Off-center Crack Research Articles

Effect of crack on shear buckling of CNTRC plates

This paper presents the buckling analysis of cracked CNTRC plates under shear loading using XFEM, focusing on the existence of the off-center cracks as the novelty of the research. For this purpose, the equivalent mechanical properties of the nanocomposites are calculated using the Eshelby-Mori-Tanaka homogenization scheme. The CNTs are assumed to be randomly oriented, experiencing the null, partial and complete agglomeration. The numerical models of the cracked CNTRC plates with center and off-center cracks are created using a calculation code prepared in MATLAB. The effect of volume fraction (VCNT = 0.0, 0.05, 0.1, 0.15, 0.20) and agglomeration of CNTs, crack length (0.0 ≤ a* ≤ 0.8), location of the crack (0.0 ≤ ey* ≤ 0.9 and 0.0 ≤ ex* ≤ 0.6), boundary conditions (SSSS, CCCC, CFCF, CSCS) and aspect ratio of cracked CNTRC plate (L* = 0.5, 1.0, 2.0) on the critical buckling coefficient and mode shape is investigated. The results show that the critical buckling mode shape is affected by the interaction effects of various cracking parameters. In addition, the CNT parameters, including the volume fraction and agglomeration, significantly affect the shear buckling capacity of the cracked CNTRC plates.

Experimental and numerical study of compressive buckling stability of plates with off-center crack

One of the criteria in the structural design is the buckling stability of the components. In cracked plates, the buckling phenomenon can be affected by the cracks. Therefore, it is important to investigate the effect of crack length and location on the buckling behavior. In this paper, the buckling stability of plates with different sizes ranging from short to long off-center cracks was studied by using the experimental and numerical methods. For this purpose, the clamped-free plate specimens of 1100 aluminum alloy with a crack in different length and locations were subjected to uniaxial compressive load. The experimental data were complemented with the numerical results obtained from extended finite element analyses, in order to further study the effect of various crack parameters in different types of boundary conditions. The agreement between the test and numerical results was quite satisfactory. Based on the results, the effect of crack eccentricity largely depends on the type of plate supports; and for the plates with two opposite free edges, the larger crack, the lower buckling stability.

Simulation of Off-center Crack Dynamic Curving Fracture with Manifold Element

On basis of introducing the method of solving the dynamic problems, this paper adopts numerical manifold method program to simulate the crack propagation of the off-center crack in the simply supported beam. The result shows that the crack propagation path obtained by the numerical manifold method is very correspondent with the experiment result, that is to say producing the evident curving fracture phenomenon. The failure of the material is the result of mixed propagation of crack mode Ⅰ and Ⅱ, and mode Ⅰ plays a dominant role. At the same time, with the increase of the off-center distance, the stress intensity factor of the crack tip gradually decreases.

Characterization of near tip stresses for a plane-strain off-center crack in a strength mismatched weld

The past two decades have seen an increasing emphasis on the development of flaw assessment procedures accounting for the state of stress (constraint) near the crack tip. In-service inspections of many nuclear power plants have revealed that cracks are most likely to occur in a weld or in the regions near the weld. In recent work, the authors have proposed a novel three-parameter scheme to characterize the crack tip opening stress, for small-scale yielding, for a crack lying at the center of a strength mismatched weld. The proposed scheme was validated with detailed finite element analyses using the modified boundary layer formulation. In the present work, the previously proposed scheme is extended to an off-center crack lying in the weld region. Apart from analyzing an off-center crack, studies are performed on an interface crack in a weld having finite width. To validate the proposed scheme, modified boundary layer analyses are carried out for a wide range of offset ratio values (ratio of the crack tip-to-weld center distance to the weld half-width), ranging from 0.33 to 0.9, and strength mismatch ratio values (ratio of yield strength of weld to yield strength of base material), ranging from 0.6 to 1.6. Our studies revealed that the proposed analytical scheme works well for all offset ratios and weld mismatch ratios. For an interface crack, crack tip stresses depend mainly on the strength mismatch ratio between the base and weld material. Practically no significant effect is observed of the weld width on the crack tip opening stress of an interfacial crack.

Assessment of an engineering approach to the evaluation of the cod of off-centered crack in pipes under bending for LBB design

In this work the applicability and the accuracy of the hodograph cone method (HCM) for estimating the COD profile of off-centered cracks in pipe under bending load has been verified by means of extensive finite element analysis. Numerical simulation results have been supported by experimental measurements. The need to develop appropriated numerical model for off-centered cracks configurations and the guidelines to follows in order to get accurate results are discussed. Experimental measures performed by means of digital image correlation (DIC) confirmed both the accuracy of the FEM model used in this work as well as the robustness of HCM. A correction for further improvement of the HCM accuracy and its extension to large crack length is proposed.

