Fatigue Crack Propagation Model Research Articles

A fatigue crack propagation model with resistance curve effects for an epoxy/copper interface

Fatigue crack propagation for copper/epoxy molding compound interfaces is modeled in this work by conducting cyclic loading on double cantilever beam test specimens. The continued increase in mechanical compliance of test specimens as the crack propagates through hundreds of cycles is used to determine the crack length and thus, the crack growth rate per cycle which is used to determine the Paris’ law constants as a function of strain energy release rate range. When monotonic debonding testing is conducted, it is seen that the critical strain energy release rate initially increases with the crack length and then stabilizes demonstrating the increasing resistance for the epoxy/copper interface. When such an increasing R-curve is used to normalize the strain energy release rate range, it is observed that the Paris’ law constants can be determined with good consistency for a wide range of specimens over different crack lengths.

Strain-based approach for fatigue crack propagation simulation of the 6061-T651 aluminium alloy

Fatigue crack growth models based on elastic-plastic stress-strain histories, at the crack tip vicinity, and strain-life damage models have been proposed. The UniGrow model is a particular case of fatigue crack propagation models. The residual stresses developed at the crack tip play a central role in these models, since they are used to assess the actual fatigue crack driving force, taking into account mean stress and loading sequential effects. The performance of the UniGrow model is assessed based on available experimental constant amplitude crack propagation data, derived for the 6061-T651 aluminium alloy. Key issues in fatigue crack growth prediction, using the UniGrow model, in particular the residual stresses evolution, are discussed. Using available strain-life data, it was possible to model the fatigue crack propagation behaviour for the AA6061-T651, taking into account the stress R-ratio effects. A satisfactory agreement was found, between the predictions and the experimental crack propagation data.

A model for high-cycle fatigue crack propagation

Abstract This paper deals with the prediction of high-cycle fatigue behavior for four different materials (7075-T6 alloy, Ti-6Al-4 V alloy, JIS S10C steel and 0.4 wt.-% C steel) using Chapetti's approach to estimate the fatigue crack propagation curve. In the first part of the paper, a single integral equation for studying the entire propagation process is determined using the recent results of Santus and Taylor, which consider a double regime of propagation (short and long cracks) characterized by the model of El Haddad. The second part of the paper includes a comparison of the crack propagation behavior model proposed by Navarro and de los Rios with the one mentioned in the first half of this work. The results allow us to conclude that the approach presented in this paper is a good and valid estimation of high-cycle fatigue crack propagation using a single equation to describe the entire fatigue crack regime.

Reliability estimation of fatigue crack growth prediction via limited measured data

In view of limited uncertainty information, a time-dependent reliability estimation procedure that combines the determined crack growth model with interval mathematics is presented as a theoretical basis for structural damage tolerance design. Firstly, by virtue of the theory of non-probabilistic interval process, an interval process model of fatigue crack propagation is investigated, in which we describe uncertain crack length a(N) at any load cycle N as interval variable and define the corresponding auto-covariance function and the correlation coefficient function to further characterize the correlation of a(N) at different cycles. By comparison of the critical crack length acritical, the uncertainty properties of the time-varying limit-state function can be given as well. Furthermore, inspired by the first-passage approach in random process theory, a new measure index of non-probabilistic time-dependent reliability is proposed as a feasible way for precisely evaluating the safe life of in-service engineering structures with crack. The corresponding solution algorithm is further discussed. Some application examples demonstrate the usage, efficiency and accuracy of the developed methodology eventually.

Determination of Initial Stages of Fatigue on the Basis of Fatigue Tensile and Fatigue Bend Testing

Fatigue crack initiation usually starts from defects or inclusion (s) in the material in the zone of stress concentration. The stress concentration zone can be at the surface of the specimen or inside the material. The fatigue crack starts to propagate, depending on stress amplitude, if the range of the stress intensity factor is higher than the fatigue threshold. The aim of this paper is to present the procedure for determining the fatigue crack initial stage by using the Wöhler S-N curve and the fatigue crack propagation parameters obtained by experiment for the loading range R=-1. Determination of the fatigue initial stage has been determined by the analysis of tensile smooth specimens and notched bending specimens. Results show that linear elastic fracture mechanics is applicable in order to establish a model for fatigue crack propagation.

