Verformungsverhalten und rechnerische Abschätzung der Ermüdungslebensdauer metallischer Werkstoffe unter mehrachsig nichtproportionaler Beanspruchung

Deformation behaviour and numerical fatigue lifetime prediction of metallic materials under multiaxial nonproportional loading The development and evaluation of a model for lifetime prediction under multiaxial nonproportional loading is the aim of the current research project. It is assumed that the technical crack initiation life is consumed by short crack growth. This phenomenon is described using a fracture mechanics based approach. Herein, the effective cyclic J‐integral is used as crack tip parameter. Crack opening levels and J‐integral values are calculated applying approximation formulas. A plasticity model that is based on the Jiang model [Jia93] and extended to describe nonproportional hardening is used to predict the deformation behaviour. Experimental investigations on tubular and notched specimens with a wide range of different loading spectra serve for the verification of the model and for the identification of damage mechanisms.     

Deformation behaviour,short crack growth and fatigue livesunder multiaxial nonproportional loading

Experimental results of a research project on short crack growth under multiaxial nonproportional loading are presented. Fatigue lives, crack growth curves and the deformation behaviour of hollow tube specimens and notched specimens were investigated under combined tension and torsion loading. The results served as basis for the development of a cyclic plasticity model [Döring R, Hoffmeyer J, Vormwald M, Seeger T. A plasticity model for calculating stress–strain sequences under multiaxial nonproportional cyclic loading. In: Comput Mater Sci. 28(3–4);2003:587–96; Döring R, Hoffmeyer J, Seeger T, Vormwald M. Constitutive modelling of nonproportional hardening, cyclic hardening and ratchetting. In: Proceedings of the seventh international conference on biaxial/multiaxial fatigue and fracture, DVM, Berlin; 2004. p. 291–6; Hoffmeyer J. Anrisslebensdauervorhersage bei mehrachsiger Beanspruchung auf Basis des Kurzrisskonzepts. PhD-Thesis, TU Darmstadt; 2004.] and a short crack model [Hoffmeyer J. Anrisslebensdauervorhersage bei mehrachsiger Beanspruchung auf Basis des Kurzrisskonzepts. PhD-Thesis, TU Darmstadt; 2004; Döring R, Hoffmeyer J, Seeger T, Vormwald M. Fatigue lifetime prediction based on a short crack growth model for multiaxial nonproportional loading. In: Proceedings of the seventh international conference on biaxial and multiaxial fatigue and fracture, DVM, Berlin; 2004. p. 253–8].Stress–strain paths including nonproportional hardening and experimental fatigue lives of the unnotched specimens under different loading cases are discussed and compared with calculations. Load-time-sequences were in-phase, 45° and 90° out-of-phase loading with constant and variable amplitudes, torsion without and with superimposed static normal stress, and strain paths like box, butterfly, diamond and cross path. For the notched specimens fatigue lives under 0° and 90° out-of-phase loading are compared with calculations based on finite element results and the short crack model. During some tests the initiation, growth and orientation of short cracks was studied using the plastic replica technique.     

Threshold stress intensity factor and crack growth rate prediction under mixed-mode loading

A new mixed-mode threshold stress intensity factor is developed using a critical plane-based multiaxial fatigue theory and the Kitagawa diagram. The proposed method is a nominal approach since the fatigue damage is evaluated using remote stresses acting on a cracked component rather than stresses near the crack tip. An equivalent stress intensity factor defined on the critical plane is proposed to predict the fatigue crack growth rate under mixed-mode loading. A major advantage is the applicability of the proposed model to many different materials, which experience either shear or tensile dominated crack growth. The proposed model is also capable to nonproportional fatigue loading since the critical plane explicitly considers the influence of the load path. The predictions of the proposed fatigue crack growth model under constant amplitude loading are compared with a wide range of fatigue results in the literature. Excellent agreements between experimental data and model predictions are observed.     

