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.     

Fatigue crack initiation prediction of cope hole details in orthotropic steel deck using the theory of critical distances

Orthotropic steel decks are vulnerable to fatigue cracking in welded connections and complex geometrical details. A total of three fatigue tests were conducted on segments of orthotropic steel deck to evaluate the fatigue performance of trough‐to‐crossbeam connections with various cut‐out configurations. In the tests, the specimens were subjected to cyclic three‐point bending load and the fatigue cracks were more likely to initiate from the cope holes in the crossbeam web rather than the trough‐to‐crossbeam fillet welds. Three‐dimensional finite element models (FEM) of the specimens were built and validated by the measured deflections and stresses. Using the validated FEM, the characteristic stresses based on the theory of critical distances (TCD) were calculated for the stress concentrations along the cope holes. The fatigue crack initiation life, predicted by the TCD‐based stress combined with the plain material S–N curve, agreed reasonably with the fatigue test results. The TCD method could further form a basis of fatigue crack propagation analysis using the fracture mechanics approaches.     

Numerical simulation of fatigue crack propagation in compressive residual stress fields of notched round bars

In this paper, the influence of the residual compressive stresses induced by roller burnishing on fatigue crack propagation in the fillet of notched round bar is investigated. A 3D finite element simulation model of rolling has allowed to introduce a residual stress profile as an initial condition. After the rolling process, fatigue loading has been applied to three‐point bending specimens in which an initial crack has been introduced. A numerical predictive method of crack propagation in roller burnished specimens has also been implemented. It is based on a step‐by‐step process of stress intensity factor calculations by elastic finite element analyses. These stress intensity factor results are combined with the Paris law to estimate the fatigue crack growth rate. In the case of roller burnished specimens, a numerical modification concerning experimental crack closure has to be considered. This method is applied to three specimens: without roller burnishing, and with two levels of roller burnishing (type A and type B). In all these cases, the computational finite element predictions of fatigue crack growth rate agree well with the experimental measurements. The developed model can be easily extended to crankshafts in real operating conditions.     

Crack closure in friction stir weldment using non‐linear model for fatigue crack propagation

The fatigue crack propagation in a friction stir‐welded sample has been simulated herein by means of two 3‐dimensional finite element method (FEM)‐based analyses. Numerical simulations of the fatigue crack propagation have been carried out by assuming a residual stress field as a starting condition. Two initial cracks, observed in the real specimen, have been assessed experimentally by performing fatigue tests on the welded sample. Hence, the same cracks have been placed in the corresponding FE model, and then a remote load with boundary conditions has been applied on the welded specimen. The material behaviour of the welded joint has been modelled by means of the Ramberg‐Osgood equation, while the non‐linear Kujawski‐Ellyin (KE) model has been adopted for the fatigue crack propagation under small‐scale yielding (SSY) conditions. Owing to the compressive nature of the residual stress field that acts on a part of the cracked regions, the crack closure phenomenon has also been considered. Then, the original version of the KE law has been modified to fully include the closure effect in the analysis. Later, the crack closure effect has also been assessed in the simulation of fatigue propagation of three cracks. Finally, an investigation of the fracture process zone (FPZ) extension as well as the cyclic plastic zone (CPZ) and monotonic plastic zone (MPZ) extensions have been assessed.     

The effect of compression stresses,stress level and stress order on fatigue crack growth of multiple site damage

Structural components are generally subjected to a wide stress spectrum over their lifetime. Service loads are accentuated at the areas of stress concentration, mainly at the connection of components. When there is a critical level of multiple site damage at connections, cracks link up to form a large crack which abruptly reduces the residual strength of the damaged structural member. Therefore, it is important to estimate the fatigue life before the cracks link up due to critical multiple site damage. In this study, the extended finite element method was applied to predict lifetime under constant amplitude cyclic loadings of fatigue tests on several multiple site damage specimens made of Al 2024‐T3. Then the multiple crack growths under service stress spectra are calculated to investigate the effects of compressive stress, stress orders and the effect of sequence cyclic loadings on stress levels by using Forman and NASGROW equations.     

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.     

