Plastic strain-controlled short crack growth and fatigue life

Constant plastic strain-controlled and constant stress-controlled tests were performed on smooth and lightly notched specimens machined from a massive forging of 42CrMo4 steel. Comparison of the fatigue life curves plotted as function of the plastic strain amplitude and stress amplitude shows a decisive role of plastic strain amplitude. Crack initiation and the kinetics of short crack growth were studied in constant plastic strain amplitude loading and the relation between the crack growth coefficient and plastic strain amplitude was established. This is equivalent to the Coffin–Manson law and shows that the Coffin–Manson law can be interpreted in terms of short crack growth.     

NUCLEATION AND SHORT CRACK GROWTH IN FATIGUED POLYCRYSTALLINE COPPER

Surface evolution in polycrystalline copper specimens with a shallow notch has been studied in interrupted constant strain amplitude cyclic loading. The inhomogeneous strain distribution close to stress amplitude saturation leads to the formation of extrusions and intrusions along persistent slip bands within the grain and also in suitably oriented grain boundaries. Numerous primary cracks within a grain or at a grain boundary are nucleated. Some cracks can grow further either by linking with existing cracks or by nucleation of new elementary cracks ahead of the crack tip. Crack growth rates of individual cracks fluctuate considerably but for each strain amplitude, which results in a saturated plastic strain amplitude, a crack growth rate of an equivalent crack can be established. This crack growth rate was found to depend strongly on the plastic strain amplitude in agreement with the Manson-Coffin law.     

Crack growth predictions using a strip‐yield model for variable‐amplitude and spectrum loading

Fatigue‐crack‐growth tests were conducted on compact, C(T), specimens made of D16Cz aluminum alloy. Constant‐amplitude tests were conducted over a range of stress ratios (R = P_min/P_max = 0.1 to 0.75). Comparisons were made between test data from middle‐crack tension, M(T), specimens from the literature and C(T) specimens. A crack‐closure analysis was used to collapse the rate data from both specimen types into a fairly narrow band over many orders of magnitude in rates using proper constraint factors. Constraint factors were established from single‐spike overload and constant‐amplitude tests. The life‐prediction code, FASTRAN, which is based on the strip‐yield‐model concept, was used to calculate the crack‐length‐against‐cycles under constant‐amplitude (CA) loading and the single‐spike overload (OL) tests; and to predict crack growth under variable‐amplitude (VA) loading on M(T) specimens and simulated aircraft loading spectrum tests on both specimen types. The calculated crack‐growth lives under CA and the OL tests were generally within ±20 % of the test results, the predicted crack‐growth lives for the VA and Mini‐Falstaff tests on the M(T) specimens were short by 30 to 45 %, while the Mini‐Falstaff+ results on the C(T) specimens were within 10 %. Issues on the crack‐starter notch effects under spectrum loading are discussed, and recommendations are suggested on avoiding these notch effects.     

Fatigue growth of short cracks in Ti-17: Experiments and simulations

The fatigue behaviour of through thickness short cracks was investigated in Ti-17. Experiments were performed on a symmetric four-point bend set-up. An initial through thickness crack was produced by cyclic compressive load on a sharp notch. The notch and part of the crack were removed leaving an approximately 50 μm short crack. The short crack was subjected to fatigue loading in tension. The experiments were conducted in load control with constant force amplitude and mean values. Fatigue growth of the short cracks was monitored with direct current potential drop measurements. Fatigue growth continued at constant R-ratio into the long crack regime. It was found that linear elastic fracture mechanics (LEFM) was applicable if closure-free long crack growth data from constant K_Imax test were used. Then, the standard Paris’ relation provided an upper bound for the growth rates of both short and long crack.The short crack experiments were numerically reproduced in two ways by finite element computations. The first analysis type comprised all three phases of the experimental procedure: precracking, notch removal and fatigue growth. The second analysis type only reproduced the growth of short cracks during fatigue loading in tension. In both cases the material model was elastic-plastic with combined isotropic and kinematic hardening. The agreement between crack tip opening displacement range, cyclic J-integral and cyclic plastic zone at the crack tip with ΔK_I verified that LEFM could be extended to the present short cracks in Ti-17. Also, the crack size limits described in the literature for LEFM with regards to plastic zone size hold for the present short cracks and cyclic softening material.     

