MECHANISMS AND FATIGUE PERFORMANCE OF TWO STEELS IN CYCLIC TORSION WITH AXIAL STATIC TENSION/COMPRESSION

Abstract— Fatigue tests conducted under fully reversed cyclic torsion, with and without superimposed axial static tension/compression loads, were carried out using hour-glass smooth specimens in laboratory air. A high strength spring steel and a 316L stainless steel, were employed to evaluate the effects of mean stress on fatigue performance. Experimental test results show that a biaxial tensile/compressive mean stress had no influence on the cyclic stress-strain response in both materials. However a biaxial tensile mean stress was found to be detrimental to fatigue life of the high strength spring steel but had no effect on the total fatigue life of 316L stainless steel. A compressive mean stress was found to be beneficial to the life of both steels. The fatigue behaviour of the two materials was investigated by experimental observations and the application of theoretical analyses of short crack growth behaviour. Based upon the analysis of surface acetate replicas it has been found that fatigue crack growth is material/stress-state dependent. A biaxial tensile static stress promoted a change in the direction of the Stage I (mode II) crack from the longitudinal direction to a plane normal to the specimen axis in the high strength steel but not in the stainless steel. Consequently a different growth behaviour of Stage I (mode II) cracks was observed for the two materials. The effect of a biaxial mean stress on fatigue crack growth behaviour of the two materials is analysed and described in some detail.     

EFFECT OF NON-PROPORTIONAL OVERLOADING ON FATIGUE LIFE

Abstract— The effect of non-proportional overloading on both low cycle and high cycle fatigue life has been studied. Low cycle multiaxial fatigue tests were performed on EN 15R (a low alloy steel) using sequential loading blocks which comprised uniaxial "ordinary" cycles and torsion "overload" cycles, and vice versa. In high cycle fatigue, the behaviour of mode I crack growth in a medium carbon steel subjected to mixed (I and II) mode overloading was examined.
Under tension-torsion sequential overloading, crack growth behaviour shows an earlier transition from Stage I to Stage II with a pronounced reduction in accumulated fatigue life. Tensile overloading on torsion cycles was found to be more damaging compared to torsion overloading on repeated tensile cycles. The crack-load interaction in sequential overloading and its influence on crack growth and fatigue life is discussed. In low strain fatigue, Stage II crack growth retardation closely relates to the overload plastic zone size, crack tip blunting and crack surface shielding. Mixed mode overloading is shown to have a significant effect only if the mode I component of overloading is large enough to keep the crack open. Under both low cycle and high cycle fatigue conditions non-proportional overloading is shown to be more damaging than proportional overloading.     

CRACK INITIATION MECHANISMS IN TORSIONAL FATIGUE

Abstract— The development of fatigue damage in Co45Ni specimens during push—pull and reversed torsion tests, performed inside a scanning electron microscope, was observed and the different stress states compared. It appeared that transgranular crack initiation and development is delayed and intergranular crack initiation promoted under torsional loading. This was explained in terms of reduced surface distortion at the emergence of persistent slip bands (PSBs) and smaller compatibility stresses at the PSB-matrix interfaces. The influence of the mechanical strength of grain boundaries on the difference between tensile and torsional fatigue lives is discussed.     

A FIRST STAGE IN THE DEVELOPMENT OF MICROMECHANICAL SIMULATIONS OF THE CRYSTALLOGRAPHIC PROPAGATION OF FATIGUE CRACKS UNDER MULTIAXIAL LOADING

Simulations of the nucleation of dislocations, glide and annihilation ahead of a fatigue crack growing along a localized slip band (a 'long' Stage I crack or a Stage II crack with a K value close to the threshold) are performed for the case of push–pull or reversed torsion loadings, ignoring, in a first approach, the effect of grain boundaries. The crack growth rates are deduced from the dislocation flux at the crack tip. An influence of the normal stress on the friction between the crack flanks as well as on the condition for dislocation emission is introduced. A slower Stage I growth rate is then predicted for reversed torsion, consistent with experimental data.     

