On the through-thickness crack with a curve front in center-cracked tension specimens

In this paper, the near-threshold fatigue behavior of physically through-thickness short cracks and of long cracks in a low alloy steel is investigated by experiments in ambient air. Physically through-thickness short fatigue cracks are created by gradually removing the plastic wake of long cracks in compact tension specimens. The crack closure is systematically measured using the compliance variation technique with numerical data acquisition and filtering for accurate detection of the stress intensity factor (SIF) at the crack opening. Based on the experimental results, the nominal threshold SIF range is shown to be dependent on the crack length and the characteristic of the crack wake which is strongly dependent on the loading history. The effective threshold SIF range and the relation between the crack propagation rate and the effective SIF range after the crack closure correction are shown to be independent on crack length and loading history. The shielding effect of the crack closure is shown to be related to the wake length and load history. The effective threshold SIF range and the relationship between the crack growth rate and the effective SIF range appear to be unique for this material in ambient air. These properties can be considered as specific fatigue properties of the couple material/ambient air environment.

There is an inherent relationship between the shape and the corresponding stress intensity factor (SIF) distribution of a crack. A typical inverse problem of linear elastic fracture mechanics about a crack, i.e. to predict the shape of a crack assuming that some information of SIF distribution is known, is presented. A finite-element based numerical procedure is used to determine the shape, correspondingly the SIF, of a mode-I planar crack based on a specified SIF distribution. The crack front is modeled using cubic splines, which are determined by a number of control-points. The crack front shape is achieved iteratively by moving control-points based on a gradientless algorithm. Numerical examples for planar cracks in through-cracked and surface-cracked plates with finite thickness and width are presented to show the validity and practicability of the proposed method. The SIFs obtained by present method are compared with the known solutions for cracks with same dimensions. The presented method is considered to be a promising alternative to the evaluation of SIFs and the prediction of shape evolution for fatigue cracks.

The Fitness-for-Service (FFS) approach requires the evaluation of the mutual impact of nonaligned, multiple cracks on each other. As such, initially one must resolve whether existing, nonaligned, parallel cracks in the structure should be treated as merged or as separate, multiple cracks for FFS evaluation. Criteria and standards found in existing literature on how to deal with multiple, nonaligned cracks are very source dependent, and those guidelines are often developed from on-site, service inspections without exact and methodical substantiation. Based on this determination, the authors previously reported on the impact of an embedded crack on an edge crack using a two-dimensional model, and, more recently using a three-dimensional (3D) model, on the impact of a semicircular surface crack on a quarter-circle corner crack. However, actual crack shapes identified using nondestructive techniques are 3D in nature, normally not semicircular, and their impact are of mutual importance. Thus, the stress intensity factor (SIF) distribution along the semi-elliptical surface crack is as significant as the SIF distribution of the corner crack in the application of FFS standards. Therefore, nonaligned cracks with varied arrangements and shapes and the SIFs along their crack fronts are considered crucial in order to obtain more practical information on the application of rules provided in FFS codes. In this study, over 330 different cases are solved and the behavior of the SIF distribution along a 3D semi-elliptic nonaligned surface crack is assessed when affected by a quarter-circle corner crack of various geometries in an infinitely large solid. For a given geometry of a quarter-circle corner crack, a detailed examination of the corner crack's impact on the 3D SIFs of the surface crack is carried out as a function of the surface crack's ellipticity, and the horizontal (H) and vertical (S) separation distances between the two cracks. The analysis was replicated for various arrangements of separation distances S and H. The results from this study are considered noteworthy to the understanding of the relation between the criteria and standards in FFS community and the consequence of their application in engineering practice. The results demonstrate that the 3D SIFs along the crack front of the semi-elliptical surface crack can be affected profoundly by the presence of the quarter-circle corner crack. The corner crack's existence may amplify or diminish the SIF of the surface crack for those points of the semi-elliptic surface crack front that approach the closest quarter-circle corner crack tip. Furthermore, when the two cracks are overlapped, the behavior of the SIF distribution as a function of separation distance is different in the vertical direction than in the horizontal direction due to a process called shielding. As the separation distances between the cracks increase in either direction, there is a separation distance after which the cracks can be treated as separate cracks, and, this distance is dependent on the relative crack lengths.

