Concurrent ratcheting–fatigue damage analysis of uniaxially loaded A‐516 Gr.70 and 42CrMo Steels

This study intends to investigate the concurrent interaction of fatigue damage and ratcheting strain in two commonly used steel alloys of (American Society for Testing and Materials) ASTM A‐516 Gr.70 and 42CrMo, respectively for pressure vessels and high grade machinery parts over uniaxial stress cycles. Ratcheting extension and fatigue damage progress were both characterized cycle‐by‐cycle over life cycles of tested materials. The interaction of ratcheting and fatigue damage was defined based on mechanistic parameters involving the effects of mean stress, stress amplitude and cyclic softening/hardening response of materials. The extent of ratcheting effect was defined by product of average ratcheting strain per cycle, and maximum stress value during a cycle, while fatigue damage was analysed based on earlier developed energy‐based models of Xia–Ellyin, and Smith–Watson–Topper. Overall damage due to ratcheting and fatigue was calibrated through a weighting factor at various mean/ cyclic amplitude stresses. An algorithm was developed to evaluate overall damage due to ratcheting and fatigue stress cycles of materials subjected to various mean and amplitude stresses. The estimated lives at different mean stresses and stress amplitudes for ASTM A‐516 Gr.70 and 42CrMo samples showed good agreements as compared with those of reported experimental data.     

Uniaxial ratcheting behavior and fatigue life models of commercial pure titanium

The uniaxial fatigue and ratcheting behavior of commercial pure titanium (CP‐Ti) was investigated by asymmetric cyclic stress‐controlled experiments at room temperature. The effects of mean stress, stress amplitude, stress ratio, and peak stress on ratcheting behavior and fatigue life were discussed. It was found that increasing mean stress, stress amplitude, and peak stress or decreasing stress ratio reduced fatigue life and promoted ratcheting behavior. The applicability of different fatigue life models was analyzed, and a new stress ratio‐related failure model was proposed based on the exponential increase of fatigue life with stress ratio. Among all the models investigated in this study, the exponential stress ratio‐related model has more advantage in fatigue life predictions for CP‐Ti under ratcheting‐fatigue interaction.     

Ratcheting‐fatigue behaviour of bainite 2.25Cr1MoV steel with tensile and compressed hold loading at 455°C

The ratcheting behaviour of a bainite 2.25Cr1MoV steel was studied with various hold periods at 455°C. Particular attention was paid to the effect of stress hold on whole‐life ratcheting deformation, fatigue life, and failure mechanism. Results indicate that longer peak hold periods stimulate a faster accumulation of ratcheting strain by contribution of creep strain, while double hold at peak and valley stress has an even stronger influence. Creep strains produced in peak and valley hold periods are noticeable and result in higher cyclic strain amplitudes. Dimples and acquired defects are found in failed specimen by microstructure observation, and their number and size increase under creep‐fatigue loading. Enlarged cyclic strain amplitude and material deterioration caused by creep lead to fatigue life reduction under creep‐fatigue loading. A life prediction model suitable for asymmetric cycling is proposed based on the linear damage summation rule.     

Ratcheting behaviour and mean stress considerations in uniaxial low-cycle fatigue of Inconel 718 at 649 °C

The ratcheting behaviour of Inconel 718 was investigated at 649 °C under uniaxial cyclic loading. Stress-control tests have been conducted at various combinations of stress amplitude and mean stress. The ratcheting strain at failure increases with increasing mean stress for a given stress amplitude and with decreasing stress amplitude for a given mean stress. Fatigue lives were correlated using three mean stress models: the Goodman equation, the Smith–Watson–Topper (SWT) parameter and the Walker parameter. It has been shown that the Goodman equation and the SWT parameter do not correlate life data, while the Walker parameter yields acceptable correlation. The SWT parameter was modified to incorporate the ratcheting effect. The new parameter is found to yield correlation similar to that of the Walker parameter.     

