Surface Cracks In Plates Research Articles

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.

Including effect of bending stress parallel to the crack plane on a developed local limit load model

A plate containing a semi-elliptical surface crack is selected as a typical surface crack case to investigate the effects of the bending stress parallel to the crack plane on the limit load and elastic-plastic J. Elastic and elastic-plastic FE analyses are used to obtain J values for the surface-cracked plate under stress normal to the crack plane or under biaxial stress plus through-thickness bending with/without bending stress parallel to the crack plane. The results show that the applied bending stress parallel to the crack plane does not affect the elastic J, and, therefore, the stress intensity factor (SIF), but it does affect the elastic-plastic J. A reference stress estimation method considering the bending stress parallel to the crack plane is developed, which shows good correlation to the elastic-plastic J for cases with/without the bending stress parallel to the crack plane. This method is then used to extend the developed local limit load model to include the effect of the bending stress parallel to the crack plane.

Assessment of surface crack growth of composite girders with concrete-filled tubular flanges and corrugated webs through substructure-based numerical modelling

This paper presents an analytical assessment of surface crack growth behaviour of composite girders with concrete filled tubular flanges and corrugated webs (CGCTFCWs) with the aid of substructure-based numerical modelling. Distinctive features of crack propagation on the tubular flanges with considerable stress gradient from lower to upper cracked tube surface interacted with the weld toes along the corrugated webs are replicated in the substructure modelling and discussed in details. Based on a favourable verification of stress intensity factors (SIFs) with reported model with semi-elliptical surface crack in plates and rectangular hollow section tube, an analytically derived substructure model of critical corrugated web-flange welded details coupled to the rest of the structure is developed. Such a model is distinguished itself from that based on original Newman and Raju equation by an amendatory of the stress gradient induced by the shifting of the neutral axis and the geometry as crack penetrated through the tube wall. Based on a parametric analysis, the SIFs significantly influenced by the corrugation depth ratio, the tube thickness-to-width ratio and the tube thickness-to-depth ratio in relation with the dimensionless crack length are demonstrated and taken into account in the derivation of a new geometry amendatory coefficient. An experimental investigation was also implemented to further examine and validate the modelling crack propagation response. The resultant fatigue fracture manner and the stress concentration of the hot spot are virtually in good correlation with the modelling results. Moreover, the relations between the crack growth increment and fatigue endurances from experimental measurement match well with these predicted by the NASGRO equation using amended SIFs, indicating that the proposed model is able to trace the distinct geometry effects of the corrugated web and the tubular flange on the crack propagation response of CGCTFCWs.

Creep fracture parameter C* solutions for semi‐elliptical surface cracks in plates under tensile and bending loads

AbstractIn order to predict and assess creep life for plate structures with semi‐elliptic surface cracks under high temperature condition, the accurate calculation of the creep fracture mechanics parameter C* is a critical step. In this paper, the effects of crack sizes, plate geometries, and material creep properties on the parameter C* have been investigated under tensile and bending loads by extensive finite element analyses. Based on the results, the creep influence functions Hc for calculating C* values were obtained and fitted into equations for surface cracks in plates under both loads. The equations have been verified by finite element calculations. The C* solutions were obtained through these equations which are suitable for wide ranges of crack sizes, plate geometries, and materials.

Two-parameter fracture prediction for cracked plates under bending

In this work, the fracture prediction method based on two-parameter J-Ad* (J-integral and a new load-independent unified constraint parameter Ad*) with considering both in-plane and out-of-plane constraints has been investigated for semi-elliptical surface cracks in plates under bending. The crack initiation locations and fracture initiation loads for different crack sizes have been comparatively predicted and analyzed by using the two-parameter J-Ad* and the conventional single-parameter J-integral. The predicted results based on the two-parameter J-Ad* approach have been verified by finite element simulation based on the GTN (Gurson–Tvergaard–Needleman) micromechanics model. The results indicate that the two-parameter approach can provide more accurate predictions. The conventional single parameter approach can produce conservative (for shorter and shallower cracks) or non-conservative (for longer and deeper cracks) results. It is recommended that in the application of the two-parameter approach, for obtaining the best prediction accuracy, the two parameters should be calculated at the crack initiation location.

