Part-through Crack Research Articles

Plastic Limit Pressure and Stress Intensity Factor for Cracked Elbow Containing Axial Semi-Elliptical Part-Through Crack

The aim of this study is to provide a solution for the plastic limit pressure and stress intensity factor of the elbows containing a part-through axial semi-elliptical crack by considering various crack sizes. The supporting system and loading conditions of the pipeline are described. The critical part of the observed pipeline was isolated for analysis and subjected to various sizes of semi-elliptical cracks. By performing numerical analysis, results were obtained for crack dimension ratios of c/a, and depth/thickness ratios of a/t. The obtained results include plastic limit pressure and stress intensity factor. The results were analyzed with a symbolic regression algorithm, and closed-form solutions for the limit pressure and stress intensity factor were proposed. To validate pipeline integrity, the Structural Integrity Assessment Procedure (SINTAP) was applied, and the FAD (Failure Assessment Diagram) was generated for cracks below the FAD function. The failure pressure was calculated by determining the points where the loading paths intersect the FAD function.

Part-through cracks computation in an Euler–Bernoulli beam model

AbstractThe reduction of the equations of a slender, brittle continuum to a one-dimensional theory and the possibility of accounting for the cracking of this body has received much attention recently. This contribution investigates the effect of cross-sectional geometry on damage localization in an Euler–Bernoulli beam. Two geometric fields characterizing the crack penetration depth on each side of the beam are introduced, from which the modulation of the bending and tensile parts of the strain energy by the crack depth is deduced. The geometry of the crack-tip envelope is obtained by energy minimization. We find that in the case of a Griffith-like dissipation potential, the characteristic size of the crack is a key element for predicting initiation at a finite external load. We can accurately predict the initiation position by regularizing the model in the spirit of Variational Brittle Fracture. Model predictions are compared against computational results obtained by the classical damage field theory.

Analytical solutions for buckling analysis of cracked plates under in-plane compressive loads: 2D refined modeling

Two refined two-dimensional (2D) crack models are developed to deal with rectangular isotropic and orthotropic plate problems with all-over part-through surface cracks under in-plane compressive loads. In the refined models, the crack terms are directly incorporated into the governing equations of cracked plates. In particular, the effect of internal in-plane forces can be investigated by theoretical analysis. The critical buckling loads of thin plates with uni-directional or bi-directional part-through cracks under uni-axial or bi-axial compressive loads can be determined analytically. In this work, different material properties, including steel, tempered glass, glass-fibre-reinforced composite, and graphite-epoxy composite, are considered. The influence of crack depth ratio and plate aspect ratio on the critical buckling loads of these structures is also presented. The analytical results are compared with those results obtained by the line-spring model and three-dimensional finite element method to verify their correctness and accuracy. The proposed models are highly effective for the buckling analysis of plates with part-through cracks.

Allowable stresses related to crack growth stability and leak-before-break for circumferentially cracked pipes governed by limit loads: Part II, Pipes subjected to bending moment

If cracks are detected in power plant pipes and the cracks are allowable, the plants can continue operating without the need for repair/replacement. The allowability of cracks is determined by means of allowable stresses, based on failure stresses. Failure bending stress at crack penetration is estimated by applying the Local Approach of Limit Load Criteria, which is based on the net-section stress approach. Using the stress at crack penetration, the allowable bending stress can be calculated for a pipe with a circumferential part-through crack. The allowable bending stress decreases with increasing crack depth and angle, as expected. However, the allowable bending stress can have one of three characters, depending on crack size: i) leak-before-break (LBB) and crack growth stability, ii) non-LBB and crack growth stability, and iii) non-LBB and crack growth instability. Character iii) represents a severe crack, and special attention needs to be paid to such a crack, even if it is allowable. Frequent non-destructive inspection and precise calculation of subcritical crack growth are recommended in order to prevent unexpected failure, especially for small-diameter thin-walled pipes. The boundaries of leak-before-break and crack growth stability can be successfully expressed by appropriate equations.