Local deformation at micro‐notches and crack initiation in an intermetallic γ‐TiAl‐alloy

The relation is studied between crack initiation from micro‐notches in a fully lamellar intermetallic γ‐TiAl alloy and the local strain field. These micro‐notches were introduced using femtosecond‐laser ablation and had dimensions below the average colony size. The specimen under investigation was then subjected to fatigue loading. Continuous monitoring using a travelling optical microscope allowed detecting microcracks at an early stage. Prior to fatigue loading, a sustained load was applied and the local strain field was determined using digital image correlation. This was supplemented by a Finite Element analysis of the notches and their neighbourhood. It was found that a crack was initiated from a notch causing high normal strains in lamella direction, whereas no crack was initiated from notches with high shear strains.     

Influence of loading path on fatigue crack growth under multiaxial loading condition

In this study, the specimens made of carbon steel S45 with an initial surface straight edge notch were subjected to combined cyclic axial‐torsion loading at room temperature. The fatigue life, surface crack extension direction and crack length were experimentally investigated. The effects of loading path, stress amplitude ratio and phase angle on the crack growth behaviour were also discussed. The results showed that, under the combination of cyclic axial and torsion loading, the tension stress amplitude had more effect on the initial crack growth path than the latter. The shear stress amplitude contributed mainly to the latter crack extension. The crack extension path was mainly determined by the stress amplitudes and the ratio of the normal stress to the shear stress, and almost independent of the mean stresses. The increase of the tension stress amplitude and shear stress amplitude would both accelerate the crack growth rate.     

THE INFLUENCE OF NOTCH PLASTICITY ON SHORT FATIGUE CRACK BEHAVIOUR

Abstract— A study has been made of fatigue crack formation and growth at the root of different notch profiles in a structural steel subjected to fully reversed tension-compression loading. The scale of stage I microstructural crack growth at notches decreased with increasing notch root strain and was comparable to the size of stage I cracks in shallow hourglass profile specimens at the same strain. Stage II crack growth rates were faster within the notch plastic field than in the elastic stress field of the bulk material.     

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.     

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.     

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.     

Microcrack growth and fatigue behavior of a duplex stainless steel

The kinetics of microcrack growth during cycling has been studied in a S32205 duplex stainless steel in the as-received and aged (100 h at 475 °C) conditions. Cylindrical specimens with a shallow notch were subjected to a constant plastic strain range of 0.3% in both thermal conditions. The characteristic features of surface damage and crack growth showed striking differences in microcrack density, nucleation location and propagation rate between the two thermal conditions even though the fatigue lives are comparable. In the as-received material, microcrack density is low and they nucleate mainly at grain and phase boundaries or second-phase particles. In the aged condition, slip markings first appear in the ferritic phase and they are the preferred site for microcrack nucleation. Crack propagation takes place along slip markings in adjacent grains for crack lengths less than 100 μm. A comparison between fatigue life and the relevant parameters of a microcrack growth law was made.     

Fatigue life prediction of engineering structures subjected to variable amplitude loading using the improved crack growth rate model

It is a difficult task to predict fatigue crack growth in engineering structures, because they are mostly subjected to variable amplitude loading histories in service. Many prediction models have been proposed, but no agreed model on fatigue life prediction adequately considering loading sequence effects exists. In our previous research, an improved crack growth rate model has been proposed under constant amplitude loading and its good applicability has been demonstrated in comparison with various experimental data. In this paper, the applicability of the improved crack growth rate model will be extended to variable amplitude loading by modifying crack closure level based on the concept of partial crack closure due to crack‐tip plasticity. It is assumed in this model that the crack closure level can instantly go to the peak/valley due to a larger compression/tensile plastic zone resulted from the overload/underload effect, and gradually recovers to the level of constant amplitude loading with crack propagation. To denote the variation in the affected zone of overload/underload, a modified coefficient based on Wheeler model is introduced. The improved crack growth rate model can explain the phenomena of the retardation due to overload and the tiny acceleration due to underload, even the minor retardation due to overload followed by underload. The quantitative analysis will be executed to show the capability of the model, and the comparison between the prediction results and the experimental data under different types of loading history will be used to validate the model. The good agreement indicates that the proposed model is able to explain the load interaction effect under variable amplitude loading.     