Split Ends and Cracking Problem During Hot Rolling of Continuously Cast Steel Billets

The paper presents a detailed analysis of split end and cracking problems that occurred during hot rolling of thermomechanically treated (TMT) grade steel bars. The major analytical tool was a multiscan computer-controlled ultrasonic image analysis system for analysis of the defects observed on transverse cut slices of the billets under investigation. The possible reasons for billet cracking during hot rolling such as a low Mn/S ratio, high casting speed, high degree of superheat, and high inclusion content in steel were analyzed. Additionally in the process parameters such as low roll diameter, high friction, and low reduction ratio were also analyzed. The cracking appeared to be associated with large surface/internal defects, axial porosity, off-centered cavities/porosities, off-centered cracks, and inclusion bands. The analysis results suggested methods to prevent such defects in continuously cast steel billets and to reduce/eliminate split end problems. The casting parameters should include: (a) Mn/S ratio >35, (b) degree of superheat <60 °C, and (c) casting speed: <3.0 m/min, where roll radius and initial thickness of the workpiece should be optimized.

Residual Strength of Panels with Cracks Based on a Plastic Hinge

The residual strength of a panel with a crack is dependent on the mode of failure. Generally, the panel will exhibit a brittle-fracture mode of failure (based on linear elastic fracture mechanics) or a mode of failure based on yielding. A common practice is to assume an elastic, perfectly plastic, material behavior, along with a net-section-yield criterion for panels that fail by yielding. However, the net-section-yield criterion is not appropriate for configurations such as panels with asymmetric geometry or loading, because equilibrium is violated. For asymmetric cases such as panels with edge cracks or off-center cracks, a plastic moment or hinge must exist, the details of which may be determined by satisfying equilibrium. The purpose of this study is to compare the experimental residual strengths of panels with edge cracks and off-center cracks with the residual strengths determined from the assumption of elastic, perfectly plastic, behavior and a plastic-moment (hinge) criterion. The material chosen for this study is 2024-T3 aluminum alloy. This material is commonly used for aircraft skin and it has a high fracture toughness, and so the mode of failure will less likely be brittle fracture. An elastic, perfectly plastic, material model was assumed, and expressions were developed for a plastic-hinge failure for panels with edge cracks as well as off-center cracks. A large number of panels with either edge cracks or off-center cracks were tested to failure, and the results were compared with the results obtained from the equations developed from the plastic-hinge assumption. The results from the plastic-hinge assumption compared favorably with the experimental results.

Scattering of anti-plane shear waves in a functionally graded material strip with an off-center vertical crack

The scattering problem of anti-plane shear waves in a functionally graded material strip with an off-center crack is investigated by use of Schmidt method. The crack is vertically to the edge of the strip. By using the Fourier transform, the problem can be solved with the help of a pair of dual integral equations that the unknown variable is the jump of the displacement across the crack surfaces. To solve the dual integral equations, the jump of the displacement across the crack surfaces was expanded in a series of Jacobi polynomials. Numerical examples were provided to show the effects of the parameter describing the functionally graded materials, the position of the crack and the frequency of the incident waves upon the stress intensity factors of the crack.

Normal impact of a piezoelectric strip with an off-center crack perpendicular to interface

The normal impact of a piezoelectric strip containing an off-center crack perpendicular to the boundaries is considered. The solution involves solving a singular integral equation in the Laplace transform domain by application of the Gauss–Jacobi integration formula. Laplace inversion is carried out numerically to obtain the dynamic energy density factors. They are greatly affected by the free boundaries of the piezoelectric strip and the material properties.

Elastic–plastic analysis of off-center cracks in cylindrical structures

This paper presents new elastic and elastic–plastic finite element solutions of the J-integral for a pipe containing off-center through-wall cracks under pure bending. The analysis is based on a three-dimensional nonlinear finite element method and small-strain theory. One hundred and five analyses were performed using the ABAQUS commercial code for a wide variety of crack sizes, off-center crack angles, and material hardening exponents. The results from these analyses show that the J-integral values at the two crack fronts of an off-center crack are unequal due to the loss of symmetry with respect to the bending plane of the pipe. In addition, the J-integral is larger, and hence, critical at the crack front which is farther away from the bending axis of the pipe. This is because, at that crack front, the tensile stress is larger and the component of the applied bending moment about the crack centerline has a further crack-opening effect. Also at this crack front, the J values can be lower or slightly higher than those of a symmetrically centered crack, depending on the crack size and off-centered angle. For the crack front that is closer to the bending axis, the J values are always lower than those of a symmetrically centered crack. This implies that the load-carrying capacity of a pipe is usually larger for an off-center crack than that for a symmetrically centered crack. Finally, based on these finite element solutions, new analytical expressions of J-integral were developed for fracture analysis of pipes containing off-center cracks.

