Showing papers in "Fatigue & Fracture of Engineering Materials & Structures in 1994"

A re-evaluation of the life to rupture of ductile metals by cyclic plastic strain

Abstract: — Experiments have been performed on specimens subjected to strain cycles similar to those experienced by sub-surface elements of material in rolling/sliding contact. It has been observed that if the strain cycle is closed then failure takes place by low cycle fatigue and the Coffin-Manson relationship may be used to predict the number of cycles to failure. If however, the strain cycle is open, so that the material accumulates unidirectional plastic strain (the situation known as “ratchetting”) a different type of failure, which is termed ratchetting failure may occur. It occurs when the total accumulated plastic strain reaches a critical value which is comparable with the strain to failure in a monotonic tension test. The number of cycles to failure under these circumstances may be estimated by dividing this critical strain by the ratchetting strain per cycle. It is suggested that low cycle fatigue and ratchetting are independent and competitive mechanisms so that failure occurs by whichever of them corresponds to a shorter life. The results of both uniaxial and biaxial tests reported in the literature have been re-evaluated and these, together with new data on biaxial tests on copper, found to be consistent with this hypothesis.

A shear stress based critical‐plane criterion of multiaxial fatigue failure for design and life prediction

Abstract: — The use of a previously presented general criterion of failure for high cycle multiaxial fatigue, τa/tA,B+σn.max/2σT= 1, is extended to cases where the shear and normal stress on the critical plane are non-proportional and also to give life predictions in the range of 104 to 106 cycles. The criterion takes account of whether case A cracks, growing along the surface, or case B cracks, growing in from the surface, occur.

Finite element analysis of specimen geometry effects on fatigue crack closure

Abstract: Elastic-plastic finite element analysis is used to study fatigue crack closure at three different crack length to width ratios for three plane stress specimen geometries: center-cracked plate, single-edge-cracked plate (tension), and single-edge-cracked plate (bend). The maximum stress to flow stress ratio, S max /σ 0 , which successfully describes closure results in many center-cracked plate configurations, does not correlate the effect of different geometries on the normalized opening stress, S open /S max . Crack opening stresses for different geometries and crack lengths are successfully correlated by a normalized stress intensity parameter, K max /K 0 , where K 0 = σ 0 √πa. The quality of the correlation is very high at small K max /K 0 , and gradually deteriorates as K max /K 0 increases beyond the small-scale yielding regime

A fatigue design parameter for spot welds

Abstract: — Mode I and mode II stress intensity factors for two half-spaces connected by a circular patch were used to develop a mixed-mode stress intensity factor (termed the stress index Ki) which can correlate the fatigue life of all spot weld geometries, base metals, and specimen dimensions. Empirical corrections were applied to Broek's equivalent stress intensity factor (Klq) to account for the weldment geometry (sheet thickness, nugget diameter, specimen width) and the effect of mean stress. The final expression, (Ki), is a measure of the notch-root stress field in the location where crack initiation and early crack growth occur. The stress index (ki) should be a useful tool for spot-weld fatigue design.

Fatigue predictions and scatter

Abstract: — Different aspects of fatigue design problems are indicated and uncertainties are listed. Scatter as observed in many laboratory studies is analyzed. It is argued that scatter of crack initiation and crack growth are different issues. Various sources of scatter are discussed and illustrative examples are presented. Comments are given on statistical distribution functions, scatter under Variable-Amplitude loading, and scatter in service. The discussion touches upon the experience and meaning of scatter of laboratory test series related to practical problems.

Fatigue crack growth in residual stress fields : experimental results and modelling

Abstract: — The paper discusses the results of fatigue crack growth rate tests conducted in the presence of residual stresses. Three different residual stress distributions, obtained by laser welds, were employed in order to characterize the crack propagation behaviour under different conditions, producing either an increase or a reduction of the stress intensity factor due to external loads. Test results are analysed by means of a non-linear numerical model (based on the weight function method) and a knowledge of the fatigue crack growth properties of the base material, free from residual stresses. The results of the analysis are discussed with reference to experimental trends, in order to clarify the predictive capabilities of the method and aspects needing further investigation.