Fatigue of engineering structures under combined nonproportional loads: An overview

Nonproportionality in fatigue is a matter of loading sequences acting on structures. In such loading cases, a life assessment‐based search of the initiation site is required. This means that for a variety of potential sites, their stress‐strain sequences must be determined and the corresponding fatigue lives have to be calculated. For the determination of local stress‐strain sequences, a superposition of the action of loads at all times for all potential sites must be performed. The superposition has not only to be performed at a particular time of a load reversal but also for a sufficiently large number of intermediate points in time. For the assessment of crack initiation under local nonproportional stress‐strain sequences, a multiaxial fatigue damage hypothesis must be specified. Due to the superiority with respect to accuracy, critical plane approaches are the favourite ones when dealing with nonproportional fatigue of ductile metals. For describing fatigue crack growth, the time sequences for the stress intensity factors corresponding to the 3 opening modes must be obtained by superposition. A mixed‐mode hypothesis must be applied to predict both the direction and the increment of crack growth at each crack front point. A first prediction trial should be based on an appropriate extension of the maximum tangential stress hypothesis. An application of a variant of the maximum shear stress hypothesis might be an amendment. Especially in the case of crack turning, the consideration of crack face contact is mandatory.     

Durability assessment via residual strength and viscoelastic observations on filled rubber compounds

Because rubber compounds are widely used under cyclic loading conditions, such as tire applications, their fatigue behaviour has been studied for a long time. Two main stages are commonly considered in studying rubber fatigue: crack nucleation and crack growth. Not many studies exist on the residual strength of rubber subsequent to fatigue loading. In this study, the residual strength method is used to model fatigue behaviour of carbon black‐filled and silica‐filled styrene‐butadiene rubber (SBR) compounds. Samples are subjected to repeated fatigue loading (ie, nonzero mean stress) using different strain amplitudes and then subjected to uniaxial constant crosshead rate, relaxation, and creep tests to assess their residual strength and viscoelastic behaviours respectively. The residual strength results are compared with typical S‐N curves. Initial relaxation rates, initial creep rates, asymptotic relaxation values, and secondary creep rates are plotted as functions of fatigue cycle number to understand the viscoelastic behaviours of carbon black and silica‐filled SBR compounds as affected by fatigue processes.     

Numerical modeling and simulation of wheel radial fatigue tests

A computational methodology is proposed for fatigue damage assessment of metallic automotive components and its application is presented with numerical simulations of wheel radial fatigue tests. The technique is based on the local strain approach in conjunction with linear elastic FE stress analyses. The stress–strain response at a material point is computed with a cyclic plasticity model coupled with a notch stress–strain approximation scheme. Critical plane damage parameters are used in the characterization of fatigue damage under multiaxial loading conditions. All computational modules are implemented into a software tool and used in the simulation of radial fatigue tests of a disk-type truck wheel. In numerical models, the wheel rotation is included with a nonproportional cyclic loading history, and dynamic effects due to wheel–tire interaction are neglected. The fatigue lives and potential crack locations are predicted using effective strain, Smith–Watson–Topper and Fatemi–Socie parameters using computed stress–strain histories. Three-different test conditions are simulated, and both number of test cycles and crack initiation sites are estimated. Comparisons with the actual tests proved the applicability of the proposed approach.     

Lebensdauerberechnung festgewalzter Kerbproben unter Axialbelastung auf der Basis eines Rißfortschrittskonzepts

Axial fatigue life calculation of fillet rolled specimens by means of a crack growth model Fillet rolling is a method which significantly improves the fatigue strength of members. Residual compressive stresses induced in the surface layer during the fillet rolling process are able to retard or prevent crack propagation. An elastic‐plastic on the J‐integral based crack growth model considering the crack opening and closure phenomenon in nonhomogeneous plastic stress fields is described. Experimentally determined crack growth curves and fracture fatigue life curves at constant amplitude loading were used to verify the developed model.     

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.     

Prediction of fatigue lifetime under multiaxial cyclic loading using finite element analysis

Life prediction for GH4169 superalloy thin tubular and notched specimens were investigated under proportional and nonproportional loading with elastic–plastic finite element analysis (FEA). A strain-controlled tension–torsion loading was carried out by applying the axial and circular displacements on one end of the specimen in the cylindrical coordinate system. Uniaxial cyclic stress–strain data at high temperature were used to describe the multi-linear kinematic hardening of the material. The comparison between FEA and experimental results for thin tubular specimen showed that the built model of FE is reliable. A fatigue damage parameter was proposed to predict the fatigue crack initiation life for notched specimen. The results showed that a good agreement was achieved with experimental data.     

