Derivation of crack closure and crack growth rate data from effective-strain fatigue life data for fracture mechanics fatigue life predictions

This study deals with the behavior of short cracks growing out of notches. Three types of load histories are used: (a) a fully-reversed constant amplitude history; (b) a periodic compressive overload history consisting of repeated load blocks containing one fully-reversed constant amplitude yield–stress magnitude cycle (the overload) followed by a group of smaller constant amplitude cycles having the same maximum stress as the overload cycle; (c) and a service strain history. Procedures are presented for deriving crack closure data and crack growth rate vs effective stress intensity factor range data from data obtained by subjecting a small number of smooth laboratory specimens to simple periodic compressive overload tests to obtain closure-free strain-life data. These procedures are illustrated in an example in which fatigue life predictions are made for a service strain history applied to notched plate specimens. The fatigue life predictions based on the measured and the derived crack closure and crack growth rate data are in good agreement with the experimentally determined fatigue lives.     

Variable amplitude fatigue of spot welds

A new method for fatigue life prediction of spot welds subjected to variable amplitude loads is proposed. The method is based on the concept of crack closure and is experimentally verified with three different specimens and four different load signals with variable amplitude. Experimental fatigue lives were found to be within a factor of three from the predicted lives. To start with, the stress intensity factor history at the spot weld is calculated with a finite element analysis. Then, crack closure is taken into account: the crack opening stress intensity factor, which is assumed to be constant, is determined from the maximum and minimum in the history. All stress intensities lower than the crack opening level are filtered from the calculated history. The filtered history is then analysed with rain flow count. Finally, fatigue life is predicted with the Palmgren–Miner cumulative damage rule together with an effective (closure‐free) curve for spot welds. In addition, single overload tests were carried out to investigate the assumption of a constant crack opening stress.     

Closure-free biaxial fatigue crack growth rate and life prediction under various biaxiality ratios in SAE 1045 steel

Biaxial fatigue tests were performed on thin-walled tubular 1045 steel specimens in a test fixture that applied internal and external pressure and axial load. There were two test series, one in which constant amplitude fully reversed strains (CAS) were applied and another in which large periodic compressive overstrain (PCO) cycles causing strains normal to the crack plane were inserted in a constant amplitude history of smaller strain cycles. Ratios of hoop strain to axial strain of λ = ?1, ?0.625, ?ν and +1 were used in each test series. Fatigue crack growth behaviours under CAS and PCO histories were compared, and revealed that the morphology of the fracture surface near the crack tip and the crack growth rate changed dramatically with the application of the compressive overstrains. When the magnitude of the compressive overstrains was increased, the height of the fracture surface irregularities was reduced as the increasing overstrain progressively flattened the fracture surface asperities near the crack tip. The reduced asperity height was accompanied by drastic increases in crack growth rate and decreases in fatigue life. Using a pressurizing device attached to the confocal scanning laser microscope (CSLM), crack opening measurements were obtained. Crack opening measurements showed that the biaxial cracks were fully open at zero internal pressure for block strain histories containing in-phase PCO cycles of yield stress magnitude. Therefore, for the shear-strained samples, there was no crack face interference and the strain intensity range was fully effective. For PCO tests (with biaxial strain ratios of ?0.625 and +1), effective strain intensity data were obtained from tests with positive stress ratios for which cracks did not close. A number of strain intensity parameters derived from well-known fatigue life parameters were used to correlate fatigue crack growth rates for the various strain ratios investigated. Predicted fatigue lifetimes based on a fatigue crack growth rate prediction program using critical shear plane parameters showed good agreement with the experimental fatigue life data.     

