High cycle thermo-mechanical fatigue: Damage operator approach

The stress-life approach is standardized and widely accepted for determining fatigue damage under stress-controlled high cycle fatigue (HCF) loading. It was first extended to non-isothermal cases by introducing an equivalent temperature approach (ETA). The paper presents its extension, that is, the damage operator approach (DOA), enabling online continuous damage calculation for isothermal and non-isothermal loading with mean stress correction. The cycle closure point, cycle equivalent temperature, threshold temperature and separate rainflow counting, obligatory for the ETA, are not necessary for the DOA any more. Both approaches are equivalent for the second and subsequent runs of block loading if temperature is constant. However, for non-isothermal cases the DOA is within the worst- and the best-case scenarios of the ETA. The approaches are compared with the simple stress history and several thermo-mechanical fatigue (TMF) cycle types.     

Improved fatigue resistance of pseudo‐elastic NiTi alloys by thermo‐mechanical treatment

Shape memory alloys are susceptible to two types of fatigue in addition to classical fatigue: 1. Pseudo‐elastic fatigue leads to an increase in the slope of the pseudo‐elastic plateau and final loss of pseudo‐elasticity 2. A change in transformation temperature. Usually the martensite temperature is lowered with the number of cycles until final loss of transformability. This paper describes measures to improve stability against both types of fatigue. Such methods are simple ageing in order to achieve precipitation in austenite, and thermo‐mechanical treatments such as ausforming that introduce lattice defects into austenite, which transforms subsequently into martensite. Another method consists in the introduction of defects into martensite by marforming plus subsequent ageing. This ageing treatment has two purposes. It increases the classical strength and restores the β‐phase from residual martensite and consequently it recreates transformability. It is shown that the last mentioned method leads to the greatest effect in respect to stabilisation against both types of fatigue. An additional effect of these treatments is a transition of localised to more homogeneous strain. Its relevance for fatigue resistance is still under investigation.     

A cumulative damage model for fatigue life estimation of high‐strength steels in high‐cycle and very‐high‐cycle fatigue regimes

A cumulative fatigue damage model is presented to estimate fatigue life for high‐strength steels in high‐cycle and very‐high‐cycle fatigue regimes with fish‐eye mode failure, and a simple formula is obtained. The model takes into account the inclusion size, fine granular area (FGA) size, and tensile strength of materials. Then, the ‘equivalent crack growth rate’ of FGA is proposed. The model is used to estimate the fatigue life and equivalent crack growth rate for a bearing steel (GCr15) of present investigation and four high‐strength steels in the literature. The equivalent crack growth rate of FGA is calculated to be of the order of magnitude of 10^?14–10^?11 m/cycle. The estimated results accord well with the present experimental results and prior predictions and experimental results in the literature. Moreover, the effect of inclusion size on fatigue life is discussed. It is indicated that the inclusion size has an important influence on the fatigue life, and the effect is related to the relative size of inclusion for FGA. For the inclusion size close to the FGA size, the former has a substantial effect on the fatigue life. While for the relatively large value of FGA size to inclusion size, it has little effect on the fatigue life.     

A weight function-critical plane approach for low-cycle fatigue under variable amplitude multiaxial loading

Low‐cycle fatigue data of type 304 stainless steel obtained under axial‐torsional loading of variable amplitudes are analyzed using four multiaxial fatigue parameters: SWT, KBM, FS and LKN. Rainflow cycle counting and Morrow's plastic work interaction rule are used to calculate fatigue damage. The performance of a fatigue model is dependent on the fatigue parameter, the critical plane and the damage accumulation rule employed in the model. The conservatism and non‐conservatism of predicted lives are examined for some combinations of these variables. A new critical plane called the weight function‐critical plane is introduced for variable amplitude loading. This approach is found to improve the KBM‐based life predictions.     

