Linear elastic fracture mechanics (LEFM) analysis of the effect of residual stress on fatigue crack propagation rate

In this research, both residual and applied stresses are converted to stress intensity factors independently and combined using the superposition principle. The fatigue crack propagation rates are predicted. Experiments using two different loading modes, constant applied stress intensity factor (SIF) range, and constant applied load modes are done for samples with and without initial tensile residual stresses. The samples with initial tensile residual stresses exhibit accelerations of the crack propagation rates. The results show that the weight function method combined with the three-component model provides a good prediction of fatigue crack propagation rates in tensile residual stress fields.     

Exact and variational theorems for fracture mechanics of composites with residual stresses, traction-loaded cracks, and imperfect interfaces

By partitioning the total stresses in a damaged composite into either mechanical and residual stresses or into initial and perturbation stresses, it was possible to derive several exact results for the energy release rate due to crack growth. These general results automatically include the effects of residual stresses, traction-loaded cracks, and imperfect interfaces. The exact energy release rate results were expressed in terms of exact solutions to reduced composite stress analysis problems. By considering the common situation where the initial stresses are known exactly, but the perturbation stresses are only known approximately, it was possible to derive rigorous upper and lower bounds to the energy release rate for crack growth. Some of the new fracture mechanics equations were applied to crack closure calculations, to fiber fracture and interfacial debonding in the fragmentation test, and to microcracking in composite laminates.     

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.     

Self-driven tunneling crack arrays—a 3D-fracture mechanics bifurcation analysis

Tunneling cracks driven by drying in a ceramic precursor confined between two glass plates represent a simple type of three-dimensional (3D) crack pattern. They arrange themselves via mutual unloading which causes some cracks to stop whereby the remaining ones get the right spacing for further propagation. By extending a 2D-model of self-driven propagation of crack arrays, a fracture mechanical bifurcation analysis for 3D-crack patterns based on calculating the post-critical contour of the alternating bifurcation mode has been developed. Shrinkage due to drying is replaced here by a simplified thermo-mechanical model based on an effective heat flow whose related temperature field and thermal stresses drive crack propagation. By means of the finite element method, the propagation velocity and the minimum spacing between the steady-state parallel tunnelling cracks are determined. Comparison of theory and experiment suggests that propagation may be non-stationary in these experiments. The observed relation between crack spacing and layer thickness, p ~ e ^2/3, follows from a scaling analysis.     

Combined action of crack closure and residual stress under periodic overloads: A fractographic analysis

The close relationship between sequence-sensitive near-tip residual stress and threshold stress intensity raises questions about load interaction models currently in use to estimate fatigue crack growth under variable amplitude loading. In an attempt to address them, experiments were performed on an Al–Cu alloy under specially designed load sequences with periodic overloads. Fractographic evidence from these tests confirms that fatigue crack closure, together with sequence sensitive variation in threshold stress intensity appear to explain all observed results. The fractographic data provide quantitative inputs for improved modeling of variable-amplitude fatigue, particularly at near-threshold crack growth rates. This study appears to suggest that conventional approaches based on the Wheeler and Willenborg residual stress models can provide reasonable estimates only by coincidence. They model the wrong parameter at lower fatigue crack growth rates and may simply not be valid at other growth rates.     

Modelling brittle crack formation at geometrical and material discontinuities using a finite fracture mechanics approach

In this study, finite fracture mechanics procedures are employed to predict crack formation at geometrical and material discontinuities in brittle elastic structures. A hybrid failure model is utilised taking into account the stress field in the undamaged structure and the energy balance for the formation of cracks. Asymptotic formulations are compared to a direct numerical implementation. Experiments carried out on notched brittle specimens exhibiting various geometries and loading-modes are analysed by means of both approaches. Additionally, free-edge effects in composite laminates are analysed. It is found that the predictions from the model agree well with experimental results.     

Finite fracture mechanics analysis of crack onset at a stress concentration in a UD glass/epoxy composite in off-axis tension

The presence of stress concentrations at holes and notches is known to reduce the strength of composite materials. Due to complexity of the damage processes at a stress raiser in a composite, different modeling approaches have been developed, ranging from empirical point and average stress criteria to involved damage mechanics or cohesive zone-based models of failure. Finite fracture mechanics approach with a coupled stress and energy failure criterion, recently developed and applied mainly to cracking in homogeneous isotropic materials, allows predicting the appearance and propagation of a crack using material strength and toughness characteristics obtained from independent tests. The present study concerns application of the finite fracture mechanics to the analysis of cracking at a notch in a UD glass/epoxy composite subjected to tensile off-axis loading. Based on UD composite strength and intralaminar toughness characterized by separate tests, finite fracture mechanics analysis provided conservative estimates of crack onset stress at the notch.     

