Vorhersagemodell für die Wachstumsraten kurzer Risse auf der Basis von Kmax‐konstant‐Versuchen an M(T)‐Proben

Prediction model for the growth rates of short cracks based on K_max‐constant tests with M(T) specimens The fatigue crack growth behaviour of short corner cracks in the Aluminium alloys Al 6013‐T6 and Al 2524‐T351 was investigated. The aim was to determine the crack growth rates of small corner cracks at stress ratios of R = 0.1, R = 0.7 and R = 0.8 and to develop a method to predict these crack growth rates from fatigue crack growth curves determined for long cracks. Corner cracks were introduced into short crack specimens, similar to M(T)‐specimens, at one side of a hole (Ø = 4.8 mm) by cyclic compression (R = 20). The pre‐cracks were smaller than 100 μm (notch + precrack). A completely new method was used to cut very small notches (10–50 μm) into the specimens with a Focussed Ion Beam. The results of the fatigue crack growth tests with short corner cracks were compared with long fatigue crack growth test data. The short cracks grew at ΔK‐values below the threshold for long cracks at the same stress ratio. They also grew faster than long cracks at the same ΔK‐values and the same stress ratios. A model was developed on the basis of K_max‐constant tests with long cracks that gives a good and conservative prediction of the short crack growth rates.     

Surface flaws behavior under tension,bending and biaxial cyclic loading

Fatigue surface crack growth and in-plane and out-of-plane constraint effects are studied through experiments and computations for the aluminum alloy D16T. A tension/bending central notched plate and cruciform specimens under different biaxial loadings with external semi-elliptical surface cracks are studied. The variation of the fatigue crack growth rate and surface crack paths is studied under cyclic tension, bending and biaxial tension–compression loading. For the experimental surface crack paths in the tested specimens, the T-stress, out-of-plane T_z factor, local triaxiality parameter h and the governing parameter for the 3D-fields of the stresses and strains at the crack tip in the form of the I_n-integral are calculated as a function of the aspect ratio by finite element analysis to characterize the constraint effects along the semi-elliptical crack front. The plastic stress intensity factor approach is applied to the fatigue crack growth on the free surface, as well as at the deepest point of the semi-elliptical surface crack front, of the tested tension/bending plate and cruciform specimens. From the results, characteristics of the fatigue surface crack growth rate as a function of the loading conditions are established.     

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.     

Propagation of physically short cracks in a bainitic high strength bearing steel due to fatigue load

Physically short cracks in a bainitic high strength bearing steel were fatigue loaded. The rapid propagation rate of early open short cracks agreed with that of long closure free cracks. After some rapid growth, the short cracks entered a transition period to the rate of growth limited long cracks. Potential drop showed that the short cracks were open to the tip throughout the growth sequence, which excluded crack face closure in the wake as the growth limiting mechanism in this material. Instead the short crack effect was related to residual stresses and other mechanisms at the crack tip. Crack manufacturing procedures were determined for straight long and short start cracks in the present material. LEFM with effective material parameters and limit compensation predicted the short crack lives.     

Small fatigue crack growth behavior of titanium alloy TC4 at different stress ratios

In this paper, the small fatigue crack behavior of titanium alloy TC4 at different stress ratios was investigated. Single‐edge‐notch tension specimens were fatigued axially under a nominal maximum stress of 370 MPa at room temperature. Results indicate that fatigue cracks in TC4 initiate from the interface between α and β phases or within α phase. More than 90% of the total fatigue life is consumed in the small crack initiation and growth stages. The crack growth process of TC4 can be divided into three typical stages, ie, microstructurally small crack stage, physically small crack stage, and long crack stage. Although the stress ratio has a significant effect on the total fatigue life and crack initiation life at constant σ_max, its effect on crack growth rate is indistinguishable at R = ?0.1, 0.1, and 0.3 when crack growth rate is plotted as a function of ?K.     

