Fatigue Crack Propagation Model Research Articles

Mechanistic model for hydrogen accelerated fatigue crack growth in a low carbon steel

Fracture by hydrogen accelerated fatigue crack growth is a severe type of environmental failure. Although fatigue crack growth has been the subject of intense investigation over several decades, a complete mechanistic and predictive model is still lacking. Such a crack growth model is even more rare in the case of hydrogen in view of the lack also of constitutive models for material deformation under cycling loading that account for the hydrogen effect. In this study, we present a model for fatigue crack propagation induced by alternating crack tip plastic blunting and re-sharpening, which in the presence of hydrogen can be accelerated by hydrogen enhanced dislocation motion and generation. The Chaboche constitutive model, which is a nonlinear kinematic hardening model capable of capturing many features of material behavior under cyclic loading, is used for the calculation of the stress and strain fields at the propagating crack tip. The Chaboche model is calibrated using a sequence of experimental data from uniaxial strain-controlled cyclic loading tests and uniaxial stress-controlled ratcheting tests with a low carbon steel, JIS SM490YB, in the absence and presence of hydrogen. The numerical simulation results indicate that the proposed crack propagation model can predict Paris law behavior and can successfully demonstrate acceleration of fatigue crack growth in the presence of hydrogen. Significantly, the profiles of the steady-state opening stress and strain ahead of the fatigue crack tip in a compact tension (C(T)) specimen were found to have sections over which they vary as ln(1/r) with distance r from the crack tip, consistent with the crack-tip strain field for a non-stationary crack.

A Physics-Based Tweedie Exponential Dispersion Process Model for Metal Fatigue Crack Propagation and Prognostics

Most structural faults in metal parts can be attributed to fatigue crack propagation. The analysis and prognostics of fatigue crack propagation play essential roles in the health management of mechanical systems. Due to the impacts of different uncertainty factors, the crack propagation process exhibits significant randomness, which causes difficulties in fatigue life prediction. To improve prognostic accuracy, a physics-based Tweedie exponential dispersion process (TEDP) model is proposed via integrating Paris Law and the stochastic process. This TEDP model can capture both the crack growth mechanism and uncertainty. Compared with other existing models, the TEDP taking Wiener process, Gamma process, and inverse process as special cases is more general and flexible in modeling complex degradation paths. The probability density function of the model is derived based on saddle-joint approximation. The unknown parameters are calculated via maximum likelihood estimation. Then, the analytic expressions of the distributions of lifetime and product reliability are presented. Significant findings include that the proposed TEDP model substantially enhances predictive accuracy in lifetime estimations of mechanical systems under varying operational conditions, as demonstrated in a practical case study on fatigue crack data. This model not only provides highly accurate lifetime predictions, but also offers deep insights into the reliability assessments of mechanically stressed components.

Multi-scale characterization of fatigue crack tip deformation and propagation in QP steel

A novel measurement method for multi-scale characterization of fatigue crack tip deformation and propagation behaviors in high strength and plasticity, multi-phase, fine-grain Quenching and Partitioning (QP) steel was proposed. The fatigue crack propagation (FCP) test system with the macro/micro images acquisition devices was built to measure the FCP rate and crack tip deformation simultaneously. First, at the mesoscale, the evolution characteristics of the crack tip deformation fields, plasticity induced crack closure (PICC) behaviors and plastic zone during the FCP process were analyzed using the sub-image stitching and matching digital image correlation (DIC) method. Then, the FCP models were established with special emphasis on the model considering the PICC effect based on the obtained crack opening load at the mesoscale. Moreover, the corresponding microscale surface crack and fracture morphologies, microstructure phase transformation and deformations were observed and analyzed by electron backscatter diffraction (EBSD) and scanning electron microscope (SEM) techniques.

