied to calculate SIFs and predict the fatigue life of engineering structural components involving surface flaws.

Numerical and experimental investigation of mixed‐mode crack growth in aluminum alloys

AbstractFatigue crack growth in Al 2024 and Al 7050 specimens was assessed experimentally and numerically. In the experimental investigation, various specimen configurations and loading conditions were used to achieve pure mode I, pure mode II, and mixed mode I/II, I/III, and I/II/III. Sample configurations were as follows: first, compact tension shear (CTS) specimen to reproduce pure mode‐I and pure initial mode‐II loading conditions; second, surface crack tension (SCT) specimen to analyze the behavior of semielliptical surface cracks in mode‐I and mixed‐mode conditions; and third, hollow cylindrical (HC) specimen with initial semielliptical surface crack to analyze fatigue crack growth under complex stress state. In the numerical study, finite element method (FEM) simulations were performed by means of FRANC3D and ABAQUS solver. The numerical predictions were validated with the experimental results. These predictions resulted to be accurate estimation of the crack growth across the broad range of the investigated loading conditions.

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.

Effects of material properties and mismatch on unified constraint parameter

In order to develop unified constraint-based fracture assessment method, it needs to investigate the effects of material properties and mismatches on the unified constraint parameter and develop the parameter solutions for cracked structures. In this work, the effects of material properties (yield strength and hardening exponent) and strength mismatch on the in-plane and out-of-plane unified constraint parameter Ad* of semi-elliptical surface cracks in homogeneous and welded plates have been investigated. The results show that the parameter Ad* does not essentially change with yield strength and hardening exponent of materials for cracks in homogeneous plates under bending and tension loads. The parameter Ad* of weld centerline cracks in welded plates under bending and tension loads is essentially independent on the strength mismatch. These advantages of Ad* are conducive to the development of its solutions for homogeneous and welded structures containing cracks. The effect of weld width on Ad* is related to loading mode, mismatch (undermatch or overmatch) and crack size. The mechanism of the influence of material properties, strength mismatch and weld width on Ad* has been explained by its definition and the crack-tip plastic strain distribution. The development and application of Ad* solutions for homogeneous and welded structures also have been discussed.

Assessment of failure probabilities and the allowable size of defects in structural elements using the criteria of fracture mechanics

The possibility of assessing the safe size of the defects of metal continuity using risk criteria are considered. Such defects occur at all stages of the life cycle of structures. Assessment of their hazard and determination of their allowable size becomes important when the defects can lead to brittle or quasi-brittle fracture. In this case, models of linear and nonlinear fracture mechanics are used. In these models, defects are considered as internal elliptical or surface semi-elliptical cracks. The stochastic variety of shapes, sizes, locations, and orientations of defects has a significant effect on the destruction mechanisms. In this regard, the relevant probabilistic problem of assessing the permissible size of defects according to the criteria of the risk of destruction comes to the fore. We consider a general approach to assessing hazard of defects by risk criteria. Two settings of the probabilistic problem of risk assessment based on of one- and two-parameter fracture criteria are presented. The risk function in the form of the probability of fracture according to a given criterion is used as the main calculated characteristic. The expression of the risk function based on one-parameter criteria of fracture mechanics is presented. The main attention is paid to the probabilistic model based on the two-parameter fracture criterion by E. M. Morozov. This criterion provides ample opportunities for analyzing fracture mechanisms with a change in the size of defects. An expression for the risk function based on the family of two-dimensional probability distributions of Lu – Bhattacharya of the Weibull type is obtained. It is shown that the correlations of the fracture mechanisms can significantly affect the values of the fracture probabilities, and, consequently, the allowable size of defects.