A NEW METHOD FOR PREDICTING FATIGUE LIFE IN NOTCHED GEOMETRIES

The objective of this paper is to develop a notch crack closure model, called NCCM, based on plasticity-induced effects and short fatigue crack growth in the vicinity of the notch, and to predict the fatigue failure life of notched geometries. By using this model the regime for non-propagating cracks (n.p.c.) and the relationship between the fatigue strength reduction factor, Kf , and the elastic stress concentration factor, Kt , under mean stress conditions, can be determined quantitatively. A crack closure model is assumed to apply in the notch regime based on an approach developed to explain the crack growth retardation behavior observed in smooth specimen geometries after an overload. Notch plasticity effects are also applied in the NCCM model. Fatigue failure life is calculated from both short fatigue crack growth in the notch region where elastic–plastic fracture mechanics (EPFM) is applied and from long fatigue crack growth remote from the notch where linear elastic fracture mechanics (LEFM) occurs. This prediction is obtained using a quantity called the effective plasticity-corrected pseudo-stress. The NCCM can be used to account quantitatively for various observed notch phenomena, including both the relationship between Kf and Kt and n.p.c. The effects of the tensile mean stress on the Kf versus Kt relationship is investigated and leads to the little recognized but technologically important observation that mean stress conditions exist where Kf can be greater than Kt . The role of notch radius and tensile mean stress on n.p.c. behavior is also explored. The model is verified using experimental data for notch geometries of aluminum alloy 2024-T3, alloy steel SAE 4130 and mild steel specimens tested at zero and tensile mean stress.     

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.     

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.     

Modellierung des Ermüdungsrisswachstums in Schweißverbindungen unter Berücksichtigung von Schweißeigenspannungen

The present paper contains research results determined within the framework of a project called IBESS (?Integrale Bruchmechanische Ermittlung der Schwingfestigkeit von Schweißverbindungen“) by the Materials Mechanics Group of the Technische Universität Darmstadt [1]. Aim is to calculate the fatigue life of welded joints by taking into account the effect of residual stresses and the influence of the weld toe geometry. Here, the fatigue life is regarded as period of short fatigue crack growth. Two and three dimensional finite element models, with cracks as initial defects, are constructed for this purpose. Fatigue crack growth analyses are performed by using the node release technique together with the finite element program ABAQUS. The welding residual stresses as well as the plasticity induced crack closure effects are considered. Structural calculations are performed in order to introduce residual stress fields in finite element models. The calculated compressive residual stress field matches the measured one especially in the weld notch area. The effective cyclic J‐integral (ΔJ_eff) is used as crack tip parameter in a relation similar to the Paris equation for the calculation of the fatigue life. For this purpose, a Python code was written for the determination of ΔJ_eff at every crack length phase. The calculated fatigue lives were compared with experimental data and a good accordance between both results was achieved. The impact of welding residual stresses on ΔJ_eff as well as on the fatigue life during short crack growth was investigated. As expected, results revealed that at lower stress amplitude, a compressive residual stress field is favorable to the fatigue life, whilst a tensile residual stress field is unfavorable. The influence of residual stresses can be neglected only for large load amplitudes.     

Crack initiation under far-field cyclic compression and the study of short fatigue cracks

A procedure involving crack initiation under far-field cyclic compression is used to study the fatigue behavior of small flaws which are ˜0.3–0.5 mm in length and are amenable to linear elastic fracture mechanics (LEFM) characterization. This technique enables the determination of the threshold stress intensity range at which crack growth begins for small flaws and provides insight into some closure characteristics. Cracks were propagated in notched specimens of a bainitic steel subjected to fully compressive remote cyclic loads, until complete crack arrest occurred after growth over a distance of only a fraction of a mm at a progressively decreasing velocity. Following this, physically small flaws were obtained by machining away the notch. For the loads examined, the results indicate that the extent of damage left at the tip of the crack grown (and arrested) under remote compression is not large enough to affect subsequent tensile fatigue crack growth, when closure effects are not significant (e.g. at high load ratios). At high load ratios, the growth of small linear elastic cracks is identical to that of corresponding long flaws subjected to the same stress intensity range, which corroborates the similitude concept implicit in the nominal use of LEFM. At low load ratios, however, short tensile cracks propagate substantially faster than the longer flaws and exhibit lower threshold stress intensity range levels. Such apparent differences in their growth rates seem to arise, to a large extent, from the differences in their closure behavior, as indicated clearly from various aspects of the compression method. Global measurements of closure, with their inherent uncertainties, however, cannot account completely for the anomalous behavior of short flaws and for the effect of load ratio on short crack growth. Closure of short flaws begins to develop after growth over a minimum distance of about 0.5 mm in this steel. The significance and limitations of the compression technique are discussed and possible mechanisms responsible for the differences between long and short fatigue cracks are outlined.     