Development of Automated Model Generation and Analysis of Surface-Cracked Plates in Bending for Interpolated Elastic–Plastic J-Integral Solutions

Abstract NASA’s Tool for Analysis of Surface Cracks (TASC) has been used since 2014 to perform elastic–plastic J-integral (J), crack mouth opening displacement (CMOD), crack front constraint, and deformation limit calculations for plates in tension. To date, no comparable database or tool exists for surface-cracked plates in bending. Existing tools and prior ASTM standards are limited to linear-elastic materials or simpler 2-D crack geometries. TASC uses a database of 600 models for interpolated solutions over a wide range of semielliptical surface crack geometries (0.2≤a/c≤1.0, 0.2≤a/t≤0.8) and material properties (100≤E/Sys≤1,000, 3≤n≤20). Here, a is the crack depth, c is the half-width of the crack, and t is the plate thickness, so that a/c is the crack aspect ratio and a/t is a normalized measurement of crack depth. E, Sys, and n are the plate’s elastic modulus, yield strength, and the Ramberg–Osgood power law hardening exponent, respectively. This report details the development of a bending model database covering the same range of crack geometries and material properties. It includes developing new criteria to determine if a model has reached sufficient plastic deformation and modifications to model boundary conditions to accurately capture the behavior of deeply cracked plates in bending. Python is the primary automation tool used in this process, including running FEACrack to create meshes, modifying material properties, iterating WARP3D boundary conditions to meet plastic deformation requirements, and converting WARP3D output into a reduced set of MATLAB-compatible data files. Bending model results from WARP3D are validated against Abaqus results for identical meshes. This report then shows the initial integration of bending models and results into the existing TASC code, laying the groundwork for a single tool for analysis of surface-cracked plates in tension or bending.

Closed-Form Stress Intensity Factor Solutions for Surface Cracks With Large Aspect Ratios in Plates

Abstract Alloy 82/182/600, which is used in light-water reactors, is known to be susceptible to stress-corrosion cracking. The depth of some of these cracks may exceed the value of half-length on the surface. Although the stress intensity factor (SIF) for cracks plays an important role in predicting crack propagation and failure, Section XI of the ASME Boiler and Pressure Vessel Code does not provide SIF solutions for such deep cracks. In this study, closed-form SIF solutions for deep surface cracks in plates are discussed using an influence coefficient approach. The stress distribution at the crack location is represented by a fourth-degree-polynomial equation. Tables for influence coefficients obtained by finite element analysis in the previous studies are used for curve fitting. The closed-form solutions for the influence coefficients were developed at the surface point, the deepest point, and the maximum point of a crack with an aspect ratio a/c ranging from 1.0 to 8.0, where a is the crack depth and c is one-half of the crack length. The maximum point of a crack refers to the location on the crack front where the SIF reaches a maximum value.

The mesh density effect on stress intensity factor calculation using ABAQUS XFEM

This paper investigates the effect of the mesh density on reliability of XFEM stress intensity factor solutions using ABAQUS by comparing with the FE solutions using detailed crack-tip mesh. For analysis, a surface-cracked plate under mechanical and thermal loading is considered. Based on comparison, the requirements of mesh density in terms of the geometric dimension or of the enrichment radius are given.

A study of Txx-stress on mixed mode I-II semi-elliptical surface crack in plates

A new finite element modeling approach is proposed in this study to analyze Txx (in-plane T-stress) on mixed mode I-II semi-elliptical surface crack in plates. Txx-stress is calculated by varying inclined angle (β), aspect ratio (a/c), relative crack depth (a/t) and the eccentric angle of ellipse (φ). As is found in this study, it is accurate and efficient to simulate mixed mode I–II crack with this new approach. As the inclined angle (β) increases, Txx-stress decreases; as a/t increases, Txx-stress varies widely in accordance with different angle of φ. Based on the stress decomposition of an arbitrary point along the crack front, it can be concluded that Txx-stress is related to sin2β, and the predicted formulas of Txx-stress match the finite element results well, which proves that the deduction of Txx-stress on surface crack in this present work is reasonable. It is also found discrepancy between Txx-stress of through crack and surface crack is great at different points along the crack front. Only in the vicinity of free surface, Txx-stress with different inclined angles is similar to that of through crack.

Three-Dimensional Mixed Mode Stress Intensity Factors for Inclined Elliptical Surface Cracks in Plates under Uniform Tensile Load

In this study, main results from parametric analyses of three-dimensional inclined elliptical surface cracks using FRAC3D are presented in terms of normalized mixed mode stress intensity factors (SIFs) along crack fronts. FRAC3D is the solver of in-house developed “Fracture and Crack Propagation Analysis System (FCPAS)” and is a finite element-based standalone program employing three-dimensional enriched finite elements. In the analyses, values of the main parameters affecting the problem, which are normalized crack depth with respect to plate thickness (a/t=0.2, 0.4, 0.6, 0.8), crack aspect ratio (a/c=0.25, 0.50, 1.0, 2.0, 4.0) and crack inclination angle (β=0°, 15°, 30°, 45°, 60°, 75°), are changed systematically in their realistic ranges to obtain a wide library of solutions representing the general problem and to develop empirical SIF equations that are valid for all values of the main parameters in their pre-determined ranges. This resulted in a total of 120 three-dimensional fracture analyses. The results show that as the inclination angle of the surface crack increases, mode-I SIF decreases along the crack front, while mode-II and mode-III SIFs increase up to β=45°, which contains the plane with maximum in-plane shear stress. For higher values of β, mode-II and mode-III SIFs start decreasing as expected. As the normalized crack depth increases, the normalized SIFs also increase. When the depth point and the free-surface point are compared with each other, it is seen that the crack aspect ratio also has big effect on the relative values of the normalized SIFs.

