A new method of crack-tip opening displacement determined based on maximum crack opening displacement

In this paper a new method is presented to determine the crack-tip opening displacement (CTOD) for the center cracked plate with uniaxial uniform tension load. The maximum crack opening displacement (MCOD) is adopted to estimate CTOD. Based on the series of calculation results by elastic–plastic finite element simulation, an explicit function expression for the CTOD versus MCOD is determined, which enables to consider the influence effects of crack geometries, plate sizes, applied loads, plane state and material properties. Hence, the presented method of CTOD determined by MCOD is suitable to any center crack finite plate of any material under uniaxial tension.     

A new method of plastic zone size determined based on maximum crack opening displacement

This paper presents a new method to determine the crack-tip plastic zone size (R_y) in the center cracked plate in tension. The maximum crack opening displacement (MCOD) is used to estimate R_y in this method. Based on the series of calculation results by finite element analysis, the explicit expression for the crack-tip plastic zone size versus MCOD is fitted by least square method. The expression enables to eliminate the influences of the yield stress of material, crack geometry, plate sizes and transverse stress. Therefore, the presented method of R_y determined by MCOD is suitable to any center crack finite plate of any material under uniaxial or biaxial tension.     

A numerical investigation on the effect of an overload on fatigue crack opening and closure behaviour

The effect of a superimposed single tensile overload or a compressive overload in a block of constant-amplitude cycles on the crack opening and closing stresses is investigated using an elastic–plastic finite element analysis. The results obtained are in basic agreement with the experimental observations. Following an applied tensile overload cycle, the crack opening and closing stresses increase instantaneously, while the imposition of a compressive overload cycle results in a small decrease of the crack opening and closing stresses. A detailed discussion of the residual stress and strain patterns caused by the plastic deformation during the overload cycle and the corresponding crack profiles is included. The main governing mechanism resulting in the change of crack growth due to an overload is pointed out.     

Prediction of crack opening stress levels for 1045 quenched and tempered steel under service loading spectra

The opening stresses of a crack emanating from an edge notch in a 1045 quenched and tempered steel specimen were measured under two different Society of Automotive Engineers (SAE) standard service load histories having different average mean stress levels. The two spectra are the Grapple Skidder history (GSH), which has a positive average mean stress, and the Log Skidder history (LSH), which has a zero average mean stress. To capture the behaviour of the crack opening stress in the material, the crack opening stress levels were measured at 900X using an optical video microscope, at frequent intervals for each set of histories scaled to two different maximum stress ranges.A crack growth analysis based on a fracture mechanics approach was used to model the fatigue behaviour of the steel specimens for the given load spectra and stress ranges. Crack growth analysis was based on an effective strain‐based intensity factor, a crack growth rate curve obtained during closure‐free loading cycles and a local notch strain calculation based on Neuber's rule.The crack opening stress (S_op) was modelled and the model was implemented in a fatigue notch model, and the fatigue lives of the specimens under the two different spectra scaled to several maximum stress levels were estimated. The average measured crack opening stresses were between 6 and 12% of the average calculated crack opening stresses. In the interest of simplifying the use of S_op in design, the average S_op was correlated with the frequency of occurrence of the cycle reducing the S_op to the average crack opening stress level. The use of an S_op level corresponding to the cycle causing a reduction in S_op to a level reached once per 10 cycles gave a conservative estimate of average crack opening stress for all the histories.     

Elastic stress intensity factors and crack opening displacements for circumferential through-walled cracked elbows

This paper provides tabulated solutions of elastic stress intensity factors and crack opening displacements for circumferential through-wall cracked elbows under internal pressure and under in-plane bending, based on extensive three-dimensional elastic finite element analyses covering a wide range of crack lengths and elbow/pipe geometries. The effect of crack length and elbow/pipe geometry on the results is discussed, with particular emphasis on the crack closure behaviour under in-plane bending.     

Stress intensity factors for surface fatigue crack in a round bar under cyclic axial loading

In this paper, the surface fatigue crack growth shape for an initial straight-fronted edge crack in an elastic bar of circular cross-section is determined through experiments under pure fatigue axial loading. Three different initial notch depths are discussed. The relations of the aspect ratio (b/c) and relative crack depth (b/D) are obtained, and it is shown that there is a great difference in the growth of cracks with different initial front shapes and crack depths. Further, using the three-dimensional finite element method, the stress intensity factors (SIFs) are determined under remote uniform tension loading. Since the relationship of b/c and b/D changes during the fatigue crack growth, the SIFs are determined for different surface crack configurations.     

