Fatigue Crack Growth Model Research Articles

Phase field modeling of fatigue crack initiation and growth under various loading situations

AbstractIn this work we illustrate the ability of a phase field model for fatigue crack growth in terms of extension capability to various amplitude loading and mean stress effects. The additional energy density contribution accounting for the energy associated with fatigue is modified in order to provide a more general model. Results obtained from numerical fatigue crack growth simulations are briefly presented and discussed.

Corrosion fatigue crack growth mechanisms in welded joints of marine steel structures

This paper presents a model of fatigue crack growth in a welded joint and a two-dimensional model of anodic dissolution based on Donahue model and anodic dissolution mechanism, respectively. In addition, a model for predicting the corrosion fatigue crack growth rate in welded joints of steel marine structures is established and crack growth mechanisms are analyzed. The results show that during early stages of crack growth, corrosion fatigue crack growth rate in welded joints is mainly controlled by corrosion action, whereas cyclic loading becomes more influential during the later stage of crack propagation. Loading frequency and effective stress ratio can affect rupture period of protective film at the corrosion fatigue crack tip and the length of corrosion crack increment, respectively, which changes the influence of corrosion action on crack growth rate. However, the impact of stress amplitude on crack growth rate is only significant when crack propagation is caused by cyclic loading. Welding residual stress not only improves the effective stress ratio of cyclic loading, but also promotes crack closure and increases corrosion fatigue crack growth rate in welded joints. Compared to corrosion action, welding residual stress has a more significant influence on crack growth caused by cyclic loading.

Single overloads FCG modeling considering damage accumulation

In this study, Fatigue Crack Growth (FCG) in a CT specimen, submitted to single overloads, is predicted by a node release numerical model, which considers the plastic strain to be the main FCG driving force. The Gauss-Tvergaard-Needleman (GTN) damage model was implemented to account for the, inevitable, growth and nucleation of microvoids in the occurrence of high levels of plastic strain. Crack closure shown to be a crucial mechanism influencing the differences between both models, as well as it explains the effects of the overloads on the FCG rate.

Fracture mechanics based fatigue life prediction for a weld toe crack under constant and variable amplitude random block loading—Modeling and uncertainty estimation

Propagation of weld toe cracks under cyclic loading is often predicted using fracture mechanics. In as welded condition, most of the propagation life is spent as a short crack, which is known to behave differently than a long crack. Several studies have been conducted with the aim of correlating the fatigue crack growth rate and the threshold condition of small cracks to the well known linear elastic crack driving force parameter ΔK, the stress intensity factor range. In many cases, the application of such models requires the quantification of material properties and model parameters that are difficult to obtain from tests, and therefore scarcely available. The present paper bypasses this inconvenience by making use of the square root of area, area, parameter proposed by Murakami. Successively, a linear elastic fracture mechanics based fatigue crack growth model is formulated for physically short and long cracks under constant and variable amplitude random block loading. The uncertainty of the model parameters is quantified in a frequentist statistical framework.

Model-driven fatigue crack characterization and growth prediction: A two-step, 3-D fatigue damage modeling framework for structural health monitoring

Prevailing fatigue damage evaluation approaches that make use of the acoustic nonlinearity of guided ultrasonic waves (GUWs) are sustained by simplified models, most of which depict three-dimensional (3-D) fatigue damage in a two-dimensional (2-D) domain [1]. Such approximation risks the evaluation accuracy. With such motivation, this study aspires to a new, two-step modeling framework, aimed at accurately characterizing and continuously monitoring fatigue damage, from its embryonic initiation, through progressive growth to formation of macroscopic crack. In the first step, a 3-D, analytical model based on the theory of elastodynamics sheds light on the generation of contact acoustic nonlinearity in GUWs under the modulation of `breathing' behavior of a non-penetrating fatigue crack, on which basis a crack-area-dependent nonlinear damage index is yielded. In the second step, a 3-D fatigue crack growth model predicts the continuous growth of the identified fatigue crack in the length and depth along crack front. The framework is validated using numerical simulation, followed with experiment, in both of which the initiation and progressive growth of a real corner fatigue crack is monitored, with continuous prediction of the crack growth in length and depth. Results have demonstrated the accuracy and precision of the developed modeling framework for characterizing embryonic fatigue damage.