Effect of crack closure on non-linear crack tip parameters

Crack closure concept has been widely used to explain different issues of fatigue crack propagation. However, some authors have questioned the relevance of crack closure and have proposed alternative concepts. The main objective here is to check the effectiveness of crack closure concept by linking the contact of crack flanks with non-linear crack tip parameters. Accordingly, 3D-FE numerical models with and without contact were developed for a wide range of loading scenarios and the crack tip parameters usually linked to fatigue crack growth, namely range of cyclic plastic strain, crack tip opening displacement, size of reversed plastic zone and total plastic dissipation per cycle were investigated. It was demonstrated that: (i) LEFM concepts are applicable to the problem under study; (ii) the crack closure phenomenon has a great influence on crack tip parameters decreasing their values; (iii) the ΔK_eff concept is able to explain the variations of crack tip parameters produced by the contact of crack flanks; and (iv) the analysis of remote compliance is the best numerical parameter to quantify the crack opening level. Therefore the crack closure concept seems to be valid. Additionally, the curves of crack tip parameters against stress intensity factor range obtained without contact may be seen as master curves.     

Small crack growth rates from simple sequences containing underloads in AA7050-T7451

Fatigue crack growth in materials that display confined slip show crack path changes that are dependant on the loading history. In these materials certain variable amplitude loading patterns can produce strong slip bands ahead of the crack tip. One of these patterns of loadings involving bands of high R cycles followed by one or two underloads also produce distinct features or progression marks on the fracture surface that have been used to delimit small blocks of constant amplitude cycles. The same loading pattern also produces strong slip bands ahead of the fatigue crack both in the plane of the crack and out of plane. These slip bands affect the direction and possibly the rate of propagation of the fatigue crack. Thus these loading patterns make an ideal marker to look at small crack growth rates in the presence of slip bands.This paper reports on the crack growth rates for a series of fatigue cracks grown in AA7050-T7451 coupons, from near initiation to near failure. The aim of this work was to generate constant amplitude crack growth data for use in predictions that is more useful for predicting crack growth lives than that obtained from long crack constant amplitude tests. Three simple sequences which applied small bands of constant amplitude loading were used in the fatigue tests preceded by a loading sequence to produce a progression mark to delimit the bands. The fatigue cracks in the coupon initiated from etch pits on the surface of the coupons. The width of the bands of constant amplitude growth in these sequences were measured under a microscope. The growth in these sequences was found to be faster than for long cracks under constant amplitude loading.     

FATIGUE LIFE PREDICTION OF WELDED JOINTS—A RE-ASSESSMENT

Abstract— Fatigue life prediction of welded joints needs an accurate and exhaustive theoretical Fracture Mechanics characterization of weld toe crack propagation. The method proposed by Albrecht et al. leads rapidly to accurate solutions of the LEFM δK-parameter. However, non-LEFM short crack behavior within the notch (weld toe) plastic zone must be taken into account. Available information on notch fatigue is surveyed, and practical cases where short crack growth is likely to occur are identified. Based on an elastoplastic finite element analysis, the LEFM validity limits and errors resulting from the misuse of LEFM in fatigue life prediction are quantified.     

Evaluation of the overload effect on fatigue crack growth with the help of synchrotron XRD strain mapping

The overload retardation effect on fatigue crack growth rate (FCGR) in titanium alloy Ti-6Al-4V is studied. Synchrotron X-ray diffraction strain mapping of near-crack tip regions of pre-cracked fatigued samples is used to determine the effective stress intensity factors experienced by the crack tip. The effective stress intensity factor values are computed by finding the best match between the experimental strain maps and linear elastic fracture mechanics (LEFM) predictions. The dependence of the effective stress intensity factor, K, on the applied load is plotted, and an interpretation of the overload retardation effect is proposed. The present approach permits to reconcile the traditional LEFM fatigue crack propagation prediction and the experimental measurement of strain fields.     