The shape of a surface crack in a plate based on a given stress intensity factor distribution

The effect of various erosion configurations on the mode I stress intensity factor (SIF) distribution along the front of a semi-elliptical crack, emanating from the deepest line of the erosion surface (DLES) at the bore of an autofrettaged, pressurized thick-walled cylinder of outer to inner radius ratio, Ro/Ri = 2, is investigated. The three-dimensional (3-D) linear elastic problem is solved via the finite element (FE) method using the ANSYS 5.2 standard code. Hill’s autofrettage residual stress field is simulated by an equivalent thermal load and the SIFs are determined by the nodal displacement method. SIF distribution along the front of semi-elliptical cracks of various crack depths to wall thickness ratios, a/t = 0.05 to 0.25, and ellipticities, a/c, ranging from 0.5 to 1.5, emanating from the DLES, are determined. Three groups of erosion geometries are considered: (a) arc erosions of constant relative depth, d/t, equal to 5 percent and with relative radii of curvature, r′/t, between 5 and 30 percent; (b) semi-elliptic erosions of constant relative depth, d/t, of 5 percent with erosion ellipticity, d/h, varying from 0.3 to 2.0; and (c) semi-circular erosions of relative depth, d/t, between 1 and 10 percent of the wall thickness. The effective SIF along the crack front results from the superposition of KIP—the SIF due to pressurization, and KIA—the negative SIF due to the autofrettage residual stress field. KIP is highly dependent on the stress concentration ahead of the DLES which directly relates to the erosion geometry. The absolute value of KIA is just slightly reduced by the presence of the erosion. Its change solely depends on, and is directly proportional to, the erosion depth. Thus, while deep cracks are almost unaffected by the erosion, the effective SIF for relatively short cracks is found to be significantly enhanced by its presence and might result in a shortening of the vessel’s fatigue life by up to an order of magnitude. Also, it is shown that 2-D analysis may lead to a nonconservative estimate of the vessel’s fatigue life.

This paper describes the application of a laboratory based experimental method [1] to three dimensional cracked body problems in pressure vessels in order to determine the crack shape and stress intensity factor (SIF) distribution along the crack front when the crack shape is not known a-priori. Results for specific problems are presented and conditions and limitation of the method are described.

3-D Stress Intensity Factors due to Full Autofrettage for Inner Radial or Coplanar Crack Arrays and Ring Cracks in a Spherical Pressure Vessel

Three-dimensional finite element models were formulated to evaluate the distribution of the elastic stress intensity factor around the periphery of cracklike flaws postulated to exist at the corners of nozzles intersecting cylindrical shells. The effect of the assumed shape of the nozzle corner flaw on the distribution of the stress intensity factor along the crack front was determined in order to indicate where initiation of crack growth is most likely to occur and what shape the crack is most likely to take subsequent to stable crack growth. This is important because of the uncertainty associated with the flaw shape and its effect on crack growth in the nozzle corner region. Stress intensity factors computed from the nozzle corner flaw models were also compared with solutions evaluated using 1) a simplified procedure similar to that given in Section XI of the ASME Boiler and Pressure Vessel Code that makes use of the stresses calculated in the absence of the flaw, 2) the method recommended specifically for nozzle corner flaws in Section III of the ASME Code, and 3) a previously published empirical formula. The results of this paper confirm the adequacy of the simplified procedure for the analysis of nozzle corner flaws of different shapes.

This thesis offers an extensive investigation of the influence of specimen thickness on the distribution of the mode-I stress intensity factor (SIF) along the fracture front of the compact tension specimen. The analysis is carried out in a fully 3D context and the characteristic of the SIF-distribution and width of the layer in the vicinity of surface breaking points where the stress intensity factor exhibits rapid variation and the layer where the SIF is nearly constant are thoroughly examined for various thicknesses of testing specimens. In the modeling, a well-known numerical technique, called a weakly-singular symmetric Galerkin boundary element method (SGBEM), is employed. The most attractive features of this technique include that the mesh generation cost is comparatively cheap since only 2D discretization on the outer boundary of the specimen and on the fracture surface is required and the calculated stress intensity factor along the fracture front is highly accurate with use of relatively coarse mesh. The latter feature results from applications of high order, special crack-tip elements in the local region surrounding the fracture front along with the use of a direct formula to extract the SIF. Extensive results are reported and discussed for specimens made from both isotropic and transversely isotropic materials.