Estimations of fatigue life and variability under random loading in aluminum Al-2024T351 using strip yield models from NASGRO

This paper is concerned with the application of the strip yield models implemented in NASGRO to estimate fatigue crack growth under random loading. The two different strip yield model options (constant constraint-loss (CCL) and variable constraint-loss (VCL)) implemented in the software are considered and compared. In addition, three crack grow rate relations, obtained from constant amplitude data, the NASGRO material database and the literature, were also considered and compared. The capacity of the models to estimate the fatigue life and variability is analyzed by comparing simulated results with experimental data of fatigue crack growth under different stationary Gaussian random load processes on compact, C(T), specimens of aluminum alloy 2024-T351. The analysis performed showed that both model options provide very similar good fatigue life predictions. The estimated fatigue lives are within ±13% of the test lives with the best option. The variability of the results due to the randomness of the load is also analyzed. In this case, the variable constraint-loss option provides better estimation than the constant constraint-loss option.     

Load sequence effects in fatigue crack growth of thick-walled welded C–Mn steel members

Many welded steel structures in marine, offshore, and infrastructural industries are subjected to variable amplitude (VA) fatigue loads. It is well known that the level and sequence of the load cycles can cause crack growth retardation or acceleration and thus influence the fatigue life. An important sequence effect is generated by a large stress cycle followed by smaller stress cycles. Whereas the effect of single large stress cycles in a further constant amplitude (CA) load on central through cracks in thin-walled aluminium sheet is well established, studies into the effects of practical VA loads on cracks in thick-walled welded steel structures are less common. This paper presents the results of CA tests with large stress peaks and VA tests on 70 mm C–Mn steel butt welded 4-point bending specimens with crack growth in thickness direction. It is demonstrated that loading by a sequence of accelerating and subsequent decelerating stress cycles cause significant retardation of the crack growth and that the same stress cycles but placed in random sequence hardly result in retarded crack growth. The obtained crack growth versus number of cycles for as-welded and stress relieved specimens have been simulated using two relatively simple crack rate retardation models, being the well-known Willenborg model and the Space-state model developed by Ray and Patankar. The latter model is also used to simulate crack growth of semi-elliptical surface cracks in welded steel structures tested by others. The Space-state model is able to predict experimental results with reasonable to good accuracy. A proposal is put forward for future improvement of the model.     

Short-crack-growth-based fatigue assessment of notched components under multiaxial variable amplitude loading

A short crack model originally proposed for multiaxial constant amplitude loading is extended and applied to multiaxial variable amplitude loading. Load sequences have a significant influence on variable amplitude life; they are taken into account using algorithms originally proposed only for uniaxial loading. The estimated fatigue lives of unnotched tubular specimens and notched shafts under different in- and out-of-phase multiaxial constant and variable amplitude load histories are compared with the experimental results. The comparison reveals that the proposed short crack approach enables sufficiently accurate estimation. Moreover, the estimated critical planes, i.e., the planes of maximum crack growth rate or minimum life, are in good agreement with the experimental observations.     

Variable amplitude fatigue of autofrettaged diesel injection parts

Experimental and analytical investigations of constant and variable amplitude fatigue life of not autofrettaged and autofrettaged components have been performed. In variable amplitude loading the new standardised CO mmon‐ RA il‐ L oad sequence CORAL has been used as well as two‐level‐tests with small cycles at high mean stresses interrupted by large cycles for the evaluation of load sequence effects. The results of the two level tests show that small cycles with amplitudes far below the fatigue limit cause fatigue damage. Life calculations have been performed according to the nominal stress approach with S‐N‐curves and improved Miner’s Rule, linear‐elastic fracture mechanics with 3D‐weight functions, elastic‐plastic fracture mechanics applying an extended strip yield‐model, and explicit 3D‐FE‐simulation of fatigue crack growth with predefined crack fronts. All approaches are appropriate for predicting realistic variable amplitude lives. From a practical point of view the explicit 3D‐FE‐simulation of fatigue crack growth is too time‐consuming. However, such simulations show that the approaches based on linear‐elastic fracture mechanics and elastic‐plastic fracture mechanics with extended strip yield‐model capture the essential physics of fatigue crack growth in a realistic way.     