Probabilistic analysis of off-center cracks in cylindrical structures

This paper presents a probabilistic methodology for fracture-mechanics analysis of off-center cracks in pipes subject to pure bending moment. It is based on: (1) a new analytical approximation of the J-integral; (2) statistical models of uncertainties in loads, material properties, and crack geometry; and (3) standard computational methods of structural reliability theory. The proposed analytical equations were applied to a probabilistic fracture-mechanics analysis of off-center cracks in pipes. The second-order reliability method was used to determine the probabilistic characteristics of the J-integral and failure probability based on the initiation of crack growth. Numerical examples are presented to illustrate the proposed methodology. The results show that the failure probability strongly depends on the off-center crack angle and is generally lower than that of a pipe with a symmetrically centered crack. Hence, simplifying an off-center crack by a symmetrically centered crack can produce significant conservatism in predicting failure probabilities. In addition, uncertainty in the off-center crack angle, if it exists, can increase the failure probability of pipes.

Crack-opening-area analyses for circumferential through-wall cracks in pipes—Part III: off-center cracks, restraint of bending, thickness transition and weld residual stresses

This is the third of three papers generated from a recent study on crack-opening-area analysis of circumferentially cracked pipes for leak-before-break applications. The first two papers [1, 2][Rahman, S., Brust, F. W., Ghadiali, N. and Wilkowski, G., Crack-opening-area analyses for circumferential through-wall cracks in pipes. Part I—Analytical models. International Journal of Pressure Vessels and Piping, (this issue). Rahman, S., Brust, F. W., Ghadiali, N. and Wilkowski, G., Crack-opening-area analyses for circumferential through-wall cracks in pipes. Part II—Model validations. International Journal of Pressure Vessels and Piping, (this issue).] dealt with crack-opening-area analysis of pipes assuming simple loading, pipe and crack geometries, and boundary conditions. This paper (Part III—Off-center cracks, restraint of bending, thickness transition, and weld residual stresses) examines several practical aspects of crack-opening-area analysis involving off-center cracks, restraint of pressure-induced bending, girth-weld nozzle cracks at thickness transition, and weld-induced residual stresses. Currently, there are no engineering methods or guidelines available to analyze pipes under these conditions. Both linear-elastic and elastic–plastic finite element analyses were conducted to determine quantitatively their effects on various crack-opening characteristics. From the results of these analyses, recommendations are made on how an off-center crack can be analyzed based on fracture-mechanics equations for a centered crack. It was found when the restraint of bending effects become important and how they should be taken into account. Cracks located in the thickness transition with thickness gradients on both sides of a nozzle girth weld were analyzed. Finally, simplified finite element simulations were performed to determine if the residual stresses should be considered and when they become important for crack-opening evaluations.

Crack-opening-area analyses for circumferential through-wall cracks in pipes—Part I: analytical models

Leak-before-break (LBB) analyses for circumferentially cracked pipes are currently being conducted in the nuclear industry to justify elimination of pipe whip restraints and jet impingement shields which are present because of the expected dynamic effects from pipe rupture. The application of the LBB methodology requires calculation of leak rates. The leak rates depend on the crack-opening area of the through-wall crack in the pipe. In addition to LBB analyses which assume a hypothetical flaw size, there is also interest in the integrity of actual leaking cracks corresponding to current leakage detection requirements in NRC Regulatory Guide 1.45, or for assessing temporary repair of Class 2 and 3 pipes that have leaks, as are being evaluated in ASME Section XI. The objectives of this study were to review, evaluate, and refine current predictive models for performing crack-opening-area analyses of circumferentially cracked pipes. A three-phase effort was undertaken to accomplish this goal. It is described here in a series of three papers generated from this study. In this first paper (Part I — Analytical models), a comprehensive review is performed to determine the current state-of-the-art in predicting crack-opening displacements for circumferentially cracked pipes under pure bending, pure tension, and combined bending and tension loads. Henceforth, new and improved analytical models and some preliminary results are presented for cases where current methods are inadequate or there are no available methods. Also, based on this review, a number of appropriate predictive models are identified for a systematic evaluation of their accuracy. The results of their evaluations will be presented and examined in the forthcoming companion papers (Part II — Model validations [1] and Part III — Off-center cracks, restraint of bending, thickness transition, and weld residual stresses) [2].

