Lebensdauerberechnung gekerbter Bauteile auf Basis der elastisch‐plastischen Schwingbruchmechanik

Fatigue life calculation of notched components based on the elastic‐plastic fatigue fracture mechanics The life of notched components is subdivided into the pre‐crack, or crack‐initiation, and crack propagation phases within and outside notch area. It is known that a major factor governing the service life of notched components under cyclic loading is fatigue crack growth in notches. Therefore a uniform elastic‐plastic crack growth model, based on the J‐Integral, was developed which especially considers the crack opening and closure behaviour and the effect of residual stresses for the determination of crack initiation and propagation lives for cracks in notches under constant and variable‐amplitude loading. The crack growth model will be introduced and verified by experiments.     

NOTCHED MEMBER FATIGUE LIFE PREDICTIONS COMBINING CRACK INITIATION AND PROPAGATION

Abstract Fatigue lives of notched members are considered to be divided into crack initiation and propagation phases. Apparent size effects caused by crack propagation through the strain gradient of the notch are accounted for if initiation is defined as a crack size within the local notch field. The extent of this field may be estimated from fracture mechanics analysis, with its size being of the order of one tenth of the notch radius. Plasticity effects must be properly handled in predicting crack initiation, but linear elastic analysis is generally satisfactory for handling the propagation phase.     

The effect of notch plasticity on the behaviour of fatigue cracks emanating from edge-notches in high-strength β-titanium alloys

The present paper is aimed at investigating the behaviour of fatigue cracks emanating from edge-notches for two different microstructures of the Ti-6246 alloy, produced by two specific thermo-mechanical treatments and defined as β-annealed and β-processed, respectively. Pulsating four point bending tests were performed on double-edge-notched specimens. The initiation and early propagation of fatigue cracks were investigated at two relatively high nominal stress levels corresponding to 88 and 58% of the 0.2% material’s yield stress. Plastic deformation at the notch tip initially produced a local stress redistribution followed by elastic shake down due to the high cyclic strain hardening rates exhibited by both microstructures, as confirmed by finite element modelling. Crack closure effects, measured by an extensometric technique, and variations in crack aspect ratio were considered in the ΔK calculation. The obtained crack growth rate data were compared with those of long cracks measured on standard C(T) specimens as well as of microcracks measured on round, unnotched S-N type of specimens to evaluate the intrinsic fatigue crack propagation resistance of the two microstructures. The contribution of notch plasticization to crack closure was estimated by finite element modelling.     

The J-integral applied to cyclic loading

The influence of notch geometry on the life to fatigue crack initiation is determined using a modified two-dimensional J-integral analysis. A notched plate that is subjected to fully reversed cyclic nominal strain control is analyzed in order to determine the strain history at the notch root. The expression for strain concentration has the same form as that obtained from the Neuber approach. After the local stress-strain history has been determined, a life prediction for fatigue crack initiation could be made. The modified J-integral and Neuber approaches are compared. Justification for the use of the modified J-integral may be found in the appendices.     

AN EXPERIMENTAL STUDY ON THE OPENING AND CLOSURE BEHAVIOUR OF FATIGUE SURFACE, CORNER AND THROUGH-THICKNESS CRACKS AT NOTCHES

Abstract— The opening and closure behaviour of surface, corner and through-thickness cracks in thin notched plates of FeE460 ( K _t= 2.5) and A15086 ( K _t= 3.4) was experimentally studied. The cracks were initiated and examined under uniaxial fully reversed constant amplitude and two-step loading. Crack opening load values were measured during crack growth in notch sections with a nonuniform stress distribution using small strain gauges glued to the specimen surface, very close to the crack tip. The results represent a comprehensive set of experimental data for crack opening load values in dependence on crack lengths a, c and load level including the influence of overloads and covering all types of cracks. The results indicate uniform relationships between crack opening load levels and all crack types. Crack opening and closure occur at nearly the same strain level, which depends on the applied load level. The crack opening load values measured at large notched specimens differ from those measured at similar smaller specimens because of the different local stress gradients.     