Micromechanical simulations of microstructure-sensitive Stage I fatigue crack growth

Simulations of dislocation dynamics at the tip of a Stage I crack are performed, taking into account the influence of the normal stress on the friction of the crack flanks and on the condition for dislocation emission at the crack tip. The interactions of the emitted dislocations with microstructural obstacles are analysed. The repeated decelerations and sometimes arrests that characterize Stage I crack growth are properly described by the model, and the differences in Stage I kinetics observed in reversed torsion and push–pull are analysed in terms of crack tip–grain boundary interactions.     

Deformation behaviour,short crack growth and fatigue livesunder multiaxial nonproportional loading

Experimental results of a research project on short crack growth under multiaxial nonproportional loading are presented. Fatigue lives, crack growth curves and the deformation behaviour of hollow tube specimens and notched specimens were investigated under combined tension and torsion loading. The results served as basis for the development of a cyclic plasticity model [Döring R, Hoffmeyer J, Vormwald M, Seeger T. A plasticity model for calculating stress–strain sequences under multiaxial nonproportional cyclic loading. In: Comput Mater Sci. 28(3–4);2003:587–96; Döring R, Hoffmeyer J, Seeger T, Vormwald M. Constitutive modelling of nonproportional hardening, cyclic hardening and ratchetting. In: Proceedings of the seventh international conference on biaxial/multiaxial fatigue and fracture, DVM, Berlin; 2004. p. 291–6; Hoffmeyer J. Anrisslebensdauervorhersage bei mehrachsiger Beanspruchung auf Basis des Kurzrisskonzepts. PhD-Thesis, TU Darmstadt; 2004.] and a short crack model [Hoffmeyer J. Anrisslebensdauervorhersage bei mehrachsiger Beanspruchung auf Basis des Kurzrisskonzepts. PhD-Thesis, TU Darmstadt; 2004; Döring R, Hoffmeyer J, Seeger T, Vormwald M. Fatigue lifetime prediction based on a short crack growth model for multiaxial nonproportional loading. In: Proceedings of the seventh international conference on biaxial and multiaxial fatigue and fracture, DVM, Berlin; 2004. p. 253–8].Stress–strain paths including nonproportional hardening and experimental fatigue lives of the unnotched specimens under different loading cases are discussed and compared with calculations. Load-time-sequences were in-phase, 45° and 90° out-of-phase loading with constant and variable amplitudes, torsion without and with superimposed static normal stress, and strain paths like box, butterfly, diamond and cross path. For the notched specimens fatigue lives under 0° and 90° out-of-phase loading are compared with calculations based on finite element results and the short crack model. During some tests the initiation, growth and orientation of short cracks was studied using the plastic replica technique.     

Shear mode fatigue crack growth in 1050 aluminium

The shear mode crack growth mechanism in 1050 aluminium was investigated using pre‐cracked specimens. A small blind hole was drilled in the centre section of the specimens in order to predetermine the crack initiation position, and a push–pull fatigue test was used to make a pre‐crack. Crack propagation tests were carried out using both push–pull and cyclic torsion with a static axial load. With push–pull testing, the main crack grew by a mixed mode. It is thus apparent that shear deformation affects the fatigue crack growth in pure aluminium. In tests using cyclic torsion, the fatigue crack grew by a shear mode. The micro‐cracks initiated perpendicular and parallel to the main crack's growth direction during the cyclic torsion tests. However, the growth direction of the main crack was not changed by the coalescence of the main crack and the micro‐cracks. Shear mode crack growth tends to occur in aluminium. The crack growth behaviour is related to a material's slip systems. The number of slip planes in aluminium is smaller than that of steel and the friction stress during edge dislocation motion of aluminium is lower than many other materials. Correlation between the crack propagation rate and the stress intensity factor range was almost the same in both push–pull and cyclic torsion with tension in this study.     

Multiaxial fatigue life prediction for a natural rubber

This study deals with the fatigue crack initiation under multiaxial non-proportional loadings in a natural rubber. Push–pull, torsion and tension-compression with a superimposed static torsion fatigue test results are presented. A short presentation of some important features concerning short fatigue crack growth is given. Two fatigue crack criteria are proposed, the first one based on the first and second invariant of the Cauchy stress tensor, the second, based on the micromechanisms of crack initiation, consist of a critical plane approach under large strain conditions using a micro to macro approach. The second criterion was found to give the best results, by predicting the fatigue lifes, crack orientations and location, even in cases with internal crack initiation.     

