EFFECT OF NOTCH STRESS FIELD AND CRACK CLOSURE ON SHORT FATIGUE CRACK GROWTH

Abstract— The growth rate of a short fatigue crack that is partly or wholly embedded within the notch plastic zone, is affected by the extent and intensity of the elastic-plastic notch stress field and closure effect. The notch stress—strain field and plastic zone were analysed by the Finite Element Method (FEM). The growth rate and the closure curve for a short fatigue crack emanating from the notch root were measured. Based on the experimental and numerical analyses, a modified Linear Elastic Fracture Mechanics (LEFM) parameter is proposed for a short through-thickness crack emanating from a notch root under elastic—plastic loading conditions.     

FATIGUE AT NOTCHES SUBJECTED TO REVERSED TORSION AND STATIC AXIAL LOADS

Reversed torsion with and without a superimposed end load has been applied to 1% Cr-Mo-V steel specimens containing sharp notches. Crack propagation was monitored by a sensitive d.c. potential drop system that measured crack depths between 25 μm and 0.6 mm from the root of the notch. Stress intensity factors do not satisfactorily correlate all the crack growth data but a strain intensity factor which is a function of material properties and notch plastic zone size shows a significant improvement and provides a single upper bound solution for both ambient and elevated temperatures. This solution permits designers to make safe lifetime assessments. At room temperature cracks initially propagate by mode II along the surface, and mode III radially but at low stresses crack growth is continued by mode I propagation. At higher stresses a transition to mode I cracking is avoided. Elevated temperature causes a brittle layer to form and in this case cracks initially propagate by mode I which then translates to mode III cracking at high stresses. Mode III thresholds are significantly higher than mode I thresholds but a constrained shear strain zone, as found at the root of notches subjected to torsion, permits the initiation and generation of a mode III crack. The application of an axial load enhances the mode III crack propagation rate since this increases the effective crack tip intensification factor.     

Fatigue crack propagation in aluminum nitride ceramics under cyclic compression

Room temperature fatigue crack growth characteristics under cyclic compressive loads were investigated in pure and 3 wt % yttria doped hot pressed aluminum nitride ceramics. A single edge-notch specimen geometry was used to induce a stable Mode I fatigue crack under cyclic compressive loads. The fatigue crack growth occurred in three stages, where the first stage is dominated by microcrack nucleation, coalescence and slow growth within the notch root. During the second stage, the crack growth is accelerated and finally, the crack growth deceleration and arrest occurred in third stage. The fatigue crack growth occurred predominantly by intergranular fracture. Insights gained from the experimental results and microscopic observations are discussed.     

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.     

Microstructure-dependent fatigue damage process zone and notch sensitivity index

The development of simulation methods for calculating notch root parameters for purposes of estimating the fatigue life of notched components is a critical aspect of designing against fatigue failures. At present, however, treatment of the notch root stress and plastic strain field gradients, coupled with intrinsic length scales of grains or other material attributes, has yet to be developed. Ultimately, this approach will be necessary to form a predictive basis for notch size effects in forming and propagating microstructurally small cracks in real structural materials and components. In this study, computational micromechanics is used to clarify and distinguish process zone for crack formation and microstructurally small crack growth, relative to scale of notch root radius and spatial extent of stress concentration at the notch. A new nonlocal criterion for the fatigue damage process zone based on the distribution of a shear-based fatigue indicator parameter is proposed and used along with a statistical method to obtain a new microstructure-sensitive fatigue notch factor and associated notch sensitivity index, thereby extending notch sensitivity to explicitly incorporate microstructure sensitivity and attendant size effects via probabilistic arguments. The notch sensitivity values obtained for a range of notch root radii using the new statistical approach presented in this study predict the general trends obtained from experimental results available in literature.     