A unified method of design for fatigue crack growth resistance in structural materials

It is well established that there are two fatigue crack tip driving forces – the cyclic, ΔK, and the static, K_max. In this study, the effects of each crack tip driving force on crack growth were evaluated for various structural materials. A unified method of design that allows for predicting the response of long and physically small fatigue cracks at positive stress ratios is introduced. Good agreement between predicted and experimental long and physically small fatigue crack growth data was obtained. The importance of this method in material and component design is discussed as part of a contemporary design philosophy.     

Experimental Investigation Into the Fatigue of Welded Stiffened 350WT Steel Plates Using Neutron Diffraction Method

Abstract: The propagation of fatigue cracks under constant amplitude cyclic loading was studied in welded stiffened steel plates. The residual stresses in the stiffened plates were measured using the neutron diffraction strain‐scanning technique. The neutron diffraction measurements indicated that, in general, the residual stresses were tensile near the welded stiffeners and compressive between the stiffeners and ahead of the starter notch tips. Fatigue testing indicated that the fatigue crack growth rates of the stiffened plates were, in general, lower than that of a corresponding unstiffened plate, especially near the notch tips, where compressive residual stresses existed. An analytical method, using Green's function, was developed to predict the fatigue crack growth rates. Reasonable accuracy was obtained.     

Fracture toughness and growth of short and long fatigue cracks in ductile cast iron EN‐GJS‐400‐18‐LT

Heavy components of ductile cast iron frequently exhibit metallurgical defects that behave like cracks under cyclic loading. Thus, in order to decide whether a given defect is permissible, it is important to establish the fatigue crack growth properties of the material. In this paper, results from a comprehensive study of ductile cast iron EN‐GJS‐400‐18‐LT have been reported. Growth rates of fatigue cracks ranging from a few tenths of a millimetre (‘short’ cracks) to several millimetres (‘long’ cracks) have been measured for load ratios R=?1, R= 0 and R= 0.5 using a highly sensitive potential‐drop technique. Short cracks were observed to grow faster than long cracks. The threshold stress intensity range, ΔK_th, as a function of the load ratio was fitted to a simple crack closure model. Fatigue crack growth data were compared with data from other laboratories. Single plain fatigue tests at R=?1 and R= 0 were also carried out. Fracture toughness was measured at temperatures ranging from ?40 °C to room temperature.     

Local strain accumulation in fatigue crack propagation process of Ti‐6Al‐4V alloy

Fatigue crack growth behaviours of the titanium alloy Ti‐6Al‐4V, with two different microstructures, at different maximum stresses were identified by digital image correlation technique. Full‐field strains were monitored around fatigue cracks after consecutive cycles in fatigue crack growth experiments. Results indicated that the Ti‐6Al‐4V alloy with a bi‐modal microstructure had a better fatigue resistance than that with a primary‐α microstructure. Typical behaviours of small cracks and the evolution of multi‐scale fatigue cracks were clarified. The strain accumulations around the micro‐notch and fatigue crack increased with increasing number of load cycles. On the basis of von Mises strain mapping, it was found that crack growth rate could be characterized by crack‐tip plastic zone size.     

A crack propagation criterion based on ΔCTOD measured with 2D‐digital image correlation technique

The fatigue cracks growth rate of a forged HSLA steel (AISI 4130) was investigated using thin single edge notch tensile specimen to simulate the crack development on a diesel train crankshafts. The effect of load ratio, R, was investigated at room temperature. Fatigue fracture surfaces were examined by scanning electron microscopy. An approach based on the crack tip opening displacement range (ΔCTOD) was proposed as fatigue crack propagation criterion. ΔCTOD measurements were carried out using 2D‐digital image correlation techniques. J‐integral values were estimated using ΔCTOD. Under test conditions investigated, it was found that the use of ΔCTOD as a fatigue crack growth driving force parameter is relevant and could describe the crack propagation behaviour, under different load ratio R.