A thermo‐damage strength model for ceramic material including an embedded crack with an arbitrarily shaped front

A fracture strength model applied at room temperature for the embedded crack was obtained based on the stress intensity factor model for embedded crack with an arbitrarily shaped front and Griffith fracture criterion. With further research on temperature effect on strength of ultra high temperature ceramics (UHTCs), a thermo‐damage strength model including the effects of temperature and crack shape was applied to each temperature phase. The fracture strengths were studied and analyzed. The conclusions were compared with the results obtained using the finite element software ABAQUS. This study will provide a theoretical basis and guidance on the design and preparation of the UHTCs.     

A rapid path‐length searching procedure for multi‐axial fatigue cycle counting

In this paper, a series of advanced searching algorithms have been examined and implemented for accelerating multi‐axial fatigue cycle counting efforts when dealing with large time histories. In a computerized calculation of the path‐length dependent cycle counting method, most of the central processor unit's (CPU) time is spent on searching for the maximum range or distance in a stress or strain space. A brute‐force search is the simplest to implement, and will always find a solution if it exists. However, its cost, in many practical problems, tends to grow exponentially as the size of the loading spectrum increases with a search time measured in the order of O(n²), where n is the number of spectrum data points. In contrast, a form of Andrew's monotone chain algorithm, as demonstrated in this paper, can remarkably reduce the solution time to the order of O(n log n). The effectiveness of the new path‐length searching procedure is demonstrated by a series of worked examples with a varying degree of non‐proportionality in multi‐axial loading history.     

High‐temperature low cycle fatigue damage assessment in near alpha IMI‐834 titanium alloy

In the present work, evolution of damage under high‐temperature (823 K) low cycle fatigue loading condition in near α IMI‐834 titanium alloy has been studied. The in situ damage has been experimentally measured during cyclic deformation using the alternating current potential drop (ACPD) technique. The measured damage curve has been compared with the damage curves calculated through mechanical variables such as cyclic modulus and stress amplitude. The ACPD damage curve has been found most sensitive towards high‐temperature low cycle fatigue damage evolution.     

Multiaxial fatigue life prediction method based on path‐dependent cycle counting under tension/torsion random loading

A path‐dependent cycle counting method is proposed by applying the distance formula between two points on the tension‐shear equivalent strain plane for the identified half‐cycles first. The Shang–Wang multiaxial fatigue damage model for an identified half‐cycle and Miner's linear accumulation damage rule are used to calculate cumulative fatigue damage. Therefore, a multiaxial fatigue life prediction procedure is presented to predict conveniently fatigue life under a given tension and torsion random loading time history. The proposed method is evaluated by experimental data from tests on cylindrical thin‐walled tubes specimens of En15R steel subjected to combined tension/torsion random loading, and the prediction results of the proposed method are compared with those of the Wang–Brown method. The results showed that both methods provided satisfactory prediction.     

Low‐cycle fatigue/high‐cycle fatigue interactions in notched Ti‐6Al‐4V*

Combined low‐cycle fatigue/high‐cycle fatigue (LCF/HCF) loadings were investigated for smooth and circumferentially V‐notched cylindrical Ti–6Al–4V fatigue specimens. Smooth specimens were first cycled under LCF loading conditions for a fraction of the previously established fatigue life. The HCF 10⁷ cycle fatigue limit stress after LCF cycling was established using a step loading technique. Specimens with two notch sizes, both having elastic stress concentration factors of K_t = 2.7, were cycled under LCF loading conditions at a nominal stress ratio of R = 0.1. The subsequent 10⁶ cycle HCF fatigue limit stress at both R = 0.1 and 0.8 was determined. The combined loading LCF/HCF fatigue limit stresses for all specimens were compared to the baseline HCF fatigue limit stresses. After LCF cycling and prior to HCF cycling, the notched specimens were heat tinted, and final fracture surfaces examined for cracks formed during the initial LCF loading. Fatigue test results indicate that the LCF loading, applied for 75% of total LCF life for the smooth specimens and 25% for the notched specimens, resulted in only small reductions in the subsequent HCF fatigue limit stress. Under certain loading conditions, plasticity‐induced stress redistribution at the notch root during LCF cycling appears responsible for an observed increase in HCF fatigue limit stress, in terms of net section stress.     