Orowan mechanism for abrupt localized flow and fracture initiation in metals ahead of an yielding notch

Plane strain elastic-plastic stresses are determined in Mises yielding solid at the root of an yielding crack like notch. This external edge notch is infinitely deep, and has a small finite (fixed) flank angle with a small tip root blunting radius. A boundary value type approach has been followed throughout, to solve this famous Orowan-lrwin problem. Firstly, a fictitious elastic stress field is calculated, considering a misfit in the bulk volume loading; these elastic stress expressions are valid when the notch is fully loaded. Secondly, the plastic stresses are determined in the compressibility gradient, maintaining the continuity of stresses and their derivatives at the yielded-unyielded interface. Our calculations reveal that: Orowan mechanism is fairly dominant below the notch root, as well as on ± 45° planes. It is concluded that the flow-localization in the Mises solid is due to a reverse slip, caused by the sudden release of a favourable critical mismatch stress concentration. Some elastic strain energy density is seen to be getting released from the bulk volume, while unloading the misfit load. The mismatch has been created entirely due to the compressibility-incompressibility difference, as suggested by Orowan.

Following Orowan, it is shown here that, before the onset of a stable crack extension, the increase in stress concentration at the notch tip root, is directly proportional to the strength of mismatch strain-localization below the notch, and inversely proportional to the plane strain plastic zone size on the crack extension plane. For a large scale yielding situation, compressive stresses and pure distortion regions are seen to occur at a far field within the plastic enclave.     

Fatigue of casting flaws at a notch root under an SAE service load history

Smooth and notched specimens of a 319 cast aluminium alloy were fatigue tested under a Society of Automotive Engineers service load history in the as-cast and hipped conditions. The hipping process, which includes subjecting the cast material to a high pressure at high temperature and then slowly cooling down to eliminate internal flaws, decreased the flaw size and improved the fatigue life of cast Al 319 smooth specimens. A 0.6-mm-diameter hole was drilled at the notch root of notched specimens to simulate a natural flaw at the notch root. Specimens with two different notch sizes were tested. Circular edge notches reduced the fatigue strength and a 0.6-mm-diameter drilled hole at the notch root resulted in a further reduction.
The fatigue lives of smooth specimens, notched specimens and notched specimens with a flaw at the notch root subjected to the service load history were predicted using the strain-life approach, an effective strain-life approach and a strain-based intensity factor crack growth model. In crack growth modelling of the fatigue life of smooth cast aluminium specimens the flaw was modelled as a circular edge notch having the same diameter as the flaw. However, in the case of a flaw at a notch root the flaw was modelled as a three-dimensional cavity subjected to the notch stress field and the crack length was predicted in the longitudinal and transverse directions of the specimen cross-section. The strain-life approach was unconservative for all specimen geometries studied. The effective strain-life approach gave good predictions for smooth and blunt notched specimens but gave very conservative predictions for the specimens with flaws in the notch roots. The crack growth calculations gave accurate predictions for all the specimen geometries.     

Short fatigue crack growth from a blunt notch in plate specimens

Short crack growth behavior from a notch including crack closure and load ratio effects was investigated. Experiments and analyses were carried out using four-point bending specimens made of SAE 1045 steel, using a blunt notch keyhole specimen geometry. The lower the load ratio, the more notch effect on short crack growth behavior was observed. Short cracks in the notch affected zone had higher growth rates than long cracks. After the crack grew out of the notch effect field, short crack growth rates merged with the long crack growth rates. Several parameters were used to correlate the short crack growth rates including stress intensity factor range, effective stress intensity factor range, and stress intensity factor range based on notch root stress.     

PREDICTION OF FATIGUE LIFETIME OF NOTCHED MEMBERS

Abstract— A simple model for the estimation of the total fatigue life of notched members is presented. The number of cycles to failure is estimated as the summation of the cyclic life spent in: (1) the initiation of a dominant fatigue crack at the notch root; (2) the very early growth of this crack within the notch plastic zone; (3) the subsequent fatigue crack growth in the elastic stress-strain field of the notch; and (4) the elastic stress field of the bulk material. Theoretical and experimental results are compared.     

Book Reviews

‘Early’ creep-fatigue crack growth rates have been measured in complex-cycle large single edge notched bend feature-specimen tests on a 1¼ CrMoV turbine casting steel at 550°C. Crack propagation rates initially accelerate with increasing distance below the stress concentration to a peak value. The depth at which this maximum occurs depends on the notch geometry and the magnitude of any superimposed primary loading. ‘Early’ creep-fatigue crack growth rates are dependent on crack size, notch root strain range and any creep damage accumulated due to primary and secondary loading.     