Marker load-aided bidirectional fatigue crack growth rate measurement via a semi-elliptical surface crack

It is always impractical to measure the fatigue crack growth rate in the thickness direction of a plate using a standard specimen because of the limited plate thickness. To address this issue, we proposed a method for crack growth rate measurements utilizing a semi-elliptical surface crack, the size of which is determined via marker bands. This method allows the crack growth rates both in the surface direction and the thickness direction to be measured in a single test. The core of the method involves the load spectrum development and the crack growth data analyses. In the load spectrum development, the number of marker load cycles in a load block is estimated through a crack growth equation including the crack closure effect, while the interval of marker load blocks is determined using the crack length measured in a pilot test. The estimated parameters can be amended using the crack growth data acquired by fractographic analyses, should unclear marker bands or unreasonable band spacing occur. In the crack growth data analyses, a closed stress intensity factor solution for a surface-cracked plate with clamped ends was developed, facilitating stress intensity factor calculations. Finally, we demonstrated an application of the proposed method, i.e. fatigue crack growth rate measurements for Ti-6Al-4 V plates. Fine and legible marker bands were observed by fractography, and the resulting da/dN-ΔK curve was consistent with the curves obtained by using standard specimens, justifying the proposed method.

A local limit load model for J prediction via the reference stress method

A local limit load model is developed for shell/plate type components with surface cracks for determining the local limit load or local reference stress used in J prediction via the reference stress J scheme for defective components. The model is a plate which contains a rectangular surface crack circumscribing the real surface defect and has the same thickness as the component at the crack location. The model is remotely loaded by the primary stresses of the component at the crack location obtained from elastic uncracked-body stress analysis. The global limit load of this model is used as the local limit load of the defective component. The model is validated using 273 cases of 3-D finite element (FE) J results for semi-elliptical surface cracks in plates, cylinders and elbows. The results show that when this local limit load is used in the reference stress J prediction scheme, the predicted J values are reasonably accurate but conservative, compared with the FE J values.

Elastic and fully plastic J-integrals for mixed mode fracture induced by inclined surface cracks in plates under biaxial loading

Mixed mode fractures can be triggered by either multi-axial stresses or inclined cracks or both. Little research has been undertaken on J-integral for inclined surface cracks in plates under biaxial loading. This paper intends to determine the elastic and fully plastic J-integral for mixed mode fracture induced by inclined surface cracks in plates under biaxial loading conditions, using three-dimensional finite element method. Various geometries, biaxiality and material properties of cracked plates, including crack depth to plate thickness ratios, inclination angles, strain hardening exponents and biaxiality ratios, are considered. From numerical results, it is found that for elastic analysis, the equivalent influence coefficients increases with the increase of the relative crack depth and the magnitude of the biaxiality ratios. It is also found that for a given crack and plate geometry, the values of normalized fully plastic J-integral h1 decrease along the whole crack front for different strain hardening exponents n with the increase of the inclination angles from 0° to 45° for uniaxial loading. It can be concluded that the method presented in the paper can determine the J-integral for inclined surface cracks in plates with reasonable accuracy. The results presented in the paper can equip practitioners for more accurate prediction of plate failures under various loads.

Cleavage fracture assessment for surface-cracked plates fabricated from high strength steels

This paper presents a combined experimental and numerical investigation to assess the probability of cleavage fracture for surface-cracked plates, using the Weibull stress framework. The proposed procedure defines a critical crack-front segment as the fracture initiation zone using the computed energy release rate. The Weibull-stress based local approach introduces a modified constraint correction function, which allows bidirectional scaling of the fracture toughness in surface-cracked specimens and the idealized 1T small-scale yielding condition. The proposed procedure predicts closely the probability of fracture for surface-cracked specimens made of three different types of steel materials.