Stress intensity factors and crack opening displacements for slanted axial through-wall cracks in pressurized pipes

This paper proposes elastic stress intensity factors and crack opening displacements (CODs) for a slanted axial through-wall cracked cylinder under an internal pressure based on detailed three-dimensional (3D) elastic finite element (FE) analyses. The FE model and analysis procedure were validated against existing solutions for both elastic stress intensity factor and COD of an idealized axial through-wall cracked cylinder. To cover a practical range, four different values of the ratio of the mean radius of cylinder to the thickness ( R _m/ t ) were selected. Furthermore, four different values of the normalized crack length and five different values of the ratio of the crack length at the inner surface to the crack length at the outer surface representing the slant angle were selected. Based on the elastic FE results, the stress intensity factors along the crack front and CODs through the thickness at the centre of the crack were provided. These values were also tabulated for three selected points, that is, the inner and outer surfaces and at the mid-thickness. The present results can be used to evaluate the crack growth rate and leak rate of a slanted axial through-wall crack due to stress corrosion cracking and fatigue. Moreover, the present results can be used to perform a detailed leak-before-break analysis considering more realistic crack shape development.     

Fatigue behaviour of a box-welded joint under biaxial cyclic loads

Multiaxial fatigue behaviour of box-welded (wrap-around) joints in a JIS SM400B steel (12-mm-thick plate) was examined using a biaxial fatigue test facility. For the specimen, two stiffeners were attached to a main plate by a CO₂ semi-automatic welding procedure. Residual stress measurements and finite element (FE) analyses were also performed. Fatigue tests were performed under both uniaxial and biaxial (mainly out-of-phase) cyclic loads, and both results were compared and examined. It was found that fatigue cracks in the biaxial fatigue test specimens were initiated at the boxing-weld toes and propagated almost in the direction of the lateral loads. This is considered to be due to the dominant direction of tensile residual stresses from welding and the stress concentration in the vicinity of the boxing-weld toe. From the relation between the strain range near a weld toe, Δε₅ , and the fatigue lives, it was found that crack initiation life, N_c , was almost equivalent in the biaxial and uniaxial fatigue tests, while the failure life, N_f , was slightly longer in the biaxial tests. However, when the fatigue lives are put in order using the stress range near a weld toe, Δσ₅ , the crack initiation life, N_c , in the out-of-phase biaxial tests (phase difference of π) is ~30% lower than in the in-phase biaxial and uniaxial tests, while the failure life, N_f , was almost equivalent in the biaxial and uniaxial tests. From these results, it is concluded that an increase in Δσ₅ (lowering of the minimum value of σ₅ ), induced by the out-of-phase lateral loads, leads to an increase in fatigue damage where the high tensile welding residual stresses exist in the vicinity of the boxing-weld toe. Finally, a simple life estimation for the biaxial fatigue tests was made using FE analyses and the results of the uniaxial fatigue tests, proving that the effects of the lateral loads should be taken into consideration.     

A crack opening stress equation for in-phase and out-of-phase thermomechanical fatigue loading

In this paper, a crack opening stress equation for in-phase and out-of-phase thermomechanical fatigue (TMF) loading is proposed. The equation is derived from systematic calculations of the crack opening stress with a temperature dependent strip yield model for both plane stress and plane strain, different load ratios and different ratios of the temperature dependent yield stress in compression and tension. Using a load ratio scaled by the ratio of the yield stress in compression and tension, the equation accounts for the effect of the temperature dependent yield stress and the constraint on the crack opening stress. Based on the scaling relation established in this paper, Newman’s crack opening stress equation for isothermal loading is enabled to predict the crack opening stress under TMF loading.     

Effect of Lüders strain on engineering crack opening displacement estimations for leak-before-break analysis: finite element study

As a companion paper to our previous paper [ Fatigue Fract. Engng Mater. Struct. 24, 243–254], this note provides further validation on the engineering crack opening displacement (COD) estimation equation based on the enhanced reference stress method against three-dimensional, elastic–plastic finite element (FE) results using actual tensile data of three typical ferritic steels exhibiting a wide range of Lüders strain. Furthermore, the resulting FE results are also compared with the GE/EPRI COD predictions. It is found that the proposed enhanced reference stress method gives overall more accurate and robust COD results than the GE/EPRI method, compared with the FE results.     

