Consideration of the residual stress distributions in fatigue crack growth calculations for assessing welded steel joints

To better understand the crack closure and propagation, an analytical model is established. The residual stress effect on fatigue crack growth equations has been considered using the residual stress intensity factor (SIF) (K_res). The joint geometries, residual stress distributions (σ_res) and residual stress ratio (R_res) were considered also. K_res are calculated using the analytical weight function (WF) method and different residual stress distributions. It is to be emphasized that the current approach is little investigated. This is because the WF has already been developed to calculate SIF for an existing crack. The current approach calculates K_res for the crack that initiates and propagates until failure. Different stress distributions have been used, and R_res is defined. The validity of using the WF has been shown. SIF due to applied load (K_app) and applied stress ratio (R_app) have been considered. Fatigue crack growth rate was investigated in accordance with the current approach. The results have been verified and benchmarked.     

Stress intensity factors for cracks in bolted joints

The mixed-mode stress intensity factors (SIFs) of the bolted joint with single and double cracks were examined. Changes in friction, clearance, applied force and crack angle were included in the nonlinear contact finite element analysis. A fine mesh was made between the contact surface and the crack tip in order to obtain an accurate solution. The least-squares method was used to determine the mixed-mode SIFs. Finite element results indicate that reasonable changes in the applied force, frictional coefficient and the clearance will not make significant changes in the normalized SIFs. The pure opening mode for cracked bolted joints does not occur at the horizontal crack but occurs at the crack with the crack angle between 0° and 22.5°. Nevertheless, using the SIF for a horizontal crack as the maximum opening-crack mode is sufficiently reliable. The maximum mode-II crack is approximately at a crack angle of 45° for both isotropic and orthotropic materials; however, at that angle the maximum mode-II SIF is only about one half of the mode-I SIF. This revised version was published online in August 2006 with corrections to the Cover Date.     

A rolling contact fatigue crack driven by squeeze fluid film

ABSTRACT A new model of surface breaking rolling contact fatigue (RCF) crack driven by a coupled action of a squeeze oil film built up in the crack interior and a pressure exerted at the external contact interface was developed. The model can be applied to the ‘nominally dry’ contact couples with an occasional presence of liquid in the crack interior (wheel/rail contact) as well as to the elastohydrodynamic lubrication (EHL) conditions. In the first case, the contact load is a result of solid/solid interaction and can be determined by solving the FE contact problem, but the liquid contained in the crack interior forms a thin film between the crack faces changing their interaction into the type of liquid/solid. This liquid is being periodically squeezed under contact load and acts as a ‘squeeze film’ known from the lubrication theory. In the second case, the liquid (lubricating oil) is permanently present in the contact area and consequently in the vicinity of the crack mouth. This creates conditions for filling the crack with oil. Similarly as in the first case, the ‘squeeze oil film’ is built between the crack faces. The contact load in this case results from a liquid/solid interaction and can be approximated by the pressure and traction distributions obtained from the numerical solution of the elastohydrodynamic contact problem. In both cases the model can be used to determine the Linear Elastic Fracture Mechanics (LEFM) crack tip stress intensity histories during cyclic loading and consequently to predict the crack growth rate and direction. An example of applying the model to the EHL case is given to explain the mechanisms and phenomena leading to the crack front loading. The cycle of rolling a roller over the crack was numerically simulated to obtain the mixed mode (I and II) SIF histories. In the analysis, the EHD pressure and traction were determined through the full solution of the EHD line contact problem accounting for the presence of a crack, whilst the pressure in the crack was found with the use of the wedge shaped squeeze oil film (SOF) model. Possible effects of the mode I and mode II stress intensity cycles on crack growth rate and direction are discussed. The solution indicates high pressure in the neighbourhood of the crack tip, exerted on the crack faces by the squeeze oil film. This leads to the ranges of the mode I and mode II SIF variations, which are larger than for the ‘dry’ and ‘fluid entrapment’ models, and can be an explanation for the crack growth rate observed in practice     

Mode II stress intensity factors for central slant cracks with frictional surfaces in uniaxially compressed plates

The effect of crack surface friction on mode II stress intensity factor (SIF) of a central slant crack in a plate uniformly loaded in uniaxial compression is quantified. A previously developed two-dimensional finite element analysis was utilised after its modification to accommodate the friction between the crack surfaces. The plane strain state was assumed. A new numerical technique was devised to avoid the iteration procedures, which had to be employed due to the existence of frictional forces.