PurposeThe fuselage riveted lap-joints are susceptible to multiple site damage (MSD) and should be considered in damage tolerance analysis. This paper aims to investigate the stress intensity factor (SIF) and crack growth simulation for lap-joints based on three-dimensional (3D) finite element analysis.Design/methodology/approachThe 3D finite element model of lap-joints is established by detailed representation of rivets and considering the rivet clamping force and friction. Numerical study is conducted to investigate the SIF distribution along the thickness direction and the effect of clamping force. A predictive method for the cracks propagation of MSD is then developed, in which an integral mean is adopted to quantify the SIF at crack tips, and the crack closure effect is considered. For comparison, a fatigue test of a lap-joint with MSD cracks is conducted to determine the cracks growth live and measure the cracks growth.FindingsThe numerical study shows that the through-thickness crack at riveted hole in lap-joints can be treated as mode I crack. The distribution of SIF along the thickness direction is inconstant and nonmonotonic. Besides, the increase in clamping force will lead to more frictional load transfer at the faying surfaces. The multiple crack growth simulation results agreed well with the experimental data.Originality/valueThe novelty of this work is that the SIF distribution along the thickness direction and the MSD cracks growth simulation for lap-joints are investigated by 3D finite element analysis, which can reflect the secondary bending, rivet clamping, contact and friction in lap-joints.

Three-dimensional finite element analysis has been carried out on the compact normal and shear(CNS) specimens under mixed-mode loading. The complex stress-intensity factor K associated with an elastic interface crack is discussed by the virtual crack extension method. The effect of Young's modulus and Poisson's ratio on stress intensity factors is discussed under various kinds of mixed-mode loading. The distribution of stress intensity factors along the crack front is investigated. A polynomial fitting is proposed to evaluate the stress-intensity factors at the midsection of CNS specimen with an interface crack subject to mixed-mode loading. It is possible to evaluate the stress-intensity factors of CNS specimen with high accuracy by the present polynomial evaluation.

Three-dimensional finite element analysis has been carried out on the compact normal and shear specimens under mixed-mode loading. The complex stress-intensity factor K associated with an elastic interface crack is discussed via three different approaches : the virtual crack extension method, the modified crack-closure integral and displacement extrapolation. The effect of Young's modulus ratio on stress intensity factors is discussed under various kinds of mixed-mode loading. The distribution of stress intensity factors along the crack front is investigated. A comparison between stress-intensity factor KI and KII, obtained by these three methods, is carried out.

A three-dimensional finite element analysis has been carried out for a compact normal and shear (CNS) specimen subjected to mixed-mode loading. The complex stress intensity factor, associated with an elastic interface crack, is discussed by the virtual crack extension method. The effect of Young's modulus and Poisson's ratio on the stress intensity factor for various kinds of mixedmode loading is discussed. The distribution of stress intensity factors along the crack front is investigated. A polynomial fit is proposed to evaluate the stress intensity factors at the midsection of the CNS specimen with an interface crack subjected to mixed-mode loading. The possibility of evaluating the stress intensity factors of CNS specimens with high accuracy by the present polynomial evaluation is demonstrated.

Variations of stress intensity factors of a semi-elliptical surface crack subjected to mode I, II, III loading

Maximum stress intensity factors of a surface crack usually appear at the deepest point of the crack, or a certain point along crack front near the free surface depending on the aspect ratio of the crack. However, generally it has been difficult to obtain smooth distributions of stress intensity factors along the crack front accurately due to the effect of corner point singularity. It is known that the stress singularity at a corner point where the front of 3 D cracks intersect free surface is depend on Poisson's ratio and different from the one of ordinary crack. In this paper, a singular integral equation method is applied to calculate the stress intensity factor along crack front of a 3-D semi-elliptical surface crack in a semi-infinite body under mixed mode loading. The body force method is used to formulate the problem as a system of singular integral equations with singularities of the form r−3 using the stress field induced by a force doublet in a semi-infinite body as fundamental solution. In the numerical calculation, unknown body force densities are approximated by using fundamental density functions and polynomials. The results show that the present method yields smooth variations of mixed modes stress intensity factors along the crack front accurately. Distributions of stress intensity factors are indicated in tables and figures with varying the elliptical shape and Poisson's ratio.