A plasticity-corrected stress intensity factor for fatigue crack growth in ductile materials under cyclic compression

For prediction of the fatigue crack growth (FCG) behavior under cyclic compression, a plasticity-corrected stress intensity factor (PC-SIF) range ΔK_pc is proposed on the basis of plastic zone toughening theory. The FCG behaviors in cyclic compression, and the effects of load ratio, preloading and mean load, are well predicted by this new mechanical driving force parameter. Comparisons with experimental data showed that the proposed PC-SIF range ΔK_pc is an effective single mechanical parameter capable of describing the FCG behavior under different cyclic compressive loading conditions.     

Local stress–strain field intensity approach to fatigue life prediction under random cyclic loading

According to the characteristic of the local behavior of fatigue damage, on the basis of stress field intensity approach, a theory of local stress–strain field intensity for fatigue damage at the notch is developed in this paper, which can take account of the effects of the local stress–strain gradient on fatigue damage at the notch. In order to calculate the local stress–strain field intensity parameters, an incremental elastic-plastic finite element analysis under random cyclic loading is used to determine the local stress–strain response. A local stress–strain field intensity approach to fatigue life prediction is proposed by means of elastic-plastic finite element method for notched specimens. This approach is used to predict fatigue crack initiation life, and good correlation was observed with U-shape notched specimens for normalized 45 steel.     

The effect of compression stresses,stress level and stress order on fatigue crack growth of multiple site damage

Structural components are generally subjected to a wide stress spectrum over their lifetime. Service loads are accentuated at the areas of stress concentration, mainly at the connection of components. When there is a critical level of multiple site damage at connections, cracks link up to form a large crack which abruptly reduces the residual strength of the damaged structural member. Therefore, it is important to estimate the fatigue life before the cracks link up due to critical multiple site damage. In this study, the extended finite element method was applied to predict lifetime under constant amplitude cyclic loadings of fatigue tests on several multiple site damage specimens made of Al 2024‐T3. Then the multiple crack growths under service stress spectra are calculated to investigate the effects of compressive stress, stress orders and the effect of sequence cyclic loadings on stress levels by using Forman and NASGROW equations.     

弯扭组合载荷下圆管半椭圆表面裂纹应力强度因子的有限元分析

对表面裂纹复合型应力强度因子的研究一直是线弹性断裂力学中的重要课题,例如弯扭组合载荷下圆管半椭圆表面裂纹应力强度因子的计算,到现在也没有一个正确的分析解。考虑到裂尖的应力奇异性,在裂纹前沿手动设置三维奇异单元,用三维有限元法中的1/4点位移法计算弯扭组合载荷下圆管表面椭圆裂纹前沿的Ⅰ型、Ⅱ型和Ⅲ型应力强度因子,并分析其随裂纹深度增加时的变化规律。运用该方法计算了有关模型的应力强度因子,并与该模型的实验值进行了比较,计算结果和实验结果吻合良好。     

On improved crack tip plastic zone estimates based on T‐stress and on complete stress fields

Cracked ductile structures yield locally to form a plastic zone (pz) around their crack tips, which size and shape controls their structural behaviour. Classical pz estimates are based solely on stress intensity factors (SIF), but their precision is limited to very low σ_n/S_Y nominal stress to yield strength ratios. T‐stresses are frequently used to correct SIF‐based pz estimates, but both SIF and SIF plus T‐stress pz estimates are based on truncated linear elastic (LE) stress fields that do not satisfy boundary conditions. Using Griffith's plate complete LE stress field to avoid such truncated pz estimates, the influence of its Williams’ series terms on pz estimation is evaluated, showing that T‐stress improvements are limited to medium σ_n/S_Y values. Then, corrections are proposed to introduce equilibrium requirements into LE pz estimates. Finally, these improved estimates are compared with pz calculated numerically by an elastic–plastic finite element analysis.     

