Limited weld residual stress measurements in fatigue crack propagation: Part II. FEM-based fatigue crack propagation with complete residual stress fields

Using a limited set of residual stress measurements acquired by neutron diffraction and an equilibrium‐based, weighted least square algorithm to reconstruct the complete residual stress tensor field from the measured residual stress data, the effect of weld residual stress on fatigue crack propagation is investigated for 2024‐T351 aluminium alloy plate joined by friction stir welding. Through incorporation of the least squares, complete equilibrated residual stress field into a finite element model of the Friction Stir Weld (FSW) region, progressive crack growth along a direction perpendicular to the welding line is simulated as part of the analysis. Both the residual stress redistribution and the stress intensity factor due to the residual stress field, K_res, are calculated during the crack extension process. Results show that (a) incorporation of the complete, self‐equilibrated residual stress field into a finite element (FE) model of the specimen provides a robust, hybrid approach for assessing the importance of residual stress on fatigue crack propagation, (b) the calculated stress‐intensity factor due to the residual stress field, K_res, has the same trend as measured experimentally by the ‘cut‐compliance method’ and (c) the da/dN results are readily explained with reference to the effect of the residual stress field on the applied stress intensity factor.     

Branch crack development from the flank of a fatigue crack propagating in mode II

The propagation of fatigue cracks in mode II often leads to the development of a branch starting from a crack flank, some distance behind the tip and not to the expected bifurcation at the crack tip. This type of branch is suggested to initiate by decohesion along a secondary slip plane and to grow in mode I due to the tensile component of the mode II stress field. Finite element calculations are performed to evaluate the stress intensity factors for the main crack and the branch as a function of the position of the latter. It is shown that the branch has a substantial shielding effect on the main crack and generates contact forces along its flanks. The simultaneous and competitive growth of the main crack and the branch in fatigue is simulated step by step using kinetic data for mode II and mode I obtained for a maraging steel.     

Growth of the corrosion layer in the vicinity of a crack propagating at a constant speed

Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 25, No. 2, pp. 66–68, March–April, 1989.     

Cyclic analysis of a propagating crack and its correlation with fatigue crack growth

Stress and strain field of a propagating fatigue crack and the resulting crack opening and closing behavior were analysed. It was found that a propagating fatigue crack was closed at tensile external loads due to the cyclically induced residual stresses. Strain range value $\text{Δ?}{}_{\mathrm{y}}$ in the vicinity of the crack tip was found to be closely related with the effective stress intensity factor range $\text{ΔK}{}_{\mathrm{eff}}$ which was determined on the basts of the analytical crack opening and closing behavior at its tip. Application of this analysis to the non-propagating fatigue crack problem and the fatigue crack propagation problems under variable stress amplitude conditions revealed that both $\text{Δ?}{}_{\mathrm{y}}$ and $\text{ΔK}{}_{\mathrm{eff}}$ were essential parameters governing fatigue crack growth rate.     

Probability of cleavage fracture for a crack propagating by fatigue

Standard fracture toughness tests use fatigue pre-cracked specimens loaded monotonically from zero to failure. Scatter in toughness (cleavage) occurs because steel is metallurgically inhomogeneous, and because each specimen has its crack tip in a different local microstructure. A probability of fracture toughness distribution can be obtained by conducting multiple repeat tests on the same steel. This is often used to make probabilistic structural fracture predictions for combinations of crack length and applied load. However, it is likely the true structural situation involves gradual extension of a fatigue crack under a cyclic load. The question then arises as to how often the probability of fracture for the structure needs to be re-calculated. It could be argued that each fatigue load cycle moves the crack tip to a new position and gives a different instantaneous probability of fracture. But if this were the case, the predicted cumulative probability of fracture would quickly tend to unity. This paper describes cold temperature, wide plate fatigue tests designed to investigate this apparent contradiction. The steel is 15 mm thick, grade A, ship plate and the tests involve propagation of a fatigue crack from 300 mm to 650 mm length under a constant amplitude fatigue cycle of 10-100 MPa at −50 °C. The cold temperature fatigue tests do not show an obviously increased probability of fracture compared with the standard monotonic load tests. Nevertheless, in view of uncertainties surrounding the issue, a cumulative probability of fracture determined at 5 mm intervals through the steel is recommended for safe structural predictions.     

Study of fatigue crack initiation in the vicinity of notches

Using the crack initiation measurements for notched specimens with various geometry (CT and axisymetric notched specimens) and different notch radii, we will try to determine the number of cycles to initiate a fatigue crack in the vicinity of stress concentration.     

An integrated methodology for separating closure and residual stress effects from fatigue crack growth rate data

To properly interpret the results of standard fatigue crack growth tests it is often necessary to incorporate corrective techniques to the ΔK applied data. This is especially true in the near‐threshold regime where long crack data need to be closure corrected to predict small crack behaviour. It is also an issue in the presence of residual stress. A methodology to separate the influence of sample size, geometry, crack length and residual stress from the standard crack growth test data to obtain a true material response is presented. Stress ratio and residual stress contributions from known combinations of assumed crack size, applied stress and residual stress are also addressed and incorporated in the fatigue crack growth behaviour.     

