XFEM analysis of the effects of voids,inclusions and other cracks on the dynamic stress intensity factor of a major crack

This paper is devoted to the extraction of the dynamic stress intensity factor (DSIF) for structures containing multiple discontinuities (cracks, voids and inclusions) by developing the extended finite element method (XFEM). In this method, four types of enrichment functions are used in the framework of the partition of unity to model interface discontinuity within the classical finite element method. In this procedure, elements that include a crack segment, the boundary of a void or the boundary of an inclusion are not required to conform to discontinuous edges. The DSIF is evaluated by the interaction integral. After the effectiveness of the implemented XFEM program is verified, the effects of voids, inclusions and other cracks on the DSIF of a stationary major crack are investigated by using XFEM. The results show that the dynamic effects have an influence on the path independence of the interaction integral, and these voids, inclusions and other cracks have a significant effect on the DSIF of the major crack.     

A direct method for calculating the stress intensity factor in BEM

The proposed algorithm employs singular crack tip elements in which the stress intensity factor appears as a degree of freedom. The additional degrees of freedom are compensated by constraint conditions which originate from imposing continuity across elements and a contour integration formula. The two benchmark problems indicate the proposed algorithm can accurately predict the stress intensity factor and the distribution of the primary and secondary variables in fracture problems.     

Fatigue tests on steel plates with longitudinal weld attachment strengthened by ultra high modulus carbon fibre reinforced polymer plate

Welded steel connections of infrastructures are susceptible to fatigue failure. Advanced carbon fibre reinforced polymer (CFRP) has been demonstrated promising for fatigue strengthening of steel structures. Limited research was conducted on CFRP strengthening of welded connections. This paper focuses on the application of ultra high modulus (UHM) CFRP plates with a modulus of 460 GPa to strengthen steel plates with longitudinal fillet weld attachment using five CFRP strengthening configurations. A series of fatigue tension tests were carried out with constant amplitude fatigue loading. Beach marking technique was adopted to record the crack propagation process. Effects of CFRP bond length, bond width and bond locations on fatigue performance of welded steel joints were investigated. The experimental results showed that UHM CFRP plates could generally increase the fatigue life of the welded steel joints. It seems better to apply CFRP on the welding side of the specimen to achieve longer fatigue life. Then, the effects of weld and weld attachment on the CFRP strengthening efficiency was further studied by comparing experimental results of non‐welded steel plates with single side UHM CFRP plate strengthening. Finally, the classification method was adopted to assess the strengthening efficiency of the UHM CFRP plate to the steel plates with longitudinal weld attachment.     

Stress intensity factors for cracked triangular cross‐section thin‐walled tubes

For one kind of finite‐boundary crack problems, the cracked equilateral triangular cross‐section tube, an analytical and very simple method to determine the stress intensity factors has been proposed based on a new concept of crack surface widening energy release rate and the principle of virtual work. Different from the classical crack extension energy release rate, the crack surface widening energy release rate can be defined by the G*‐integral theory and expressed by stress intensity factors. This energy release rate can also be defined easily by the elementary strength theory for slender structures and expressed by axial strains and loads. These two forms of crack surface widening energy release rate constitute the basis of a new analysis method for cracked tubes. From present discussions, a series of stress intensity factors are derived for cracked equilateral triangular cross‐section tubes. Actually, the present method can also be applied to cracked polygonal tubes.     

Assessing the accuracy of fatigue life in surface‐cracked straight pipes

The demonstration of leak before brake (LBB) based on fracture mechanics requires information on the initial size of a defect, initiation of crack growth from the inherent defect and subsequent crack growth rates. In the present paper the prediction methodologies have been tested for three different full scale pipes geometry experimentally tested data. The prediction accuracy of two SIF solutions available in the literature has also been judged. The effect of fatigue crack closure and corrections needed in the numerical prediction methodology using FEM have also been included. The results showed that the FEM could fairly predict the fatigue crack initiation and crack growth life of full‐scale piping components having a constant depth crack profile.     