The crack inclination angle varied between zero and 75° measured from the horizontal direction. The coefficient of friction of the crack surfaces changed from zero to 1. In case of relatively sliding crack surfaces, mode II SIF existed. As is well known, the resulting mode II SIF decreased with increasing the coefficient of friction of the crack surfaces. Further, mode II SIF increased with increasing crack line inclination angle and then decreased after reaching a maximum value. The angle corresponding to that maximum SIF increased as the coefficient of friction of the crack surfaces increased.     

A mode II weight function for subsurface cracks in a two-dimensional half-space

The general properties of a mode II Weight Function for a subsurface crack in a two‐dimensional half‐space are discussed. A general form for the WF is proposed, and its analytical expression is deduced from the asymptotic properties of the displacements field near the crack tips and from some reference cases obtained by finite elements models. Although the WF has general validity, the main interest is on its application to the study of rolling contact fatigue: its properties are explored for a crack depth range within which the most common failure phenomena in rolling contact are experimentally observed, and for a crack length range within the field of short cracks. The accuracy is estimated by comparison with several results obtained by FEM models, and its validity in the crack depth range explored is shown.     

Fatigue Life Estimation of Structural Components Using Macrofibre Composite Sensors

Abstract: Recently, a number of different structural health monitoring (SHM) techniques have been developed for the online inspection of air, land and sea engineering structures. Various smart materials are employed for detecting eminent damage in situ. Fatigue cracks in structural components are the most common cause of structural failure when exposed to fatigue loading. Fatigue design of structural components is typically accomplished either using a set of stress cycle (S‐N) data obtained from prior fatigue tests or using the fracture mechanics approach. The fracture mechanics approach considers the fatigue life of structures as a summation of crack initiation life and crack propagation life. The stress intensity factor (SIF) is required for the estimation of fatigue crack propagation life from the linear elastic fracture mechanics (LEFM) perspective. However, the accurate prediction of the SIF is difficult especially when the geometry or the boundary conditions of a structure becomes complex. In this study, a SHM application of macrofibre composite (MFC) sensors is presented. A set of MFC sensors is used for the real‐time measurement of the SIF. The measured values of the SIF are later used for the prediction of the crack propagation life. The impedance‐based SHM technique using the same set of MFC sensors is employed for the detection of crack initiation life.     

SIFs of CCT plate repaired with single‐sided composite patch

Constant amplitude load fatigue tests are performed to obtain crack propagation data for LF2‐aluminium centre crack tension (CCT) plates un‐repaired and repaired with single‐sided composite patches. Then, the James–Anderson method, an experimental method, is used to obtain the stress intensity factor (SIF) formula for the repaired CCT plates with carbon–fibre composite patches. At last, crack propagation life prediction and finite element (FE) calculation are carried out to validate the experimental SIF formula. It is shown that the present SIF formula can exactly predict the fatigue‐crack propagation life of the patched CCT plates and is close to the FE results, which implies the effectivity of the experimental SIF formula in the present paper.     

An efficient stress intensity factor solution scheme for corner cracks at holes under bivariant stressing

This paper summarizes the development of an efficient stress intensity factor (SIF) solution scheme applicable to a corner crack (CC) in a rectangular section subjected to arbitrary stressing on the crack plane. A general bivariant weight function (WF) formulation developed previously for a CC in a plate was extended to address a CC at a hole. Two supplemental algorithms were developed to achieve a substantial reduction in the computational time necessary for practical application. The new SIF solution scheme was validated by comparison with more than 180 three‐dimensional (3D) boundary element (BE) solutions.     