Low cycle fatigue behavior and life prediction of a directionally solidified alloy

Low cycle fatigue behavior and life prediction of a directionally solidified alloy

Fatigue Reliability Assessment for Orthotropic Steel Decks: Considering Multicrack Coupling Effects

Multiple fatigue cracks are generally present in practical engineering due to the existence of welding; the size and number of cracks of orthotropic steel bridge decks are greatly uncertain. The component failure conditions caused by these cracks may have correlations. Currently, it is still a challenging issue to develop a physical model of multiple fatigue crack propagation in bridge decks and perform a fatigue reliability assessment, which is also the motivation that drives the innovation of this study. A fatigue reliability evaluation method is presented for orthotropic steel bridge decks, considering the coupling effect of multiple cracks and the randomness of vehicle loading. A numerical simulation method for multifatigue crack growth is developed by combining the ABAQUS and FRANC3D programs. The equivalent crack depth under different spacing and depths of collinear cracks is calculated by using numerical simulation and the multicrack equivalent characterization method. The critical damage accumulation function of multiple fatigue cracks is established using linear elastic fracture mechanics. Subsequently, the critical damage accumulation function of multiple fatigue cracks is established based on linear elastic fracture mechanics. In order to solve the time-consuming problem of traditional Monte Carlo method, the iHL-RF method and AK-MCS method are developed for fatigue reliability analysis. The results show that compared with the single-crack model, the fatigue reliability of orthotropic steel deck will be crucially reduced considering the coupling effect of double cracks. The MCS, iHL-RF and AK-MCS methods can effectively solve the fatigue reliability analysis problem. Compared with the MCS method, the reliability calculation time based on AK-MCS method is significantly reduced. The AK-MCS method-based method reduces the time for calculating the reliability of orthotropic steel decks by 50% compared with the iHL-RF method. The reliability analysis of orthotropic steel deck bridge based on AK-MCS method is proved to be efficient and accurate.

Constraints-related microscopic fatigue crack propagation behaviour of polycrystalline alloys

Based on the microscopic polycrystalline fatigue crack propagation (MPFCP) model, the MPFCP behaviours of GH4169 alloy under different micro-notch depths and lengths (constraints) were studied from aspects of MPFCP path, MPFCP rate and stress distribution. The influences of the initial crack angle on MPFCP behaviour were further explored. It was observed that the grain boundary, the grain size and the stress state were different during crack propagation under different constraints, resulting in different MPFCP paths. The MPFCP path was straighter under high constraints, and the MPFCP rate was related to the micro-notch size and the loading direction. The crack tip needed more stress accumulation at low constraints than under high constraints to ensure smooth MPFCP behaviour. The influence of the initial crack angle on the MPFCP path was mainly reflected in the grain interior where the initial crack was located. The initial crack angle had a greater influence on the MPFCP rate than on the MPFCP path.

Peridynamic study of fatigue failure of engineered cementitious composites

Fatigue crack propagation is crucial in studying fatigue in engineered cementitious composites (ECC). This paper established a peridynamics (PD)-based fatigue crack propagation model for ECC, incorporating the “cycle broken bonds number” to enhance calculation efficiency. First, the PD fatigue crack propagation model was constructed, and the validity of the model was verified by simulating the fatigue crack propagation path of an inclined edge crack in the plate. Secondly, an improved PMB model considering the strain softening stage was used to model the ECC cement matrix, and the fibers were modeled as one-dimensional cyclic dynamic rods to establish a PD fully discrete model of ECC. At the same time, an interface exponential friction attenuation model was introduced. Then, the effectiveness and validness of the fully discrete model were verified by simulating single fiber pull-out tests and uniaxial tensile tests of ECC specimens. Finally, the fatigue crack propagation forms of ECC beams with mid span Type I cracks under three-point bending fatigue loads were studied, and the effects of fiber volume fraction, stress level, and fiber length on the crack propagation forms and structural deflection of ECC beams under four-point bending fatigue loads were investigated.