SEMI-ELLIPTICAL FATIGUE CRACK GROWTH UNDER ROTATING OR REVERSED BENDING COMBINED WITH STEADY TORSION

Abstract— An analysis of the influence of steady torsion loading on fatigue crack growth rates under rotating or reversed bending is presented. Mixed-mode (I + III) tests were carried out on cylindrical specimens in DIN Ck45k steel and results are compared for two different testing machines: rotary bending and reversed bending obtained by cyclic Mode I (Δ K ₁) with or without superimposed static Mode III ( K _III) loading, simulating the real conditions on power rotor shafts where many failures occur. The growth and shape evolution of semi-elliptical surface cracks, starting from a chordal notch on the cylindrical specimen surface, was measured for several Mode III/ Mode I ratios. Results have shown that the steady Mode III loading superimposed on the cyclic mode I leads to a significant reduction in the crack growth rates. It is suggested that this retardation is related to an increase of plastic zone size near the cylindrical surface in association with the interlocking of rough fracture surfaces, friction and fretting debris, leading to a decrease of the ΔK effective at the crack tip profile due to the "crack closure effect". This work provides a contribution to a better understanding of crack growth rates under mixed-mode load conditions thereby allowing one to predict remaining lifetimes and to estimate the risks of pre-cracked rotor shafts.     

Behaviour of short cracks in alloy 800HT under biaxial fatigue

Biaxial in phase fatigue tests were carried out on thin walled tube specimens of alloy 800HT at ambient temperature. The loading modes included tension, torsion, and combined tension—torsion with a tensile/shear plastic strain range ratio Δ?p/Δγp = 3^1/2. The influence of effective strain amplitudes and biaxiality on the initial growth of fatigue cracks was investigated using the replica technique. The results indicated that the loading conditions strongly affected the growth rates of short cracks. In torsion the cracks grew significantly more slowly than under axial or biaxial loading. A mean tensile stress perpendicular to the shear crack promoted its growth and reduced the fatigue life. The growth of the cracks could be described by the ΔJ integral for axial and biaxial loading; the integration predicted the fatigue life under axial and biaxial loading correctly. However, significantly conservative lifetime predictions were obtained for pure torsional loading since ΔJ does not include crack closure and crack surface rubbing.

MST/3234     

Surface crack and cracks networks in biaxial fatigue

Semi-elliptical fatigue crack growth in 304 L stainless steel, under biaxial loading, was investigated. Compared to those of through-cracks under uniaxial loading, the growth rate of surface cracks is increased by a non-singular compressive stress and reduced by a tensile stress, when R = 0. Plasticity-induced crack closure under biaxial loading was investigated through 3D finite element simulations with node release. Roughness and phase-transformation-induced closure effects were also discussed. The interactions in two-directional crack networks under biaxial tension were investigated numerically. It appears that the presence of orthogonal cracks should not be ignored. The beneficial influence of interaction-induced mode-mixities was highlighted.     

THE EFFECT OF BIAXIAL STRESS STATE AND CHANGES OF STATE ON FATIGUE CRACK GROWTH BEHAVIOUR

Abstract— The effect of biaxial loading on the fatigue crack growth properties for a stainless steel has been examined. From comprehensive experiments, a significant biaxial stress effect on crack growth was found when the stress level was high and the crack was short. In this paper, the critical region where the effect of biaxial stress appears was clarified quantitatively. Moreover, the effect of changing the biaxial stress condition on fatigue crack growth behaviour was investigated. Significant acceleration of crack growth was observed just after the uniaxial or equibiaxial stress condition was changed to the shear stress condition. This acceleration seems to be due to the change of plastic zone shape at the crack tip.     

