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.     

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.     

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.     

拉—拉疲劳下15MnMoVN多裂纹扩展研究

为分析单裂纹或多裂纹在裂纹面承受疲劳拉伸载荷作用下尖端应力强度因子变化规律和裂纹形貌变化以及疲劳寿命情况,以含不同初始长深比的半椭圆单裂纹或双裂纹的薄片试样为研究对象,对试样在应力比R=0.1的疲劳拉伸载荷下单裂纹或双裂纹情况进行了仿真分析。建立含裂纹试样的有限元模型,仿真分析了裂纹在扩展过程中尖端应力强度因子的分布情况,并将单裂纹扩展结果与双裂纹相互作用影响下的结果进行了对比研究;进行含裂纹试样的疲劳实验,分析了含单裂纹或双裂纹的试样的断裂面的形成原因,并验证仿真结果正确性。结果表明,裂纹面之间的相互作用会逐渐影响裂纹的扩展方向、扩展速率以及在扩展过程中尖端应力强度因子的变化趋势;而且初始形貌为半椭圆形的双裂纹在相互作用影响下会逐渐过渡到半圆形。     

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.     

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.     

Analysis of the stress intensity factor dependence with the crack velocity using a lattice model

In this work, the influence of crack propagation velocity in the stress intensity factor has been studied. The analysis is performed with a lattice method and a linear elastic constitutive model. Numerous researchers determined the relationship between the dynamic stress intensity factor and crack propagation velocity with experimental and analytical results. They showed that toughness increases asymptotically when the crack tip velocity is near to a critical. However, these methods are very complex and computationally expensive; furthermore, the model requires the use of several parameters that are not easily obtained. Moreover, its practical implementation is not always feasible. Hence, it is usually omitted. This paper aims to capture the physics of this complex problem with a simple fracture criterion. The selected criterion is based on the maximum principal strain implemented in a lattice model. The method used to calculate the stress intensity factor is validated with other numerical methods. The selected example is a finite 2D notched under mode I fracture and different loads rates. Results show that the proposed model captures the asymptotic behaviour of the SIF in function of crack speed, as reported in the aforementioned models.     

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.     

Research on fatigue crack propagation behaviour of 4003 ferritic stainless steel based on infrared thermography

Fatigue crack propagation (FCP) behaviour of 4003 ferritic stainless steel was investigated using infrared thermography. Four stages of superficial temperature evolution were observed during the FCP tests: an initial temperature decrease stage, a temperature equilibrium stage, a slow temperature increase stage and an abrupt temperature increase stage; a thermal model is developed to explain the observed temperature evolution. The experimental results indicate that: when the range of stress intensity factor (ΔK) is at a low level where the crack is located in slow propagation region, thermoelastic effect will be in dominant status; when the ΔK is at a high level where the crack is located in stable propagation region, the temperature rise can be used to describe FCP rate. The fatigue fracture surfaces were examined using scanning electron microscope (SEM) in order to understand the effect of the fatigue mechanisms on temperature variation.     

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.     

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.     

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.     

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.     

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.     

Experimental and numerical investigation of fatigue crack growth in the cracked gear tooth

The numerical simulation was conducted to analyse the fatigue crack growth in gear with the finite element codes ansys (ANSYS, Inc. Canonsburg, Pennsylvania, USA.) and franc 3d (Fracture Analysis Consultants, Inc. Ithaca, New York, USA.), and the corresponding fatigue test was also carried out. During the simulation, the location of maximal stress induced by the external force was first determined by the code ansys , and then the obtained results were imported into the franc 3d to analyse the crack growth. The analysed results were input into the codes ansys and franc 3d again to compute the stress and the stress intensity factor in the following steps. After several rounds of analysis, the results of the fatigue crack propagation were obtained. The investigations show that the crack mode I is dominant during the crack growth and the stress intensity factor K_I raises with increase of crack growth length and a series of quarter‐elliptical cross sections of the ruptured gear tooth are obtained. The simulation results are in good accordance with experimental findings.