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.     

Observations and modeling of the small fatigue crack behavior of an extruded AZ61 magnesium alloy

The objective of this paper is to quantify the microstructurally small fatigue crack growth of an extruded AZ61 magnesium alloy. Fully reversed and interrupted load-controlled tests were conducted on notched specimens that were taken from the material in the longitudinal and transverse orientations with respect to the extrusion direction. In order to measure crack growth, replicas of the notch surface were made using a dual-step silicon-rubber compound at periodic cyclic intervals. By using microscopic analysis of the replica surfaces, crack initiation sites from numerous locations and crack growth rates were determined. A marked acceleration/deceleration was observed to occur in cracks of smaller length scales due to local microheterogeneities consistent with prior observations of small fatigue crack interaction with the native microstructure and texture. Finally, a microstructure-sensitive multistage fatigue model was employed to estimate the observed crack growth behavior and fatigue life with respect to the microstructure with the most notable item being the grain orientation. The crack growth rate and fatigue life estimates are shown to compare well to published findings for pure magnesium single crystal atomistic simulations.     

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.     

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.     

Crack extension by alternating shear

A comparison of the slip line flow field at the tip of a sharp crack and of a blunted crack shows that a sharp crack can be extended by alternating shear until it becomes blunted. Crack tip blunting is associated with high strain concentration and fracture by hole growth and coalescence. Crack extension by alternating shear has been obtained in fully plastic, plane strain sharply notched, singly and doubly grooved tensile specimens. Electron fractography shows crack extension by alternating shear at the tip of cleavage and fatigue cracks. It is shown that fatigue crack propagation is the result of repeated cyclic crack extension by alternating shear.     

The effect of bi-modal and lamellar microstructures of Ti-6Al-4V on the behaviour of fatigue cracks emanating from edge-notches

This paper is aimed at evaluating the influence of bi‐modal and lamellar microstructures on the behaviour of small cracks emanating from notches in α+β titanium Ti‐6Al‐4V alloy. Pulsating four point bending tests were performed at a nominal stress ratio of 0.1 and a frequency of 15 Hz on double‐edge‐notched specimens. The conditions of initiation and early propagation of fatigue cracks were investigated at two relatively high nominal stress levels corresponding to 88 and 58% of the 0.2% material yield stress. Crack closure effects were measured by an extensometric technique and discussed. Variations in crack aspect ratio were determined and considered in the ΔK calculation. Corresponding results were discussed by considering the effect of the yielded region at the notch tip calculated by elastic–plastic finite element modelling of the fatigue tests. The importance of the bi‐modal and lamellar microstructures on the material damage was highlighted and correlated to the observed oscillations in the crack growth rate. The crack growth rate data obtained were compared with those measured using standard C(T) specimens (long crack).     

Local stress–strain field intensity approach to fatigue life prediction under random cyclic loading

According to the characteristic of the local behavior of fatigue damage, on the basis of stress field intensity approach, a theory of local stress–strain field intensity for fatigue damage at the notch is developed in this paper, which can take account of the effects of the local stress–strain gradient on fatigue damage at the notch. In order to calculate the local stress–strain field intensity parameters, an incremental elastic-plastic finite element analysis under random cyclic loading is used to determine the local stress–strain response. A local stress–strain field intensity approach to fatigue life prediction is proposed by means of elastic-plastic finite element method for notched specimens. This approach is used to predict fatigue crack initiation life, and good correlation was observed with U-shape notched specimens for normalized 45 steel.     