An improved multiaxial high‐cycle fatigue criterion based on critical plane approach

Several groups of fatigue damage parameters are discussed and then an improved multiaxial high‐cycle fatigue criterion based on critical plane defined by the plane of maximum shear stress range is presented in this paper. A compromising solution to consider the mean normal stress acting on the critical plane is also proposed. The new fatigue criterion extends the range of metallic materials which is valid for the ratio 1.25 < f_?1/t_?1 < 2. The predictions based on the presented model show a good agreement with test data.     

Predicting damage and failure under low cycle fatigue in a 9Cr steel

Experimental data have been generated and finite element models developed to examine the low cycle fatigue (LCF) life of a 9Cr (FB2) steel. A novel approach, employing a local ductile damage initiation and failure model, using the hysteresis total stress–strain energy concept combined with element removal, has been employed to predict the failure in the experimental tests. The 9Cr steel was found to exhibit both cyclic softening and nonlinear kinematic hardening behaviour. The finite element analysis of the material's cyclic loading was based on a nonlinear kinematic hardening criterion using the Chaboche constitutive equations. The models’ parameters were calibrated using the experimental test data available. The cyclic softening model in conjunction with the progressive damage evolution model successfully predicted the deformation behaviour and failure times of the experimental tests for the 9Cr steels performed.     

Simulation based microstructural optimization of thermo‐mechanically treated steel components

A simplified approach for the simulation based estimation of the phase distribution in a thermo‐mechanically treated steel component is presented. A key aspect of the approach is the time‐temperature relation for each volume element. Based on a forming simulation with a commercial tool the numerically calculated temperature evolution in the component is analyzed with an in‐house code. The code allows estimating the local phase distribution after the forming process with the help of the continuous‐cooling‐diagram of the material used. A first validation fits well with the existing phase distribution in the component, even though the phase transition in the component is critical in terms of time, deformation and local chemical composition of the material used.     

Multi‐scale experimental study on fatigue damage behaviour and its effect on structural nonlinear response

Experimental analyses on the structural response caused by local fatigue damage accumulation in welded details are accomplished to perform failure process and nonlinear effect analysis at different structural levels. The experiment is carried out by using welded compact tension (CT) specimens and a scaled truss specimen, and all of them have a notch at the weld toe to facilitate damage initiation. Cyclic loads are applied to those specimens to generate accumulative fatigue damage, respectively. The process of fatigue accumulation including initiation and propagation of fatigue cracks in the welded detail and resultant structural responses of CT specimens and the truss are measured with integration of multiple testing techniques. Multi‐scale experimental results show that microscopic‐/mesoscopic‐concentrated strain and extension of plastic zone in the vicinity of notch tip are both affected significantly by the fatigue damage accumulation and present appreciable nonlinear behaviour; however, the macroscopic response such as the frequency and stiffness parameters of the welded truss specimen are less sensitive to the low‐level fatigue damage. It is concluded that the fatigue failure of the welded truss is a multi‐scale progressive process due to fatigue damage trans‐scale evolving, in which the local meso‐damage firstly affects local strain of plastic zone in the vicinity of the notch tip, and then fatigue damage evolving from meso‐ to macro‐scale affects nonlinear responses of the damaged components; lastly, the fatigue failure could be expected as the results of the propagation of macroscopic fatigue cracks.     

An analysis of thermal gradient impact in thermal–mechanical fatigue testing

Thermal–mechanical fatigue (TMF) testing is a good method to decrease the number of isothermal tests for non‐isothermal behaviour laws identification. Based on experimental results of the TMF Standard European Working Group, this study aims to investigate the impact of thermal gradients on mechanical heterogeneity within the gage length specimen. The quality of the TMF test is examined by an energy criterion related to error bounds for nonlinear behaviour. A sensitivity analysis is then made for a given behaviour law identified on a TMF test to answer to the above question. Moreover the geometric instability phenomenon, already noticed by Sheffler and Coffin, is modelled herein.     