A review of modelling small-crack behavior and fatigue-life predictions for aluminum alloys

Abstract: The small-crack effect, where small fatigue cracks grow faster and at lower stress-intensity factors than large cracks, has been found to be significant for many materials and loading conditions. In this paper, plasticity effects and crack-closure modelling of small fatigue cracks are reviewed. A crack-closure model with a cyclic-plastic zone-corrected effective stress-intensity factor range (related to the cyclic J-integral) and microstructural data on crack-initiation sites were used to calculate small-crack growth rates and fatigue lives for unnotched and notched specimens made of two aluminum alloys. The crack-closure transient from the plastic wake was shown to be the dominant cause of the small-crack effect and plasticity effects on the cyclic-plastic zone-corrected stress-intensity factor range were negligible except at extremely high stress levels. Small-crack growth rates and fatigue lives under both constant-amplitude and spectrum loading from tests and analyses agreed well.

Cyclic plasticity in type 316l austenitic stainless steel

Abstract: — The cyclic stress-strain response of two heats of austenitic stainless steel 3 16L was experimentally studied under a wide range of cyclic plastic strain amplitudes. Three domains on the cyclic stress- strain curve were found. In the middle domain the plateau behaviour corresponds to fatigue softening. The domain at low plastic strain amplitudes is characterized by stabilized behaviour and the domain of the highest plastic strain amplitudes by continuous hardening. Individual domains were correlated with observed dislocation structures. The existence of the plateau can be related to the localization of the cyclic strain into persistent slip bands. A Manson-Coffin plot of the material over a wide cyclic amplitude range is curved and can be approximated by a double logarithmic dependence.

A micro and macro approach to the energy dissipation rate model of stable ductile crack growth

Abstract: — The equations for the energy dissipation rate, D per unit area of crack growth, for plasticity and fracture combined, are presented for equilibrium crack extension in a real elastic-plastic material. These relationships are a necessary condition for stable growth. The term D is identical to G for lefm and to the rate at which work is done for the rigid-plastic limit. Crack growth is seen at both micro- and macro-levels as a two stage process of damage accumulation in a process zone followed by actual separation as a micro-instability at the crack tip. Some examples of the behaviour of ductile metals are cited in support at both micro- and macro-level. For the fully plastic case, D reduces strongly with growth. Relationships with conventional rising R-curves are stated for contained and uncontained yield.

The role of cavity growth mechanisms in determining creep-rupture under multiaxial stresses

Abstract: — The effect of stress state on the time and strain to failure has been considered in terms of currently accepted models of cavity growth. It is shown that the increasing contributions of compressive stress cause changes in cavity growth mechanisms which lead to increases in ductility. A tensile component of stress is necessary to provide the driving force for cavity growth by diffusion of vacancies and hence only strains in the presence of a tensile stress can lead to creep-dominated failure in creep-fatigue. Equivalent stress functions for isochronous stress rupture have been derived in terms of the cavity growth models and their corresponding relationships for calculating damage in terms of strain fractions developed. It is shown that it is difficult to discriminate between the various models on the basis of available experimental data. However, the analysis allows data to be assessed within the framework of physically based mechanisms and suggests methods which lead to conservative lower bound estimates of endurance. It is concluded that the shape of the isochronous creep rupture locus depends on the controlling process of cavity growth and that a detailed analysis of uniaxial creep ductility is necessary to obtain a complete description of the multiaxial behaviour. In many instances such an analysis will prove more valuable than simply performing creep tests over a limited range of stress states. Increasing contribution of principal stress to the failure process leads to a greater value for the equivalent stress in the presence of a compressive component compared with the von Mises equivalent value. However, the equivalent stress is reduced in the tensile quadrant of bi-axial stress. Hence the degree of conservatism arising from using the von Mises equivalent stress will vary with stress and may become slightly non-conservative. The relationship between equivalent stress functions for application in a time fraction assessment of creep and the calculation of creep damage by a strain fraction method has been demonstrated. Finally, guidance is given on how a limited data base of uniaxial rupture properties can be used to obtain a conservative estimate of behaviour under multiaxial loading.