Global limit load solutions for plates with surface cracks under combined biaxial forces and cross-thickness bending

Lower bound limit load solutions for surface cracks in plates under combined end force, cross-thickness bending moment and tensile/compressive membrane stress parallel to the crack are derived based on the von Mises yield criterion. From these solutions, particular limit loads for plates with extended surface cracks and through-thickness cracks or uncracked plates under the same loading conditions are obtained. The limit load solutions for surface cracks in plates under combined tension and bending due to Lei and Fox can be reproduced from the solutions in this paper by setting the stress parallel to the crack plane to zero.

Effect of Compressive Residual Stress on Fatigue Crack Propagation

Fatigue failures have sometimes taken place in weld joints due to stress concentration and tensile residual stress at the weld toe. Therefore managements of fatigue crack initiation and propagation contribute to the enhancement of the fatigue life of welded steel structures.The hammer peening process is well known as one of methods to improve the fatigue life of weld joints by generating the compressive residual stress field near the weld toe where recognized as the fatigue crack initiation site. With respect to the fatigue life estimation of the welded steel structure which applied the compressive residual stress field near the weld toe, it is important not only fatigue life estimation for the fatigue crack initiation but also that for the fatigue crack propagation. However there is few research work which deal with the fatigue crack estimation in the compressive residual stress field.In this study, mechanism of fatigue crack propagation in the compressive residual stress field was clarified by experimental observation of crack propagation from a surface crack after hammer peening. Morphology of a propagating surface crack in plate and gusset weld joint specimens were measured by the beach mark method. As a result, it was clarified that morphology of surface crack propagated in the compressive residual stress field was different from that in neutral stress filed. And this phenomenon was clearly observed especially under the low stress intensity factor condition.

Limit load solutions of plates with extended surface cracks under combined biaxial forces and cross-thickness bending

Lower bound limit load solutions for extended surface cracks in plates with free ends (pin-loaded) under combined biaxial positive/negative force/stress and positive/negative through-thickness bending are developed based on the lower bound limit load theorem and both Tresca and Mises criteria. An existing Mises limit load solution for extended surface cracks in plates with fixed ends under combined biaxial tension and positive moment is extended to general solutions for combined biaxial positive/negative force/stress and positive/negative through-thickness bending moment. Corresponding reference stress expressions are also derived and presented.

An equivalent thickness conception for evaluation of corner and surface fatigue crack closure

The out-of-plane constraint-based equivalent thickness conception developed previously for corner cracks is extended here to surface-cracked plates based on systematical finite element simulations for the purpose to evaluate the plasticity-induced fatigue closure of corner and surface cracks. A semi-analytical solution for equivalent thickness of semi-elliptic surface cracks is obtained by numerical analyses of three-dimensional stress fields near the crack borders and comparing with that of ideally straight-through cracks in plates of finite thickness. The fatigue opening stresses of corner and surface cracks are evaluated based the recognized equations of straight-through cracks using the equivalent thickness conception. Comparison against available finite element and experimental results shows that the developed method can provide satisfied prediction of fatigue closure for both corner and surface cracks.

A global limit load solution for plates with surface cracks under combined end force and cross-thickness bending

A global limit load solution for rectangular surface cracks in plates under combined end force and cross-thickness bending is derived, which allows any combination of positive/negative end force and positive/negative cross-thickness moment. The solution is based on the net-section plastic collapse concept and, therefore, gives limit load values based on the Tresca yielding criterion. Solutions for both cases with and without crack face contact are derived when whole or part of the crack is located in the compressive stress zone. From the solution, particular global limit load solutions for plates with extended surface cracks and through-thickness cracks under the same loading conditions are obtained. The solution is consistent with the limit load solution for surface cracks in plates under combined tension and positive bending due to Goodall & Webster and Lei when both the applied end force and bending moment are positive. The solution reduces to the limit load solution for plain plates under combined end force and cross-thickness bending when the crack vanishes.

Nondestructive Damage Detection of Two Dimensional Plate Structures Using Modal Strain Energy Method

AbstractA nondestructive detection method of surface cracks in two dimensional plate structures using modal strain energy method is investigated in this paper. Experimental modal analysis (EMA) is conducted on an aluminum alloy 6061 thin plate to obtain the mode shapes before and after damage under a completely free boundary condition. The measured mode shapes are used to compute the strain energy of the plate. Limited by the measured points, a differential quadrature method is employed to compute the partial differential terms in strain energy formula. A damage index is then defined based on strain energy ratio of the plate before and after damage. This damage index is employed to identify the location of surface crack in plate structure. A finite element analysis (FEA) is also performed to access this approach and demonstrate a feasible process for the experimental work. Good correlation between FEA and EMA results is obtained. The damage index obtained from both FEA and EMA successfully identify the location of surface crack in the aluminum plate. Only few measured mode shapes of the plate are required in this method, which provides a quick, flexible, inexpensive and nondestructive technique to identify the damagein local and global 2D plate structures.