Biaxial fatigue for proportional and non‐proportional loading paths

In order to study the use of a local approach to predict crack‐initiation life on notches in mechanical components under multiaxial fatigue conditions, the study of the local cyclic elasto‐plastic behaviour and the selection of an appropriate multiaxial fatigue model are essential steps in fatigue‐life prediction. The evolution of stress–strain fields from the initial state to the stabilized state depends on the material type, loading amplitude and loading paths. A series of biaxial tension–compression tests with static or cyclic torsion were carried out on a biaxial servo‐hydraulic testing machine. Specimens were made of an alloy steel 42CrMo4 quenched and tempered. The shear stress relaxations of the cyclic tension–compression with a steady torsion angle were observed for various loading levels. Finite element analyses were used to simulate the cyclic behaviour and good agreement was found. Based on the local stabilized cyclic elastic–plastic stress–strain responses, the strain‐based multiaxial fatigue damage parameters were applied and correlated with the experimentally obtained lives. As a comparison, a stress‐invariant‐based approach with the minimum circumscribed ellipse (MCE) approach for evaluating the effective shear stress amplitude was also applied for fatigue life prediction. The comparison showed that both the equivalent strain range and the stress‐invariant parameter with non‐proportional factors correlated well with the experimental results obtained in this study.     

A fatigue damage indicator parameter for P91 chromium‐molybdenum alloy steel and fatigue pre‐damaged P54T carbon steel

Two grades of structural steel were subjected to fully reversible, constant stress amplitude cyclic loading. The local strain response of the material was measured and recorded during the test, with the applied testing technique enabling the monitoring of hysteresis loop variation for the narrowest cross‐section of the hourglass specimen. Changes in hysteresis loop width, representing the local inelastic response of the material, were recorded in order to monitor the density of structural imperfections. Material ratcheting behaviour was observed as changes in the mean strain for selected load cycles. Ratcheting was attributed to local deformation of the material in the vicinity of imperfections such as voids or inclusions, as well as deformation induced by the propagation of microcracks. Definitions of a damage indicator parameter and damage parameter were proposed. The fatigue behaviour of the two investigated grades of steel was finally illustrated in the form of damage curves for different stress amplitudes and for undamaged and fatigue pre‐damaged material.     

Ratcheting and fatigue properties of the high-nitrogen steel X13CrMnMoN18-14-3 under cyclic loading

High-nitrogen steel X13CrMnMoN18-14-3 has been used in manufacturing expanding metallic stents with 0.1 mm diameter, and such medical implant is subjected to complicated and asymmetrical cyclic loading during service. But there is no test data published for the thin wire of the material under cyclic loading. In this study, a series of tests were conducted on X13CrMnMoN18-14-3 stainless steel under uniaxial cyclic loading with mean tensile stress. The yield stress and ultimate strength were higher than that of large size specimen with diameters of 5 mm and 7 mm. The effects of stress amplitude, mean stress, loading history and stress rate on the ratcheting behavior of high-nitrogen steel were analyzed, respectively. It can be concluded that the ratcheting strain amplitude and ratcheting strain rate of X13CrMnMoN18-14-3 steel increases with increasing stress amplitude or mean stress correspondingly. At the meantime, experimental results reveal that the material exhibits a strong memory of the previous loading history, the stress cycling with higher stress amplitude or mean stress greatly restrains the ratcheting of subsequent stress cycling with lower ones. The ratcheting strain rate was very sensitive to the applied cyclic stress rate, and the accumulation of ratcheting strain under stress rate of 21.2 MPa/s is much faster than that under stress rate of 106 MPa/s. In addition, comparison of the fatigue life between bulk specimen and thin wire indicates that the size effect has significant influence on fatigue properties of the material. In the case of the test conducted under stress amplitude of 400 MPa, the fatigue life of small specimen is approximately ten times longer than that of bulk specimen under the same loading conditions.     