Vergleichende Untersuchungen zur Anrisslebensdauervorhersage gekerbter Proben mit dem Örtlichen Konzept und dem Nennspannungskonzept am Beispiel des Stahls Cm15

Comparative Investigations on Service Life Assessment of Notched Specimens Based on the Local Strain and the Nominal Stress Approach to Fatigue for a Steel SAE 1017 It is still unclear whether the strain based approach to fatigue or the stress based approach to fatigue should be preferred for service life assessment of notched components. In order to clarify the similarities and differences between these concepts stress and strain controlled fatigue experiments have been performed with notched specimens. It has been found, that stress and strain controlled fatigue testing results in the same number of cycles until failure. Essential for this correlation is that the cyclic stable strain amplitude at the notch root is taken for the entry into the strain‐life diagram in both cases. Starting from an elastic‐plastic analysis of the material behaviour at the notch root it is shown, how the strain‐life curve can be converted into a stress‐life curve. Based on that result service‐life is calculated from both approaches mentioned above. The calculation gives nearly the same service‐lives for both cases, but overestimates the measured data. It becomes obvious, that a S‐N curve determined under one‐level loading doesn’t provide a proper basis for service life assessment. While strain or stress‐life curves always contain crack initiation phase as well as crack propagation phase, the fatigue process under irregular loads is mainly governed by crack propagation. As a consequence, the damage per cycle is underestimated for loads near the fatigue limit, if Miner’s rule is used.     

EXAMINATION OF SHORT-CRACK MEASUREMENT AND MODELLING UNDER CYCLIC INELASTIC CONDITIONS

The opening and closure behaviour of short fatigue cracks is seen as one of the important phenomena which control fatigue life of components where a major part of life consists of the growth of short cracks. Therefore attempts are undertaken to experimentally assess and to model the behaviour of short cracks with respect to opening and closure. In this paper crack opening results obtained by Sunder et al. through SEM evaluation of striation patterns of 2000 series aluminium alloys are examined and compared to predictions using a model recently developed for fatigue life prediction based on fracture mechanics of short cracks. Sunder's technique for crack opening measurements involves particular load sequences with increasing and decreasing load ranges applied to notched specimens with naturally nucleated surface cracks where crack opening levels are identified by steady-state striation widths for increasing load ranges. A detailed review of Sunder's results, however, indicates a number of inconsistencies and contradictions which are discussed. Opening and closure behaviour of short fatigue cracks, in particular for inelastic conditions, is compared to predictions obtained with the above-mentioned model which incorporates a constant strain opening and closure assumption. For inelastic conditions that may develop at notches this assumption means that cracks would close at considerably lower stress levels as compared to the opening stress which becomes important when effective (local) stress-strain ranges are to be determined for fatigue life prediction under spectrum loading. The constant strain assumption is supported by a number of experimental observations from the literature as discussed in the paper. The approximative nature of this assumption and further details of the model are pointed out which show a need for further developments.     

Ratcheting and fatigue behavior of a copper alloy under uniaxial cyclic loading with mean stress

Stress-control fatigue tests have been conducted on a copper alloy at room temperature with and without mean stress. Ratcheting strain was measured to failure under four sets of stress amplitude and mean stress. The ratcheting strain versus cycle curve is similar to the conventional creep curve under static load consisting of primary, steady-state and tertiary stages. The steady-state rate and ratcheting strain at failure increase with mean stress for a given stress amplitude and with stress amplitude for a given mean stress. Ratcheting strain increases as the stress rate decreases. The S–N curve approach and mean stress models of Smith–Watson–Topper and Walker yielded good correlation of fatigue lives in the life range of 10²–10⁵ cycles.     

Application of a modified Wheeler model to predict fatigue crack growth in Fibre Metal Laminates under variable amplitude loading

This paper presents the investigation regarding fatigue crack growth prediction in Fibre Metal Laminates under variable amplitude fatigue loading. A recently developed constant amplitude analytical prediction model for Fibre Metal Laminates has been extended to predict fatigue crack growth under variable amplitude loading using the modified Wheeler model based on the Irwin crack-tip plasticity correction and effective stress intensity factor range (ΔK_eff). The fatigue crack growth predictions made with this model have been compared with crack growth tests on GLARE center-cracked tension specimens under selective variable amplitude loading as well as flight simulation loading. The accuracy of the model is discussed in comparison with the experimental fatigue crack growth data.     

