Semi-elliptical Surface Cracks In Plates Research Articles

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.

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.

J-integral and limit load analysis of semi-elliptical surface cracks in plates under tension

Systematic detailed non-linear finite element (FE) analyses are described for semi-elliptical surface cracks in plates under tension. Limit load solutions are obtained from the FE J results through the reference stress method. The results show that the type of the relationship between J and the limit load mainly depends on the ratio a/ t, where a is the crack depth and t the thickness of the plate. For a/ t≤0.5, J for any position along the crack front can be predicted by the reference stress method using a single limit load value, except for the points very close to the plate surface. For a/ t=0.8, J can only be approximately estimated because no single limit load value can be found to satisfy all the FE J solutions along the crack front. However, for all cases considered, the maximum J value along the crack front can still be predicted by using the global limit load in the reference stress method. The limit load data obtained from this work can be well predicted by a global limit load equation developed by Goodall and Webster.

J-integral and limit load analysis of semi-elliptical surface cracks in plates under bending

Systematic detailed linear and non-linear finite element (FE) analyses are performed for semi-elliptical surface cracks in plates under bending. Limit load (moment) solutions are obtained from the FE J results via the reference stress method. The FE results show that the Newman and Raju stress intensity factor equation is reasonably accurate and the Yagawa et al. J solution may significantly under estimate J for bending load. The relationship between J and the limit load is found to be dependent on the ratio a/ t and a/ c, where a and c are the depth and the half-length of the crack and t is the plate thickness. For a/ t≤0.5 with a/ c=0.2, J for any position along a crack front can be predicted by the reference stress method using a single limit load value except for the points very close to the plate surface. For all other cases, it can only be approximately estimated by the reference stress method because a limit load value that can satisfy all the FE J solutions along the crack front cannot be found. However, for all the cases examined, the maximum J along the crack front can be well predicted by the reference stress method when a proper global limit load is used. The Goodall and Webster global limit load equation is extended to any crack depth. The limit load data obtained in this paper can be well reproduced by the extended equation.

J-integral and limit load analysis of semi-elliptical surface cracks in plates under combined tension and bending

Systematic detailed finite element (FE) analyses are performed for semi-elliptical surface cracks in plates under combined tension and bending. The Newman and Raju stress intensity factor solution is confirmed and non-linear J solutions are generated and expressed as the EPRI type h 1 function for a wide range of geometry factors and ratios of bending to tensile load. Limit load solutions are obtained from the FE J results through the reference stress method. The results show that relationship between J and the limit load depends on a/ t, a/ c and the load ratio λ. Here a and c are the depth and half-length of the crack and t is the plate thickness. When both tension and bending are effective (e.g. λ=0.5), for a/ t≤0.5 and a/ c=0.2, J for any position along a crack front can be predicted by the reference stress method using a single limit load value except for the points very close to the plate surface. For all other cases analysed, it can only be approximately estimated by the reference stress method because a limit load value that can satisfy all the FE J solutions along the crack front cannot be found. However, for all the cases, the maximum J along the crack front can be well predicted by the reference stress method when a proper global limit load is used. The FE limit load data can be well predicted by the extended Goodall and Webster solution.

Distributions of SIFs for symmetrical part-elliptical and semi-elliptical surface cracks in plates subjected to crack face shear loading

The distributions of SIF s K II, K III and their ratios along crack fronts of symmetrical part-elliptical (PE) surface cracks with a critical inclination angle β c in plates subjected to uniform crack face shear loading were evaluated using three-dimensional FEM. The results are then compared with the corresponding results obtained for semi-elliptical (SE) surface cracks. The differences between PE and SE cracks in distributions of K II, K III are small at positions where ϕ/ ϕ c ⩽0.625, but are appreciable at positions where ϕ/ ϕc >0.625. The distribution of the K II/ K III ratio is mainly dependent on the crack aspect ratio a/ c and the crack front inclination angle β. The ratios K II/ K III at the corner points of the PE cracks with β = 66.8° and ν = 0.3 vary from 2.06 to 2.21 for geometries in this study. However for SE cracks they vary from 19 to 35. The PE cracks are very different from the SE cracks.