Crack growth in ferroelectric ceramics under electric loading

Summary A crack with growth in ferroelectric ceramics under purely electric loading is analyzed. The crack tip stress intensity factor for the growing crack under small scale conditions is evaluated by employing the model of nonlinear domain switching. The electrical fracture toughness is obtained from the result of the stress intensity factor. It is shown that the ferroelectric material can be either toughened or weakened as the crack grows. Fatigue crack growth in a ferroelectric material under cyclic electric loading is also examined. The incremental fatigue crack growth under cyclic electric loading is obtained numerically. The fatigue crack growth rate is affected strongly by the electrical nonlinear behavior. It is found that the curve of fatigue crack growth rate versus electric field intensity factor is linear on the log-log plot at intermediate values of the electric field intensity factor.     

Numerical simulation of constraint effects in fatigue crack growth

The computational analysis of constraint effects on fatigue crack growth is discussed. An irreversible cohesive zone model is used in the computations to describe the processes of material separation under cyclic loading. This approach is promising for the investigation of fatigue crack growth under constraint as the energy dissipation due to the formation of new crack surface and cyclic plastic deformation is accounted for independently. Fatigue crack growth in multi-layer structures under consideration of different levels of T-stress are conducted with a modified boundary layer model. Fatigue crack growth is computed as a function of layer thickness and T-stress for constant and variable amplitude loading cases.     

Messung und Modellierung der Lebensdauer der Legierung AlCuMg2 unter zweistufiger Schwingbeanspruchung

Fatigue lifetime investigations on Aluminium 2024 under two stage cyclic loading by means of experiments and three microstructural models The aim of this work is to achieve information about the development of fatigue failure in the aluminium alloy 2024. The attention was focused on short fatigue cracks under cyclic loading and the occurring load sequence effects on lifetime under two‐level cyclic loading. Following the experiments, a revision of three different microstructural crack growth models, which were found in the literature, was made. Based on the data of constant‐level cyclic loading, predictions of two‐level cyclic loading behaviour were made and compared with the experimentally measured crack propagation rates and reached lifetimes.     

Monotonic and Cyclic Deformations of Case‐Hardened Steels Including Residual Stress Effects

Abstract: Monotonic and cyclic deformations of case‐hardened steel specimens under axial loading were investigated experimentally and analytically. A finite element (FE) model for the case‐hardened specimens was constructed to study multiaxial stresses due to different plastic flow behaviour between the case and the core, as well as to evaluate residual stress relaxation and redistribution subsequent to cyclic loading. The multiaxial stress is shown to increase the effective stress on the surface, and, therefore, unfavourable to yielding or fatigue crack nucleation. The residual stresses are shown to relax or redistribute, even in the elastic‐behaving region, when any part of a case‐hardened specimen or component undergoes plastic deformation. Multi‐layer models were used to analyse and predict monotonic and cyclic deformation behaviours of the case‐hardened specimen based on the core and case material properties, and the results are compared with the experimental as well as FE model results. The predicted monotonic stress–strain curves were close to the experimental curves, but the predicted cyclic stress–strain curves were higher than the experimental curves.     

A computationally efficient cohesive zone model for fatigue

A cohesive zone model has been developed for the simulation of both high and low cycle fatigue crack growth. The developed model provides an alternative approach that reflects the computational efficiency of the well‐established envelop‐load damage model yet can deliver the accuracy of the equally well‐established loading‐unloading hysteresis damage model. A feature included in the new cohesive zone model is a damage mechanism that accumulates as a result of cyclic plastic separation and material deterioration to capture a finite fatigue life. The accumulation of damage is reflected in the loading‐unloading hysteresis curve, but additionally, the model incorporates a fast‐track feature. This is achieved by “freezing in” a particular damage state for one loading cycle over a predefined number of cycles. The new model is used to simulate mode I fatigue crack growth in austenitic stainless steel 304 at significant reduction in the computational cost.     

Elastic–plastic fatigue crack growth analysis under variable amplitude loading spectra

Most fatigue loaded components or structures experience a variety of stress histories under typical operating loading conditions. In the case of constant amplitude loading the fatigue crack growth depends only on the component geometry, applied loading and material properties. In the case of variable amplitude loading the fatigue crack growth depends also on the preceding cyclic loading history. Various load sequences may induce different load-interaction effects which can cause either acceleration or deceleration of fatigue crack growth. The recently modified two-parameter fatigue crack growth model based on the local stress–strain material behaviour at the crack tip [1,2] was used to account for the variable amplitude loading effects. The experimental verification of the proposed model was performed using 7075-T6 aluminum alloy, Ti-17 titanium alloy, and 350WT steel. The good agreement between theoretical and experimental data shows the ability of the model to predict the fatigue life under different types of variable amplitude loading spectra.     

