Micromechanical modeling of short fatigue cracks

This paper gives an overview over the micromechanical modeling approaches of short fatigue cracks. Until now many approaches have been presented in the literature, which differ significantly in their degree of complexity ranging from simple empirical or analytical models to complex models based on numerical solutions. In recent years different trends were observed: On the one hand detailed models are presented, which describe the propagation of a microstructurally short fatigue crack in a physically sound way based on discrete dislocations. However, their application is somewhat limited due to their complexity regarding the application in real microstructures. Thus, another trend is to develop models closely related to experimental research work to identify and focus on the main aspects of short fatigue crack growth.     

Micromechanical finite element modelling of thermo-mechanical fatigue for P91 steels

In this paper, the cyclic plasticity and fatigue crack initiation behaviour of a tempered martensite ferritic steel under thermo-mechanical fatigue conditions is examined by means of micromechanical finite element modelling. The crystal plasticity-based model explicitly reflects the microstructure of the material, measured by electronic backscatter diffraction. The predicted cyclic thermo-mechanical response agrees well with experiments under both in-phase and out-of-phase conditions. A thermo-mechanical fatigue indicator parameter, with stress triaxiality and temperature taken into account, is developed to predict fatigue crack initiation. In the fatigue crack initiation simulation, the out-of-phase thermo-mechanical response is identified to be more dangerous than in-phase response, which is consistent with experimental failure data. It is shown that the behaviour of thermo-mechanical fatigue can be effectively predicted at the microstructural level and this can lead to a more accurate assessment procedure for power plant components.     

A methodology for strain-based fatigue reliability analysis

A significant scatter of the cyclic stress–strain (CSS) responses should be noted for a nuclear reactor material, 1Cr18Ni9Ti pipe-weld metal. Existence of the scatter implies that a random cyclic strain applied history will be introduced under any of the loading modes even a deterministic loading history. A non-conservative evaluation might be given in the practice without considering the scatter.A methodology for strain-based fatigue reliability analysis, which has taken into account the scatter, is developed. The responses are approximately modeled by probability-based CSS curves of Ramberg–Osgood relation. The strain–life data are modeled, similarly, by probability-based strain–life curves of Coffin–Manson law. The reliability assessment is constructed by considering interference of the random fatigue strain applied and capacity histories. Probability density functions of the applied and capacity histories are analytically given. The methodology could be conveniently extrapolated to the case of deterministic CSS relation as the existent methods did. Non-conservative evaluation of the deterministic CSS relation and availability of present methodology have been indicated by an analysis of the material test results.     

Cyclic fatigue of ZTC — Micromechanical modelling

Crack bridging is an important mechanism in zirconia toughened ceramics (ZTC). A micromechanical model describing the toughening induced by this mechanism is first briefly recapitulated. The metastable tetragonal zirconia precipitates in the ceramic matrix transform to monoclinic phase under high stresses due to macrocracks in the matrix. The toughening of the latter results not only from this phase transformation but also because the precipitates impede the progress of the macrocrack and trap it. The combined effect of these two mechanisms in the bridged zone ahead of the open macrocrack is modelled by a distribution of nonlinear springs whose stiffness is determined from the transformation and geometrical characteristics of the precipitates.

Next, a micromechanical model is developed in two steps for the crack growth rate in ZTC under cyclic loading. In the first step, a model for the growth rate of a single sharp crack in a t → m phase transforming material is established. In the next step, this model is combined with the above mentioned crack bridging model. The resulting model predicts not only the crack growth rate, but also the stepwise growth pattern of the crack front under cyclic loading that has been observed in ZTC.     

Micromechanical simulations of microstructure-sensitive Stage I fatigue crack growth

Simulations of dislocation dynamics at the tip of a Stage I crack are performed, taking into account the influence of the normal stress on the friction of the crack flanks and on the condition for dislocation emission at the crack tip. The interactions of the emitted dislocations with microstructural obstacles are analysed. The repeated decelerations and sometimes arrests that characterize Stage I crack growth are properly described by the model, and the differences in Stage I kinetics observed in reversed torsion and push–pull are analysed in terms of crack tip–grain boundary interactions.     

