An improved damage model using the construction technology of virtual load spectrum and its statistical analysis

In this work, an improved damage model based on construction technology of virtual load spectrum is developed. A predetermined reliability index is used as the termination criterion to calculate the fatigue life, and the results of statistical analysis have shown that the accuracy of fatigue life prediction result has been greatly improved. The model is targeting cyclic loading applications. The main advantage of the model is the use of construction technology of virtual load spectrum for expanding load spectrum and the Monte Carlo method for correcting fatigue damage. Another advantage concerns the link between predetermined reliability criterion and the fatigue life, which puts forward a new method of calculating fatigue life. The convergence proof of the model is presented, and physical experiment data are shown for validation. Several illustrative examples are presented to confirm the accuracy and efficiency of the proposed damage model.     

A cumulative damage theory for fatigue crack initiation and propagation

A method for evaluating the cumulative damage resulting from the application of cyclic stress (or strain) sequences of varying amplitude is presented. Both the crack initiation and propagation stages of the fatigue failure process are included. The development is based on the concept of plastic strain energy dissipation as a function of cyclic life. The damage accumulated at any stage is evaluated from a knowledge of the fatigue limit in the initiation phase and an ‘apparent’ limit obtained through fracture mechanics for the propagation phase. The proposed damage theory is compared with two-level strain cycle test data of thin-walled specimens, and is found to be in fairly good agreement.     

Fatigue crack initiation life estimation in a steel welded joint by the use of a two-scale damage model

This work deals with the fatigue behaviour of S355NL steel welded joints classically used in naval structures. The approach suggested here, in order to estimate the fatigue crack initiation life, can be split into two stages. First, stabilized stress–strain cycles are obtained in all points of the welded joint by a finite element analysis, taking constant or variable amplitude loadings into account. This calculation takes account of: base metal elastic–plastic behaviour, variable yield stress based on hardness measurements in various zones of the weld, local geometry at the weld toe and residual stresses if any. Second, if a fast elastic shakedown occurs, a two-scale damage model based on Lemaitre et al. 's work is used as a post-processor in order to estimate the fatigue crack initiation life. Material parameters for this model were identified from two Wöhler curves established for base metal. As a validation, four-point bending fatigue tests were carried out on welded specimens supplied by 'DCNS company'. Two load ratios were considered: 0.1 and 0.3. Residual stress measurements by X-ray diffraction completed this analysis. Comparisons between experimental and calculated fatigue lives are promising for the considered loadings. An exploitation of this method is planned for another welding process.     

Woven fabric composites—part II: Characterization of macro‐crack initiation loads for global damage analysis

In Part 2, finite element techniques are developed to additionally investigate the global damage of woven fabric composites, focusing on plain weaves. The homogenized elastic properties of the original undamaged and the damaged woven fabric composites from the micromechanical homogenization and the micromechanical progressive damage analysis investigated earlier in Part 1 are subsequently employed in the present global damage analysis. The theory of continuum damage mechanics is utilized in the global damage analysis. The damage variables, the most important material properties of the continuum damage mechanics, are measures of average material degradation at a macro‐mechanics scale. In the present study, these damage variables are calculated numerically using the results from the micromechanical damage analysis in Part 1, instead of being obtained experimentally. Subsequently, a finite element formulation for the global damage analysis of woven fabric composites is developed to predict the initiation loads of macro‐cracks. Copyright © 2001 John Wiley & Sons, Ltd.     