Effects of off-centered cracks and restraint of induced bending caused by pressure on the crack-opening-area analysis of pipes

Current models for the crack-opening-area analysis of pipes with circumferential through-wall cracks are based on various idealizations or assumptions which are often necessary to simplify the mathematical formulation and numerical calculation. This paper focuses on the validity of two such assumptions that involve off-centered cracks and the restraint of induced bending caused by pressure, and quantifies their effects on the crack-opening area analysis of pipes. Finite element and/or simple estimation methods were employed to compute the center-crack-opening displacement and crack-opening shape for a through-wall-cracked pipe, considering off-centered cracks and the restraint of induced bending caused by pressure. The results of the analyses show that, for both cases, the crack-opening area can be reduced significantly. For pipes with off-centered cracks, the crack-opening area can be evaluated from analyses of symmetrically centered cracks and assuming elliptical profile. For pipes with complete restraint of the induced bending caused by pressure, the reduction in crack-opening area depends on the crack size. When the crack size is small, the restraint effects can be ignored. However, when the crack size is large, the restrained crack opening can be significantly smaller than the unrestrained crack opening, depending on the length of pipe involved; hence, it may be important for the crack-opening-area and leak-rate analyses.

On the fracture path and the intergranular phosphorus distribution in phosphorus-doped FeSi symmetrical bicrystals

A high-resolution scanning Auger micropobe analysis was carried out on matching fracture surfaces of symmetrical Σ = 5 (013) bicrystals of Fe-3 wt%Si doped with 270 ppm phosphorus which were grown from seeds by floating-zone melting. The phosphorus distribution on some regions of a fracture surface was found to alternate between high and low concentrations; these alternations were often associated with deformation bands, such as mechanical twins. The reverse pattern was found on the matching region on the opposite fracture surface. This confirms a hypothesis made earlier that the inhomogeneous phosphorus concentrations found on fracture surfaces are the result of off-center crack propagation through a laterally extended phosphorus distribution along the grain boundary and the switching of the crack path from one side to the other upon an encounter with a grain-boundary step caused by a deformation band. In the regions of unequal division of the P-enriched region by the fracture, a 2:1 ratio of phosphorus concentrations was found. The total width of the region was deduced to be about five atomic planes from observations of sputtering rates and an analysis based on simple logic.

Surface small crack growth behaviour in low-cycle fatigue at elevated temperature and application limit of macroscopic crack growth law: Okazaki, M., Yada, T. and Endoh, T. Nucl. Eng. Des. Jan. (II) 1989 111, (1), 123–134

This is the third of three papers generated from a recent study on crack-opening-area analysis of circumferentially cracked pipes for leak-before-break applications. The first two papers1, 2[Rahman, S., Brust, F. W., Ghadiali, N. and Wilkowski, G., Crack-opening-area analyses for circumferential through-wall cracks in pipes. Part I—Analytical models. International Journal of Pressure Vessels and Piping, (this issue). Rahman, S., Brust, F. W., Ghadiali, N. and Wilkowski, G., Crack-opening-area analyses for circumferential through-wall cracks in pipes. Part II—Model validations. International Journal of Pressure Vessels and Piping, (this issue).] dealt with crack-opening-area analysis of pipes assuming simple loading, pipe and crack geometries, and boundary conditions. This paper (Part III—Off-center cracks, restraint of bending, thickness transition, and weld residual stresses) examines several practical aspects of crack-opening-area analysis involving off-center cracks, restraint of pressure-induced bending, girth-weld nozzle cracks at thickness transition, and weld-induced residual stresses. Currently, there are no engineering methods or guidelines available to analyze pipes under these conditions. Both linear-elastic and elastic–plastic finite element analyses were conducted to determine quantitatively their effects on various crack-opening characteristics. From the results of these analyses, recommendations are made on how an off-center crack can be analyzed based on fracture-mechanics equations for a centered crack. It was found when the restraint of bending effects become important and how they should be taken into account. Cracks located in the thickness transition with thickness gradients on both sides of a nozzle girth weld were analyzed. Finally, simplified finite element simulations were performed to determine if the residual stresses should be considered and when they become important for crack-opening evaluations.