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

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

Crack growth and residual stress in Al-Li metal matrix composites under far-field cyclic compression

The growth of cracks under far-field cyclic compressive loading in aluminium-lithium (Al-Li) alloys reinforced with SiC particulates is investigated in notched compact tension specimens (CT). When cracks were initiated from the root of the notch, progressive deceleration occurred with the initial crack growth being largest. After crack arrest, analysis indicated that the initial residual stress diminished as the crack became non-propagating and at arrest the crack faces appeared to be open. When the crack closure loads were determined, it was shown that not all the stress amplitude produced crack growth and opening. This effect of crack closure was enhanced for small stress fields when the effective stress intensity dropped to the fatigue threshold of the alloy. For large residual stress fields the effective stress intensity range was well above the threshold and the initial crack growth rates were largest in the alloy containing the reinforcement particles. A residual strain model was used to determine the residual stress introduced in the root of the notch from the first compressive preload. It is shown that the fatigue crack growth was confined to a region of tensile stress within the residual stress field and the initial crack propagation rates were enhanced by the presence of the reinforcement. A dependence of the stress magnitude on growth rates was also established — the greater the residual stress at the root of the notch the larger the growth rates. The reinforcement had an additional amplification effect in terms of tensile distance from the notch. The effective stress intensity range, K, was investigated using compliance measurements and a model is introduced which explains the underlying features and mechanism of accelerated growth in both alloys, taking into account the reinforcement phase, plastic zone-size dependence and the residual stress field of the MMC.     

The growth of short fatigue cracks ahead of a notch in high strength steel

This paper is concerned with the short crack growth behaviour in notched specimens of high strength steels mainly used for automotive parts. Attention is focused on the appropriate estimation of the stress intensity range ΔK, when the short cracks grow in the stress field of a notch and attempts are made to investigate whether this is appropriate or whether further allowance may have to be made for short crack effects at low ΔK.The stress distribution for the notch in bending was taken into account for the estimation of ΔK. This enabled us to produce a more precise evaluation of short crack growth in the stress field of the notch. Our findings are that the short cracks, which propagate in the notch field, grow faster at low ΔK when their lengths are extremely short compared with the notch root radius. The short crack effect at low ΔK in the notch stress field is analysed by expressing the crack growth data in terms of the parameter, ΔK_s, in which stress gradient ahead of the notch is taken into account.     

Fatigue life prediction of notched members based on local strain and elastic-plastic fracture mechanics concepts

Fatigue life predictions for notched members are made using local strain and elastic-plastic fracture mechanics concepts. Crack growth from notches is characterized by J-integral estimates made for short and long cracks. The local notch strain field is determined by notch geometry, applied stress level and material properties. Crack initiation is defined as a crack of the same size as the local notch strain field. Crack initiation life is obtained from smooth specimens as the life to initiate a crack equal to the size of cracks in the notched member. Notch plasticity effects are included in analyzing the crack propagation phase. Crack propagation life is determined by integrating the equation that relates crack growth rate to ΔJ from the initiated to final crack size. Total fatigue life estimates are made by combining crack initiation and crack propagation phases. These agree within a factor of 1.5 with measured lives for the two notch geometries.     

Failure of a Porous Solid from a Deep Notch

A finite strain finite element method is used to examine the stress state near the tip of a deep notch in an elastic-plastic porous solid. The notch is loaded in mode I plane strain tension and small scale yielding is assumed. Two rate independent strain hardening material models are used: a version of the Gurson model (1977) and the more recent FKM model developed by Fleck, Kuhn and McMeeking (1992). Under increasing K _I, void growth is initially stable and independent of mesh dimension. Localization of plastic flow sets in at a finite value K _i, and the deformation field is mesh-size dependent thereafter. The initiation of crack growth at the notch root is assumed to occur when a critical level of porosity is attained. The results show that the shape of the plastic zone for both the Gurson and the FKM material is highly dependent on the initial porosity. In the case of low initial porosity, the plastic zone shape is similar to that of a fully dense material; at higher initial porosities the plastic zone is concentrated ahead of the notch tip. The effect of the initial void volume fraction on the porosity field and the critical stress intensity factor is studied, and the mesh-size dependence of the results is discussed. The analysis is useful for prediction of the notched strength of porous metals. This revised version was published online in August 2006 with corrections to the Cover Date.     