Micromechanical analysis of fatigue cracks in cord–rubber composites

Analyses of two different types of cracks due to fatigue of cord–rubber composites is carried out using micromechanical two-dimensional (2D) and three-dimensional (3D) finite element analysis. The fracture parameter, tearing energy (TE)/J-integral that characterizes the severity of crack tip stresses in rubber composites, is computed from the finite element results of stresses and strains. The results obtained are validated with existing analytical methods in the literature. Numerical results of J-integral values are presented for two crack types, and crack sizes under transverse strain and shear strain loading conditions. The results presented illustrate that crack type, loading, and crack size have a strong effect on the values of J-integral. The results of the J-integral should help our understanding in estimating the severity of local failures in cord–rubber composites.     

Micromechanical study of the loading path effect in high cycle fatigue

In this work, an analysis of both the mechanical response at the grain scale and high cycle multiaxial fatigue criteria is undertaken using finite element (FE) simulations of polycrystalline aggregates. The metallic material chosen for investigation, a pure copper, has a Face Centred Cubic (FCC) crystalline structure. Two-dimensional polycrystalline aggregates, which are composed of 300 randomly orientated equiaxed grains, are loaded at the median fatigue strength defined at 10⁷ cycles. In order to analyse the effect of the loading path on the local mechanical response, combined tension–torsion and biaxial tension loading cases, in-phase and out-of-phase, with different biaxiality ratios, are applied to each polycrystalline aggregate. Three different material constitutive models assigned to the grains are investigated: isotropic elasticity, cubic elasticity and crystal plasticity in addition to the cubic elasticity. First, some aspects of the mechanical response of the grains are highlighted, namely the scatter and the multiaxiality of the mesoscopic responses with respect to an uniaxial macroscopic response. Then, the distributions of relevant mechanical quantities classically used in fatigue criteria are analysed for some loading cases and the role of each source of anisotropy on the mechanical response is evaluated and compared to the isotropic elastic case. In particular, the significant influence of the elastic anisotropy on the mesoscopic mechanical response is highlighted. Finally, an analysis of three different fatigue criteria is conducted, using mechanical quantities computed at the grain scale. More precisely, the predictions provided by these criteria, for each constitutive model studied, are compared with the experimental trends observed in metallic materials for such loading conditions.     

Micromechanical interactions in a superduplex stainless steel subjected to low cycle fatigue loading

Micromechanical interactions in an austenitic‐ferritic SAF 2507 steel under lowcycle fatigue loading was studied by experiment and simulation. Neutron diffraction measurements of residual lattice strains were made on specimens unloaded from different cyclic deformation stages, namely cyclic hardening, softening and saturation. With self‐consistent modelling, the micromechanical behaviour of the constituent phases was studied for the first loading cycle. The evolution of the residual lattice strain distributions with cyclic loading and the development of phase stresses have been analysed with respect to the initial residual stress field and the different mechanical properties of the constituent phases.     

Analytical methodology for predicting fatigue life distribution of fuselage splices

Methodologies to predict fatigue life distribution of fuselage splices, measured as the number of cycles to visible cracks, were developed in this work. Modeling procedures using three dimensional nonlinear finite element (FE) analysis were developed to obtain the stress state at the rivet hole. Contact surfaces, which include friction effects, were used to simulate the rivet to hole and skin to skin interactions. The squeezing force (SF) resulting from the riveting process and the coefficient of friction (CF) used for the contact surfaces were taken as random variables. Analytical expressions for local stress as a function of the squeezing force and coefficient of friction were developed using a response surface technique along with limited FE analyses. Based on the calculated local stresses, a strain-life approach was employed to predict fretting fatigue crack nucleation at the rivet hole. A Monte Carlo simulation was developed, which integrated the two random variables into the models, to determine the fatigue life distribution to visible cracks. Results from the simulation showed that the predicted fatigue life distribution correlated very well with the existing test data. Further sensitivity studies indicated that the squeezing force has a stronger influence on the life distribution than the coefficient of friction.     