Stress intensity factor estimation for unbalanced rotating cracked shafts by artificial neural networks

The knowledge of the stress intensity factor (SIF) values along a crack front is essential to calculate the crack growth rate and the remaining life of a mechanical component. In the case of a rotating shaft, usually it presents disalignments, which modify the SIF data with regard to a balanced one. This paper presents the use of an artificial neural network (ANN) for estimating the SIF at the crack front in an unbalanced shaft under rotating bending, previously, a quasi‐static numerical (finite element) model, which simulates a rotating shaft, has been developed to create the training cases for the ANN. The obtained results allow to study the influence of the unbalance of rotating shafts in the crack breathing mechanism and will allow to predict the influence of this behaviour on the values of the SIF and in the propagation of cracks.     

Influence of effective stress intensity factor range on mixed mode fatigue crack propagation

ABSTRACT The behaviour of fatigue crack propagation of rectangular spheroidal graphite cast iron plates, each consisting of an inclined semi‐elliptical crack, subjected to axial loading was investigated both experimentally and theoretically. The inclined angle of the crack with respect to the axis of loading varied between 0° and 90°. In the present investigation, the growth of the fatigue crack was monitored using the AC potential drop technique, and a series of modification factors, which allow accurate sizing of such defects, is recommended. The rate of fatigue crack propagation db/dN is postulated to be a function of the effective strain energy density factor range, ΔS_eff. Subsequently, this concept is applied to predict crack growth due to fatigue loads. The mixed mode crack growth criterion is discussed by comparing the experimental results with those obtained using the maximum stress and minimum strain energy density criteria. The threshold condition for nongrowth of the initial crack is established based on the experimental data.     

Computation of the stress intensity factors of sharp notched plates by the fractal‐like finite element method

The fractal‐like finite element method (FFEM) is an accurate and efficient method to compute the stress intensity factors (SIFs) of different crack configurations. In the FFEM, the cracked/notched body is divided into singular and regular regions; both regions are modelled using conventional finite elements. A self‐similar fractal mesh of an ‘infinite’ number of conventional finite elements is used to model the singular region. The corresponding large number of local variables in the singular region around the crack tip is transformed to a small set of global co‐ordinates after performing a global transformation by using global interpolation functions. In this paper, we extend this method to analyse the singularity problems of sharp notched plates. The exact stress and displacement fields of a plate with a notch of general angle are derived for plane‐stress/strain conditions. These exact analytical solutions which are eigenfunction expansion series are used to perform the global transformation and to determine the SIFs. The use of the global interpolation functions reduces the computational cost significantly and neither post‐processing technique to extract SIFs nor special singular elements to model the singular region are needed. The numerical examples demonstrate the accuracy and efficiency of the FFEM for sharp notched problems. Copyright © 2008 John Wiley & Sons, Ltd.     

Effects of the transverse stress on biaxial fatigue crack growth predicted by plasticity-corrected stress intensity factor

The transverse stress has an important effect on the biaxial fatigue crack behavior. However, the experimental evidence has provided conflicting indications: it is sometimes considered to increase, decrease or have no effect. These complex phenomena cannot be rationally explained by the existing mechanical models. The effect of the transverse stress on the fatigue crack growth behavior is still one of the most puzzling questions in biaxial fatigue. Physically, this effect is a transverse stress induced plasticity phenomenon. In this paper, a plasticity-corrected stress intensity factor (PC-SIF) is proposed to describe the effect of transverse stress on biaxial fatigue. By use of this new crack driving force some important phenomena associated with transverse stress are predicted. Comparisons with experimental results showed that the PC-SIF as an effective mechanical parameter is capable of predicting the effects of the crack length, the stress level, cyclic stress ratio, biaxial stress ratio and phase difference on the biaxial fatigue crack growth. Consequently, the alleged conflicting experimental results have been rationally explained by the PC-SIF.     

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.     