Contending Remaining Useful Life Algorithms

Operational readiness, reliability and safety are all enhanced through condition monitoring. That said, for many assets, there is still a need for a prognostic capability to calculate remaining useful life (RUL). RUL allows operation and maintenance personnel to better schedule assets, and logisticians to order long lead time part to help improve balance of plant/asset availability. While a number of RUL techniques have been reported, we have focused on fatigue crack growth models (as opposed to physics or deep learning of based models). This paper compares the performance of stress intensity models (linear elastic model, e.g. Paris’ Law), to Head’s theory (geomatical similarity hypothesis) and to Dislocation/Energy theories of crack growth. It will be shown that these models differ mainly in the crack growth exponent, and that this leads to large differences in the estimation of RUL during early state fault propagation, though the results of all three models converge as the RUL is shorted.

Digital twin approach for intelligent operation planning and health management of mechanical systems

The digital twin paradigm aims to fuse information obtained from sensor data, physics models, and operational data for a mechanical component in use to make well-informed decisions regarding health management and operations of the component. In this work, we discuss a methodology for digital-twin-based operation planning in mechanical systems to enable: a) cost-effective maintenance scheduling, and b) resilient operations of the system. As properties of mechanical systems, as well as their operational parameters, loads and environment are stochastic in nature, our methodology includes probabilistic damage diagnosis, probabilistic damage prognosis, and system optimization under uncertainty. As an illustrative example, we consider the problem of fatigue crack growth in a metal component. We discuss a probabilistic, ultrasonic-guided-wave-based crack diagnosis framework that can handle both aleatory and epistemic uncertainties in the diagnosis process. We build a high-fidelity, finite element model to simulate the piezoelectric effect and ultrasonic guided wave propagation. We use test data obtained by conducting diagnostic experiments on the physical twin to calibrate the error in the diagnosis model. We perform Bayesian diagnosis of crack growth using the corrected diagnosis model, considering data corrupted by measurement noise, and fuse the information from multiple sensors. We build a finite-element-based high-fidelity model for crack growth under uniaxial cyclic loading, and calibrate a phenomenological (low-fidelity) fatigue crack growth model using the high-fidelity model output as well as data from fatigue loading experiments performed on the physical twin. We use the resulting multi-fidelity model in a probabilistic crack growth prognosis framework; thus achieving both accuracy and computational efficiency. Lastly, we utilize the damage diagnosis framework along with the damage prognosis model to optimize system operations under diagnostic and prognostic uncertainty. We perform simulation as well as laboratory experiments that show how the digital twin of the component of interest can be used for intelligent health management and operation planning for mechanical systems.

Probabilistic life prediction for FCG degradation process of turbine disc with small sample data

A probabilistic fatigue crack growth (FCG) life prediction is conducted on a turbine disc considering small sample data involving material properties and geometric dimensions in this study. Wiener process with two transformed time scales is used to quantify the time-varying dispersion of FCG degradation process. The accuracy of Weiner process model is verified by using the FCG experimental data for standard compact tension (CT) specimens. Then, FCG tests on the component-like specimens are conducted to establish the time-varying FCG model considering geometrical features. During this process, Bootstrap method is introduced to expand the small test samples into larger Bootstrap samples. Meanwhile, the dispersion for geometric dimensions of the small sample is described by using probability box method. Finally, probabilistic FCG analysis is conducted on a turbine disc through using quasi-Monte Carlo sampling method. Results show that the average relative error between the lower bound of Ns and Na is within 20%, and the average relative error between the upper bound of Ns and Na is less than 15%, which further demonstrates the accuracy of probabilistic FCG method.