Generation and analysis of FCG data using a single specimen and Kmax–ΔK testing matrix

A custom method to generate fatigue crack growth (FCG) data requires testing of multiple specimens at different load ratios, R, and the application of a load shedding procedure from pre-cracking level to threshold. In this paper, a novel method of testing has been investigated which utilizing a single specimen and a testing matrix in terms of K_max and ΔK values corresponding to predetermined R-ratios for which FCG data are recorded. Automatic K-controlled tests on 2324-T39 Al alloy were conducted using both increasing and decreasing ΔK procedures while K_max was kept constant. Results show that the increasing ΔK procedure gives less scatter than decreasing ΔK procedure. Also, fatigue crack growth curves near the threshold region obtained from increasing ΔK are above the curves obtained from decreasing ΔK procedure. These differences are explained by means of interaction between cyclic plastic zones and their effect on fatigue damage. The procedure with increasing ΔK demonstrated minimal interaction effects and hence it is recommended for efficient FCG data generation. The proposed procedure reduces testing time, the overall scatter associated with multiple samples and eliminates possible uncertainty linked to the load shedding procedure and its effects on threshold.     

On the fatigue damage micromechanisms in Si‐solution–strengthened spheroidal graphite cast iron

Graphite nodules in spheroidal graphite cast iron (SGI) play a vital role in fatigue crack initiation and propagation. Graphite nodules growth morphology can go through transitions to form degenerated graphite elements other than spheroidal graphite nodules in SGI microstructure. These graphite particles significantly influence damage micromechanisms in SGI and could act differently than spheroidal graphite nodules. Most of the damage mechanism studies on SGI focused on the role of spheroidal graphite nodules on the stable crack propagation region. The role of degenerated graphite elements on SGI damage mechanisms has not been frequently studied. In this work, fatigue crack initiation and propagation tests were conducted on EN‐GJS‐500‐14 and observed under scanning electron microscope to understand the damage mechanisms for different graphite shapes. Crack initiation tests showed a dominant influence of degenerated graphite elements where early cracks initiated in the microstructure. Most of the spheroidal graphite nodules were unaffected at the early crack initiation stage, but few of them showed decohesion from the ferrite matrix and internal cracking. In the crack propagation region, graphite/ferrite matrix decohesion was the frequent damage mechanism observed with noticeable crack branching around graphite nodules and the crack passing through degenerated graphite elements. Finally, graphite nodules after decohesion acted like voids which grew and coalesced to form microcracks eventually causing rapid fracture of the remaining section.     

A stochastic damage accumulation model for crack initiation in high-cycle fatigue

A stochastic damage accumulation model for crack initiation in high-cycle fatigue is proposed. It is assumed that the fatigue damage is accumulated in the form of dislocations under the repeated stress and that the slip band crack is initiated when the strain energy due to a local pile-up of dislocations exceeds a critical value. The size of an initiating crack is the cell size, derived from a probabilistic argument and its depth is determined in relation to the stored dislocation energy. Our theoretical results are compared with the experimental data from a low-carbon steel S20C in order to examine the consistency of our model.     

Numerical stress and crack initiation analysis of the compressor blades after foreign object damage subjected to high-cycle fatigue

This paper presents results of the complex stress and crack initiation analysis of the PZL-10 W turbo-engine compressor blade subjected to high cycle fatigue (HCF). A nonlinear finite element method was utilized to determine the stress state of the blade during the first mode of transverse vibration. In this analysis, the numerical models without defects and also with V-notches were defined. The quality of the numerical solution was checked by the convergence analysis. Obtained results were next used as an input data into crack initiation (ε–N) analyzes performed for the load time history equivalent to one cycle of the transverse vibration. In the fatigue analysis the different methods such as: Neuber elastic–plastic strain correction, linear damage summation and Palmgreen–Miner rule were utilized. As a result of ε–N analysis, the number of load cycles to the first fatigue crack appearing in the compressor blades was obtained. Moreover, the influence of the blade vibration amplitude on the number of cycles to the crack initiation was analyzed. Values of the fatigue properties of the blade material according to Baumel–Seeger and Muralidharan methods were calculated. The influence of both the notch radius and values of the UTS of the blade material on the fatigue behavior of the structure was also considered. In the last part of work, the finite element results were compared with the results of an experimental vibration HCF tests performed for the compressor blades.     