Physical meaning of ΔKRP and fatigue crack propagation in the residual stress distribution field

Previous papers have shown ΔK_RP to be a useful parameter describing fatigue crack propagation behavior, where ΔK_RP is an effective stress intensity factor range corresponding to the excess RPG load (re-tensile plastic zone's generated load) in which the retensile plastic zone appears under the loading process. In this paper, the relationship between ΔK_RP and the zone size ( ) (which is smaller between the tensile plastic zone at maximum load and the compressive plastic zone at minimum load) was investigated using a crack opening/closing simulation model so as to consider a physical meaning of ΔK_RP. As a result, it becomes clear that ΔK_RP dominates the zone size where fatigue damage mostly occurs. This result supports the following crack propagation equation

where C and m are material constants.Simulation and fatigue crack propagation tests were then carried out for compact tension (CT), center cracked tension (CCT) and four points bend (4PB) specimens under constant amplitude loading to obtain C and m values for HT-50 steel. Fatigue crack propagation tests were also carried out under constant amplitude loading using CCT specimens with residual stress distribution due to flame gas heating at the center line or edge lines. The T specimen introduced tensile residual stress at the tip of a notch, and the C specimen introduced compressive residual stress. It therefore becomes clear that tensile residual stress leads to a decrease in RPG load, while compressive residual stress leads to increase in RPG load, and that the simulation results are in good agreement with the experimental RPG load. It also becomes clear that simulated crack growth curve using the simulated and the above equation is in good agreement with the experimental curve. It is understood that tensile residual stress creates only a slight increase in crack propagation rate and compressive residual stress create a big decrease a crack propagation rate.     

Plane stress dynamic plastic field near a propagating crack tip

In this paper the asymptotic solution to the plane stress dynamic plastic field surrounding a propagating crack tip is given. The perfectly plastic model and Mises yield condition as well as J₂ flow theory are adopted. The force of inertia is considered in the equations of motion. The asymptotic expansions of displacements, strains and stresses are given and solved for the dominant terms. The results show that strain possesses ln (A/r) singularity at the crack tip. Finally, the stress distribution surrounding the crack tip are given numerically.

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Résumé On fournit dans cette étude une solution asymptotique pour le champ de déformations pastiques dynamiques sous contraintes planes qui entoure l'extrémité d'une fissure au cours de sa propagation. On adopte comme hypothèse un modèle parfaitement plastique, la conditions de passage en plasticité de von Mises et la théore de l'écoulement J₂. Dans les équations de mouvement, on considère la force d'inertie. Les développements asymptotiques des déplacements, des déformations et des contraintes sont fournis et résolus pour leur termes principaux. Les résultats montrent qu'à l'extrémité d'une fissure, la déformation présente une singularité de caractère ln A/Y. Enfin, on fournit une expression numérique de la distribution des contraintes dans la zone enrobant l'extrémité de la fissure.

     

Numerical simulation of fatigue crack propagation in compressive residual stress fields of notched round bars

In this paper, the influence of the residual compressive stresses induced by roller burnishing on fatigue crack propagation in the fillet of notched round bar is investigated. A 3D finite element simulation model of rolling has allowed to introduce a residual stress profile as an initial condition. After the rolling process, fatigue loading has been applied to three‐point bending specimens in which an initial crack has been introduced. A numerical predictive method of crack propagation in roller burnished specimens has also been implemented. It is based on a step‐by‐step process of stress intensity factor calculations by elastic finite element analyses. These stress intensity factor results are combined with the Paris law to estimate the fatigue crack growth rate. In the case of roller burnished specimens, a numerical modification concerning experimental crack closure has to be considered. This method is applied to three specimens: without roller burnishing, and with two levels of roller burnishing (type A and type B). In all these cases, the computational finite element predictions of fatigue crack growth rate agree well with the experimental measurements. The developed model can be easily extended to crankshafts in real operating conditions.     

A fracture mechanics approach to estimate the fatigue endurance of welded t-joints including residual stress effects

Residual stresses and weld defects play a major role in the fatigue behaviour of welded structures, so these effects need to be accounted for in a theoretical analysis. A simplified engineering procedure based on linear‐elastic fracture mechanics is applied to estimate the fatigue behaviour, particularly the limit of endurance. Local geometrical irregularities and pre‐existing flaws, which are typical for this kind of weld, are covered by an overall notch intensity factor instead of a specific stress intensity factor, so the initial flaw size is not needed explicitly in the analysis. The effect of residual stresses can be easily included. The cut‐compliance method was applied to measure the residual stress distribution on the cross‐section of the weld. A welded T‐joint was used as a benchmark. Unexpectedly, compressive residual stresses were found to prevail in the root region. According to the analysis, they contribute to the endurance limit of the considered joint by about 50%. This result was confirmed by fatigue tests where a significant decrease in the fatigue strength after a post‐weld stress relieving heat treatment was observed.     