The fatigue resistance of peened 7050‐t7451 aluminium alloy—repair and re‐treatment of a component surface

Abstract: — Metal and glass-bead peening treatments, widely used throughout the aircraft industry to enhance the fatigue performance of many steels and titanium alloys, are now being routinely applied to high-strength aluminium-alloy components. This paper describes the effects of peening on the fatigue life of 7050 aluminium alloy material, which is representative of alloys used for many components in modern military aircraft. Using simulated service loading, two proposed peening/re-peening procedures were evaluated and compared with both the original peened surface and a simple hand-polished surface. The results show that optimisation of peening parameters to reduce surface damage can provide a substantial improvement in fatigue life over both the original peening treatment and the polished surface treatment, however, poor control of peening procedures, or unnecessary “overpeening” can lead to a relatively poor fatigue life. For re-peened surfaces, a procedure incorporating a polishing step, designed to repair any damage from the severe peening applied initially, gave the best fatigue performance. Results are discussed in relation to the stability of the residual surface stresses under fatigue loading, the surface roughness, and the number and types of defects introduced by the peening treatments.

Statistical investigation of the behaviour of small cracks and fatigue life in carbon steels with different ferrite grain sizes

Abstract: — In order to study the relation between the scatter characteristics of small crack growth behaviour and fatigue life, rotatory bending fatigue tests of smooth specimens were carried out using 0.21% carbon steels of different ferrite grain sizes. Fifteen to eighteen specimens were fatigued at each stress amplitude, and the initiation and propagation behaviour of the cracks which led to the final fractures were examined for all the specimens. The physical basis of scatter in fatigue life was investigated, based on the successive observation of fatigue damage on the surface using the plastic replica technique, followed by an analysis of the data assuming a Weibull distribution. A statistical investigation of the physical basis of scatter in relation to the ferrite grain size was performed, i.e. the distributions for crack initiation life, crack propagation life, fatigue life and growth rate of small cracks. Finally, the fluctuation of crack growth rate was studied in relation to the application of a crack growth law for microstructurally small cracks.

Analyzing ductile fracture using dual dilational constitutive equations

Abstract: — By adopting a suggestion made by Thomason, a new failure criterion for the Gurson-Tvergaard model has been recently introduced by the authors. In this study, a method based on the Gurson-Tvergaard constitutive model and the new failure criterion is applied to the analysis of ductile fracture. The main features of the method are that the material failure is a natural process of the development of Thomason's dual dilational constitutive responses, and the void volume fraction corresponding to the failure by void coalescence is not necessarily a material constant and is not needed to be fitted beforehand. Furthermore, void nucleation parameter(s) can be numerically fitted from experimental tension results. This method has been implemented into the ABAQUS finite element program via a user material subroutine and is applied to the prediction of tension problems conducted by the authors. In the analyses, two strain-controlled void nucleation models have been studied and compared. The void nucleation parameters corresponding to the two models have been calibrated. The crack initiation of both smooth and notched axisymmetric tensile specimens are well predicted by the method. Finally, several critical issues in the analysis of ductile fracture are discussed.

Application of energy dissipation rate arguments to stable crack growth

Abstract: — Energy dissipation rate, D, and crack tip opening angle (CTOA) have been related for large amounts of ductile crack growth in a fully plastic two-dimensional model of real elastic plastic material. Several J-type rising R-curves have been constructed and related, some based on the cumulative energy dissipated and some as a characterising term that relates closely to the far-field J contour value. These two meanings co-exist but the relationship is geometry dependent. For deep notch bend (DNB) cases the non-dimensional group Lα/r* (where L is normalised load, α is CTOA and r* defines the position of the instantaneous centre of rotation) governs the value of dJ. Certain DNB cases where R-curves vary with size are resolved by this group rather than by CTOA itself whereas for centre-cracked tension there is a higher value of CTOA than for DNB.