FATIGUE STRENGTH OF A ROTOR STEEL SUBJECTED TO TORSIONAL LOADING SIMULATING THAT OCCURRING DUE TO CIRCUIT BREAKER RECLOSING IN AN ELECTRIC POWER PLANT

Abstract— The fatigue strength of notched specimens of a rotor steel was examined under variable torsional loading which simulates turbine-generator oscillations resulting from the high speed reclosing of transmission-line circuit breakers. The local stress-strain response at a notch root was analysed using Neuber's rule and the resulting complex strain sequences applied to smooth specimens. Using the rain flow analysis and the linear summation rule, fatigue lives of the smooth specimens were successfully predicted from constant amplitude fatigue life data in association with the cyclic stress-strain curve obtained by the incremental step method. Experimental crack initiation lives for notched specimens subjected to variable torsional loading were in excellent agreement with the theoretical curves derived from results on smooth specimens. According to the view that fatigue damage is equated to crack length, the propagation life of a mode II crack along the notch root was predicted to be actually coincident with the life to crack initiation at the notch root denned in this study, i.e. the life at the stage of finding a continuous circumferential crack.     

Prediction of fatigue crack growth and residual life using an exponential model: Part II (mode-I overload induced retardation)

Almost all load bearing components usually experience variable amplitude loading (VAL) rather than constant amplitude loading (CAL) during their service lives. A single overload cycle introduced in a constant amplitude fatigue loading retards fatigue crack growth and increases residual fatigue life. Although many models have been proposed on this subject, but life prediction under these complex situations is still under constant improvement. The present study aims at evaluating retardation in fatigue life due to application of a single tensile overload spike by adopting an exponential model. The proposed model calculates not only parameters related with overload induced retardation in fatigue crack growth, but also residual life in case of 7020-T7 and 2024-T3 aluminum alloys with reasonable accuracy without integration of rate equation. The model also covers stage-II and stage-III of post-overload period.     

Fatigue crack initiation life estimation in a steel welded joint by the use of a two-scale damage model

This work deals with the fatigue behaviour of S355NL steel welded joints classically used in naval structures. The approach suggested here, in order to estimate the fatigue crack initiation life, can be split into two stages. First, stabilized stress–strain cycles are obtained in all points of the welded joint by a finite element analysis, taking constant or variable amplitude loadings into account. This calculation takes account of: base metal elastic–plastic behaviour, variable yield stress based on hardness measurements in various zones of the weld, local geometry at the weld toe and residual stresses if any. Second, if a fast elastic shakedown occurs, a two-scale damage model based on Lemaitre et al. 's work is used as a post-processor in order to estimate the fatigue crack initiation life. Material parameters for this model were identified from two Wöhler curves established for base metal. As a validation, four-point bending fatigue tests were carried out on welded specimens supplied by 'DCNS company'. Two load ratios were considered: 0.1 and 0.3. Residual stress measurements by X-ray diffraction completed this analysis. Comparisons between experimental and calculated fatigue lives are promising for the considered loadings. An exploitation of this method is planned for another welding process.     

Variable amplitude fatigue of adhesively-bonded pultruded GFRP joints

The fatigue behavior of adhesively-bonded pultruded GFRP joints subjected to variable amplitude loading patterns was experimentally investigated. The failure mode of the examined joints was found to be similar to that under constant amplitude loading. The acceleration or retardation of the crack propagation rate due to the load interaction effects was thoroughly investigated by monitoring crack propagation during the variable amplitude loading. The fatigue life of the joints was predicted using classic fatigue life prediction methodology. Existing models for characterizing the fatigue behavior of the examined joints were employed together with the linear Palmgren–Miner’s rule for the prediction of fatigue life. A simple modification was incorporated into the applied methodology to take into account the load interaction effects introduced under the variable amplitude loading. Comparison of the life predictions to experimental data proved that the introduced modification can significantly improve the accuracy of the classic life prediction methodology.     