Fatigue crack propagation assessment based on residual stresses obtained through cut-compliance technique

Crack growth rate versus crack length curves of heavily overloaded parent material specimens and fatigue crack propagation curves of friction‐stir‐welded aluminium samples are presented. It is shown that in both cases the residual stresses have a strong effect on the crack propagation behaviour under constant and variable amplitude loading. As a simplified engineering approach, it is assumed in this paper, that in both cases residual stresses are the main and only factor influencing crack growth. Therefore fatigue crack propagation predictions are performed by adding the residual stresses to the applied loading and by neglecting the possible effects of overloading and friction stir welding on the parent material properties. For a quantitative assessment of the residual stress effects, the stress intensity factor due to residual stresses K_res is determined directly with the so‐called cut‐compliance method (incremental slitting). These measurements are particularly suited as input parameters for the software packages AFGROW and NASGRO 3.0, which are widely used for fatigue crack growth predictions under constant and variable amplitude loading. The prediction made in terms of crack propagation rates versus crack length and crack length versus cycles generally shows a good agreement with the measured values.     

A Continuum Mechanics Approach for Crack Initiation and Crack Growth Predictions

Very often, different approaches are used for crack initiation and crack growth predictions. The current article introduces a recently developed approach that can be used for the predictions of both crack initiation and crack propagation. A basic assumption is that both crack nucleation and crack growth are governed by the same fatigue damage mechanisms and a single fatigue damage criterion can model both stages. A rule is that any material point fails to form a fresh crack if the total accumulated fatigue damage reaches a limit. For crack initiation predictions, the stresses and strains are obtained either directly from experiments or though a numerical analysis. For the prediction of crack growth, the approach consists of two steps. Elastic‐plastic stress analysis is conducted to obtain the detailed stress‐strain responses. A general fatigue criterion is used to predict fatigue crack growth. Compact specimens made of 1070 steel were experimentally tested under constant amplitude loading with different R‐ratios and the overloading influence. The capability of the approach to predict both crack initiation and the crack growth under these loading conditions was demonstrated by comparing the predictions with the experimental observations.     

Numerical investigation of fatigue characteristics of concrete pavement

In concrete pavements, fatigue is one of the major causes of distress. Repeated loads result in the formation of cracks. The propagation of these cracks cause internal progressive damage within the structure, which ultimately leads to failure of the pavement due to fatigue. This paper presents a theoretical investigation of crack propagation within concrete pavement and its fatigue characteristics under cyclic loading. A numerical fatigue performance model has been developed for this purpose. The model is based on fictitious crack approach for the propagation of cracks and stress degradation approach for estimating the bridging stress under cyclic loading. Using the numerical model, a parametric study has been performed for a typical concrete pavement to evaluate its fatigue characteristics for different foundation strengths. The method can be used for prediction of crack propagation in concrete pavement under cyclic loading and gives an estimate of the incremental damage or the entire crack history of the pavement.     

A numerical analysis of constraint effects in fatigue crack growth by use of an irreversible cohesive zone model

The analysis of constraint effects in fatigue crack growth in multi-layer structures is discussed. The process of material separation under cyclic loading is described by a cohesive zone model (CZM) with an irreversible constitutive relationship. The traction–separation behavior does not follow a predefined path, but is dependent on the evolution of the damage dependent cohesive zone properties. A modified boundary layer model is used in simulations of fatigue crack growth along the centerline crack of the metal layer sandwiched between two elastic substrates. Fatigue crack growth is computed for a series of values of metal layer thickness under constant and variable amplitude loading conditions. The results of the computations demonstrate that certain combinations of load magnitude, layer thickness and material properties results in significant constrain effects in fatigue crack growth. The influence of these constraint effects on fatigue crack growth rates and on crack closure processes is determined. The evolutions of the traction–separation law, the accumulated and current plastic zones, as well as the stress fields during the crack propagation are discussed.