Fatigue life prediction of heat-treated carbon steels and low alloy steels based on a small crack growth law

Abstract: — Since heat-treated high strength steels are often used as materials for machines and structures that operate under severe service conditions, it is important to evaluate their fatigue life. Hence the growth law of a small fatigue crack must be known in order to estimate the fatigue life of machines and structures since the life of such members is controlled mainly by the behaviour of a small crack. The growth rate of a small crack can not be predicted usually by linear elastic fracture mechanics, but can be determined uniquely by the term σnal, where σa is stress amplitude, l is crack length and n is a material constant. In this paper, the small-crack growth law of heat-treated carbon steels and low alloy steels was studied. An effective and convenient method based on a small-crack growth law, dl/dN=C3(σa/σa)nl is proposed, where σu is the ultimate tensile strength, for predicting the small crack propagation life of heat- treated steels with different tensile strength levels, together with a method for determining the fatigue life of plain members.

Fatigue crack growth in nickel‐based superalloys at 500‐700°c. ii: direct‐aged alloy 718

Abstract: — The effects of cyclic frequency, hold time, and stress-intensity factor range (ΔK) on rates of fatigue crack growth in air at 500°C and 700°C have been studied for the direct-aged version of the nickel-based superalloy 718. The main effects were similar to those observed for Waspaloy (Part I), namely: (i) small effects of cyclic frequency and hold time at 500°C, (ii) higher rates of crack growth at lower cyclic frequencies at high ΔK at 700°C, and (iii) lower rates of crack growth at low ΔK (and higher ΔK thresholds) for longer hold times at 700°C. For DA 718, there was no increase in crack growth rates with increasing hold times (0–60 s) at high ΔK at 700°C (unlike the large increases reported for standard processed Alloy 718). Metallographic and fractographic observations showed that crack growth was predominantly transgranular at 500°C, and predominantly intergranular at 700°C except at 2 Hz at high ΔK. The precise intergranular crack path, extent of branching, and fracture-surface appearance depended on ΔK, wave-form and cycle-period. The mechanisms responsible for the observed effects, and possible explanations for the different behaviour of DA 718 and standard processed Alloy 718, are discussed.

Theoretical and experimental studies of fretting‐initiated fatigue failure of aeroengine compressor discs

Abstract: — A finite element analysis and fatigue crack growth studies are made of dovetail joints in aeroengine compressor discs. Three aspects are examined: the first deals with the finite element stress analysis of the critical geometrical features and interface conditions of different dovetail configurations, thus enabling an assessment to be made of the critically loaded regions in the disc. The second deals with the prediction of the direction of potential fatigue cracks, which were allowed to initiate in the finite element model at the regions where fretting damage is most likely to occur, using an incremental crack tracking criterion. The third is concerned with the verification of the above modelling techniques with fatigue tests on a uniaxial back-to-back arrangement, which attempts to simulate the stress fields of a rotating disc.

Fatigue crack growth in nickel-based superalloys at 500-700°c. i: waspaloy

Abstract: — The effects of cyclic frequency, hold time, and stress-intensity-factor range (δK) on rates of fatigue crack growth in air at 500-700°C have been studied for Waspaloy—a nickel-based superalloy used for gas-turbine engine discs. The main effects observed were: (i) higher rates of crack growth for lower cyclic frequencies at high δK at 600 and 700°C. and (ii) lower rates of crack growth at low δK (and higher δK thresholds) for longer hold times at 700°C, compared with those at a baseline frequency of 2 Hz. Metallographic and fractographic observations suggested that the effects of cyclic frequency and hold time could be rationalised in terms of the competing effects of enhancement of cracking due to creep and inhibition of cracking caused by oxide-induced crack closure, fracture-surface-roughness induced crack closure, and crack-branching/deflection. Possible mechanisms for promoting intergranular and transgranular cracking at low cyclic frequencies or long hold times are discussed.

A study of the internal parameters of ductile damage theory

Abstract: — In this paper the Rousselier ductile damage model is used to simulate the softening behaviour of notched bars and crack growth in a pre-cracked specimen of an A508 pressure vessel steel. The effect of the internal parameters needed to represent the damage on the calculated results is studied. The interactions between these parameters and their effects on the calibration process are discussed. The effect of the cell size on the values of the damage parameters obtained during calibration and on the response of the specimens is briefly reviewed.