Fatigue life analysis and predictions for NR and SBR under variable amplitude and multiaxial loading conditions

This paper investigates the effects of variable amplitude loading conditions on the fatigue lives of multiaxial rubber specimens. Two filled rubber materials were used and compared to investigate the effects of strain-crystallization on crack development NR, which strain crystallizes, and SBR, which does not. The applicability of Miner’s linear damage rule for predicting fatigue lives of variable amplitude tests in rubber and the use of both scalar and plane-specific equivalence parameters to characterize fatigue life results were also investigated. A fatigue life prediction approach that utilizes normal strain to find the critical plane and the cracking energy density on that plane to determine fatigue life is introduced and compared to other approaches. The effects of load sequence and temperature on fatigue life, as well as differences in fatigue lives using both stiffness and critical crack length failure criteria are discussed.     

Analysis of fatigue crack growth in an attachment lug based on the weight function technique and the UniGrow fatigue crack growth model

A generalised step-by-step procedure for fatigue crack growth analysis of structural components subjected to variable amplitude loading spectra has been presented. The method has been illustrated by analysing fatigue growth of planar corner crack in an attachment lug made of Al7050-T7451 alloy.Stress intensity factors required for the fatigue crack growth analysis were calculated using the weight function method. In addition, so-called “load-shedding” effect was accounted for in order to determine appropriate magnitudes of the applied stress intensity factors. The rate of the load shedding was determined with the help of the finite element (FE) method by finding the amount of the load transferred through the cracked ligament. The UniGrow fatigue crack growth model, based on the material stress–strain behaviour near the crack tip, has been used to simulate the fatigue crack growth under two variable amplitude loading spectra. The comparison between theoretical predictions and experimental data proved the ability of the UniGrow model to correctly predict fatigue crack growth behaviour of two-dimensional planar cracks under complex stress field and subjected to arbitrary variable amplitude loading.     

Elastic–plastic fatigue crack growth analysis under variable amplitude loading spectra

Most fatigue loaded components or structures experience a variety of stress histories under typical operating loading conditions. In the case of constant amplitude loading the fatigue crack growth depends only on the component geometry, applied loading and material properties. In the case of variable amplitude loading the fatigue crack growth depends also on the preceding cyclic loading history. Various load sequences may induce different load-interaction effects which can cause either acceleration or deceleration of fatigue crack growth. The recently modified two-parameter fatigue crack growth model based on the local stress–strain material behaviour at the crack tip [1,2] was used to account for the variable amplitude loading effects. The experimental verification of the proposed model was performed using 7075-T6 aluminum alloy, Ti-17 titanium alloy, and 350WT steel. The good agreement between theoretical and experimental data shows the ability of the model to predict the fatigue life under different types of variable amplitude loading spectra.     

A third-order state-space model for fatigue crack growth

A second‐order state‐space model of fatigue crack growth in ductile alloys was presented by Patankar et al., 1 - 4 where the crack length and the crack opening stress were treated as two state variables. Simulation results showed that this model gave good predictions when compared with experimental data for aluminium alloy 7075‐T6 and 2024‐T3 at constant‐amplitude load as well as with overloads. These model predictions were, however, poor for cases with over/under load or under/over load sequences where load excursion effects were underestimated. A third‐order state‐space model is presented is this paper that is believed to be more accurate for predictions of fatigue crack growth for ductile alloys under various loadings. The constraint factor calculated from an algebraic equation in the second‐order state‐space model is treated as the third state variable in this model. Through simulations, it is shown that the third‐order state‐space model gives better predictions than the second‐order state‐space model and FASTRAN II, especially when the effects of over/under load and under/over load are necessary considerations.     

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.