Theoretical model of fatigue crack growth of a thermoelectric pn-junction bonded to an elastic substrate

Thermoelectric materials and devices have wide applications in micro/nano-structured materials and structures. Under the time-varying thermal loadings, the thermoelectric devices can failure by fatigue accumulation. Fatigue crack propagations at the interface of the thermoelectric pn-junction and at the interface between the thermoelectric layer and the elastic substrate are analyzed in this paper. Influence of the temperature dependence of material properties on the fatigue life is discussed. The fatigue crack is more prone to propagation at the interface between thermoelectric layer and substrate rather than at the interface of the thermoelectric pn-junction. The fatigue life gradually increases to a constant with the external electrical resistance. Fatigue lives of the thermoelectric devices with temperature-dependent material properties are much shorter than those with constant material properties. A simplified but useful expression of the fatigue life as functions of the thermal loadings and the crack length is presented.

Uncertainty theory based reliability modeling for fatigue

The study of the fatigue crack growth law is usually carried out by the fatigue crack growth experiments (FCGE), and is expressed by the fatigue crack growth model. Epistemic uncertainties exist in FCGE with small samples. Generally, Bayesian method, interval probability method, and fuzzy probability method are presented to quantify the epistemic uncertainty in the case of small samples. However, the expression of the epistemic uncertainty in most studies is greatly influenced by subjective information, and there are interval expansion problems in the calculation. Therefore, the problem of how to quantify the epistemic uncertainties in FCGE with small samples has not been well solved. Under such circumstance, a novel uncertain measure is used to quantify such epistemic uncertainty in this paper, which is belong to uncertainty theory proposed by Prof. Baoding Liu. Firstly, the fatigue crack growth model proposed by Zhang is introduced as the foundation of modeling. Then, the sources of uncertainties in FCGE are analyzed and the uncertainties are quantified based on the uncertainty theory. Finally, a belief reliability model of fatigue crack growth is proposed, in which the associated reliability function is derived, and the uncertain statistics for the parameter estimations is presented. The case study illustrates the proposed methodology and the corresponding discussions show that the uncertainty theory contributes to more stable reliability evaluation than probability theory when quantifying the epistemic uncertainty, and the influence of the material scatter on fatigue reliability should be emphasized.

Crack growth prediction for irradiated stainless steels under the combined fatigue-creep loading

A methodology is presented in this study for estimating the crack growth of austenitic stainless steel Types 304, 304L, 316, and 316L, which are commonly used as structural materials in nuclear pressure vessels. These structural components are typically subjected to neutron irradiation and combined loadings, including repeated mechanical stresses (i.e., fatigue) resulting from startups and shutdowns, as well as creep due to on-load periods at elevated temperature. In this study, the fatigue crack length was estimated using a strip-yield based fatigue crack growth model. The model is extended to include the effects of creep deformation in a presence of hold- times, and expanded to include the effects of irradiation. Reasonable crack growth estimations are obtained for selected materials under various combined loading conditions when compared to the experimental data available in the literature.

Study on the Overload and Dwell-Fatigue Property of Titanium Alloy in Manned Deep Submersible

With the rapid development of ocean technology, the deep-sea manned submersible is regarded as a high-tech equipment for the exploration and exploitation of ocean resources. The safety of manned cabin has a decisive effect on the whole system. Ti-6Al-4V with the superior strength-to-weight ratio and corrosion resistance has been used for the manned cabin. The manned cabin experiences loading spectrum with different maximum stresses and different dwell time during their service life. The load sequence effects on dwell fatigue crack growth behavior of Ti-6Al-4V under different dwell time are investigated experimentally in this paper. The experimental results show that the crack tip plastic zone is enlarged by the dwell time and the overload retardation zone increases with dwell time under the same overload rate. A dwell fatigue crack growth model is proposed by modifying the crack tip plastic zone under the loading history with combinations of the single overload and dwell time factors are included in the modified model. Based on the experimental data, the overload retardation zone and the crack growth rates of Ti-6Al-4V are predicted by the modified model. A reasonable model for the load sequence effect on the dwell fatigue crack growth rates of Ti-6Al-4V is verified.