Fatigue crack growth driven by electric fields in piezoelectric ceramics and its governing fracture parameters

Fatigue crack growth test for piezoelectric ceramics was performed under cyclic electric loading. Double cantilever beam specimen, which was made of two different piezoelectric ceramics, with a through notch was used. The specimens were, varying the amplitude and the mean value, subjected to various cyclic electric fields. It was found that crack growth behavior is greatly dependent on the amplitude and mean value of cyclic electric field and materials. Crack growth rate decreased as electric field increased and finally stopped. Crack growths under the positive, the negative and the shifted electric field were very slow compared to that under fully reversed electric field. However, threshold for the crack propagation did not depend greatly on materials. Then, as possible governing fracture parameters, CED and electric displacement intensity factor were chosen based on the results of electromechanical finite element analysis within linear framework and their closed form equations were also obtained considering the influences of electric boundary conditions inside the notch. Finally, the parameters were correlated with crack growth rate measured experimentally by employing Paris law type equation.     

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.     

Initiation and short crack growth in austenitic–ferritic duplex steel‐effect of positive mean stress

The effect of the mean stress on the crack initiation and short crack growth of austenitic–ferritic duplex steel has been studied. High mean stresses and stress amplitudes result in appreciable mean strain relaxation and long‐term hardening. Mean stress produces unidirectional slip bands and slip steps that serve as nuclei for persistent slip bands and persistent slip markings. It leads to the acceleration of the crack initiation and production of a high density of cracks. Crack linkage contributes to the growth of short cracks. The concept of equivalent crack was used to describe the crack growth. The kinetics of short crack growth with positive mean stress is similar to that in symmetric loading, that is, exponential growth is observed. Positive mean stress results in earlier crack initiation and in the acceleration of the crack growth rate. Both factors contribute to the decrease of the fatigue life.     

Development of numerical model for the determination of crack opening and closure loads,for long cracks

A two‐dimensional finite element (FE) model has been developed for determining crack opening and closure stresses, with the eventual aim of investigating plasticity induced closure effects on crack growth under variable amplitude loading. An issue with model verification is obtaining accurate experimental values of crack opening and closure loads. Validation was therefore carried out using experimental data from constant amplitude loading tests, recently obtained by the authors 1 , 2 where there was good confidence in the accuracy of the opening and closing loads. Elastic–perfect plastic and work hardening material properties were investigated to determine the effect they had on crack growth. The modelling considered long cracks by dividing the crack into consecutive small lengths. For this purpose, the restart capability included in the ABAQUS code was employed. In addition, a mesh refinement strategy was optimised to reduce the memory requirements for the thousands of cycles analysed. This enabled both long crack lengths and small element sizes to be studied which has not been done in the literature before. The FE results were in good agreement with most of the experimental results, and possible reasons are given for some of the minor discrepancies observed.     

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.     

Short‐crack thresholds and propagation in an AISI 4340 steel under the effect of SP residual stresses

The effect of residual stresses induced by shot‐peening in a high‐strength AISI 4340 steel has been studied with the purpose of deriving a consistent fatigue model incorporating the results of fatigue crack growth experiments in the threshold region for a broad range of load ratio (R‐ratio ranging from ?2.5 to 0.7), and the effect of short cracks by means of a modified El‐Haddad model. The proposed model, taking into account the effect of crack closure and being capable to assess the conditions for fatigue propagation of short cracks partially embedded in the shot‐peened surface layer, was validated against constant amplitude fatigue experiments conducted in the endurance strength region, ie, for fatigue lives up to 10⁷ cycles, with micronotched specimens in the presence of shot‐peening residual stresses. The proposed model was also validated by comparing the results of fatigue crack propagation simulations with fatigue crack growth experiments under variable amplitude loading, experimentally reproducing the combined effect of service fatigue loads and shot‐peening residual stresses.     

Multiaxial notch fatigue life prediction based on pseudo stress correction and finite element analysis under variable amplitude loading

A new computational methodology is proposed for fatigue life prediction of notched components subjected to variable amplitude multiaxial loading. In the proposed methodology, an estimation method of non‐proportionality factor (F) proposed by authors in the case of constant amplitude multiaxial loading is extended and applied to variable amplitude multiaxial loading by using Wang‐Brown's reversal counting approach. The pseudo stress correction method integrated with linear elastic finite element analysis is utilized to calculate the local elastic‐plastic stress and strain responses at the notch root. For whole local strain history, the plane with weight‐averaged maximum shear strain range is defined as the critical plane in this study. Based on the defined critical plane, a multiaxial fatigue damage model combined with Miner's linear cumulative damage law is used to predict fatigue life. The experimentally obtained fatigue data for 7050‐T7451 aluminium alloy notched shaft specimens under constant and variable amplitude multiaxial loadings are used to verify the proposed methodology and equivalent strain‐based methodology. The results show that the proposed methodology is superior to equivalent strain‐based methodology.