Morphological aspects of fatigue crack propagation Part II—effects of stress biaxiality and welding residual stress

In order to maintain structural integrity of welded structures, it is of great importance to evaluate the fitness for serviceability of the structural components, in which fatigue cracks are found during in-service inspections. Crack propagation paths are sometimes prerequisite for the proper estimation of fatigue crack propagation, because curved crack paths and sharp crack turning could occur at the intersections of structural members mainly due to stress biaxiality of repeated loads. In order to investigate this fatigue crack-growth behavior, fatigue crack-propagation tests and numerical simulation are carried out under various biaxial stress range ratios. Morphological mode transitions of fatigue failures are observed in experiments and also by computer simulation. Although simulated modes of failures are in fairly good agreement with the experimental results, discrepancies are sometimes observed for the crack-propagation lives. In order to investigate this problem, the welding residual stresses in the test specimens are measured, and the fatigue crack-propagation lives are quantitatively examined in terms of the combined effects of residual stress distribution and crack paths.     

Fracture mechanics analysis of a crack in a residual stress field

The standard definition of the J integral leads to a path dependent value in the presence of a residual stress field, and this gives rise to numerical difficulties in numerical modelling of fracture problems when residual stresses are significant. In this work, a path independent J definition for a crack in a residual stress field is obtained. A number of crack geometries containing residual stresses have been analysed using the finite element method and the results demonstrate that the modified J shows good path-independence which is maintained under a combination of residual stress and mechanical loading. It is also shown that the modified J is equivalent to the stress intensity factor, K, under small scale yielding conditions and provides the intensity of the near crack tip stresses under elastic-plastic conditions. The paper also discusses two issues linked to the numerical modelling of residual stress crack problems-the introduction of a residual stress field into a finite element model and the introduction of a crack into a residual stress field.     

A note on the plastic zone size ahead of the propagating fatigue crack

Crack length and plastic zone size measurements were made on a limited number of mild steel tensile specimens of ASTMGS No.3.5 and No. 7.0 grain size for various stress amplitudes and various mean stresses. The data are in agreement with the predictions of Bilby, Cottrell and Swinden concerning the static yielding, and indicate that maximum shearing stress rather than shear stress amplitude should be used for best correlation.

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Zusammenfassung An einer beschränkten Anzahl Zugprüflingen aus weichem Stahl der Korngrösse ASTMGS N 3,5 und No 7,0 wurden Risslänge und Grösse der plastischen Zone an der Risspitze bei verschiedenen Spannungsamplituden und verschiedenen mittleren Spannungen gemessen.Die erhaltenen Daten stimmen mit den von Bilby, Cottrell und Swinden für den Fall des statischen Versagens vorhergesagten Daten überein und zeigen an, dass im Hinblick auf eine gute Uebereinstimmung mit der Theorie eher die maximale Schubspannung als die Schubspannungsamplitude verwendet werden soll.

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Résumé Sur un nombre limité d'éprouvettes de traction d'un acier doux, dont la grosseur du grain ASTM était de 3,5 et de 7,0, on a mesuré la longueur de la fissure de fatigue, et l'étendue de la zone de déformation plastique précédant celle-ci, en fonction de diverses amplitudes de la tension alternée, et de divers niveaux de la tension moyenne.Les résultats sont en accord avec les prédictions de Bilby, Cottrell et Swinden concernant l'élongation statique et montrent que pour obtenir une corrélation optimale il convient de considérer la contrainte maximale de cisaillement plutôt que l'amplitude de la tension appliquée.

     

Plastic strain distribution at the tip of a fatigue crack. application to fatigue crack closure in the threshold regime

The fatigue crack growth rate behaviour of a Co-33 wt pct Ni alloy was investigated at room temperature down to the threshold regime using CT specimens for two load ratios 0.1 and 0.3. Cyclic equivalent plastic strain distributions along an axis normal to the crack plane were experimentally determined over the whole range of crack growth rates using two techniques microhardness and a quantitative metallographic technique applied to twins, both calibrated on low cycle fatigue specimens. These experimental values were compared with theoretical curves as obtained from the monotonic plane strain finite element analysis of Tracey and adapted to cyclic loading according to the procedure proposed by Rice. A good agreement was found in stage II crack growth in the vicinity of the crack tip but a discrepancy was observed in the low crack growth rate regime, indicative of crack closure. It was possible to determine the effective amplitude of the stress intensity factor which accounts for this discrepancy and an intrinsic crack growth law was obtained which obeys Paris equation and which applies in the whole crack growth rate range independently of the load ratio.