A methodology and criterion for acrylic bone cement fatigue tests

Acrylic bone cement is used as a fixing device in total hip arthroplasty and it is based on polymethyl-methacrylate. Fatigue failure of the cement is the primary cause of loosening of cemented arthroplasties. Pores form in the acrylic material during mixing and curing, and an analysis of the fatigue life of the cement requires the elimination of the critical macropores, defined as having a diameter > 1 mm, which may bias the outcome of tests. Previous workers have rejected fatigue specimens either on a qualitative basis or at a specified pore size level. However various different thresholds have been considered but currently there is no quantitative criterion to define them. This investigation proposes a quantitative criterion for establishing a critical macropore size rejection threshold for fatigue specimens, and discusses the effectiveness of this criterion based on fatigue tests of radiopaque cement specimens.     

One-way Fluid Structure Interaction modelling methodology for boiler tube fatigue failure

A modelling methodology developed for dealing with fatigue failures on large boiler tube assemblies, as used by power generation industries, is described. Boiler tube fatigue failures are resultant to a coupled combination of fluid flow and heat transfer mechanisms, inducing thermal expansion leading to fatigue failure. A combination of modelling tools is effectively combined for one-way Fluid Structure Interaction, solving for and extracting stress results efficiently. A one dimensional fluid solver is used to approximate and model the thermal flow components. The study case considered implemented the developed methodology on a quarter boiler hopper section made up of 3022 tube and membrane structure with a collective length of 4787 m. Operating conditions are iteratively adjusted in the one dimensional pipe flow model until a correlation is formed with instrumented data. This validated model enables further use for various postulated plant conditions and operational sequences through transient start-up conditions. The boiler tube temperatures obtained from the one dimensional model are transferred and used as boundary conditions in a full three dimensional finite element analysis where deformations are solved for and stress results obtained due to thermal expansion within the boiler tube walls and the adjacent support structure. The model is used for redesign of sections of the boiler to reduce stress in those areas and subsequently reduce fatigue failures.     

A 'crack-like' notch analogue for a safe-life fretting fatigue design methodology

Various analogies have recently been proposed for comparing the stress fields induced in fretting fatigue contact situations, with those of a crack and a sharp or a rounded notch, resulting in a degree of uncertainty over which model is most appropriate in a given situation. However, a simple recent approach of Atzori–Lazzarin for infinite‐life fatigue design in the presence of a geometrical notch suggests a corresponding unified model also for fretting fatigue (called Crack‐Like Notch Analogue model) considering only two possible behaviours: either ‘crack‐like’ or ‘large blunt notch.’ In a general fretting fatigue situation, the former condition is treated with a single contact problem corresponding to a Crack Analogue model; the latter, with a simple peak stress condition (as in previous Notch Analogue models), simply stating that below the fatigue limit, infinite life is predicted for any size of contact. In the typical situation of constant normal load and in phase oscillating tangential and bulk loads, both limiting conditions can be readily stated. Not only is the model asymptotically correct if friction is infinitely high or the contact area is very small, but also remarkably accurate in realistic conditions, as shown by excellent agreement with Hertzian experimental results on Al and Ti alloys. The model is useful for preliminary design or planning of experiments reducing spurious dependences on an otherwise too large number of parameters. In fact, for not too large contact areas (‘crack‐like’ contact) no dependence at all on geometry is predicted, but only on three load factors (bulk stress, tangential load and average pressure) and size of the contact. Only in the ‘large blunt notch’ region occurring typically only at very large sizes of contact, does the size‐effect disappear, but the dependence is on all other factors including geometry.     