Fatigue crack growth in ductile materials under cyclic compressive loading

Abstract: — Mode I fatigue crack growth has been studied in notched specimens of 7017-T651 aluminium alloy subjected to fully compressive cyclic loads. The specimens were first subjected to a deliberate compressive preload which causes plastic deformation at the notch tip. On unloading, this region developed a residual tensile stress field and on subsequent compressive cyclic loading in laboratory air, a fatigue crack was nucleated at the notch and grew at a diminishing rate until it stopped. The final crack length increased with an increase in the value of the initial compressive preload and with an increase in the negative value of the applied cyclic mean load. To gain a better understanding of crack growth in residual stress fields, the magnitude and extent of residual stress induced from compressive preloads have been analysed. This was achieved when extending the notch by cutting while recording the change in the back face strain. From residual strain models it was found that the fatigue crack growth was confined to a region of tensile cyclic stress within the residual stress field. The effective stress intensity range was investigated at selected mean loads and amplitudes, for correlating purposes, using both the compliance technique and by invoking the crack growth rate behaviour of the alloy. Finally, a brief discussion of the fracture morphology of cracks subjected to cyclic compression is presented.

The relation between crack blunting and fatigue crack growth rates

Abstract: — Previous work has shown that the inclusion of the strain energy released by crack blunting leads to an energy minimum for fatigue crack growth that can be used to predict stage II fatigue crack growth. The present work assumes a polynomial relation between crack blunting and crack extension to derive an expression for the rate of fatigue crack growth that is dependent upon only the applied ΔK, E, σys, Kc, and the exponent p in the relation between crack blunting and crack extension. This expression is thought to be generally valid since it accurately predicts fatigue crack growth rates for a wide variety of titanium, nickel, aluminium and steel alloys. A unique characteristic of the model is its ability (for long crack, slow crack growth) to account for the different slope for different materials in the Paris Law region of the da/dN vs. δK curve. The model specifically shows that this slope, m, is dependent solely upon the exponent, p, in the relation between crack blunting and crack extension.

The measurement of surface breaking cracks by the electrical systems acpd/acfm

Abstract: — The successful implementation of a fracture mechanics approach to the in-service structural integrity assessment of welded and machined components requires an accurate and reliable NDT method for detecting and sizing surface breaking cracks. This paper discusses and compares the crack depth sizing abilities of two theoretically-based NDT techniques: alternating current potential difference (ACPD) and alternating current field measurement (ACFM). Surface fatigue cracks of high and low aspect ratio are used in the investigation. It is demonstrated that ACPD is capable of accurately sizing long shallow cracks and that ACFM provides accurate crack depth predictions for small deep cracks.

Microstructural and environmental effects on fatigue crack propagation in duplex stainless steels

Abstract: Fatigue crack initiation and propagation in duplex stainless steels are strongly affected by microstructure in both inert and aggressive environments. Fatigue crack growth rates in wrought Zeron 100 duplex stainless steel in air were found to vary with orientation depending on the frequency of crack tip retardation at ferrite/austenite grain boundaries. Fatigue crack propagation rates in 3.5% NaCl solution and high purity water are increased by hydrogen assisted transgranular cyclic cleavage of the ferrite. The corrosion fatigue results are interpreted using a model for the cyclic cleavage mechanism.

Fracture and life prediction under thermal-mechanical strain cycling

Abstract: — Thermal-mechanical cyclic strain tests were carried out under in-phase and out-of-phase conditions on a ferritic 1 CrMoV steel in the temperature range 315 to 565°C and two different batches of a 316 stainless steel in the temperature range 400 to 625°C. The results were compared with isothermal data. In general, lives for in-phase thermal-mechanical tests were lower than for equivalent isothermal tests. This was substantiated by metallographic examination which indicated greater intergranular damage for the in-phase specimens. The addition of a tensile dwell to the in-phase condition caused even greater differences. Three life prediction methods were used: the ductility exhaustion and a modified strain range partitioning approach gave reasonable estimates of life, whilst the linear life fraction method produced poor prediction.