Weld root crack propagation under mixed mode I and III cyclic loading

This study examined fatigue propagation behaviour and fatigue life of weld root cracks under mixed mode I and III loading. Fatigue tests were performed on butt-welded joints with a continuous lack-of-penetration (LOP) inclined at angles of 0°, 15°, 30° or 45° to the normal direction of the uniaxial cyclic load. Branch and/or co-planar crack propagation was observed, depending on the initial mode I stress intensity factor (SIF) range. Co-planar crack propagation predominated when the SIF range was large. The fatigue crack propagation mode affected fatigue life; the life of branch crack propagation was longer than that of co-planar crack propagation. Using an initial equivalent SIF range based on a maximum strain energy release rate criterion, the results obtained from the 0°, 15°, 30°, and 45° specimens indicated almost the same fatigue lives, despite the different inclination angles.     

Extended structural criterion for numerical simulation of crack propagation and coalescence under compressive loads

An extension of the Neuber-Novozhilov structural fracture propagation criterion is presented for mode I (tensile) and mode II (shear) propagation under compressive loads. In addition to allowing numerical simulation of crack growth, the criterion can be used to model change of propagation mode, crack branching, and coalescence. The criterion can be applied effectively when the SIF is calculated accurately (at least three significant digits). A numerical method is suggested for this purpose that consists of complementing the complex variable hypersingular boundary element method (CVH-BEM) with special procedures for automatically tracing crack propagation and coalescence. The CVH-BEM code with the structural criterion has been used to investigate crack propagation in compression for both small and non-small fracture process zone (FPZ). The results of numerical experiments are in agreement with the analytical conclusions available for the case of small FPZ that indicates the possibility of three distinct patterns of crack propagation under external compressive loads. These are: (i) smooth curvilinear tensile (wing) cracks, (ii) stair-step propagation pattern with changing modes, and (iii) in plane shear propagation. The numerical study also indicates that when the critical size of the FPZ is large enough, the non-singular terms in the expansion of the stress functions strongly influence the crack trajectories. Specifically, this occurs when the size of the FPZ approaches a quarter of the half-length of the initial crack. Calculations for a closed initial crack in a half-space under compression illustrate the general features of crack propagation. Although the dominant direction of crack growth is that of the applied compressive stress, the pattern of propagation strongly depends on the particular geometry, critical size of the FPZ, and the ratio of shear-to-tensile microscopic strength.     

A method for tracking internal crack propagation in railhead

This paper presents a method for tracking two-dimensional propagation of internal cracks, in particular vertical split head (VSH) defects, due to contact loading in railhead. Generalised curved crack is assumed to have present in the railhead and its propagation is simulated by solving interaction of arbitrary shaped cracks successively. Furthermore, the finite shape of the rail section is also modelled as the continuous distribution of dislocation within an infinite plane. Crack propagation is simulated using the criterion of vanishing of Mode II stress intensity factors (SIF) at crack tips. Examples are provided for tracking the propagation of pre-existing internal cracks in railheads turning into VSH defects under centric contact loading.     

Crack propagation in notched specimens of porous silicon carbide under cyclic loading

Notched specimens of porous silicon carbide with porosity 37% were fatigued under four‐point bending at frequencies of 30 and 0.3 Hz. The fatigue life expressed in terms of time was rather insensitive to the test frequency, while that expressed in terms of cycles was much shorter for the case of 0.3 Hz than for 30 Hz. A time‐dependent mechanism of stress corrosion cracking was mainly responsible for crack propagation, and stress cycling enhanced the crack‐propagation mechanism. The crack length was estimated from the change in compliance of the specimen. The crack‐propagation curve was divided into stages I and II. In stage I, the crack‐propagation rate decreased even though the applied stress intensity factor became larger with crack extension, and then turned to increase in stage II. The transition from stage I to II took place at a crack extension of around 0.8 mm. This anomalous behaviour is caused by crack‐tip shielding due to microcracking and asperity contact. Fractographic observations showed that the fracture path was along the binder phase between silicon carbide particles, or more precisely along the interface between particles and binders.     