Modified CCS fatigue crack growth model for the AA2019-T851 based on plasticity-induced crack-closure

Several fatigue cracks growth laws have been suggested over the past 50years. Recently, a fatigue crack propagation law was proposed by Castillo-Canteli-Siegele (CCS model) based on the assumption that fatigue crack growth takes the form of a Gumbel cumulative distribution function. Besides many physical aspects, the fatigue crack propagation laws need to account for fatigue crack opening and closure effects. Thus, in this paper a modification of the CCS fatigue crack growth law is proposed to account for the crack opening and closure effects, as well as the stress R-ratio effect, Rσ. The fatigue crack opening and closure effects are taken into account using a plasticity-induced crack-closure model. Other fatigue crack closure models can also be used in the proposed modification of the CCS crack growth model through the quantitative parameter U=ΔKeff/ΔK. This modified CCS crack propagation model using the effective stress intensity factor range, ΔKeff, is a new version of an explicit fatigue crack propagation model, supported by mathematical and physical assumptions. In this paper, the proposed model is applied using the fatigue crack growth data and mechanical properties that were collected for the 2219-T851 aluminium alloy. Based on the plasticity-induced crack-closure model, which was first formulated by Newman, and in this paper modified with a boundary correction factor, Fw, the crack opening stress intensity factor, Kop, and quantitative parameter U are determined. The results showed a good agreement between the proposed modification of the CCS fatigue crack propagation model taking into account the plasticity-induced crack-closure model with the boundary correction factor and experimental results of the fatigue crack propagation data for the 2219-T851 aluminium alloy.

Quantitative fractography and modelling of fatigue crack propagation in high strength AerMet®100 steel repaired with a laser cladding process

Ultra-high strength steels employed in safety-critical applications, such as AerMet®100 used in aircraft landing gear structures, are managed on very conservative rejection criteria for small defects and repair options are limited. A novel repair technique using laser cladding has recently been developed. In the present paper we report a study of the fatigue endurance of AerMet®100 steel components repaired by the laser cladding process, and a fracture mechanics based model to predict the fatigue endurance of repaired components. Three different types of samples were tested; baseline AerMet®100 sample with a small electro-discharge machining notch to initiate a crack, as-clad repaired, and as-clad repaired followed by heat treatment to relieve residual stresses. The specimens were subjected to cyclic loading under a special sequence consisting of constant amplitude segments at two different stress-ratios (ratio of minimum to maximum cyclic stress). The test results showed that the crack propagation lives from a common initial depth of 0.25mm for the as-clad samples were significantly longer than the baseline samples by a factor of three to four. The longer life is attributed to the beneficial compressive residual stresses resulting from the repair process. The model predictions are found to correlate well with the results of quantitative fractography measurements from samples tested under variable amplitude cyclic loads.

Probabilistic model of fatigue crack propagation and estimation of probability-confidence bounded a–N curves

ABSTRACTThe fatigue crack growth model is expressed as a function of mechanical properties. The uncertainties associated with the crack growth process are incorporated assuming them as random variable following a statistical distribution. The effect of material nonhomogeneity is included in the model through a random process parameter of Gaussian type. Assuming fatigue life as a random variable, probability-confidence bounded mean crack growth relation is developed and an algorithm is presented. The model is validated through the experimental and predicted results from several data sets.

A Development in the Finite Volume Method for the Crack Growth Analysis without Global Remeshing

Crack growth analysis has remained one of the challenging problems in the fracture mechanics of structures. On the other hand, the fatigue crack growth is a common phenomenon in the components of structures like airplanes, navies and fluid storages where the fracture due to crack should be considered in the design of these structures. In this paper, the finite volume method (FVM) is extended for the modeling of static and fatigue crack propagation for two-dimensional problems. In the present method, due to the crack growth, no global remeshing is needed where only a cell dividing near the crack tip can be used which is easy to implement during the analysis. The accuracy of the method is studied by solving several benchmark problems and the results obtained are compared with the available analytical and numerical results. It is observed that the results obtained have good accuracy comparing with the references results.

Stochastic modelling and prediction of fatigue crack propagation using piecewise-deterministic Markov processes

Fatigue crack propagation is a stochastic phenomenon due to the inherent uncertainties originating from material properties, environmental conditions and cyclic mechanical loads. Stochastic processes thus offer an appropriate framework for modelling and predicting crack propagation. In this paper, fatigue crack growth is modelled and predicted by a piecewise-deterministic Markov process associated with deterministic crack laws. First, a regime-switching model is used to express the transition between the Paris regime and rapid propagation that occurs before failure. Both regimes of propagation are governed by a deterministic equation whose parameters are randomly selected in a finite state space. This one has been adjusted from real data available in the literature. The crack growth behaviour is well-captured and the transition between both regimes is well-estimated by a critical stress intensity factor range. The second purpose of our investigation deals with the prediction of the fatigue crack path and its variability based on measurements taken at the beginning of the propagation. The results show that our method based on this class of stochastic models associated with an updating method provides a reliable prediction and can be an efficient tool for safety analysis of structures in a large variety of engineering applications. In addition, the proposed strategy requires only little information to be effective and is not time-consuming.