A methodology for the fatigue design of notched castings in gray cast iron

Fatigue failures of machine components remain a topic of relevant importance in the industrial world. They usually occur from geometrical features such as holes, notches, corners and grooves, whose actual influence is not well estimated in the design phase. Cast parts made in gray cast iron are typical examples of components difficult to design in fatigue because they are simultaneously characterized by complex geometries and microstructure. In this contribution the issue is discussed starting from the failure analysis of a cyclically pressurized hydraulic component. The work consists of an experimental procedure, i.e. the fatigue characterization of the material on specimens extracted from cast parts, and of a numerical design activity, i.e. the prediction of life time according to the critical distance method [Taylor D. Crack modelling: a technique for the fatigue design of components. Engng Fail Anal 1996;3(2):129-36]. The implication is that cracks and localized damage begin to appear in the microstructure of gray cast iron at sharp notches from the first cycles of loading. In order to obtain a correct prediction, the fatigue design should adopt fracture mechanics arguments to determine non-propagating conditions.     

A methodology for predicting creep/fatigue crack growth rates in Ti 6246

A methodology has been developed which is capable of predicting creep/fatigue crack growth rates at ambient and elevated temperatures in Ti 6246. Predictions are based on finite element analysis and strain-control testing of plain specimens. The prediction of fatigue crack growth rates for a given crack configuration and cyclic plastic zone size is assumed to be consistent with the processes leading to crack initiation in plain specimens. Such an assumption leads to the conclusion that a similar stress–strain profile will lead to similar lives in both the plain specimens and in the cyclic plastic zone ahead of a crack in a notched specimen. Therefore, fatigue crack growth results from the accumulation of damage in the cyclic plastic zone ahead of the crack tip. Once the damage accumulated in this element of material becomes critical, the crack propagates through the damaged region into a new region of virgin material where the process of damage accumulation begins again. The creep/fatigue model is described and assessed with reference to measured fatigue crack growth rate data for Ti 6246 at 20 °C and 500 °C.     

A crystal plasticity based methodology for fatigue crack initiation life prediction in polycrystalline copper

Fatigue failure is the dominant mechanism that governs the failure of components and structures in many engineering applications. In conventional engineering applications due to the design specifications, a significant proportion of the fatigue life is spent in the crack initiation phase. In spite of the large number of works addressing fatigue life modelling, the problem of modelling crack initiation life still remains a major challenge in the scientific and engineering community. In the present work, we present a methodology for estimating fatigue crack initiation life using macroscale loading conditions and the microstructural phenomenon causing crack initiation. Microstructure sensitive modelling is used for predicting potential crack initiation life by employing randomly generated representative microstructures. The microstructural parameters contributing to crack initiation life are identified and accounted for by computing lattice level energy dissipation during fatigue crack initiation. This model is coupled with experimental results to improve the predictive capabilities and identification of potentially damaging weak points in the microstructures. The estimated values for crack initiation life were found to be in good agreement with the experimentally observed values of initiation life. The results have shown that this kind of approach could be successfully used to predict crack initiation life in polycrystalline materials. This work successfully provides an approach for estimating crack initiation life based upon numerical computations accounting for the microstructural phenomenon.     

Mechanical properties and biocompatibility of plasma-nitrided laser-cut 316L cardiovascular stents

The effect of surface modification of laser-cut 316L cardiovascular stents by low-T plasma nitriding was evaluated in terms of mechanical properties and biocompatibility of the stents. The plasma nitriding was performed at 400, 450 or 500 °C using various ratios of nitrogen–hydrogen gas mixtures. The flexibility and radial strength were measured in crimped and expanded state of the stents, respectively. The mechanical properties could be adjusted and improved by plasma nitriding conducted at temperatures lower than 450 °C and/or nitrogen content less than 10% in the treatment gas. An osteoblast cell culture model system was utilized to investigate the effect of plasma nitriding of the stents on the biological response towards the stents, using biological criteria such as cell viability, alkaline phosphatase and nitric oxide production. In terms of cell viability and alkaline phosphatase production, the plasma nitriding procedure did not appear to negatively affect the biocompatibility of the 316L steel stents. However, in terms of nitric oxide production that was slightly increased in the presence of the plasma-nitrided stents, an indirect improvement in the biocompatibility could possibly be expected.