Probabilistic prediction models for crack initiation and progression of spray sealed pavements

Cracking is one of the primary distress modes in spray (chip)-sealed pavement surface performance and its prediction is a major concern for pavement engineers. In order to identify, manage and asses effectively and efficiently cracked pavement at a network level, a probabilistic modelling approach is utilised to develop cracking initiation and progression models. This study aims to predict the probability of pavement cracks occurring using a binary logistic model and cracks progression over time using an ordinal logistic regression model. These models have been developed to take into account the effect of variations among observations, among sections and among highways. Readily available historical time series data (from 2004 to 2011) from 40 highway segments have been collected and prepared for modelling. These time series include surface cracking as a performance parameter and traffic loading, expansion potential of subgrade soil, climate condition, condition of drainage system and pavement strength as predictor parameters. Cracking data include all types of cracking: transverse, longitudinal and crocodile cracking and is reported as a percent of the affected area. The study estimates the probability of crack initiation at a certain time and predicts the probability of a pavement maintaining its current level of cracking. It is found that with the 50% estimated probability, about 82% of the observations are correctly predicted by the crack initiation model and 65% of the observations are correctly predicted by the crack progression model. The study has concluded that the effect of time is stronger than the other variables on crack initiation and progression. Also, the effect of traffic loading is stronger than the effect of initial pavement strength in crack initiation phase. However, the effect of pavement strength at any time is stronger than the effect of traffic loading in crack progression phase. The predicted probabilities have been successfully validated using another data-set from the same network and the results indicate that the developed probability models are well estimating the crack conditions and have the ability to predict future conditions accurately.     

Analysing the onset of multiple site damage at mechanical joints

A detailed analysis has been performed on the onset of multiple site damage at mechanical joints. The crack initiation is analysed based on non-linear stress analyses and the crack closure model. It has been found that the stress-strain response at the joint can have a stabilised linear relation under fatigue loading even if considerable plastic yield has occurred. This makes it possible to analyse the post yield multiple crack initiation based on fracture mechanics solutions for the crack growth in a residual stress field. Weight function method has been used to solve stress intensity factors and Green's functions for the crack growth analyses according to a strip yield crack closure solution. In this analysis, the small crack behaviour as well as the post yield effect have been accounted for. Intrinsic material parameters have been extensively used so that the method is not limited to the specified problems. Together with the crack growth analyses, a probabilistic model has been developed to account for uncertainties in initial flaw, stochastic crack propagation, geometrical inconsistency, as well as variation in the fatigue load. According to the probabilistic solution, important information about the onset of multiple site damage, e.g. the probability of crack occurrence, and the probability of crack break-through etc., are predicted as a function of the stress and the construction of joint. One example is provided to illustrate the procedure and to highlight problems in dealing with the onset of multiple site damages at mechanical joints.     

Probabilistic analysis of multi-site damage in aircraft fuselages

 Most aircraft fleets nowadays are operating under the concept of damage tolerance, which requires an aircraft to have sufficient residual strength in the presence of damage in one of its principal structural elements (PSE) during the interval of service inspections. The residual strength however is significantly reduced due to multi site damage (MSD). In the present paper, a probabilistic framework for the computation of the failure probability is developed. The MSD problem of a PSE is considered, where the uncertainties in crack initiation and crack growth as well as yield stress and fracture toughness are described by random variables. For the crack growth calculations the finite element alternating method [1], which avoids a remeshing of the finite element problem, is used. After specifying link up and failure criteria, importance sampling is employed to obtain the probability of failure of the PSE due to MSD. Received: 29 July 2002 / Accepted: 18 December 2002     

A novel accumulative fatigue damage model for multiaxial step spectrum considering the variations of loading amplitude and loading path