Interfacial damage in fibre‐reinforced composites subjected to tension fatigue loading

ABSTRACT The interfacial behaviour of fibre‐reinforced composites subjected to tension fatigue loading is studied based on the shear‐lag model. The governing equations of this problem are obtained and solved. In order to describe the interfacial debonding, the Paris fatigue crack growth formula as well as a modified degradation model for the coefficient of friction is adopted. Finally some important values related to interfacial debonding are obtained. In the present investigation, Poisson's contraction is considered.     

Three‐dimensional thermal response and thermo‐mechanical fatigue analysis for a large LCD TV frame mould in steam‐assisted rapid heat cycle moulding

Rapid heat cycle moulding (RHCM) is a newly developed moulding technique to improve the surface appearance of plastic parts and eliminate the polluting secondary operations such as primers and painting. In steam‐assisted RHCM, the mould surface temperature should be thermally cycled by alternatively cycling the high temperature steam and cooling water in the heating/cooling channels of the mould. The mould design is of great importance for RHCM because it not only has a great effect on the heating/cooling efficiency and hence the productivity but also directly affects the mould surface temperature uniformity and accordingly the final part quality. Furthermore, the service life of the RHCM mould with steam heating is also very much dependent on the mould structure or the layout of the heating/cooling channels as the fatigue crack is likely to occur at the wall of the heating/cooling channels under combined thermal cycling and mechanical loading. In this study, an RHCM mould for a type of 52‐inch LCD TV frame was designed. A three‐dimensional (3D) transient thermal analysis was performed to determine the thermal response efficiency of the designed RHCM mould cavity and investigate the factors affecting the heating efficiency. Then, by using the results obtained from the heat transfer simulation, the thermal‐structure coupling analysis comprehensively considering the cavity pressure and clamp force was conducted to analyse the stress distribution in the mould cavity, which is helpful to find the weak position in the mould cavity. We found that the spots where the maximum stresses occur are similar to the region where fatigue cracks come into being in the actual RHCM mould. Based on the simulation results, the mechanism of the cavity cracks formation on the cavity surface was proposed. Finally, the fatigue analysis was conducted to predict the fatigue life of the RHCM mould. The analysis results show that the regions at the top edges of the heating/cooling channels have the lowest fatigue life and safety factor. The discrepancy between the available life predicted by simulation and the actual service life of the RHCM mould is also discussed.     

Low‐cycle fatigue life behaviour of BS 460B and BS B500B steel reinforcing bars

This paper investigates the low‐cycle fatigue resistance of BS 460B and BS B500B steel reinforcing bars and proposes models for predicting their fatigue life based on plastic‐strain (?_ap) and total‐strain (?_a) amplitudes. Constant‐amplitude, strain‐controlled low‐cycle fatigue tests were carried out on these bars under cyclic load with a frequency of 0.05 Hz. The maximum applied axial strain amplitude (?_s,max) ranges from 3 to 10% with zero and non‐zero mean strains. The strain ratios (R = ?_s,min/?_s,max) used are R =?1, ?0.5 and 0. Hysteresis loops were recorded and plastic and total strain amplitudes were related to the number of reversals (2N_f) to fatigue failure and models for predicting the number of reversals to fatigue failure were proposed. It is concluded that the predicted fatigue life of these bars is very accurate when compared with the measured experimental fatigue life results for wide range of values of strain ratios. It is also observed that based on plastic‐strain amplitude, BS B500B consistently has a longer life (higher number of cycles to failure) than those of BS 460B for all R values; however, at low plastic‐strain amplitudes they tend to behave similarly, irrespective of R value. Other observations and conclusions were also drawn.