A NOTE ON MODELLING SHORT FATIGUE CRACK BEHAVIOUR

Based upon experimental short fatigue crack growth data and adopting the Brown–Hobson model, new crack growth equations have been derived in an attempt to describe more precisely short fatigue crack growth behaviour that separates the physically small crack regime from the long crack regime. An empirical model for physically small crack growth was developed by employing elastic–plastic fracture mechanics parameters.
By considering the proposed approach to short fatigue crack modelling, a new second 'microstructural' threshold condition has been established using only short fatigue crack growth data. In the case of fatigue in an aggressive environment it is suggested that three transition (threshold) conditions can be identified representing: (i) a stress-assisted pitting/pit-to-crack transition; (ii) a microstructurally short shear crack/physically small tensile crack transition; and (iii) a physically small crack/long crack transition.
A comparison of this approach with that of existing models has been made, and predictions of total fatigue lifetime using the model have been presented. A reasonable agreement has been observed between predicted and experimental crack growth rates.     

THE SIGNIFICANCE OF CRACK TIP DEFORMATION FOR SHORT AND LONG FATIGUE CRACKS

Abstract— The behaviour of physical short mode I cracks under constant amplitude cyclic loading was investigated both numerically and experimentally. A dynamic two-dimensional elastic-plastic finite element technique was utilised to simulate cyclic crack tip plastic deformation. Different idealisations were investigated. Both stationary and artificially advanced long and short cracks were analysed. A parameter which characterises the plastically deformed crack tip zone, the strain field generated within that zone and the opening and closure of the crack tip were considered. The growth of physically short mode I cracks under constant amplitude fully reversed fatigue loading was investigated experimentally using conventional cast steel EN-9 specimens. Based on a numerical analysis, a crack tip deformation parameter was devised to correlate fatigue crack propagation rates.     

The application of microstructural fracture mechanics to various metal surface states

The fatigue crack initiation period, previously thought to be a necessary precursor to fatigue crack propagation and eventual failure, is considered here to be a negligible phase in the fatigue failure of polycrystalline metals. Rather this period is considered to be the propagation of a defect of microstructural dimensions by a variety of processes. The significance of this alternative view is examined in relation to corrosion fatigue, models of short crack growth, different loading modes, and the enhancement of fatigue resistance by surface shot-peening treatments. In both inert and aggressive environments, the fatigue lifetime of plain steel specimens of various strengths and treatments is predominantly determined by the early propagation of short cracks of microstructural dimensions. Microstructural fracture mechanics, rather than continuum mechanics, can quantify both pit growth and Stage I shear crack growth behavior before the defect reaches the dominant microstructural barrier which controls the fatigue behavior of the material. The important processes that determine lifetime are those that are strongly dependent on the synergism between the aggressive environment and cyclic stresses; these are the pitting, Stage I and the Stage I-to-Stage II crack propagation processes. A model has been produced to quantify these three important stages of lifetime named above. Under torsion loading, where Stage I cracks prefer to propagate along the surface, an intermittent series of deceleration/acceleration events of crack growth occur across the first few grain boundaries until the defect is blocked in its further development by a major microstructural barrier. When this barrier is breached, the environmentally-assisted Stage I crack rapidly becomes a Stage II crack. Under push-pull loading, the Stage I environmentally-assisted crack can propagate faster into the bulk material and, as a consequence, the transition to a Stage II environmentally-assisted crack is rapid thereby eliminating the need for the intermittent process observed under torsion loading. With no environmentally-assisted fatigue processes (i.e., testing in air) reversed torsion and push-pull loading test data can best be correlated by a von Mises criterion. Corrosion fatigue lifetimes can best be correlated by a Rankine (tensile stress) criterion. Shot-peening enhances the corrosion fatigue resistance of polycrystalline metals by inducing residual compressive stresses in the surface and creating numerous and more rapidly formed microcracks. This is probably caused by the presence of variously oriented plastically deformed bands within the surface microstructure and “short crack-short crack” interactions both of which delay the progress of the dominant crack toward its final Stage II phase. The present work is published according to the kind permission of the Royal Society in London. In 1997, Prof. K. J. Miller celebrated his 65th birthday. Congratulations of the Editorial Board on this occasion are presented at the end of this issue. Research Institute for the Integrity of Structures, Sheffield University (SIRIUS), England. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 33, No. 1, pp. 9–32, January–February, 1997.     