In this paper, based on the process of the fatigue crack initiation and the critical plane theory, a continuous stress parameter was proposed to quantify the driving force of the fatigue crack initiation for the fully reversed multiaxial fatigue loading. In this stress parameter, the shear stress amplitude and normal stress amplitude on the critical plane were combined with the variable coefficients which were affected by the normalized fatigue life and the loading non‐proportionality. Owing to these coefficients, for the multiaxial loadings with different non‐proportionalities, the driving force of the fatigue crack initiation during the whole life could be described. After that, a novel accumulative fatigue damage model was established for the multiaxial two‐stage step spectrum. In this model, the accumulative damage was calculated according to the variation of the proposed stress parameter on the critical plane. Considering the directionality of the multiaxial fatigue damage, for the spectrum in which the loading path was variable, the damage accumulation was carried out on the critical planes of the both loadings, and the larger one was chosen as the final accumulative fatigue damage. In order to verify the new model, up to 41 different multiaxial two‐stage step spectrum loading tests on 2024‐T4 aluminium alloy were collected. The new model, as well as other five commonly used models, was applied to calculate the accumulative fatigue damage. The final results showed that, compared with other commonly used models, the new model had the most accurate results with the smallest scatters.     

On the estimation of fatigue life in notches differentiating the phases of crack initiation and propagation

Over the last three decades, a variety of models have been developed in order to predict the life of components under fatigue. Some of the models are based on the definition of the fatigue process as a combination of the phases of crack initiation and crack propagation, considering component life as the sum of the duration of each phase. Other models consider only one of the phases; some consider only initiation while others only propagation, though in this case, from cracks with lengths in the order of the microstructural dimensions. This article will carry out a comparative analysis of the methods that consider life as the sum of the duration of both phases. In this same line, it proposes yet another method, which simulates crack growth according to damage theories. In analysing the behaviour of each model, this paper will describe various elements: the prediction that each of them produces regarding notched specimens submitted to testing, the advantages and inconveniences of each, and lastly, the possibilities of applying each of the models to more realistic geometries.     

Modelling of load interaction and overload effect on fatigue damage of steel bridges

This paper studies the effects of load sequence and interaction, and overloading effect on the fatigue damage of bridges on the basis of a non-linear fatigue damage model. The model is derived from the theory of continuum damage mechanics for high-cycle fatigue. Fatigue behaviour at two levels of constant stress range is first discussed in detail. The formulation for the effective fatigue strength of the predamaged members is then derived, and the results predicted by the model are compared with the experimental data for two stress level tests and other results obtained from linear and double linear fatigue damage models. The variation of cycle ratio and fatigue life due to overloading is secondly investigated; the equations for evaluating the effect of overloading on fatigue damage accumulation on bridges at normal traffic loading are then derived. It has been demonstrated that the developed model can well describe the effect of load sequence and interaction and has also been verified by comparing the predicted results obtained by the model with the experimental data based on two levels of stress tests. The effect of accidental overloading on the fatigue damage of existing bridges can also be evaluated using the model. The model is applied to evaluate the fatigue damage and service life of the Tsing Ma Bridge, an essential portion of the transport network for the Hong Kong airport, under normal traffic loading and possible accidental overloading.     

Probabilistic analysis of fatigue crack propagation in finite size specimens

By taking into account the effect due to the finiteness of the specimen's size, stochastic fatigue crack propagation processes are investigated on the basis of a Markov approximation method. Since the limiting property proved by Koiter causes a particular kind of singularity on the governing equation, the so-called death point must be introduced into the range of finite crack size. In the present study, the Fokker-Planck equation in a generalized sense is derived for such a particular case, and the influence of the specimen's size on the statistical properties of the residual life of the component is clarified by the use of numerical calculations.     

Physics‐based multiscale damage criterion for fatigue crack prediction in aluminium alloy

In this paper, a physics‐based multiscale approach is introduced to predict the fatigue life of crystalline metallic materials. An energy‐based and slip‐based damage criterion is developed to model two important stages of fatigue crack initiation: the nucleation and the coalescence of microcracks. At the microscale, a damage index is developed on the basis of plastic strain energy to represent the growing rate of a nucleated microcrack. A statistical volume element model with high computational efficiency is developed at the mesoscale to represent the microstructure of the material. Also, the formation of a major crack is captured by a coalescence criterion at mesoscale. At the macroscale, a finite element analysis of selected test articles including lug joint and cruciform is conducted with the statistical volume element model bridging two scale meshes. A comparison between experimental and simulation results shows that the multiscale damage criterion is capable of capturing crack initiation and predicting fatigue life.     