The fatigue crack propagation in nanocrystalline materials in the hydrogen environment

In this article, the effect of the external corrosion environment on dislocation emission is introduced, and the microscopic mechanism of fatigue crack propagation (FCP) in a hydrogen environment is studied. Meanwhile, based on the discrete distributed dislocation method, the corrosion FCP model of nanocrystal materials is established. In the framework of our model, the FCP is mainly determined by the irreversibility of the crack tip dislocation. The research results indicate that the aggregation of hydrogen atoms at the crack tip (CT) promotes the dislocations emission and increases the FCP rate. Meanwhile, considering the application of materials in different hydrogen circumstances, the effects of changes in the distance between hydrogen atoms and the crack tip and the radius of hydrogen atoms on crack propagation rate are studied. The results show that the accumulation of hydrogen atoms at the crack tip promotes the fatigue crack growth rate in nanocrystalline materials. Compared with the air environment, the maximum increase in crack propagation rate is about 45% under the action of hydrogen environment. Meanwhile, increasing the grain size and dislocation emission angle helps to increase the crack propagation rate. The research in this paper provides a theoretical basis for evaluating the corrosion fatigue life of metal materials.

A novel peridynamic fatigue crack propagation model based on two-parameter remaining-life formulation

A novel peridynamic fatigue crack propagation model based on two-parameter remaining-life formulation

The interaction of crack and dislocations in cyclic loading in the body-centered cubic (BCC) crystal

In engineering, the mode of fatigue crack propagation in crystals is very important for studying the first stage of fatigue crack propagation. In this paper, a model of fatigue crack propagation in crystals is established by using the discrete dislocation method. The propagation rate of fatigue cracks in different crystals and the dislocation movement and distribution on the slip plans (SP) in front of cracks during loading and unloading are obtained by calculation the model. The effects of different dislocation motion behaviors on fatigue crack growth rate during loading and unloading are analyzed, including dislocation emission, rebound and annihilation. Compared with the case without considering dislocation shielding effect, the influence of dislocation shielding effect on fatigue crack propagation is given. At the same time, the effects of different grain sizes and different grain boundary (GB) angles on fatigue crack propagation are studied.

Jk-integral applied to mixed-mode fatigue crack propagation and life prediction in metal welding interface

In this paper, an innovative fatigue crack propagation model of metal welding interface is investigated based on the concept of Jk-integral (k = 1, 2) in elastic–plastic material, including the prediction of crack propagation path and life. In order to validate the effectiveness of the present fatigue model, the experiments of mixed-mode interface fatigue cracks are carried out on compact tensile shear specimens of N36 zirconium alloy using DIC methods. The results demonstrate that the fatigue crack only propagates along the interface under mode I loading where the relationship between the crack growth rate da/dN and ΔJ1 (the J1-integral range per loading cycle) is logarithmic linear. As for mode I/II mixed-mode loading, interface cracks start to propagate along the interface when J1 reaches Jint-C (the interface fracture toughness). When Jtotal (the vector sum of J1 and J2) reaches Jsub-C (the substrate fracture toughness), the crack deflects to the substrate in the Jtotal direction. In this case, da/dN shows a two-stage logarithmic linear relation with ΔJtotal (the Jtotal-integral range per loading cycle) under mixed-mode loading, and the critical Jtotal at the beginning of crack deflection is approximately matching the specific value. The theoretical deflection angle (i.e. the Jtotal direction) calculated from the corresponding J1 and J2 at the beginning of crack deflection is wellconsistentwiththe actual deflection angle observed in experiments. Moreover, the model can clearly describe the two-stage process from the crack propagation along the interface to the crack deflection to the substrate under mixed-mode loading. It is concluded that the proposed fatigue model based on Jk-integral can accurately predict the fatigue crack propagation path and lifetime of metal welding interface.

Fatigue crack propagation model and life prediction for pantographs on High-Speed trains under different service environments

The fatigue crack growth of a weld toe on the upper arm of a pantograph was investigated to predict the fatigue crack propagation life of the pantograph under normal and corrosive conditions. First, samples were subjected to four-point bending tests and simulations under the two conditions, and Paris law parameters were obtained. Second, constant-amplitude loads were determined through the equivalent treatment of variable-amplitude loads. Based on the Paris model, crack propagation was simulated using the finite element method for the two environments, and results showed a relationship between the crack length a and the stress intensity factor KI. The service life of the pantograph was predicted using the Paris law. Results indicated that the pantograph could run about 958,000 km and 7,660 km in normal and corrosive environments, respectively, after the development of its fatigue crack from a surface crack into a through-thickness crack.