A weight function for 2D subsurface cracks under general loading conditions

A procedure for evaluating the fracture mechanics parameters of a subsurface two-dimensional crack parallel to the boundary in an elastic half plane is presented. A Weight Function (WF) with a matrix structure is proposed, to account for the coupling effects between modes I and II, typical in non-symmetrical problems. In order to face any loading condition, the WF was formulated by symmetric and anti-symmetric components and the ‘multiple reference loading’ approach was used to derive their analytical expressions. To this purpose, a parametric Finite Element (FE) analysis was set up and the Stress Intensity Factors (SIFs) were determined for several independent loading conditions. The analysis was carried out for different ratios between crack length and in-depth position and, consequently, the dependence of the WF on this parameter was studied. The WF accuracy was assessed by considering different loading and the method applied for evaluating the SIFs produced by a point-like load travelling on the semi-plane surface. The results indicated that the correct fracture mechanics analysis requires crack closure (either complete or partial) to be taken into account. Consequently, the crack opening displacement (COD) components under general loading conditions have to be evaluated. On the basis of the WF, the related Green Function (GF) was also derived by which the COD components can be efficiently evaluated for any applied load including the contact due to crack closure.     

A notch stress intensity approach applied to fatigue life predictions of welded joints with different local toe geometry

In the Notch Stress Intensity Factor (N‐SIF) approach the weld toe region is modelled as a sharp V‐shaped corner and local stress distributions in planar problems can be expressed in closed form on the basis of the relevant mode I and mode II N‐SIFs. Initially thought of as parameters suitable for quantifying only the crack initiation life, N‐SIFs were shown able to predict also the total fatigue life, at least when a large part of the life is spent as in the propagation of small cracks in the highly stressed region close to the notch tip. While the assumption of a welded toe radius equal to zero seems to be reasonable in many cases of practical interest, it is well known that some welding procedures are able to assure the presence of a mean value of the weld toe radius substantially different from zero. Under such conditions any N‐SIF‐based prediction is expected to underestimate the fatigue life. In order to investigate the degree of conservatism, a total of 128 fillet welded specimens are re‐analysed in the present work by using an energy‐based N‐SIF approach. The local weld toe geometry, characterised by its angle and radius, has been measured with accuracy for the actual test series. The aim of the work is to determine if the N‐SIF‐based model is capable of taking into account the large variability of the toe angle, and to quantify the inaccuracy in the predictions due to the simplification of setting the toe radius equal to zero.     

Critical study of existing solutions for a penny-shaped interface crack, comparing with a new boundary element solution allowing for frictionless contact

A numerical study of the fundamental problem of a pressurized penny-shaped crack at the interface of two dissimilar half spaces is carried out allowing for the possibility of frictionless contact between crack faces. A new, highly accurate axi-symmetric formulation of the boundary element method (BEM) for the solution of elastic contact problems is employed. The correctness and accuracy of available predictions of different kinds for several key characteristics of the solution of this problem are checked. First, comparison of the BEM results for the near-tip contact length shows a very good agreement with some existing predictions. Second, the global solution obtained by BEM is compared with existing asymptotic solutions, obtained with both the open and the frictionless contact models. BEM results show that at the closest neighborhood to the crack tip the global solution of the problem is governed by the first term of the asymptotic solution of the frictionless contact model (up to a distance of the order of a fraction of the near-tip contact length). After a small transition region, in an adjacent surrounding zone whose extent is almost independent of the near-tip contact length, the global solution of the problem is governed by the first term of the asymptotic solution of the open model. As a result of the comparison presented, the regions in which the classical fracture parameters, stress intensity factor (SIF) and energy release rate, can be accurately obtained from the global numerical solution of a crack of this kind have been determined. Third, BEM results and previous estimations show certain discrepancies with a recently published closed form solution of the near-tip contact length and the mode II SIF of the frictionless contact model. A new closed form expression of this mode II SIF, derived from the asymptotic solution of the open model, is proposed in this paper.     