Effects of Shot‐Peening on Fretting Fatigue Crack Growth Behavior in Ti‐6Al‐4V

Abstract: The effects of shot‐peening on fretting fatigue crack growth behaviour in titanium alloy, Ti‐6A1‐4V were investigated. Three shot‐peening intensities: 4A, 7A and 10A were considered. The analysis involved the fracture mechanics and finite element sub‐modelling technique to estimate crack propagation lives. These computations were supplemented with the experimentally measured total fretting fatigue lives of laboratory specimens to assess the crack initiation lives. Shot‐peening has significant effect on the initiation/propagation phases of fretting fatigue cracks; however this effect depends upon the shot‐peening intensity. The ratio of crack initiation and total life increased while the ratio of the crack propagation and total life decreased with an increase of shot‐peening intensity. Effects of residual compressive stress from shot‐peening on the crack growth behaviour were also investigated. The fretting fatigue crack propagation component of the total life with relaxation increased in comparison to its counterpart without relaxation in each shot‐peened intensity case while the initiation component decreased. Improvement in the fretting fatigue life from the shot‐peening and also with an increase in the shot‐peening intensity appears to be not always due to increase in the crack initiation resistance from shot‐peened induced residual compressive stress.     

Fatigue crack initiation assessment of welded joints accounting for residual stress

The impact of residual stresses on the fatigue crack initiation life of welded joints is evaluated by the finite element method. The residual stresses of nonload‐carrying cruciform joints, induced by welding and ultrasonic impact treatment, are modelled by initial stresses, using the linear superposition principle. An alternative approach of using modified stress‐strain curves in the highly stressed zone is also proposed to account for the residual stress effect on the local stress‐strain history. An evaluation of the fatigue crack initiation life of welded joints based on the local strain approach is carried out. The predicted results show the effect of residual stresses and agree well with published experimental results of as‐welded and ultrasonic impact treated specimens, demonstrating the applicability of both approaches. The proposed approaches may provide effective tools to evaluate the residual stress effect on the fatigue crack initiation life of welded joints.     

Coupled FEM–DBEM approach on multiple crack growth in cryogenic magnet system of nuclear fusion experiment ‘Wendelstein 7‐X’

At the Max Planck Institute for plasma physics in Greifswald, Germany, the world's largest nuclear fusion experiment of modular stellarator type Wendelstein 7‐X has started plasma operation. The hot hydrogen plasma is confined in a plasma vessel by an electromagnetic field generated by 50 non‐planar and 20 planar superconducting coils. The superconducting coils are encased in cast stainless steel housings. The coils are bolted onto a central support ring and welded together by so called lateral support elements (LSEs). In this paper, a procedure, based on a global–local finite element method (FEM)–dual boundary element method (DBEM) approach, is developed to simulate the propagation of multiple cracks detected in LSEs and undergoing a fatigue load spectrum. The global stress analysis on the superconducting coils is performed by FEM whereas the sub‐modelling approach is adopted to solve the crack propagation in the DBEM environment. The boundary conditions applied on the DBEM submodel are the displacements calculated by the FEM global analysis, in correspondence of the cut surfaces (there are no body forces nor external loads applied on the submodel volume). Two cracks are simultaneously introduced, and a linear elastic fracture mechanics analysis is performed. Results in terms of cracks growth rates and evolving crack shapes are provided, and the residual life of the component is forecast.     

Stress intensity factor solutions for estimation of fatigue lives of laser welds in lap-shear specimens

Fatigue behavior of laser welds in lap-shear specimens of high strength low alloy (HSLA) steel is investigated based on experimental observations and two fatigue life estimation models. Fatigue experiments of laser welded lap-shear specimens are first reviewed. Analytical stress intensity factor solutions for laser welded lap-shear specimens based on the beam bending theory are derived and compared with the analytical solutions for two semi-infinite solids with connection. Finite element analyses of laser welded lap-shear specimens with different weld widths were also conducted to obtain the stress intensity factor solutions. Approximate closed-form stress intensity factor solutions based on the results of the finite element analyses in combination with the analytical solutions based on the beam bending theory and Westergaard stress function for a full range of the normalized weld widths are developed for future engineering applications. Next, finite element analyses for laser welded lap-shear specimens with three weld widths were conducted to obtain the local stress intensity factor solutions for kinked cracks as functions of the kink length. The computational results indicate that the kinked cracks are under dominant mode I loading conditions and the normalized local stress intensity factor solutions can be used in combination with the global stress intensity factor solutions to estimate fatigue lives of laser welds with the weld width as small as the sheet thickness. The global stress intensity factor solutions and the local stress intensity factor solutions for vanishing and finite kinked cracks are then adopted in a fatigue crack growth model to estimate the fatigue lives of the laser welds. Also, a structural stress model based on the beam bending theory is adopted to estimate the fatigue lives of the welds. The fatigue life estimations based on the kinked fatigue crack growth model agree well with the experimental results whereas the fatigue life estimations based on the structural stress model agree with the experimental results under larger load ranges but are higher than the experimental results under smaller load ranges.     