Mean stress effect on fatigue strength of stainless steel

Influence of mean stress on fatigue life and fatigue limit was investigated for Type 316 stainless steel. The results for prestrained specimens revealed that fatigue life was almost the same in the same strain range regardless of stress amplitude, maximum peak stress and mean strain. The fatigue life was shortened when applying the mean stress for the same strain range, whereas it was increased for the same stress amplitude. It was shown that the reduction in fatigue life was brought about by the change in the effective strain range, which was caused by the increase in minimum peak stress and the ratcheting strain. The fatigue life could be predicted conservatively even if the mean strain was applied by assuming the effective strain range to be equal to the total strain range (by assuming the crack mouth to be never closed). It was concluded that the mean stress correction was not necessary for the load-controlled cyclic loading and for the region where the ratcheting strain was constrained.     

Torsional fatigue with axial constant stress for Sn–3Ag–0.5Cu lead-free solder

A series of multiaxial ratcheting–fatigue interaction tests have been carried out on Sn–3Ag–0.5Cu lead-free solder specimens. All tests were conducted under cyclic shear strain with the constant axial stress at the room temperature with the shear strain rate of 5 × 10⁻³ s⁻¹. It was found that the ratcheting strain increased with increasing axial stress and shear strain amplitude while the fatigue life decreased at the same time. The ratcheting strain rate was linear with axial stress in double logarithmic coordinate. The Ohno–Wang II constitutive model was employed to simulate the stress–strain responses. Several fatigue life prediction models were applied to predict the multiaxial ratcheting–fatigue life of the Sn–3Ag–0.5Cu lead-free solder. The Gao–Chen model which adopted the maximum shear strain and the ratcheting strain rate as the damage parameter predicted the multiaxial ratcheting fatigue life well.     

Effect of axial ratcheting deformation on torsional low cycle fatigue life of lead-free solder Sn–3.5Ag

Multiaxial fatigue tests were conducted on Sn–3.5Ag solder specimens under axial/torsional loading at room temperature. It was found that the ratcheting strain increased while the fatigue life decreased with the increase of axial stress and shear strain amplitude. A power relationship of ratcheting strain rate versus fatigue life was observed. Equivalent strain approach and critical plane approaches were evaluated with fatigue life data obtained in the tests. Since those approaches excluded the consideration of the ratcheting strain and mean stress, the methods for fatigue life prediction were improper for multiaxial fatigue with ratcheting strain. Coffin model, considered the effect of ratcheting on fatigue life depending on the ratio of ratcheting strain to material ductility, brought the fatigue life predictions on non-conservative side if the ratcheting deformation was large. For this reason, a model with the maximum shear strain range and axial ratcheting strain rate was proposed as a new damage parameter. The new model could not only describe the fatigue life in torsion test, but also predicted torsional fatigue life of the lead-free solder with axial ratcheting.     

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.     

Mean stress and ratcheting corrections in fatigue life prediction of metals

Ratcheting occurs easily because of the presence of mean stress during the stress‐control fatigue of engineering components. For ductility exhaustion dominated fatigue failure, a new fatigue life prediction model is developed by introducing the mean ratcheting strain rate to incorporate the effects of ratcheting and mean stress on fatigue life. The prediction accuracy of the proposed model was compared with that of the generalised damage parameter, Xia–Kujawski–Ellyin, Walker and Goswami models. Specifically, the model predictions and tested lives were compared using nine sets of experimental data from the literature. In the statistical analysis of these five models, the proposed model provides the highest accuracy and robust life predictions with the lowest model prediction errors.     