A Boussinesq wedge analysis of the tensile stress region in a rail head beneath compressive and traction point loads

Investigations into the causes of damage to rail heads and on rolling contact fatigue, date back a considerable time and are described in a large number of expertise literature on the many different aspects of this complex problem. The present paper is prompted by the naïve observation that fatigue crack propagation is more likely to occur in a tensile stress environment than in a highly compressive one and it therefore seeks to locate a region of radial or longitudinal tensile stresses on a rail head during the rectilinear motion of the train, providing favourable conditions for mode I or mixed‐mode crack propagation.     

Estimation of three‐dimensional stress intensity factor for structural ‘T’ details

Three‐dimensional (3D) opening mode stress intensity factors (SIFs) for structural steel‐welded ‘T’ details were investigated by the finite element method. A 3D shape‐dependent correction factor is proposed for semi‐elliptical surface cracks. The aspect ratio (a/c) of a semi‐elliptical crack plays a key role in the approximation of 3D‐SIF values, and in the present study, it was estimated for a 3D crack analysis. The estimated 3D‐SIF was determined through a correlation between the a/c ratio and the two‐dimensional SIF for semi‐elliptical cracks in the thickness direction adjacent to the web‐flange junction of a welded ‘T’. The resulting equation can be used to estimate the 3D‐SIF values from the two‐dimensional SIF without much ambiguity.     

Effect of vertex singularities on stress intensities near plate free surfaces

The stress intensity factor (SIF) distribution along the front of a through‐the‐thickness crack is significantly influenced by the presence of the 3D corner (vertex) singularities. All past 3D finite element studies indicated that for mode I, SIF rapidly decreases near the free surface and for mode II, it sharply increases. From the previous numerical simulations, it is unclear what the limiting values of SIF near the surface are and whether these values are infinite or bounded at the vertex point. In this paper, we conduct a careful finite element study and propose a theoretical equation, which describes the SIF behaviour near the vertex. We demonstrate that the asymptotic behaviour of SIF near the surface is governed by the difference in the strength of the corner and edge singularities. Furthermore, we validate our numerical approach and calculations by utilising the invariant properties of J‐integral.     

Neural approach to estimate the stress intensity factor of semi‐elliptical cracks in rotating cracked shafts in bending

In the last decades, neural network approach has often been used to study various and complex engineering problems, such as optimization or prediction. In this paper, a methodology founded on artificial neural networks (ANNs) was used to calculate the stress intensity factor (SIF) in different points of the front of a semi‐elliptical crack present in a rotating shaft, taking into account the shape and depth of the crack, the angle of rotation, and the location of the point in the front. In the event of rotating machines, such as shafts, it is crucial to know the SIF along the crack front because this parameter, according to the Paris Law, is related to the performance of the crack during its propagation. Previously, it was necessary to achieve the data for the ANN training, for this a quasi‐static numerical model was made, which simulates a rotating cracked shaft with a semi‐elliptical crack. The numerical solutions cover a wide range of crack depths and shapes, and rotation angles. The values of the SIF estimated by the ANNs were contrasted with other solutions available in the literature finding a good agreement between them. The proposed neural network methodology is an alternative that offers a very good option for the SIF estimation, because it is efficient and easy to use, does not require high computational costs, and can be used to analyse the propagation of cracks contained in rotating shafts by means of the Paris Law taking into account the nonlinear behaviour of the shaft.