Evaluation of fatigue crack initiation life from a notch

Local strain at the notch-root and its effect on fatigue crack initiation was investigated in four metals by the real-time, fine-grid method. Special attention was focused on local notch-root strain behaviour until crack initiation. From the application of strain hysteresis at the notch root, the maximum strain under loading conditions during each cycle was investigated in detail. One of the main results was that the maximum strain value at the first cycle of the fatigue test coincided with that at crack initiation. Maximum strain defined from the cyclic strain changes at the notch root was proposed as one possible parameter for estimating fatigue crack initiation life. Based on the curvilinear relationship between maximum strain and number of cycles to crack initiation, a new life evaluation method for fatigue crack initiation is proposed. This approach differs fundamentally from the usual fracture mechanics method based on the stress intensity factor.     

Fatigue crack initiation at notches in SA 333 piping steel

Abstract

In this paper are reported two recent investigations into crack initiation at notch roots using techniques developed for remote monitoring of crack growth in high–temperature water environments. In the first, a notched compact–type specimen of a carbon steel, SA 333 Gr. 6, was monitored for crack initiation (defined as a 0·076 mm crack at the notch root) in a variety of water chemistries and testing conditions. The mechanical conditions at the notch root have been analysed using the Neuber–notch method, enabling a direct comparison to be made with the strain–controlled fatigue data curves used for a smooth specimen in the ASME Boiler and Pressure Vessel Code, Section III. In the second investigation a different method was considered for monitoring crack initiation. A modification of the electrical–potential technique, called the reversing dc electrical potential method, was used to obtain quantitative information on the initiation and early growth of small surface cracks in notched bars of a high–strength alloy at elevated temperature. Results obtained by the method are presented and discussed.

MST/72     

Notch effect on torsional fatigue of austenitic stainless steel: Comparison with low carbon steel

Notch effect in austenitic stainless steel under cyclic torsion is quite different depending on the superposition of static tension. In pure torsion, the rubbing of the serrated factory-roof type crack faces delays the crack growth along the notch root. Thus, the lifetime in notched specimen becomes longer than in smooth specimen. However, in cyclic torsion with static tension, the flat crack path and mean tensile stress reduce the influence of the crack face contact. Accordingly, shorter lifetime resulted from higher strain concentration at the notch root. Crack growth in low carbon steel under cyclic torsion is highly affected by the ferrite/pearlite banded microstructure besides the addition of static tension. Because of a small amount of the crack face contact, the reduction of lifetime in notched specimen is revealed irrespective of superposition of static tension.     

Direct observation and modelling of the crack–fibre interaction process in continuous fibre-reinforced ceramics: model experiment

The effect of the matrix–fibre interface bonding and debonding condition on the crack growth behaviour in a fibre-reinforced ceramic matrix composite was studied using a model glass fibre-reinforced PMMA matrix composite. The crack growth process from a centre notch is monitored using a compression splitting test. From direct observation three characteristic stages can be identified in the crack growth process of the composite, namely elastic constraint (stage I), matrix crack bowing (stage II) and crack bridging (stage III). Partial interface debonding occurs at the end of stage I and cylindrical interface debonding occurs at the end of stage II. The crack growth rate is accelerated just after the onset of interface partial debonding and this indicates that a debonded interface reduces the crack growth resistance. The partial interface debonding which occurs before fibre breaking plays an important role on the crack growth mechanism.     

Notch effect on creep–fatigue life for Sn–3.5Ag solder

This paper studies the creep–fatigue crack initiation and failure lives of Sn–3.5Ag solder notched specimens focused on the multiaxial strain at the notch root. Push–pull creep–fatigue tests were performed using three circumferential notched specimens using four kinds of creep–fatigue strain waveforms. Multiaxial strains at the notched section were calculated by finite element (FE) analysis under four kinds of creep–fatigue loading. Creep–fatigue damage laws were applied for evaluating the crack initiation and failure lives using the multiaxial strains obtained by the FE analysis. von Mises equivalent strain at the notch root estimated the crack initiation lives with a large scatter as well as the failure lives. Instead, the mean value of von Mises equivalent strain over the cross section of the notch root estimated the crack initiation and failure lives with a small scatter.