Mechanisms and modeling of low cycle fatigue crack propagation in a pressure vessel steel Q345

The fatigue process near crack is governed by highly concentrated strain and stress in the crack tip region. Based on the theory of elastic–plastic fracture mechanics, we explore the cyclic J-integral as breakthrough point, an analytical model is presented in this paper to determine the CTOD for cracked component subjected to cyclic axial in-plane loading. A simple fracture mechanism based model for fatigue crack growth assumes a linear correlation between the cyclic crack tip opening displacement (ΔCTOD) and the crack growth rate (da/dN). In order to validate the model and to calibrate the model parameters, the low cycle fatigue crack propagation experiment was carried out for CT specimen made of Q345 steel. The effects of stress ratio and crack closure on fatigue crack growth were investigated by elastic–plastic finite element stress–strain analysis of a cracked component. A good comparison has been found between predictions and experimental results, which shows that the crack opening displacement is able to characterize the crack tip state at large scale yielding constant amplitude fatigue crack growth.

Prediction of fatigue crack growth in a ship detail under wave-induced loading

Fatigue life prediction based on fracture mechanics has become the focus of research on the strength of ship structures; however, it is difficult to summarize a general formula for calculating stress intensity factors (SIF) for cracks in ship details, and the application of fatigue crack propagation (FCP) theory is limited to simple structures and simple loads in some way. To address this problem, in the present study, the SIF of a crack in a ship detail was calculated by combining a PATRAN finite element model for the whole ship with the advantages of ANSYS for SIF calculation, incorporating a macrocode written to achieve the transformation. The method was validated by comparison with existing empirical formulas. Also a method of generating the ship fatigue loading spectrum is demonstrated based on the design wave approach. Finally, an example is given of combining the unique curve model of FCP with the proposed SIF calculation method and the fatigue loading spectrum generation method, to predict the fatigue life of a welded hatch corner joint in a vessel with large hatch openings. This serves as a reference for fatigue assessment of other complex ship details.

Numerical Modeling of the Surface Fatigue Crack Propagation Including the Closure Effect

Presently modeling of surface fatigue crack growth for residual life assessment of structural elements is almost entirely based on application of the Linear Elastic Fracture Mechanics (LEFM). Generally, it is assumed that the crack front does not essentially change its shape, although it is not always confirmed by experiment. Furthermore, LEFM approach cannot be applied when the stress singularity vanishes due to material plasticity, one of the leading factors associated with the material degradation and fracture. Also, evaluation of stress intensity factors meets difficulties associated with changes in the stress state along the crack front circumference. An approach proposed for simulation the evolution of surface cracks based on application of the Strain-life criterion for fatigue failure and of the finite element modeling of damage accumulation. It takes into account the crack closure effect, the nonlinear behavior of damage accumulation and material compliance increasing due to the damage advance. The damage accumulation technique was applied to model the semi-elliptical crack growth from the initial defect in the steel compact specimen. The results of simulation are in good agreement with the published experimental data.

Proposal of a fatigue crack propagation model taking into account crack closure effects using a modified CCS crack growth model

This paper proposes a modification of the fatigue crack growth model proposed by Castillo-Canteli-Siegele (CCS) to take into account crack opening and closure effects as well as the influence of the stress R-ratio. The theoretical model to obtain the effective stress intensity range, ΔKeff, which takes into account the effects of the mean stress and the crack closure and opening effects proposed by Correia et al. was taken in consideration in this new proposal. This last model is based on the same initial assumptions of the analytical models proposed by Hudak et al. and Ellyin. This modified CCS crack propagation model is a new version of an explicit fatigue crack propagation model, supported by mathematical and physical assumptions.

A relative crack opening time correlation for corrosion fatigue crack growth in offshore structures

AbstractA considerable amount of research has been carried out on the prediction of mean stress effects on fatigue crack growth in structures. Newer types of structure are now being developed for use in highly dynamic, harsh marine environments, particularly for renewable energy applications. Therefore, the extent to which mean stresses can enhance corrosion‐assisted fatigue damage in these structures needs to be better understood. A new theoretical model that accounts for mean stress effects on corrosion fatigue crack growth is proposed. The model is developed based on the relative crack opening period per fatigue cycle and by considering only the damaging portion of the stress cycle. The baseline data for the modelling exercise are the data obtained at a stress ratio of 0.1 in air and seawater tests conducted on compact tension specimens. The model is validated by comparison with experimental data and with other fatigue crack propagation models. The proposed model correlates fairly well with experimental data and the other models examined.