Short fatigue crack path determinants in polycrystalline Ni-base superalloys

Abstract: Fifty seven short fatigue cracks in the Ni-base superalloy AP1 have been examined, to ascertain how the paths taken by growing fatigue cracks are determined. The observations were made on the surface of a smooth specimen, and on the exposed fracture surfaces. Three dimensional reconstructions of the vulnerable microstructures in the vicinity of the cracks were produced. Initiation occurred in mode II, with the lines of intersection of the initiation sites with the specimen top surface orientated at approximately 45° to the tensile axis. These initiation sites developed in slip bands which crossed a large grain and at least one other grain via a grain boundary with a low angle of misorientation. 'River markings' on one of the initiation facets, indicated that the crack first opened from the top centre of the initiation grain. Subsequent to initiation, the growth paths of these cracks are related to the misorientations of the grains and the progress of the crack front.

A frequency response method for calculating stress intensity factors due to thermal striping loads

Abstract: — When incompletely mixed hot and cold fluid streams pass adjacent to the surface of a component or a structure, they can cause thermal fatigue damage. An analytical model, based on linear elastic fracture mechanics and the frequency response method, is presented for the assessment of thermal fatigue damage. Various shapes of surface temperature-time histories, represented by their power spectral densities, are examined. The model is compared with an alternative method based on the impulse response method and good agreement is found. This kind of thermal fatigue is of particular concern in various types of nuclear reactors and rapid shut-downs of hot plant. The model proposed is intended as an engineering design tool and has been developed as a computer code known as “TBL”.

Use of the distributed dislocations method to determine the t-stress

Abstract: — This paper demonstrates a method to determine the elastic T-stress for a semi-infinite half-plane containing a surface-breaking crack which is loaded by an arbitrarily distributed far-field tension. The method consists of representing the crack by a continuous distribution of edge dislocations and forming singular integral equations to determine the equilibrium dislocation distributions. By numerically solving the integral equations, stress intensity factors and T-stresses are obtained for the example case of a crack which is normal and inclined to the free-surface of a half-plane and loaded by a uniform far-field tension.

Effect of relative slip amplitude on fretting fatigue of high strength steel

Abstract: — The effect of relative slip amplitude on fretting fatigue in high strength steel was studied at various contact pressures using fretting pads of various lengths. Under a given contact pressure, the fretting fatigue life showed a minimum at a certain relative slip amplitude. Under a fixed pad length, the life also showed a minimum at a certain contact pressure. A map of fretting fatigue life versus contact pressure and relative slip amplitude was obtained using the data of this study. The map indicated that both the phenomena which showed a minimum life in relation to slip dependence and contact pressure dependence were the same, as were the underlying mechanisms. The minimum life was interpreted in terms of local stress concentration at the fretted area.

Fretting patterns in a conductor–clamp contact zone

Abstract: — Cyclic bending fatigue tests have been performed on a typical electrical conductor held by a suspension clamp. Surface damage of the aluminium wire has been induced during short duration tests. Various degradation zones have been characterized between wire layers and the clamp. Metallographic examination has shown that two process zones are critical with respect to fretting crack nucleation. Fatigue tests at different bending amplitudes have shown that the wire breaks in these critical zones.

An engineering assessment of fatigue crack growth of irregularly oriented multiple cracks

Abstract: — Knowledge of the behaviour of interacting and irregularly oriented multiple cracks is very limited. The recharacterisation rules for such cracks are usually empirical. In order to provide more reasonable rules for an engineering assessment of fatigue growth of irregularly oriented multiple cracks, this paper first studies the mechanics of fatigue growth of two-dimensional non-coplanar cracks. Uniaxial and biaxial fatigue testing on specimens with various multiple cracks are then carried out. Possible errors in the assessment of the cracks using the current rules are discussed. An improved procedure for the fatigue life assessment is developed.