Evaluation of leak flow rate and jet impingement related to leak before break: Yano, T., Matsushima, E. and Okamoto, A. Nucl. Eng. Des. Jan. (II), 1989 111, (1), 197–205

This is the third of three papers generated from a recent study on crack-opening-area analysis of circumferentially cracked pipes for leak-before-break applications. The first two papers1, 2[Rahman, S., Brust, F. W., Ghadiali, N. and Wilkowski, G., Crack-opening-area analyses for circumferential through-wall cracks in pipes. Part I—Analytical models. International Journal of Pressure Vessels and Piping, (this issue). Rahman, S., Brust, F. W., Ghadiali, N. and Wilkowski, G., Crack-opening-area analyses for circumferential through-wall cracks in pipes. Part II—Model validations. International Journal of Pressure Vessels and Piping, (this issue).] dealt with crack-opening-area analysis of pipes assuming simple loading, pipe and crack geometries, and boundary conditions. This paper (Part III—Off-center cracks, restraint of bending, thickness transition, and weld residual stresses) examines several practical aspects of crack-opening-area analysis involving off-center cracks, restraint of pressure-induced bending, girth-weld nozzle cracks at thickness transition, and weld-induced residual stresses. Currently, there are no engineering methods or guidelines available to analyze pipes under these conditions. Both linear-elastic and elastic–plastic finite element analyses were conducted to determine quantitatively their effects on various crack-opening characteristics. From the results of these analyses, recommendations are made on how an off-center crack can be analyzed based on fracture-mechanics equations for a centered crack. It was found when the restraint of bending effects become important and how they should be taken into account. Cracks located in the thickness transition with thickness gradients on both sides of a nozzle girth weld were analyzed. Finally, simplified finite element simulations were performed to determine if the residual stresses should be considered and when they become important for crack-opening evaluations.

Effects of treatments on mechanical properties of titanium alloy castings: Eylon, D., Froes, F.H. and Barice, W.J. SAMPE Q. Jan. 1989 20, (2), 42–45

Current models for the crack-opening-area analysis of pipes with circumferential through-wall cracks are based on various idealizations or assumptions which are often necessary to simplify the mathematical formulation and numerical calculation. This paper focuses on the validity of two such assumptions that involve off-centered cracks and the restraint of induced bending caused by pressure, and quantifies their effects on the crack-opening area analysis of pipes. Finite element and/or simple estimation methods were employed to compute the center-crack-opening displacement and crack-opening shape for a through-wall-cracked pipe, considering off-centered cracks and the restraint of induced bending caused by pressure. The results of the analyses show that, for both cases, the crack-opening area can be reduced significantly. For pipes with off-centered cracks, the crack-opening area can be evaluated from analyses of symmetrically centered cracks and assuming elliptical profile. For pipes with complete restraint of the induced bending caused by pressure, the reduction in crack-opening area depends on the crack size. When the crack size is small, the restraint effects can be ignored. However, when the crack size is large, the restrained crack opening can be significantly smaller than the unrestrained crack opening, depending on the length of pipe involved; hence, it may be important for the crack-opening-area and leak-rate analyses.

Realistic cycle fatigue strength of spherical graphite cast iron (spharoguss) under the influence of corrosion: Fischer, E., Mahnig, F. and Walter, H.P. Konstr. Giessen 1988 13, (2), 16–24 (in German)

Current models for the crack-opening-area analysis of pipes with circumferential through-wall cracks are based on various idealizations or assumptions which are often necessary to simplify the mathematical formulation and numerical calculation. This paper focuses on the validity of two such assumptions that involve off-centered cracks and the restraint of induced bending caused by pressure, and quantifies their effects on the crack-opening area analysis of pipes. Finite element and/or simple estimation methods were employed to compute the center-crack-opening displacement and crack-opening shape for a through-wall-cracked pipe, considering off-centered cracks and the restraint of induced bending caused by pressure. The results of the analyses show that, for both cases, the crack-opening area can be reduced significantly. For pipes with off-centered cracks, the crack-opening area can be evaluated from analyses of symmetrically centered cracks and assuming elliptical profile. For pipes with complete restraint of the induced bending caused by pressure, the reduction in crack-opening area depends on the crack size. When the crack size is small, the restraint effects can be ignored. However, when the crack size is large, the restrained crack opening can be significantly smaller than the unrestrained crack opening, depending on the length of pipe involved; hence, it may be important for the crack-opening-area and leak-rate analyses.