The influence of roller burnishing on the fatigue crack propagation in notched round bars—Experimental observations under three-point bending

Roller burnishing involves a local plastic deformation on the surface that permits the fatigue strength of structures to be increased. Crack propagation is delayed by the introduction of compressive residual stresses. In this way, the process is particularly useful in the presence of stress concentrators, for example in the fillets of crankshafts or in notched shafts. Crack propagation in round bars has been widely investigated, experimentally and numerically. However, the aim of the present work is to study roller burnished notched shafts (whose groove approaches the fillets of crankshafts) loaded in three‐point bending. Experimentally, a sequence of destructive interrupted tests has been performed to obtain the crack kinetics and shapes during fatigue life. Thus, the beneficial influence of roller burnishing has been confirmed on both crack initiation and propagation. Some cracks were even stopped by compressive residual stresses. Otherwise, the crack shape observed was very original : cracks propagated first at the edge of the coupon and then, into the depth of the shaft. Multicracking and crack closure have been pointed out and appear to be of great importance.     

SHORT FATIGUE CRACK GROWTH IN PLAIN AND NOTCHED SPECIMENS OF AN 8090 Al-Li ALLOY

Abstract— Fatigue tests on notched and plain specimens were carried out under a combined acoustic and optical microscope. Crack initiation in plain specimens occurs invariably at inclusions which act as sites of stress concentration. Short crack propagation behaviour shows the usual pattern of accelerations and retardations associated with microstructural variations. Growth can only be sustained if the applied stress is sufficiently high to overcome the microstructural barriers. For the notched specimens the extent of the notch tip and crack tip plastic zone sizes control crack propagation. A short crack will continue to propagate only if its own plastic zone can sustain growth as the crack tip extends beyond the notch zone, otherwise it becomes non-propagating. Notch plastic zones are calculated using both approximate and accurate solutions. Some microstructural effects are discussed.     

Ermüdungsrißwachstum in Kerben

Fatigue Crack Growth in Notches Nowadays it is wellknown that an important part of the fatigue life time, usually differenciated in crack initiation and crack growth, is often controlled by fatigue crack growth of cracks in notches. An elastic-plastic on the J-integral based crack growth model considering the crack opening and closure phenomenon will be described to determine crack growth of cracks in notches between crack initiation and failure. Experimental results and finite element analysis were used to verify the developed model.     

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.     

Investigating creep rupture and damage behaviour in notched P92 steel specimen using a microscale modelling approach

Idealized random grains separated by pseudo grain boundaries were generated by using Voronoi tessellation to simulate the polycrystalline microstructure. Combined with finite element analyses, this approach made it possible to addressing crack initiation and progressive failure due to crack growth in notched bar geometries of P92 steel at high temperature. The calculations provided good predictions for creep rupture lives of notched specimen with different notch radii and external stress. Simultaneously, irregular crack growth shape, intergranular crack mode, and wedge cracks at triple grain interaction were captured in the model. The crack initiation positions were found to be influenced by notch radius and applied stress causing high stress triaxiality at the subgrain level. Furthermore, the preferential crack growth directions were changed as the notch varied from sharp to blunt.     

Micromechanical analysis of mechanical heterogeneity effect on the ductile tearing of weldments

The objective of this study is determination of the effect of mechanical heterogeneity on ductile crack initiation and propagation in weldments using micromechanical approach. Welded single-edge notched bend (SENB) specimens were experimentally and numerically analysed. Material properties of welded joint zones were estimated using a combined experimental and numerical procedure; strains on a smooth tensile specimen were determined using ARAMIS stereometric measuring system in order to obtain true stress – true strain curves. High-strength low-alloyed steel was used as base metal, in quenched and tempered condition. J–R curves and crack growth initiation values of fracture mechanics parameter were experimentally and numerically obtained for specimens with a pre-crack in the heat-affected zone (HAZ) and weld metal (WM). The complete Gurson model (CGM) was used in prediction of J–R curves and crack growth initiation. It is shown that the resistance to crack initiation and growth can be predicted using micromechanical analysis, and that the results are significantly affected by mechanical heterogeneity of the weldment.     

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