Shear mode threshold for a small fatigue crack in a bearing steel

The fatigue behaviour of small, semi‐elliptical surface cracks in a bearing steel was investigated under cyclic shear‐mode loading in ambient air. Fully reversed torsion was combined with a static axial compressive stress to obtain a stable shear‐mode crack growth in the longitudinal direction of cylindrical specimens. Non‐propagating cracks less than 1 mm in size were obtained (i) by decreasing the stress amplitude in tests using notched specimens and (ii) by using smooth specimens in constant stress amplitude tests. The threshold stress intensity factor ranges, ΔK_IIth and ΔK_IIIth, were estimated from the shape and dimensions of non‐propagating cracks. Wear on the crack faces was inferred by debris and also by changes in microstructure in the wake of crack tip. These effects resulted in a significant increase in the threshold value. The threshold value decreased with a decrease in crack size. No significant difference was observed between the values of ΔK_IIth and ΔK_IIIth.     

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.     

Axial fatigue of a gas-nitrided quenched and tempered AISI 4140 steel: effect of nitriding depth

Fatigue testing under fully reversed axial loading (R=?1) and zero‐to‐tension axial loading (R= 0) was carried out on AISI 4140 gas‐nitrided smooth specimens. Three different treatment durations were investigated in order to assess the effect of nitriding depth on fatigue strength in high cycle fatigue. Complete specimens characterization, i.e., hardness and residual stresses profiles (including measurement of stabilized residual stresses) as well as metallographic and fractographic observations, was achieved to analyse fatigue behaviour. Fatigue of the nitrided steel is a competition between a surface crack growing in a compressive residual stress field and an internal crack or ‘fish‐eye’ crack growing in vacuum. Fatigue life increases with nitriding depth until surface cracking is slow enough for failure to occur from an internal crack. Unlike bending, in axial fatigue ‘fish‐eye’ cracks can initiate anywhere in the core volume under uniform stress. In these conditions, axial fatigue performance is lower than that obtained under bending and nitriding depth may have no more influence. In order to interpret the results, special attention was given to the effects of compressive residual stresses on the surface short crack growth (closure effect) as well as the effects of internal defect size on internal fatigue lives. A superimposed tensile mean stress reduces the internal fatigue strength of nitrided steel more than the surface fatigue strength of the base metal. Both cracking mechanisms are not equally sensitive to mean stress.     

A new testing method to obtain mode II fatigue crack growth characteristics of hard materials

Flaking type failure in rolling‐contact processes is usually attributed to fatigue‐induced subsurface shearing stress caused by the contact loading. Assuming such crack growth is due to mode II loading and that mode I growth is suppressed due to the compressive stress field arising from the contact stress, we developed a new testing apparatus for mode II fatigue crack growth. Although the apparatus is, as a former apparatus was, based on the principle that the static K_I mode and the compressive stress parallel to the pre‐crack are superimposed on the mode II loading system, we employ direct loading in the new apparatus. Instead of the simple four‐point‐shear‐loading system used in the former apparatus, a new device for the application of a compressive stress parallel to the pre‐crack has been developed. Due to these alterations, mode II cyclic loading tests for hard steels have become possible for arbitrary stress ratios, including fully reversed loading (R=?1); which is the case of rolling‐contact fatigue. The test results obtained using the newly developed apparatus on specimens made from bearing steel SUJ2 and also a 0.75% carbon steel, are shown.     

A TEST METHOD FOR MODE II FATIGUE CRACK GROWTH RELATING TO A MODEL FOR ROLLING CONTACT FATIGUE

Abstract— From fractographic observations of specimens that have failed due to rolling contact fatigue, it has been concluded that the first stage of damage is the formation of mode II fatigue cracks parallel to the contact surface due to the cyclic shear stress component of the contact stress. Although these initial subsurface cracks, in both metals and ceramics, are produced in a direction parallel to the cyclic shear stress, cracks eventually grow in a direction close to the plane of the maximum tensile stress if we apply a simple mode II loading to them. The difference between crack growth in simple mode II loading and crack growth due to rolling contact fatigue is, we suppose, whether or not there is a superimposed compressive stress. Based on this hypothesis, we developed an apparatus to obtain the intrinsic characteristics of mode II fatigue crack growth, and developed a simplified model of subsurface crack growth due to rolling contact fatigue.
Some results in terms of da/dN versus ΔK_II relations have been obtained using this apparatus on specimens of steel and aluminum alloys. Fractographs of the mode II fatigue fracture surfaces of the various materials are also provided.