Fatigue of beta titanium alloy at 20, 482 and 648 °C

Fatigue life of fibrous metal matrix composites is limited by the distribution of fibre strengths, the fibre‐matrix interfacial strength, and the fatigue resistance of the matrix. The aim of this work is to provide fatigue results for a beta titanium alloy over a range of temperatures and stresses that can be used as input for predicting fatigue life of a titanium matrix composite. Stress controlled tests having fatigue ratios between ?1 and ?0.2 were conducted on a limited number of samples machined from unreinforced laminated Ti‐15Mo‐3Al‐2.7Nb‐0.2Si (TIMETAL^®21S) sheets to represent as closely as possible the in situ matrix material. Stress control was used to enable quantification of strain ratcheting for tensile mean stresses and a fast loading rate was used to minimize time‐dependent (creep) deformation. Stress amplitude‐life data at 20, 482 and 648 °C for fully reversed loading are well fit by a power law. Normalizing the stress amplitude with respect to the power law coefficient appears to account for the temperature dependence of the S–N curves. As the tests had large strains and lives were in the low‐cycle fatigue range, strain range at the half‐life was also correlated to life. For tensile mean stress cycling at 482 and 648 °C, the rate of strain ratcheting per cycle increased to failure; shakedown was not observed.     

Steady ratcheting strains accumulation in varying temperature fatigue tests of PMMA

The evolutions of ratcheting strains of polymethyl methacrylate (PMMA) at different temperatures and stress levels were experimentally investigated. A steady ratcheting strain growth region with a constant rate was observed in all specimens, which occupied significant part of total fatigue failure life. Experimental results also showed that the steady ratcheting growth rate varied with applied temperatures and loading. In this paper, theory of thermally activated process for glassy polymers was used to describe the plastic deformations during the cycle. Based on the correlations between ratcheting strains per cycle and hysteresis loop energy, a new ratcheting strains accumulative model for polymer materials was developed, which quantificationally elucidated the effects of temperature, loading frequency, mean stress and stress amplitude on the accumulative rate of ratcheting strains. Comparing the predications from the proposed model with experimental ratcheting strain data of PMMA, it was found that the model could describe the steady ratcheting strain accumulative behaviors under arbitrary temperatures and loading conditions exactly.     

Experimental study on the whole‐life heterogeneous ratchetting and ratchetting‐fatigue interaction of SUS301L stainless steel butt‐welded joint

Uniaxial fatigue tests of butt‐welded joint, made from SUS301L stainless steel, were carried out under asymmetric stress‐controlled cyclic loading conditions in this work. The effects of stress amplitude and mean stress on the whole‐life heterogeneous ratchetting and fatigue life of the butt‐welded joint were investigated, respectively, for the specified subzones. The experimental observations show that the whole‐life inhomogeneous ratchetting strain concentrating in a specific fusion zone (denoted as the FZ‐1 subzone) of the welded joint becomes more significant as the stress level increases; the fatigue failure also occurs in the FZ‐1 subzone, and the fatigue life depends on both the applied mean stress and stress amplitude and is determined by the combination of ratchetting damage and fatigue one in the localized FZ‐1 subzone.     

Fretting fatigue under variable loading below fretting fatigue limit

The fatigue limit diagram provides the critical condition of non‐failure against fatigue under constant amplitude loading. The fatigue limit diagram is usually considered to give the allowable stress if every stress component is kept within the fatigue limit diagram. In the case of variable amplitude fretting fatigue, however, this study showed that fatigue failure could occur even when all stresses were within the fatigue limit diagram. An example of such a condition is a repeated two‐step loading such as when the first step stress is R=?1 and the second step stress has a high mean value. The reason why such a phenomenon occurs was investigated. A non‐propagating crack was formed by the first step stress even when well below the fatigue limit. The resultant non‐propagating crack functioned as a pre‐crack for the second step stress with a high mean value. Consequently, fatigue failure occurred even when every stress was within the fatigue limit diagram of constant amplitude loading. The fatigue limit diagram obtained in constant amplitude fatigue test does not necessarily guarantee safety in the case of variable amplitude loading in fretting fatigue.     