Allowable stresses related to crack growth stability and leak-before-break for circumferentially cracked pipes governed by limit loads: Part I, Pipes subjected to tensile loading

When cracks are found in high toughness ductile pipes governed by limit loads at in-service inspections, and the applied stresses at the cracked locations are less than the allowable stresses, the cracks are allowable. The allowable stresses are generally determined in combination with failure stresses and safety factors. Failure of pipes with circumferential part-through cracks subjected to tensile loading occurs in a two-step sequence: first there is the onset of crack penetration, and then there is the break after the crack penetration. The Local Approach of Limit Load Criteria, which is based on the net-section stress approach, can estimate both crack penetration and break stresses for high-toughness ductile pipes. Using the Local Approach of Limit Load Criteria, allowable tensile stresses based on crack penetration stresses are determined by means of safety factors for plant service level conditions. The allowable stresses decrease with increasing crack angles and depths. The characters of the allowable tensile stresses are found to vary with changing sizes of crack angles and depths. These different characters involve the presence/absence of two parameters: leak-before-break (LBB) and crack growth stability. The crack size boundary on LBB vs non-LBB can be expressed by appropriate equations containing crack depths and angles. In addition, the boundaries of crack growth stability/instability are also expressed by crack depths and angles. These boundaries are taken into consideration during non-destructive inspection and crack growth evaluation.

Safety assessment of allowable through-wall crack angles for pipes subjected to tensile loading

Fully plastic collapse stresses for high toughness ductile pipes with circumferential cracks subjected to tensile loading can be predicted by means of Limit Load Criteria based on the net-section stress approach. The Limit Load Criteria are provided by the ASME Code Section XI. Allowable membrane stresses for part-through cracks were determined by plastic collapse stresses in combination with safety factors. The allowable stresses decrease with increasing angles of the part-through cracks. When crack angles are large, the allowable stresses of the part-through cracks are larger than the collapse stresses of through-wall cracks. For such large cracks, allowable stresses greater than the collapse stresses cause instability, and are thus detrimental to pipe integrity, especially in thin-wall pipes, even though the stresses are allowed. In order to avoid the anxiety associated with this, it is necessary to establish maximum allowable crack angles. This paper proposes maximum allowable crack angles for allowable stresses based on the collapse stresses of through-wall cracks. The maximum allowable crack angles can be expressed by equations for various service level conditions.

A novel procedure to evaluate the performance of failure assessment models

The quantification for overall performance of failure assessment models (FAM) is a challenging task. In the first part of this paper, we propose a novel procedure to evaluate FAM's overall performance based on reliability engineering and system safety. This procedure is composed of three parts: 1. proposing the evaluation index system for FAM's performance based on the uncertainty of Prediction Accuracy (PA); 2. calculating the FAM's overall performance scores, which contains three steps: determining the weights of the criteria in the evaluation index system; calculating the decision matrix for different FAMs; and computing FAM's overall performance; 3. analyzing the evaluation results to give recommendations. In the second part of this paper, we demonstrate the application of the novel procedure to evaluate the performance of 9 FAMs for the integrity assessment of pipes containing axial-oriented part-through cracks on the outer surface. This evaluation is based on 250 well-documented pipe burst experiments. The results show that: R6-Option 2A-local solution (2016) gives the best overall prediction. In addition, different Multi-Criteria Decision Making (MCDM) methods have different focuses. VIKOR and TOPSIS are more considering the impact of high weight criteria, especially VIKOR. SWM and PROMETHEE II care more about FAM's overall performance.

Aeroelastic instability of an inverted cantilevered plate with cracks in axial subsonic airflow

This paper reports a mathematical modeling and theoretical instability analysis of an inverted cantilevered plate in the effect of both cracks and subsonic axial flow. The plate model is clamped at the trailing edge but free at the other and contains an arbitrary number of all-over part-through cracks. It focuses on an analysis methodology of such a plate aeroelastic instability problem and its convergent numerical solutions. We apply the Possio integral equation for fluids and the fracture mechanics for cracks’ modeling, respectively. We transfer the instability problem into a mathematical function approximation problem in the state-space formulation, avoiding the difficulty of solving the plate slope function directly because of the discontinuities caused by cracks. According to the Stone-Weierstrass theorem, the slope function of the cracked plate is expanded as a linear combination of polynomial functions, including the cracks’ effect. The numerical solution of the plate slope function is finally solved by the least square method. The numerical analysis shows that the critical flow speed significantly decreases as the crack flexible coefficient increases. The change of critical dynamic pressure and instability modes of the cracked plates has been theoretically analyzed and analytically expressed in terms of the crack parameters. The present modeling and analysis strategy has potential applications for investigations of other engineering problems, which can naturally exhibit plate-like systems with inverted configurations and discontinuity.