Effects of stress ratio and temperature on fatigue crack growth in a Ti–6Al–4V alloy

Fatigue thresholds and fatigue crack growth (FCG) rates in corner notched specimens of a forged Ti–6Al–4V aero-engine disk material were investigated at room temperature and 350 °C. The threshold stress intensity range, ΔK_th, was determined by a method involving a step change in stress ratio (the ‘jump in’ method). It was found that for three high stress ratios (R=0.7–0.9), where crack closure effects are widely accepted to be negligible, there were similar ΔK_th values at room temperature and 350 °C under the same R. For a given temperature, ΔK_th was observed to decrease from 3.1 to 2.1 MPam with R increasing from 0.7 to 0.9. The fatigue crack growth rate was influenced by increasing temperature. For high stress ratios, FCG rate at 350 °C was higher than that at room temperature under the same ΔK. For a low stress ratio (R=0.01), higher temperature led to higher FCG rates in the near-threshold regime, but showed almost no effect at higher ΔK. The influence of stress ratio and temperature on threshold and FCG rates was analysed in terms of a K_max effect and the implication of this effect, or related mechanisms, are discussed. In light of this, an equation incorporating the effects of the K_max and fatigue threshold, is proposed to describe FCG rates in the near-threshold and Paris regimes for both temperatures. The predictions compare favourably with experimental data.     

A new solution for 3D crack extension based on linear elastic stress fields

A solution to the 3D stress field based on the maximum tangential stress (MTS) criterion is presented in this paper. The solution allows for the estimation of the critical crack plane, the direction of growth in terms of both twist and tilt angles and the equivalent crack driving force for a given mixed-mode loading condition. It also shows the graphical relationship between the three different stress intensities for a given driving force. Initial results have shown good correlation with experimental data obtained from literature.     

Studies of elastic and elastic–plastic J integral for mixed mode cracked plate under biaxial loading

Analyses of I–II mixed mode central cracked plate by finite element method are performed in this paper, and some different phenomena are found. First for I–II mixed mode crack, the distribution of J integral along crack tip thickness depends on biaxiality factors because of the existence of vertex (corner) singularity, which is unlike that for mode I or mode II crack. Then J integrals at middle layer keep constant for any cracked plates with different inclined angles β when the biaxiality ratio is equal to 1 or ?1, which implies that the inclined angle or the extent of I–II mixed mode has no effect on the J integral for positive or negative equal axial loading conditions. And the decreasing trend of J integral with the inclined angle β for biaxiality ratio λ being between?1 and 1 is just opposite with that for biaxiality ratio λ being larger than 1 and smaller than ?1. Finally, proposed h₁ (a/W, n, λ, β) of cracked plate with different inclined angles under different biaxial loading are calculated.     

Fatigue life prediction based on crack closure for 6156 Al-alloy laser welded joints under variable amplitude loading

A fatigue prediction approach is proposed using fracture mechanics for laser beam welded Al-alloy joints under stationary variable amplitude loading. The proposed approach was based on the constant crack open stress intensity factor in each loading block for stationary variable amplitude loading. The influence of welding residual stress on fatigue life under stationary variable amplitude was taken into account by the change of crack open stress intensity factor in each loading block. The residual stress relaxation coefficient β = 0.5 was proposed to consider the residual stress relaxation for the laser beam welded Al-alloy joints during the fatigue crack growth process. Fatigue life prediction results showed that a very good agreement between experimental and estimated results was obtained.     

Improved hybrid displacement function (IHDF) element scheme for analysis of Mindlin–Reissner plate with edge effect

For a Mindlin–Reissner plate subjected to transverse loadings, the distributions of the rotations and some resultant forces may vary very sharply within a narrow district near certain boundaries. This edge effect is indeed a great challenge for conventional finite element analysis. Recently, an effective hybrid displacement function (HDF) finite element method was successfully developed for solving such difficulty 1 , 2 . Although good performances can be obtained in most cases, the distribution continuity of some resulting resultants is destroyed when coarse meshes are employed. Moreover, an additional local coordinate system must be used for avoiding a singular problem in matrix inversion, which makes the derivations more complicated. Based on a modified complementary energy functional containing Lagrangian multipliers, an improved HDF (IHDF) element scheme is proposed in this work. And two new special IHDF elements, named by IHDF‐P4‐Free and IHDF‐P4‐SS1, are constructed for modeling plate behaviors near free and soft simply supported boundaries, respectively. The present modeling scheme not only greatly improves the precision of the numerical results but also avoids usage of the additional local Coordinate system. The numerical tests demonstrate that the new IHDF element scheme is an effective way for solving the challenging edge effect problem in Mindlin–Reissner plates. Copyright © 2016 John Wiley & Sons, Ltd.