Microstructure-Scale In-Situ Image Correlation-Based Study of Grain Deformation and Crack Tip Displacements in Al–Cu Alloys

Abstract Mechanistic understanding based on experimental measurements of grain and crack tip deformation at relevant length scales is critical for improvement of physics-based modeling of microstructurally-sensitive fatigue crack propagation and for the computationally-assisted design of more durable materials. In this study, single-crystal, bi-crystal, and large-grain multi-crystal specimens of Al–Cu alloys are fabricated, characterized using electron backscattered diffraction (EBSD), and mechanically tested. In addition to conventional optic al–imaging based 3D image correlation (IC), scanning electron microscope (SEM) based high-resolution 2D IC is used to measure displacements within grain interiors, near crack tips, and grain boundaries. The use of micro-scale IC and EBSD-based experiments is discussed as they relate to the development of crystal-plasticity-based finite element models (CP–FEMs). This article specifically highlights experimental methods that have been developed to obtain the relevant data needed for CP–FEM calibration and validation.

최대하중조건에 따른 Mg-Al-Zn 합금의 확률변수 잔차를 이용한 확률론적 피로균열전파모델 평가

본 논문의 주 목적은 최대하중조건을 변화시키면서 확률변수의 잔차를 이용하여 확률론적 피로균열전파모델들을 평가하고, Mg-Al-Zn 합금의 피로균열성장거동의 변동성을 묘사하기에 적합한 확률론적 모델을 제시하는 것이다. 평가에 사용된 모델은 피로균열성장의 변동성을 나타내기 위하여 실험적 피로균열전파모델인 Paris-Erdogan 모델, Walker 모델, Forman 모델과 수정 Forman 모델에 확률변수를 도입한 모델이다. 최대하중조건에 따른 Mg-Al-Zn 합금의 피로균열전파거동의 확률적 변동성을 묘사하기에 적합한 모델은 ‘확률론적 Paris-Erdogan 모델’과 ‘확률론적 Walker 모델’임을 밝혔으며, 최대하중조건이 피로균열성장의 확률적 변동성에 미치는 영향 또한 고찰하였다.

Probabilistic S-N Field Assessment for a Notched Plate Made of Puddle Iron From the Eiffel Bridge with an Elliptical Hole

Probabilistic fatigue models are required to account conveniently for several sources of uncertainty arising in the prediction procedures for structural details, such as the scatter in material behaviour. In this paper, a procedure to derive probabilistic S-N fields for structural details [1] is applied to a notched geometry with elliptic central hole made of puddle iron from the Eiffel bridge, based on the local approaches supported by the probabilistic ɛa–N or Smith–Watson–Topper (SWT)–N fields [1,2]. This procedure suggests an extension of the fatigue crack propagation model proposed by Noroozi et al. [3,4] to structural details, in order to cover both the fatigue crack initiation and fatigue crack propagation, based on local strain approaches to fatigue. Both fatigue crack initiation and fatigue crack propagation mechanisms are accounted for in the proposed approach. The numerical results are compared with available experimental S-N fatigue data for the notched plate under consideration.

Modelling probabilistic fatigue crack propagation rates for a mild structural steel

A class of fatigue crack growth models based on elastic–plastic stress–strain histories at the crack tip region and local strain-life damage models have been proposed in literature. The fatigue crack growth is regarded as a process of continuous crack initializations over successive elementary material blocks, which may be governed by smooth strain-life damage data. Some approaches account for the residual stresses developing at the crack tip in the actual crack driving force assessment, allowing mean stresses and loading sequential effects to be modelled. An extension of the fatigue crack propagation model originally proposed by Noroozi et al. (2005) to derive probabilistic fatigue crack propagation data is proposed, in particular concerning the derivation of probabilistic da/dN-?K-R fields. The elastic-plastic stresses at the vicinity of the crack tip, computed using simplified formulae, are compared with the stresses computed using an elasticplastic finite element analyses for specimens considered in the experimental program proposed to derive the fatigue crack propagation data. Using probabilistic strain-life data available for the S355 structural mild steel, probabilistic crack propagation fields are generated, for several stress ratios, and compared with experimental fatigue crack propagation data. A satisfactory agreement between the predicted probabilistic fields and experimental data is observed.

Modeling of Corrosion Fatigue Crack Growth of X70 Pipeline Steel and Numerical Simulation of Crack Propagation

To solve the problem that the change of curve slop was not considered in the common corrosion fatigue crack growth, a new corrosion fatigue crack propagation model based on Pairs formula was established in this paper; which corrected parametersCandnof Paris formula at the same time. Based on the fatigue crack propagation experimental data of X70 pipeline steel in hydrogen sulfide corrosive environment, the key parameters of the model were fitted. Based on the new model, a FRANC3D software was used, and the corrosion fatigue crack propagation processes of X70 pipeline steel in corrosive solution were simulated. It was demonstrated that the simulated fatigue crack growth processes obtained by the boundary element method were very close to the test results, and the maximum error is less than 10%. Therefore, boundary element method can be used to predict the life of corrosion fatigue on the project.