Investigation of small fatigue crack initiation and growth behaviour of nickel base superalloy GH4169

Surface replication method was utilized to monitor the small fatigue crack initiation and growth process of single‐edge‐notch tension specimens fabricated by nickel base superalloy GH4169. Three different stress levels were selected. Results showed that small fatigue cracks of nickel base superalloy GH4169 initiated from grain boundaries or surface inclusions. The small fatigue crack initiation and growth stages took up about 80–90% of the total fatigue life. Multiple major cracks were observed in the notch root, and specimen with more major cracks seemed to have smaller fatigue life under the same test conditions. At the early growth stage, small crack behaviour might be strongly influenced by microstructures; thus, the crack growth rates had high fluctuations. However, the stress level effect on the small fatigue crack growth rates was not distinguishable for the three different stress levels. And no clear differences were found among the crack initiation lives by using replication technique.     

FATIGUE CRACK GROWTH UNDER MIXED-MODE I AND II LOADING

Abstract— Mixed-mode fatigue crack growth has been studied using four point bend specimens under asymmetric loads. A detailed finite element analysis provides the stress intensity factors for curved cracks under different mixed-mode load conditions. Both fatigue crack growth direction and crack growth rate are studied. The maximum tangential stress and the minimum strain energy density criteria were found to provide satisfactory predictions of the crack growth directions. An effective stress intensity factor was used to correlate the fatigue crack growth rates successfully. It is found that the use of mode I fatigue crack growth rate properties results in a conservative crack growth rate prediction for mixed-mode load conditions.     

Fatigue behaviour of friction stir welded AA2024‐T3 alloy: longitudinal and transverse crack growth

The fatigue crack growth properties of friction stir welded joints of 2024‐T3 aluminium alloy have been studied under constant load amplitude (increasing‐ΔK), with special emphasis on the residual stress (inverse weight function) effects on longitudinal and transverse crack growth rate predictions (Glinka's method). In general, welded joints were more resistant to longitudinally growing fatigue cracks than the parent material at threshold ΔK values, when beneficial thermal residual stresses decelerated crack growth rate, while the opposite behaviour was observed next to K_C instability, basically due to monotonic fracture modes intercepting fatigue crack growth in weld microstructures. As a result, fatigue crack growth rate (FCGR) predictions were conservative at lower propagation rates and non‐conservative for faster cracks. Regarding transverse cracks, intense compressive residual stresses rendered welded plates more fatigue resistant than neat parent plate. However, once the crack tip entered the more brittle weld region substantial acceleration of FCGR occurred due to operative monotonic tensile modes of fracture, leading to non‐conservative crack growth rate predictions next to K_C instability. At threshold ΔK values non‐conservative predictions values resulted from residual stress relaxation. Improvements on predicted FCGR values were strongly dependent on how the progressive plastic relaxation of the residual stress field was considered.     

The effect of residual stresses arising from laser shock peening on fatigue crack growth

Residual stresses have in the past been introduced to manipulate growth rates and shapes of cracks under cyclic loads. Previously, the effectiveness of shot peening in retarding the rate of fatigue crack growth was experimentally studied. It was shown that the compressive residual stresses arising from the shot peening process can affect the rate of crack growth. Laser shock peening can produce a deeper compressive stress field near the surface than shot peening. This advantage makes this technique desirable for the manipulation of crack growth rates. This paper describes an experimental program that was carried out to establish this effect in which steel specimens were partially laser peened and subsequently subjected to cyclic loading to grow fatigue cracks. The residual stress fields generated by the laser shock peening process were measured using the neutron diffraction technique. A state of compressive stress was found near the surface and tensile stresses were measured in the mid-thickness of the specimens. Growth rates of the cracks were observed to be more affected by the tensile core than by the compressive surface stresses.     

Influence of residual stresses from shot peening on fretting fatigue crack growth

One method to improve fretting fatigue life is to shot peen the contact surfaces. Experimental fretting life results from specimens in a Titanium alloy with and without shot peened surfaces were evaluated numerically. The residual stresses were measured at different depths below the fretting scar and compared to the corresponding residual stress profile of an unfretted surface. Thus, the amount of stress relaxation during fretting tests was estimated. Elastic–plastic finite element computations showed that stress relaxation was locally more significant than that captured in the measurements. Three different numerical fatigue crack growth models were compared. The best agreement between experimental and numerical fatigue lives for both peened and unpeened specimens was achieved with a parametric fatigue growth procedure that took into consideration the growth behaviour along the whole front of a semi‐elliptical surface crack. Furthermore, the improved fretting fatigue life from shot peening was explained by slower crack growth rates in the shallow surface layer with compressive residual stresses from shot peening. The successful life analyses hinged on three important issues: an accurate residual stress profile, a sufficiently small start crack and a valid crack growth model.     