Automated System for Analyzing Stress Intensity Factors of Three-Dimensional Cracks: Its Application to Analyses of Two Dissimilar Semi-Elliptical Surface Cracks in Plate

This paper describes a new automated system for analyzing the stress intensity factors (SIFs) of three-dimensional cracks. A geometry model containing one or several three-dimensional cracks is defined using a commercial CAD system, DESIGNBASE. Several local distributions of node density are chosen from the database of the present system, and then automatically superposed on one another over the geometry model by using the fuzzy knowledge processing. Nodes are generated by the bucketing method, and ten-noded quadratic tetrahedral solid elements are generated by the Delaunay method. A user imposes material properties and boundary conditions onto parts of the geometry model such as loops and edges by clicking them with a mouse and by inputting values. For accurate analyses of the stress intensity factors, finer elements are generated in the vicinity of crack tips, thanks to the fuzzy knowledge processing. The singular elements such that the midpoint nodes near crack front are shifted at the quarter-points are automatically placed along the three-dimensional crack front. The complete finite element model generated is given to a commercial finite element code, MARC, and a stress analysis is performed. The stress intensity factors are calculated using the displacement extrapolation method. To demonstrate practical performances of the present system, two dissimilar semi-elliptical surface cracks in a plate subjected to uniform tension are solved, and their interaction effects are discussed in detail. It is shown from the results that ASME Boiler and Pressure Vessel Code, Section XI, Appendix A gives a conservative stress intensity factor for two identical adjacent surface cracks and for two dissimilar adjacent surface cracks.

Stress intensity factors for semi-elliptical surface cracks in plates and cylindrical pressure vessels using the hybrid boundary element method

At first, a hybrid boundary element method used for three-dimensional linear elastic fracture analysis is established on the basis of the first and the second kind of boundary integral equations. Then the concerned basic theories and numerical approaches including the discretization of boundary integral equations, the divisions of different boundary elements, and the procedures for the calculations of singular and hypersingular integrals are presented in detail. Finally, the stress intensity factors of surface cracks in finite thickness plates and cylindrical pressure vessels are computed by the proposed method. The numerical results show that the hybrid boundary element method has very high accuracy for the analysis of surface crack.

Three-dimensional fully plastic solutions for semi-elliptical surface cracks

Nonlinear finite element analyses of semi-elliptical surface cracks are performed with the fully plastic condition, where the power-law hardening materials and the deformation theory of plasticity are assumed. To satisfy the incompressibility condition of a plastic material, two kinds of numerical techniques (the penalty function method and the Uzawa algorithm) are employed. The local distributions and the global values of the J- integral are obtained using the virtual crack extension technique for various configurations of semi-elliptical surface crack in plate subjected to uniform tension and bending, respectively. These solutions are given in the form of polynomials with geometric parameters of crack and the strain hardening exponent. Finally, an estimation scheme for the J- integral of surface crack in a plate subjected to mixed loading of tension and bending is proposed.

Stress intensity factors for semi-elliptical surface cracks in a plate under tension based on the Isida's solution

The stress intensity factor solution given by Isida et al. for semi-elliptical surface cracks in plates is improved and extended. The data tabulated for the ranges 0≤a/t≤0.6 and 0.25≤a/c≤1.0 were checked using the energy relation and found to be superior to solutions available in the literature.

Assessment of stress intensity factor and aspect ratio variability of surface cracks in bending plates

In this paper, a closed-form solution for the stress intensity factor ( K) of semielliptical surface cracks in plates subjected to pure bending, obtained by Newman and Raju using 3D finite elements, is critically evaluated. This solution is compared to a recommended solution by the Society of Experimental Stress Analysis (SESA). It is also compared to photoelastic K measurements. In addition, in this study the aspect-ratio variability of surface cracks under fatigue loading is predicted and compared with experimental data and also with the predictions of other empirical equations proposed by Porten, Kawahara and Kurihara, and lida. Finally, the usefulness of this equation for the prediction of fatigue life of surface cracks is evaluated by a comparison with experimental results.

Stress-intensity factors for a wide range of semi-elliptical surface cracks in finite-thickness plates

Surface cracks are among the more common flaws in aircraft and pressure vessel components. Accurate stress analyses of surface-cracked components are needed for reliable prediction of their crack growth rates and fracture strengths. Several calculations of stress-intensity factors for semi-elliptical surface cracks subjected to tension have appeared in the literature. However, some of these solutions are in disagreement by 50–100%. In this paper stress-intensity factors for shallow and deep semi-elliptical surface cracks in plates subjected to tension are presented. To verify the accuracy of the three-dimensional finite-element models employed, convergence was studied by varying the number of degrees of freedom in the models from 1500 to 6900. The 6900 degrees of freedom used here were more than twice the number used in previously reported solutions. Also, the stress-intensity variations in the boundary-layer region at the intersection of the crack with the free surface were investigated.

An experimental investigation into the mechanics of deep semielliptical surface cracks in mode i loading

An experimental investigation was made of the surface deformation and extent of plastic yielding associated with relatively deep semielliptical surface cracks in plates subjected to tensile loading. Data were gathered from sheet Ti-6A1-4V and Fe-3Si, the latter material being employed to study, by the electrolytic etching technique, the plastic zones in various planes intersecting the crack. Available analytical models were applied to calculate the stress intensity factors, and the experimental data were used to examine various models for predicting plastic zone sizes.