Fatigue crack growth in a welded rail under the influence of residual stresses

The effect of welding residual stresses on fatigue crack growth in rail welds is studied. Finite element analysis is used to calculate residual stresses in a flash-butt welded rail. The calculated residual stresses are found to be in good agreement with experimentally determined residual stresses in a welded rail. The redistribution of residual stresses in the welded rail is simulated for a straight track, during heavy-haul operation conditions, using a train-track model. Fatigue crack growth of defects in the weld region is studied using fracture mechanics. In the investigation, a number of parameters such as the axle load, crack location, crack size and rail temperature are varied.     

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.     

Fatigue crack initiation assessment of welded joints accounting for residual stress

The impact of residual stresses on the fatigue crack initiation life of welded joints is evaluated by the finite element method. The residual stresses of nonload‐carrying cruciform joints, induced by welding and ultrasonic impact treatment, are modelled by initial stresses, using the linear superposition principle. An alternative approach of using modified stress‐strain curves in the highly stressed zone is also proposed to account for the residual stress effect on the local stress‐strain history. An evaluation of the fatigue crack initiation life of welded joints based on the local strain approach is carried out. The predicted results show the effect of residual stresses and agree well with published experimental results of as‐welded and ultrasonic impact treated specimens, demonstrating the applicability of both approaches. The proposed approaches may provide effective tools to evaluate the residual stress effect on the fatigue crack initiation life of welded joints.     

Discrete fractal fracture mechanics

A modification of the classical theory of brittle fracture of solids is offered by relating discrete nature of crack propagation to the fractal geometry of the crack. The new model incorporates all previously considered theories of fracture processes, in particular the Griffith [Griffith AA. The phenomenon of rupture and flow in solids. Philos Trans Roy Soc Lond 1921;A221:163-398] theory, its contemporary extension known as LEFM and the most recently developed Quantized Fracture Mechanics (QFM) by Pugno and Ruoff [Pugno N, Ruoff RS. Quantized fracture mechanics. Philos Mag 2004;84(27):2829-45]. Using an equivalent smooth blunt crack for a given fractal crack, we find that assuming that radius of curvature of the blunt crack is a material property, the crack roughens while propagating. In other words, fractal dimension at the crack tip is a monotonically increasing function of the nominal crack length, i.e., the presence of the Mirror-Mist-Hackle phenomenon is analytically demonstrated.     

Residual stress induced crack tip constraint

This paper studies the effect of welding residual stresses on the near tip stress field in single edge notched bending and tensile specimens. A combined effect of mechanical stresses by the applied load and residual stress on the crack tip constraint is analyzed. Three initial residual stress distributions were considered. It has been shown that the crack tip stress field is strongly influenced by the residual stresses and a new parameter, R, is proposed to characterize the residual stress induced crack tip constraint. The results therefore suggest a three-parameter approach (CTOD, Q and R) to characterize the crack tip stress field in the presence of residual stress where CTOD sets the size scale over which large stresses and large strains develop, and the geometry constraint parameter Q and the new residual stress induced constraint parameter R control the actual crack tip constraint level. For the cases analyzed, R is in general positive, which indicates that residual stress can enhance the crack tip constraint. However, the results also indicate that the R decreases towards zero and the effect of residual stress on crack tip constraint can be neglected when a full plastic condition is approached in the specimen.     

Interaction of welding residual stresses and warm pre-stressing on brittle fracture of a pipe containing an internal semi-elliptical crack

Residual stresses (RS) due to welding process, may change the load bearing capacity of cracked components. These stresses can also affect the benefit of warm pre-stressing (WPS) cycles which are used for improving structure behaviour. RS are obtained from a two-passes welding simulation of a pipe and verified by experiments. A semi-elliptical internal crack at the weld line is considered. Redistribution of RS field after introducing the crack shows a significant tensile RS are remained at the crack tip. Two common WPS cycles, load-cool-fracture (LCF) and load–unload-cool-fracture (LUCF), are applied using the model at room and low temperature subjected to axial loading. Using local approach to fracture shows that welding RS dramatically raise the fracture probability. LCF has more influence on reducing the fracture probability in comparison with LUCF. The interaction of welding RS and WPS cycles still improves the fracture properties, however, welding RS cause to decrease the benefit of WPS. Comparing RS distributions on crack-tip shows that applying WPS cause to release a significant amount of welding RS and therefore, WPS can be very useful for welded structures. The near crack-tip opening stresses at a same fracture load are further studied for all cases.     

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.     