Fatigue growth prediction of center slant crack in rectangular plate

This paper presents a numerical prediction model of mixed‐mode crack fatigue growth in a plane elastic plate. It involves a formulations of fatigue growth of multiple crack tips under mixed‐mode loading and a displacement discontinuity method with crack‐tip elements (a boundary element method) proposed recently by Yan is extended to analyse the fatigue growth process of multiple crack tips. Due to an intrinsic feature of the boundary element method, a general growth problem of multiple cracks can be solved in a single‐region formulation. In the numerical simulation, for each increment of crack extension, remeshing of existing boundaries is not necessary. Crack extension is conveniently modelled by adding new boundary elements on the incremental crack extension to the previous crack boundaries. At the same time, the element characters of some related elements are adjusted according to the manner in which the boundary element method is implemented. As an example, the present numerical approach is used to analyse the fatigue growth of a centre slant crack in a rectangular plate. The numerical results illustrate the validation of the numerical prediction model and can reveal the effect of the geometry of the cracked plate on the fatigue growth.     

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).     

Synchrotron diffraction investigation of the distribution and influence of residual stresses in fatigue

This paper presents some results obtained from synchrotron diffraction investigations into two somewhat related areas of interest to the fatigue community. Firstly, the influence of fatigue cycling on the distribution and magnitude of residual strains and stresses and, secondly, the residual strains and stresses engendered around a growing fatigue crack. Its main premise is that modern tools such as automated synchrotron strain scanning offer the potential for more complete insight into the distribution of residual strains and stresses and their influence on fatigue performance. The first part of the work was accomplished using friction‐stir welded (FSW) and metal‐inert gas (MIG) welded specimens. The particular interest in these specimens was obtaining detailed knowledge regarding as‐welded variation in residual stresses between specimens, the location of peak values relative to local microstructure and stress concentrations, and of their modification during fatigue cycling. Such information may indicate a route forward to the selection of welding process parameters for optimised fatigue performance. The second part of the work considered an established fatigue crack in a compact tension (CT) specimen and examined the ability of synchrotron diffraction to characterize the stresses associated with the plastic enclave around a fatigue crack. This work is of interest in the context of better knowledge of crack‐tip shielding by plasticity‐induced closure and its incorporation into life prediction methodologies.     

Fatigue crack growth through a residual stress field introduced by plastic beam bending

We present predictions and measurements of fatigue crack growth rates in plastically bent aluminium 2024‐T351 beams. Beam bending and fatigue were carefully controlled to minimize factors other than residual stress that could affect the fatigue crack growth rate, such as large plastic strains or residual stress relaxation. The residual stress introduced by bending was characterized by a bending method and by the slitting method, with excellent agreement between the two methods. Crack growth rates were predicted by three linear elastic fracture mechanics (LEFM) superposition based methods and compared to experimental measurements. The prediction that included the effects of partial crack closure correlated with experimental data to within the variability normally observed in fatigue crack growth rate testing of nominally residual stress free material. Therefore, we conclude that crack growth through residual stress fields may be predicted using the concept of superposition as accurately as crack growth through residual stress free material, provided that the residual stress is accurately known, the residual stress remains stable during fatigue, the material properties are not changed by the introduction of residual stress, and that the effect, if any, of partial crack closure is taken into account.     

Foreign object damage and fatigue crack threshold: Cracking outside shallow indents

Foreign Object Damage (FOD) usually happens when objects are ingested into jet engines powering military or civil aircraft. Under extreme conditions, FOD can lead to severe structural damage. More commonly it produces local impacted sites of the fan and compressor airfoils, lowering fatigue life of these components. FOD is a prime cause for maintenance and repair in aircraft engines. In this paper, a framework for analyzing FOD and its effect on fatigue cracking is established. A finite element analysis is used to identify three relevant regimes of FOD related to the depth of penetration into the substrate, and to determine the residual stresses. Most of the emphasis in this paper focuses on fatigue cracks emerging from shallow indentations, which are generally expected to be of most practical concern. Full three-dimensional finite element solutions are obtained for semi-circular surface cracks emerging from specific locations at the indentation revealing the influence of the residual stress on the stress intensity factor distribution. For shallow indents, a relatively simple dimensionless formula for the relation between the residual stress intensity factor, the crack size, and the indentation width are developed. These results, together with results for the intensity factor variations due to cyclic loading, have been used to address the question: To what extent do the residual stresses caused by the FOD reduce the critical crack size associated with threshold fatigue crack growth? Formulas for the critical crack size are obtained. Specific results are presented for the blade alloy, Ti-6Al-4V, revealing that FOD can reduce the critical crack size by as much as 60%.