Stress intensity factor computation using the method of fundamental solutions: mixed‐mode problems

The method of fundamental solutions is applied to the computation of stress intensity factors in linear elastic fracture mechanics. The displacements are approximated by linear combinations of the fundamental solutions of the Cauchy–Navier equations of elasticity and the leading terms for the displacement near the crack tip. Two algorithms are developed, one using a single domain and one using domain decomposition. Numerical results are given. Copyright © 2006 John Wiley & Sons, Ltd.     

Stress intensity factors for three‐dimensional weld toe cracks using weld toe magnification factors

In welded components, particularly those with complex geometrical shapes, evaluating stress intensity factors is a difficult task. To effectively calculate the stress intensity factors, a weld toe magnification factor is introduced that can be derived from data obtained in a parametric study performed by finite element method (FEM). Although solutions for the weld toe magnification factor have been presented, these are applicable only to non‐load‐carrying cruciform or T‐butt joints, due possibly to the requirement of very complicated calculations. In the majority of cases for various welded joints, the currently used weld toe magnification factors do not adequately describe the behaviour of weld toe cracks. In this study, the weld toe magnification factor solutions for the three types of welded joints such as cruciform, cover plate and longitudinal stiffener joints were provided through a parametric study using three‐dimensional finite elements. The solutions were formed with exponents and fractions that have polynomial functions in terms of a/c and a/t – that is, crack depths normalised by corresponding half crack lengths and specimen thickness. The proposed weld toe magnification factors were applied to evaluate the fatigue crack propagation life considering the propagation mechanisms of multiple‐surface cracks for all welded joints. It showed good agreement within a deviation factor of two between the experimental and calculated results for the fatigue crack propagation life.     

Numerical simulations and experimental measurements of the stress intensity factor in perforated plates

A numerical procedure, which combines two hybrid finite element formulations, was developed to analyse the stress intensity factors in cracked perforated plates with a periodic distribution of holes and square representative volume elements. The accuracy of the method in predicting the stress intensity factor was verified by a comparison with experimental measurements, carried out by a photoelasticity method, and by commercial finite element software. Several simulations were executed by varying both the crack length and the hole diameters, and the effects of the holes on the stress intensity factor are illustrated. The method shows high accuracy and efficiency, as small differences were observed when compared with the traditional finite element method, notwithstanding a strong reduction in degrees of freedom and mesh complexity.     

State‐of‐the‐art review on extended stress intensity factor concepts

The stress intensity factor concept for describing the stress field at pointed crack or slit tips is well known from fracture mechanics. It has been substantially extended since Williams' basic contribution (1952) on stress fields at angular corners. One extension refers to pointed V‐notches with stress intensities depending on the notch opening angle. The loading‐mode‐related simple notch stress intensity factors K₁, K₂ and K₃ are introduced. Another extension refers to rounded notches with crack shape or V‐notch shape in two variants: parabolic, elliptic or hyperbolic notches (‘blunt notches’) on the one hand and root hole notches (‘keyholes’ when considering crack shapes) on the other hand. Here, the loading‐mode‐related generalised notch stress intensity factors K_1ρ, K_2ρ and K_3ρ are defined. The concepts of elastic stress intensity factor, notch stress intensity factor and generalised notch stress intensity factor are extended into the range of elastic–plastic (work‐hardening) or perfectly plastic notch tip or notch root behaviour. Here, the plastic notch stress intensity factors K_1p, K_2p and K_3p are of relevance. The elastic notch stress intensity factors are used to describe the fatigue strength of fillet‐welded attachment joints. The fracture toughness of brittle materials may also be evaluated on this basis. The plastic notch stress intensity factors characterise the stress and strain field at pointed V‐notch tips. A new version of the Neuber rule accounting for the influence of the notch opening angle is presented.     