Prediction and evaluation of fatigue life for mechanical components considering anelasticity‐based load spectrum

To accurately predict the degraded fatigue life of components under random loads, anelasticity effect of metal on life estimation needs to be explored. Weighting coefficient and dynamic elastic modulus are introduced to modify the calculation process of the model. By establishing an equal‐amplitude fatigue median surface and applying Miner linear fatigue cumulative damage theory, a fatigue life prediction model of the component under random loads is proposed. The model can be used to calculate the degraded fatigue life of components, which provides a theoretical basis for life estimation under random load spectrum. The two‐dimensional load spectrum is compared with the unprocessed two‐dimensional load spectrum and the one‐dimensional program spectrum in life prediction results. With the comparison of the target life and simulation life and the data calculated by the model of the automobile front stabilizer bar, it is concluded that the data obtained by the modified model are more reasonable and accurate.     

A study of local deformation and damage of dual phase steel

Deformation and fracture behavior of Dual Phase (DP) high strength steel were investigated by means of a microstructure based Finite Element (FE) modeling. Representative Volume Elements (RVEs) were applied to consider effects of various microstructure constituents and characteristics. Individual stress–strain curves were provided for ferrite, martensite as well as transformation induced Geometrically Necessary Dislocations (GNDs) taking into account in the RVEs. Principally, the GNDs occurred around phase boundaries during quenching process due to the austenite–martensite transformation. Flow behaviors of individual phases were defined on the basis of dislocation theory and partitioning of local chemical composition. Then, flow curves of the examined DP steel were predicted. Furthermore, the Gurson–Tvergaard–Needleman (GTN) model was used to represent ductile damage evolution in the microstructure. Occurrences of void initiation were characterized and damage parameters for RVE simulations were hence identified. Finally, influences of the GNDs, local stress and strain distributions and interactions between phases on predicted crack initiation in the DP microstructure were discussed and correlated with experimental results.     

An improved crack tracking algorithm with self-correction ability of the crack path and its application in a continuum damage model

In this paper, a new procedure for predicting the crack propagation and fracture behavior in quasi-brittle materials is presented based on continuum damage mechanics. Several crack tracking algorithms are widely used for failure analysis, among which the local tracking algorithm is very simple and easy to implement with low computational cost. However, in the prediction of crack growth with the traditional local tracking algorithm, it can be often seen that the sharp changes in the crack path such as U-turns can occur. An improved local tracking algorithm with self-correction ability of the crack path is proposed to overcome these difficulties of the traditional crack tracking algorithms. A continuum damage model, in addition to the present crack tracking algorithm, can greatly enhance the performance of failure prediction in quasi-brittle materials. The present approach has the advantages that it can well predict the crack propagation path and can avoid mesh size and mesh bias dependence without the embedment of discontinuities or nodal enrichment. The present model is incorporated into ANSYS by the ANSYS Parameter Design Language to simulate the initiation and propagation of the discrete crack in engineering applications. The numerical results by this model are compared with the ones by the extended finite element method and experiments, and good agreements are achieved.     

Probabilistic assessment of weld fatigue damage for a nonlinear combination of correlated stress components

Estimation of fatigue damage for welds which are subjected to multiple stress components is addressed. Each component is represented by a separate stress cycle distribution of the Weibull type, and the effect of correlation between the different components is addressed. Three different types of bivariate Weibull distributions are considered. These are of the following categories: (i) The Nataf model (ii) The NKR model and (iii) The Plackett model. Comparison is made between the fatigue damage obtained by application of the different models for different levels of correlation and with different SN-curve exponents. Extension from the bivariate case to higher dimensions is also briefly discussed.