Vibration analysis of cracked plates resting on elastic foundation via moving least squares differential quadrature method

In this work, moving least squares differential quadrature scheme is employed to formulate and solve the free vibration analysis of cracked plates resting on the Winkler–Pasternak elastic foundation. Two types of cracks as a part-through surface and internal crack are studied in a rectangular plate. Formulation of the problem is dependent on transverse shear deformation theory and line spring model. Also, continuous weight functions around the crack are produced by diffraction method. Boundary conditions are augmented in the equation of motion and the problem is converted to a discrete eigenvalue problem. The accuracy and efficiency of the present results is validated by comparing with exact, experimental and numerical results. Moreover, the effects of different boundary conditions, crack length, crack depth and foundation parameters on the vibration frequencies and mode shapes are examined in detail. The obtained results may be used for structural health monitoring.

Allowable Cracks Related to Penetration for Part-Through Cracks in Pipes Subjected to Bending Stresses

Abstract Fully plastic collapse stresses for circumferentially part-through cracked pipes subjected to bending stresses are estimated by limit load criteria provided by the ASME Code Section XI. Allowable crack depths were determined by using the limit load criteria and that are tabulated in the ASME Code Section XI for different plant service-level conditions. On the other hand, crack penetration bending stresses for part-through cracked pipes were estimated by using the local approach of limit load criteria. By using these criteria, the study presented in this paper obtained allowable crack depths at penetration for circumferentially part-through cracked pipes. Comparing the allowable crack depths obtained by both methods for each service level, it is evident that the allowable crack depths at penetration calculated by the local approach of limit load criteria are almost always smaller than those at fully plastic collapse stresses calculated by the limit load criteria. It was found that the allowable crack depths provided by the ASME Code Section XI are less conservative for crack penetrations.

Fatigue crack growth for through and part-through cracks in additively manufactured Ti6Al4V

Critical aerospace parts require damage tolerance analysis to determine the inspection intervals in-service. Such analyses, based on linear fracture mechanics, require that the fatigue crack growth (FCG) rate relation to the stress intensity factor range is applicable independent of geometry and stress. FCG rates for laser powder bed fusion Ti6Al4V material for conventional compact tension (CT) specimens have therefore been compared to FCG rates for specimens with a crack configuration more technically relevant from an industrial and engineering perspective. The FCG rates corresponded very well and data obtained with CT-specimens can therefore be considered relevant for general damage tolerance predictions.

Comparison of J Integral Assessments for Cracked Plates and Pipes.

The purpose of this article is to compare two predictive methods of J integral assessments for center-cracked plates, single-edge cracked plates and double-edge cracked plates produced from X52 and X70 steels, and a longitudinally cracked pipe produced from X70 steel. The two methods examined are: the GSM method and the Js procedure of the French RCC-MR construction code, designated here as the FC method. The accuracy of J integral predictions by these methods is visualized by comparing the results obtained with the “reference” values calculated by the EPRI method. The main results showed that both methods yielded similar J integral values, although in most cases, the GSM predictions were slightly more conservative than the FC predictions. In comparison with the “reference” values of the J integral, both methods provided conservative results for most crack configurations, although the estimates for cracks of a relative length smaller than 1/8 were not found to be so conservative. The prediction of burst pressures for external longitudinal semielliptical part-through cracks in X70 steel pipe showed that the magnitudes of predicted burst pressures came very close to each other, and were conservative compared to FEM (finite element method) calculations and experimentally determined burst pressures.