Radial locations of strain gages for accurate measurement of mode I stress intensity factor

Strain gage methods are popular in experimental determination of stress intensity factors (SIFs). Radial location of gages with respect to the crack tip plays an important role in accuracy of strain measurements and thus accurate determination of SIFs. The present work proposes a finite element based simple, accurate and consistent method for determination of the limiting value of the radial distance (r_max) of a strain gage. This parameter is in turn useful in deciding the valid strain gage location for accurate measurement of opening mode SIF. The results obtained from the present investigation agree well with the theoretical predictions and could be used for experimental determination of SIFs for both single ended and double ended cracked specimens. The r_max values of center cracked and edge cracked plates with different crack length to width ratio are estimated. The results of the present investigation show that the relative size of the crack length and net ligament length strongly influences the r_max value and the effect of Poisson’s ratio is marginal on the r_max value.     

Rim Thickness Effects on Gear Crack Propagation Life

Analytical and experimental studies were performed to investigate the effect of gear rim thickness on crack propagation life. The FRANC (FRacture ANalysis Code) computer program was used to simulate crack propagation. The FRANC program used principles of linear elastic fracture mechanics, finite element modeling, and a unique re-meshing scheme to determine crack tip stress distributions, estimate stress intensity factors, and model crack propagation. Various fatigue crack growth models were used to estimate crack propagation life based on the calculated stress intensity factors. Experimental tests were performed in a gear fatigue rig to validate predicted crack propagation results. Test gears were installed with special crack propagation gages in the tooth fillet region to measure bending fatigue crack growth. Good correlation between predicted and measured crack growth was achieved when the fatigue crack closure concept was introduced into the analysis. As the gear rim thickness decreased, the compressive cyclic stress in the gear tooth fillet region increased. The retarded crack growth and increased the number of crack propagation cycles to failure. This revised version was published online in August 2006 with corrections to the Cover Date.     

Measuring residual stress and the resulting stress intensity factor in compact tension specimens

The measurement of residual stress through the remaining ligament of a compact tension specimen was studied. In the crack compliance method, a slot or notch is successively extended through the part, and the resulting strain is measured at an appropriate location. By using a finite element simulation of a specimen preloaded beyond yield, three techniques for determining the original residual stress from the measured strains were compared for accuracy and sensitivity to measurement errors. A common beam-bending approximation was substantially inaccurate. The series expansion method proved to be very versatile and accurate. The fracture mechanics approach could determine the stress intensity factor caused by the residual stresses with a very simple calculation. This approach offers the exciting possibility of determining the stress intensity factor prior to a fatigue or fracture test by measuring strains during the specimen preparation.     

Analytical calculation of stress intensity factor of cracked steel I-beams with experimental analysis and 3D digital image correlation measurements

An analytical method to calculate the stress intensity factor for cracked steel I-beams under both bending moment and axial load is presented. The method is based on the approach of crack surface widening energy release rate. The crack surface widening energy release rate is formulated by a G^∗-integral and elementary strength theory of materials. Comparisons between the analytical results and results available in the literature for specific cases demonstrate the validity of the methodology. Furthermore, the fatigue and fracture behavior of the steel I-beam are experimentally investigated. The fatigue crack growth rate, residual deflection and stiffness reduction of a cracked beam under cyclic loading are studied. A three-dimensional digital image correlation system is used to illustrate the stress evolution pattern and the plasticity zone around the crack tip using image processing technique, thereby providing further verification of the theoretical models.     

On the Mode I stress intensity factor for an external circular crack with fibre bridging

This paper presents a theoretical analysis of an external matrix crack located in a unidirectional fibre-reinforced elastic solid modelled as a transversely isotropic material. The presence of matrix cracking with fibre continuity introduces bridging action that has an influence on the stress intensity factors at the crack tip of the external crack. This paper presents a model for the bridged crack, where the fibre ligaments induce a constant displacement-dependent traction constraint over the external crack. This gives rise to a Fredholm integral equation of the second kind, which can be solved in an approximate fashion. We examine the specific problem where the bridged external circular crack is loaded by a doublet of concentrated forces. Numerical results are presented to illustrate the influence of the fibre–matrix modular ratio and the location of the loading on the bridged-crack opening mode stress intensity factor.