The effect of a residual stress field on fracture initiation in RPV steel

Whether flaws in structures containing residual (secondary) stresses will extend under particular operational (primary) loads depends on the extent to which the residual stress field affects: (a) the nature and distribution of initiators; (b) the combined (primary + secondary) stresses and strains experienced by potential initiators. This paper compares fractographic data from specimens loaded by only a primary stress with data from specimens also containing a tensile residual stress field. Three‐dimensional elastic–plastic finite element calculations are used to characterize the stress–strain conditions at the initiation sites at the onset of brittle fracture. The introduction of a residual stress changes the dominant stage in fracture nucleation from microcrack extension to particle cracking. This offsets some of the decrease in fracture toughness expected when the residual stress field increases specimen constraint.     

Fatigue crack growth through a residual stress field introduced by plastic beam bending

We present predictions and measurements of fatigue crack growth rates in plastically bent aluminium 2024‐T351 beams. Beam bending and fatigue were carefully controlled to minimize factors other than residual stress that could affect the fatigue crack growth rate, such as large plastic strains or residual stress relaxation. The residual stress introduced by bending was characterized by a bending method and by the slitting method, with excellent agreement between the two methods. Crack growth rates were predicted by three linear elastic fracture mechanics (LEFM) superposition based methods and compared to experimental measurements. The prediction that included the effects of partial crack closure correlated with experimental data to within the variability normally observed in fatigue crack growth rate testing of nominally residual stress free material. Therefore, we conclude that crack growth through residual stress fields may be predicted using the concept of superposition as accurately as crack growth through residual stress free material, provided that the residual stress is accurately known, the residual stress remains stable during fatigue, the material properties are not changed by the introduction of residual stress, and that the effect, if any, of partial crack closure is taken into account.     

Fatigue crack growth in residual stress fields

A fatigue crack growth (FCG) model for specimens with well-characterized residual stress fields has been studied using experimental analysis and finite element (FE) modeling. The residual stress field was obtained using four point bending tests performed on 7050-T7451 aluminum alloy rectangular specimens and consecutively modeled using the FE method. The experimentally obtained residual stress fields were characterized using a digital image correlation technique and a slitting method, and a good agreement between the experimental residual stress fields and the stress field in the FE model was obtained. The FE FCG models were developed using a linear elastic model, a linear elastic model with crack closure and an elastic–plastic model with crack closure. The crack growth in the FE FCG model was predicted using Paris–Erdogan data obtained from the residual stress free samples, using the Harter T-method for interpolating between different baseline crack growth curves, and using the effective stress intensity factor range and stress ratio. The elastic–plastic model with crack closure effects provides results close to the experimental data for the FCG with positive applied stress ratios reproducing the FCG deceleration in the compressive zone of the residual stress field. However, in the case of a negative stress ratio all models with crack closure effects strongly underestimate the FCG rates, in which case a linear elastic model provides the best fit with the experimental data. The results demonstrate that the negative part of the stress cycle with a fully closed crack contributes to the driving force for the FCG and thus should be accounted for in the fatigue life estimates.     

Fracture mechanics of surface fatigue crack growth by ductile striation space measurement in notched Waspaloy

Ductile striation space (DSS), a parameter to predict actual cracks in both direction of length and depth, is proposed for the surface fatigue crack behaviors on notched Waspaloy. Three different lengths (1, 2 and 4 mm) of artificial notches are formed as the initial surface crack for an applied maximum stress of 1,103 MPa at the stress ratio R of 0.05. These notches are similar with the appearance of the surface cracks found from the survey of compressor disk. The results show that, all initial crack sites in the depth direction started from the multiple origination sites. The DSS parameter was clearly confirmed, and it also proves the high effectiveness of the measurement in the range of the stress intensity factors for acquiring the crack growth rate on the fractured surface. The surface cracks on Waspaloy at room temperature in an atmosphere perfectly follow the relation of ΔK versus da/dN and db/dN, even though there are, respectively, earlier and later timing differences on the initiation of cracks for the notch sizes of 1 and 4 mm. The results of ΔK versus da/dN and db/dN relations show a similar slope for three different kinds of notches.     

Evolution of residual stresses with fatigue crack growth in integral structures with crack retarders

Bonded straps are investigated for their ability to retard a growing fatigue crack in metallic structures. The evolution of the residual stresses in the vicinity of the strap with fatigue crack growth has been studied. Cracks were grown in single edge-notched tension (SEN(T)) specimens reinforced with either a titanium or a carbon fibre reinforced plastics (CFRP) strap. The residual stress evolution has been measured in situ during crack growth using neutron diffraction, and modelled with a finite element approach. The peak residual stresses induced by the mismatch of the coefficient of thermal expansion between the strap and plate materials were seen to be fairly constant with crack growth. Good correlation between the experimental and the modelling results was found, except at very long crack lengths for a specimen that exhibited considerable fracture surface roughness at long crack lengths. The difference was attributed to wedging of the fracture surface changing the expected stress state, rather than any effect of the strap.