Study of plate vibrating in fluids having part-through crack at random angles and locations

This study presents the vibration characteristics of plate with part-through crack at random angles and locations in fluid. An experimental setup was designed and a series of tests were performed for plates submerged in fluid having cracks at selected angles and locations. However, it was not possible to study these characteristics for all possible crack angles and crack locations throughout the plate dimensions at any fluid level. Therefore, an analytical study is also carried out for plate having horizontal cracks submerged in fluid by adding the influence of crack angle and crack location. The effect of crack angle is incorporated into plate equation by adding bending and twisting moments, and in-plane forces that are applied due to antisymmetric loading, while the influence of crack location is also added in terms of compliance coefficients. Galerkin’s method is applied to get time dependent modal coordinate system. The method of multiple scales is used to find the frequency response and peak amplitude of submerged cracked plate. The analytical model is validated from literature for the horizontally cracked plate submerged in fluid as according to the best of the authors’ knowledge, literature lacks in results for plate with crack at random angle and location in the presence of fluid following validation with experimental results. The combined effect of crack angle, crack location and fluid on the natural frequencies and peak amplitude are investigated in detail. Phenomenon of bending hardening or softening is also observed for different boundary conditions using nonlinear frequency response curves.

Identification and severity estimation of a breathing crack in a plate via nonlinear dynamics

Cracks in mechanical structures are normally fatigue cracks which open and close (hence called breathing cracks) upon excitation thus introducing nonlinearity. These nonlinear cracks, particularly early cracks are difficult to identify and hence may lead to catastrophic failure of the whole structure, if remain undetected. Breathing cracks in beam-like (1D) structures have been modeled and identified successfully to date. However, these types of nonlinear cracks are difficult to identify in plate-like (2D) structures. Researchers have modeled open part-through cracks analytically in plates, but it still needs to be explored in case of breathing part-through and through-cracks. This paper presents the mathematical modeling of a breathing part-through crack in a plate based on piecewise equations. Further, in order to identify this crack, a proposed enhancement of the Hilbert transform from 1 to 2D structure is presented. The cracked plate model is that of a bilinear oscillator with two frequencies corresponding to two stiffness regions indicating breathing. The piecewise equations used to model breathing crack, are combined by considering its dynamic characteristics at the stiffness interface. The breathing frequency obtained is validated analytically, numerically as well as by simulated experiments. The results indicate that the proposed method successfully identified the nonlinear breathing crack. Another important finding is that instantaneous frequency obtained can be related to severity estimation of crack.

Elastic-plastic solutions for corner and surface cracks emanating from stress concentrators

Three-dimensional (3D) constraint effects for part-through cracks, such as corner and surface cracks, emanating from stress concentrators play important role in damage tolerance design of structures, but have hardly been investigated in the frame of 3D elastic–plastic fracture theory. Here the ability of current elastic–plastic solutions to describe 3D constraints and their effects on crack tip fields of corner and surface cracks emanating from stress concentrators are systematically analyzed using finite element (FE) method. Distribution of the out-of-plane constraint factor Tz and corresponding in-plane constraint parameters QT and AT can quantify the effect of stress concentration on crack tip fields. Good agreement between 3D elastic–plastic solutions (J-Tz, J-Tz-QT, J-Tz-AT) and FE results is obtained for four typical specimens at relatively high and low loading levels, showing that these solutions can serve as the theory foundation for advanced damage tolerant analyses of engineering structures.

Fracture toughness assessment of axial partially through cracks in X65 and X70 steel pipes

This paper presents analysis of fracture assessment methods of axial partially-through crack in X65 and X70 steel pipes with internal pressure. Two analytical methods Folin–Ciocalteu method (FC method) and Gauss–Seidel method (GS method)) are used to make assessment for two steel pipes (steel X65 and X70). Finite Element model of X65 and X70 steel full-scale pipes with axial part-through crack was established. In this work, a comparison is made between results obtained from FC and GS methods and finite element model with previous experimental results. The GS is more conservative assessment method as it provides smaller crack depth (a) corresponding to (Jcr). Finite Element model in case of steel X70 is more conservative than the analytical methods and its results close to the experimental values.