Mean stress effects on low‐cycle fatigue for a precipitation‐hardening martensitic stainless steel in different tempers

The objective of this study is to investigate the effects of mean stress and ageing treatment on the low‐cycle fatigue (LCF) behaviour of a precipitation‐hardening martensitic stainless steel (PHMSS). Uniaxial LCF tests were conducted under strain control with three strain ratios, R = ?1, 0 and 0.5 on specimens heat‐treated to three different tempers, i.e. solution‐annealed (SA), peak‐aged (H900) and overaged (H1150) conditions. Experimental results indicated that under a strain ratio of R = ?1, specimens in H900 temper exhibited longer LCF lifetimes than those in SA and H1150 tempers. However, this advantage for H900 over SA and H1150 tempers disappeared at higher strain ratios (R = 0 and 0.5) due to the greater sensitivity to mean stress effects in H900 temper. For a given temper at high strain amplitudes, the LCF lifetimes under the three applied strain ratios did not show significant differences as a result of the mean stress relaxation effect. However, at low strain amplitudes, cyclic loading at R = ?1 generated longer LCF lifetimes in comparison to R = 0 and 0.5 due to the absence of detrimental tensile mean stress. LCF lifetime data obtained for the given PHMSSs under various combinations of strain ratio and heat treatment were well correlated with a strength‐normalized Smith–Watson–Topper (SWT) parameter in a log–log linear model.     

Experimental and theoretical studies on thermo‐mechanical fatigue test for aluminium cast alloy

Evaluation of the thermo‐mechanical behaviour and prediction of the service life of cast aluminium alloys are important for the design of automobile engine cylinder heads. In this study, cast Al alloy specimens are extracted from cylinder heads and subjected to in‐phase thermo‐mechanical cyclic loading. The hysteresis curves related to stress and strain were recorded under the individual thermo‐mechanical loading conditions. The number cycles to failure corresponding to multiple mechanical strain and temperature ranges were obtained. It is found that the cyclic stress amplitude decreases and the cyclic softening rate increases with increasing maximum temperature rise. A modified fatigue‐creep model based on energy conservation has been developed for prediction of the fatigue life of cylinder heads. The proposed method shows good agreement with the well‐established Ostergren model and low standard deviations. In summary, the proposed method described in this study provides an option for prediction of the thermo‐mechanical behaviour of metals.     

Comparative analysis of fatigue life predictions in central notched specimens of Al–Mg–Si alloys

The fatigue behaviour of an Al–Mg–Si alloy was studied using notched specimens. Fatigue tests were conducted at two stress ratios R= 0 and R= 0.4 on thin plates with a central hole. Constant and block variable loading amplitudes were applied to the specimens using a servo‐hydraulic machine. The applicability of the local strain approach method to the prediction of the fatigue life was investigated for this type of discontinuity. Two methods, the equivalent strain energy density approach and a modified stress–strain intensity field approach, were used to predict the fatigue strength. For the second one an elastic–plastic finite element analysis was carried out in order to obtain the local strain and stress distributions near the notch root. Based on Miner's rule an equivalent stress was used to correlate the fatigue lives for the variable amplitude histories. The experimental results were compared with the predicted results obtained by the two methods investigated and better agreement was found with the stress–strain field intensity approach, while the strain energy approach gave more conservative results. Miner's rule gives a good correlation between the variable amplitude and constant amplitude results.     

True stress-controlled ratcheting behavior of 304LN stainless steel

Cyclic plastic deformation response of materials under asymmetric stress cycling is known as ratcheting. Combined effect of fatigue and permanent tensile strain accumulation results in early failure of materials during ratcheting. For this reason, ratcheting should be emphasized in the safety assessment and life estimation of engineering structures. Engineering and true stress-controlled ratcheting behavior of 304LN stainless steel has been carried out at room temperature. Effects of stress amplitude, mean stress, and their histories (i.e., step loading) on the ratcheting behavior are analyzed in this investigation. It is noticed that under true stress-controlled ratcheting experiments, ratcheting life increases in presence of mean stress, and hysteresis loop area and plastic strain energy decreases with the increasing mean stress. A comparison has also been drawn in between the true and engineering stress-controlled tests, and massive differences in ratcheting life and strain accumulation were found. Ratcheting strain accumulation ceases in descending step loading, is noticed in this work.