Microscopic fatigue crack propagation model for polycrystalline alloys

In the present work, using the crystal plasticity finite element method in combination with the extended finite element method, a microscopic polycrystalline fatigue crack propagation (MPFCP) model based on the total cumulative shear strain was developed. MPFCP processes were reproduced well by the MPFCP model. The MPFCP behaviors of micro-single edge notched tensile (M−SENT) and micro-central cracked tension (M-CCT) model specimens under different constraint conditions were analyzed using the new model. Furthermore, the effects of grain orientation on the MPFCP rate and path were discussed. It was found that with the increase of constraints, the number of cycles required for the same MPFCP length increased for both M−SENT and M-CCT model specimens. A crack length of a = 100 μm was the transition length from the microstructurally small crack stage to the physically small crack stage. The diversity of grain orientation distribution had a significant influence on the MPFCP path and rate within each grain.

Identification of the parameters contained in a cyclic cohesive zone model for fatigue crack propagation

Cyclic cohesive zone models provide a useful tool to describe fatigue driven crack propagation, covering a wide range of engineering applications. For a proper use of these models, particular attention must be devoted to the correct calibration of the parameters contained, considering that some of these can be characterized by a large variability and/or by the absence of a precise physical meaning so that they are not amenable to a direct measurement. This paper proposes a robust inverse analysis procedure, to investigate the identifiability of the model parameters governing the fatigue induced damage evolution, in a recently proposed cyclic cohesive zone model. A novel control for compact test specimens providing more meaningful experimental information is proposed. The identification problem is formulated by considering fatigue crack propagation curve and deformations measurements in a discrete number of points of the specimen surface as input data of the inverse algorithm. The finite element operator, adopted to simulate the experimental tests, has been substituted by a proper calibrated meta model to reduce the computational cost of the forward operator and, thus, to solve the inverse problem in a stochastic context through Monte Carlo like procedures. Representative results, obtained starting from virtual data affected by different levels of noise, are reported to highlight the identifiability of the model parameters on the basis of the experimental data adopted. Indications regarding the minimum number of measurements needed to make the inverse problem well-posed are also provided, supporting possible planning of measurements setups for laboratory investigations.

Multi-scale modelling of fatigue crack propagation due to liquid droplet impingement

We develop a sequential multi-scaling framework for studying the problem of fatigue crack propagation due to liquid droplet impingement. The scope is limited to a hypothetical material and a hypothetical liquid. The multi-scaling is achieved by handshaking the atomistic scale molecular dynamics (MD) simulations with the continuum scale smoothed particle hydrodynamics (SPH). The handshaking, in turn, is performed by evaluating the material, the fracture and the loading properties from MD simulations, and using them as inputs in the continuum scale SPH model. Due to the qualitative agreement of the pressure developed in the fluid and the substrate between the MD simulations and already published results, the liquid droplet impact in SPH is simulated through appropriate surface stresses. Further, we incorporate the pseudo-spring approach within the SPH model to develop a methodology for studying mixed-mode fatigue crack propagation. Our methodology provides good agreement with the existing literature for several cases. Lastly, we calculate the fatigue life of an edge-cracked specimen due to liquid droplet impingement.

Prediction of fatigue crack propagation based on dynamic Bayesian network

To address the problem of low prediction accuracy in the current research on fatigue crack propagation prediction, a prediction method of fatigue crack propagation based on a dynamic Bayesian network is proposed in this paper. The Paris Law of crack propagation and the extended finite element method (XFEM) are combined to establish the state equation of crack propagation. The uncertain factors of crack propagation are analyzed, and the prediction model of fatigue crack propagation based on the dynamic Bayesian network is constructed. A Bayesian inference algorithm based on the combination of Gaussian particle filter and firefly algorithm is proposed. The fatigue experiment of the specimen with the pre-cracks is carried out to test the correlation between the fatigue load cycles and the crack propagation depth. The experimental results show that the crack propagation prediction method proposed in this paper can effectively improve the prediction accuracy of crack propagation depth.