Failure bending stresses for pressurized pipes with circumferentially part-through cracks

Stress corrosion cracks detected in austenitic stainless pipes were circumferential cracks at inside of the pipes. Failure stresses for the cracked pipes were developed by net-section stress concept. Limit Load Criterion provided by the ASME Code based on the net-section stress concept can estimate fully plastic collapse stress, which is called as failure stress. Local Approach of Limit Load Criteria for estimating stress at crack penetration had developed for a part-through cracked pipe based on the Limit Load Criteria. Advanced Local Approach of Limit Load Criteria for estimating stress at crack penetration is newly developed based on the Local Approach in this paper. In comparing with experimental stresses of pipe crack penetrations, the Limit Load Criteria give un-conservative estimation, and the Local and the Advanced Local Approaches are close to the experimental stresses. In addition, the Advanced Local Approach always gives higher stresses than the Local Approach for internal cracks, and it is shown that the Advanced Local Approach is beneficial for thick wall pipes with large angle cracks.

Attractor Based Analysis of Centrally Cracked Plate Subjected to Chaotic Excitation

The presence of part-through cracks with limited length is one of the prevalent defects in the plate structures. Due to the slight effect of this type of damages on the frequency response of the plates, conventional vibration-based damage assessment could be a challenging task. In this study for the first time, a recently developed state-space method which is based on the chaotic excitation is implemented and nonlinear prediction error (NPE) is proposed as a geometrical feature to analyze the chaotic attractor of a centrally cracked plate. For this purpose using line spring method (LSM) a nonlinear multi-degree of freedom model of part through cracked rectangular plate is developed. Tuning of Lorenz type chaotic signal is conducted by crossing of the Lyapunov exponents’ spectrums of nonlinear model of the plate and chaotic signal and in the next step by varying the tuning parameter to find a span in which a tangible sensitivity in the NPE could be observable. Damage characteristics such as length, depth and angle of crack are altered and variation of proposed feature is scrutinized. Results show that by implementation of the tuned chaotic signal, tangible sensitivity and also near to monotonic behavior of NPE versus damage intensity are achievable. Finally, the superiority of the proposed method is examined through the comparison with the frequency-based method.

A Non-Classical Analytical Approach for Vibration Analysis of Isotropic and Fgm Plate Containing a Star Shaped Crack

ABSTRACTA non-classical analytical model for vibration analysis of thin isotropic and FGM plate containing multiple part-through cracks (star shaped) of arbitrary orientation is proposed. A plate containing four concentric cracks of arbitrary orientation in the form of continuous line is considered for analysis. The proposed governing equation is derived based on classical plate theory and modified couple stress theory. Line spring model is modified to accommodate all the crack terms. The application of Berger’s formulation introduces nonlinearities in the governing equation and then the Galerkin’s method is applied for solving final governing equation. Results for fundamental frequencies for different values of crack length, crack orientation, gradient index and material length scale parameters are presented for two different boundary conditions. Furthermore, to study the phenomenon of bending hardening/softening in a cracked plate, the frequency response curves are plotted for the parameters stated above. Based on the outcomes of this study, it can be concluded that stiffness of the plate is severely affected by the presence of multiple cracks and the stiffness goes on decreasing with increase in number of cracks thereby affecting the fundamental frequency.

Equivalent thickness-based three dimensional stress fields and fatigue growth of part-through cracks emanating from a circular hole

Accurate characterization of stress states is essential to assess structural integrity and predict fatigue crack growth life. Strong three dimensional constraints always raise at cracks and holes, but have never been investigated in the frame of three dimensional fracture theory for part-through cracks emanating from a hole. Here the three dimensional constraint and its effect on crack tip fields of corner and surface cracks emanating from a circular hole in tensile plates are comprehensively analyzed using finite element method. Distributions of the out-of-plane constraint factor Tz are strongly dependent on relative circular hole size and relative thickness parameters, but the K-Tz description of the stress field remains efficient with the present of circular hole. The equivalent thickness conception based on Tz distributions is applied to crack tip stress field description. Based on the equivalent thickness conception and plasticity-induced fatigue crack closure model, evaluation of fatigue growth of corner crack emanating from a circular hole is demonstrated and validated against test data in the literature.