Time-Dependent Sensitivity of Structural Reliability Assessment to Multi-Source Uncertainties Using Lamb Wave

Abstract This article investigates the time-dependent sensitivity of structural reliability assessment to multisource uncertainties using Lamb wave. To precisely model the influence of local damage on the structure in the course of damage growth, a surface damage effect model is proposed to obtain the equivalent elasticity modulus, which can be coupled with the structure model. The evolution of the surface damage is modeled using the fatigue crack propagation model. Furthermore, by setting up the component and structure failure criteria, the time-dependent reliability model of the structure under multisource uncertainties from Lamb wave detection and material properties is established. The method of score function is employed to evaluate the sensitivity index, which is defined as the derivative of the reliability with respect to the distribution parameters of uncertain variables. A spatial truss structure is used to demonstrate the overall procedure. Numerical results show that the sensitivities indices are time and damage size dependent. The sensitivity contributions from Lamb wave quantification model and the material properties are comparable when the crack size is relatively small. When the crack grows to a larger size, the reliability assessment result is much more sensitive to uncertainties associated with material properties.

Prediction of fatigue crack propagation lives based on machine learning and data-driven approach

Numerous influence factors will lead to the inaccurate prediction of fatigue crack propagation (FCP) life of the metal structure based on the existing FCP model, while the prediction method based on machine learning (ML) and data-driven approach can provide a new idea for accurately predicting the FCP life of the metal structure. In response to the inconvenience of the online prediction method and the inaccuracy of the offline prediction method, an improved offline prediction method based on data feedback is presented in this paper. FCP tests of reduced scale models of balcony opening corners in a cruise ship are conducted to obtain experimental data with respect to the a-N curves. The crack length corresponding to the cycle is trained using a support vector regression (SVR) and back propagation neural network (BP NN) algorithms. FCP prediction lives of test specimens are performed according to the online, offline, and improved offline prediction methods. Effects of the number of feedback data, the sequence length (SL) in the input set, and the cycle interval on prediction accuracy are discussed. The generalization ability of the proposed method is validated by comparing the prediction results with the experimental data in the literature. The larger the number of feedback data, the higher the prediction accuracy. The results show that 1/5 and 1/2 feedback data are needed in the SVR and BP NN algorithm with SL is 5, respectively. Furthermore, the SVR algorithm and SL=5 are recommended for FCP life prediction using the improved offline prediction method.

Numerical modelling of a new FCP model and a correlation of the FCP rate with the constraint

Fatigue and constraint are two important factors affecting fracture behavior of materials and life of structures. Some researchers have attempted to describe the fatigue crack propagation (FCP) behavior based on the two-parameter constraint theory. However, there is still no consensus regarding the effect of the constraint on the FCP rate. A correlation between the constraint and the FCP rate must be established. Thus, in this study, a new FCP model was developed by numerical simulations and verified by experiments. Then, the FCP behavior for compact tension (CT) and single edge-notched tensile (SENT) specimens with different in-plane and out-of-plane constraints was studied by numerical simulations using the new FCP model. The trends and essence of the FCP behavior under different constraints were finally clarified. In detail, a linear correlation of the FCP rate with the constraint was established for the first time by using the unified constraint parameter, Ap. Ap was not only extended for use in both monotonic and fatigue loading, but this paper also emphasizes that the FCP rate was largely dependent on the area surrounded by the equivalent plastic strain (εp) isoline at the crack tip rather than the length of the plastic zone. The results show that Ap can be employed to reveal the constraint effect in fatigue deeply and extensively.

A two-dimensional ordinary state-based peridynamic model for surface fatigue crack propagation in railheads

Based on ordinary state-based peridynamic theory, a 2D peridynamic model has been established to investigate fatigue crack propagation in railheads. The proposed model is verified in terms of rail deformation under a quasi-static load and the ductile material-related fatigue failure model. Good agreements have been achieved between a finite element model and the experimental results. With the proposed model, the effects of the initial crack angle, initial crack length and wheel-rail friction coefficient on crack propagation in railheads are studied. This research provides a new method for studying crack propagation in railheads.