Cumulative Damage Modeling with Recurrent Neural Networks

Maintenance of engineering assets (for example, aircraft, jet engines, and wind turbines) is a profitable business. Unfortunately, building models that estimate remaining useful life for large fleets is daunting due to factors such as duty cycle variation, harsh environments, inadequate maintenance, and mass production problems that cause discrepancies between designed and observed lives. We model cumulative damage through recurrent neural networks. Besides architectures such as long short-term memory and gated recurrent unit, we introduced a novel physics-informed approach. Essentially, we merge physics-informed and data-driven layers. With that, engineers and scientists can use physics-informed layers to model well understood phenomena (for example, fatigue crack growth) and use data-driven layers to model poorly characterized parts (for example, internal loads). A numerical experiment is used to present the main features of the proposed physics-informed recurrent neural network. The problem consists of predicting fatigue crack length for a fleet of aircraft. The models are trained using full input observations (far-field loads) and very limited output observations (crack length data for only a portion of the fleet). The results demonstrate that our proposed physics-informed recurrent neural network can model fatigue crack growth even when the observed distribution of crack length does not match the fleet distribution.

Probabilistic modeling of fatigue crack growth and experimental verification

Stochastic fatigue crack growth (FCG) modeling is vital for fatigue reliability and durability analyses of engineering components. To characterize the statistical properties of FCG process, the Yang–Manning model was introduced to calculate the crack exceedance probability and fatigue life distribution to reach any crack size; however, it is only applicable for failure probability analyses of pre-cracking specimens. According to this, a new probabilistic fatigue life model considering the distribution of initial crack sizes was proposed. Experimental data of Al 2024-T3 alloy and 30NiCrMoV12 steel were utilized for model validation and comparison. Results show that the proposed probabilistic model works well for FCG analysis with independent cracks. In addition, the Yang–Manning model was extended to consider the crack coalescence issue under multiple cracks condition, which shows a sound conformity to experimental data.

Mixed-mode fatigue crack growth using cohesive zone modeling

In order to capture nonlinear crack tip behavior and account for mixed-mode fatigue crack growth, a cohesive zone based fatigue crack growth model is proposed in conjunction with the Park-Paulino-Roesler (PPR) traction-separation relationship. The model clearly defines five stages during arbitrary fatigue loading: softening, unloading, reloading, contact, and complete failure. The cohesive traction-separation relationship is based on the PPR fracture potential, while the fatigue damage is accumulated by introducing two conjugate damage measures. One damage measure is associated with the rate of separation, while the other is related to the rate of traction (or local stress). Additionally, two model constants are introduced to control the normal contact condition, which may be associated with physical conditions such as crack closure, crack face roughness, and oxidation of fracture surface. Furthermore, computational simulations of the proposed fatigue crack growth model are performed for a simple mode-I test, double cantilever beam test, modified mixed-mode bending test, and three-point bending test. The observed computational results lead to stable and consistent fatigue crack growth.

A procedure to generate design load-time histories for fatigue strength assessment of offshore structures

This paper presents general procedures to generate loading histories for fatigue strength assessment of offshore structures based on a storm model and seasonal wave data. Using hindcast wave data of 11 years at one point in the North Atlantic Ocean, the relations among the storm duration, storm crest and the number of levels in a storm are formulated and the statistics of storm duration are obtained. One year, including four seasons is chosen as the reference period of the loading history. Based on the generated loading histories, fatigue crack propagation analyses are performed on a tubular T-joint using a fatigue crack growth model considering the load interaction and R-ratio effect. The crack size uncertainty caused by randomly generated loading histories is investigated. The proposed procedures can lead to a good agreement with the observed significant wave height distribution. The generated loading histories result in median crack growth curves, comparing with those from measured wave data. The crack size is subjected to considerable uncertainty after a period of crack propagation. Ignoring the load interaction effect leads to faster crack growth, which may be the most convenient way to achieve a conservative fatigue crack propagation analysis using only one generated load history.

Analytical modeling of fatigue crack propagation based on cyclic hardening and a characteristic damage length

An analytical fatigue crack growth model is developed, which combines effectively a cyclic energy dissipation approach and the strain energy density theory. The model uses cyclic material properties and relies on cyclic hardening for fatigue crack growth rate prediction. Fatigue crack propagation occurs incrementally by a characteristic damage length, which is in the length scale of striation spacing in commercial aluminum alloy, supporting the model’s physical background. Analytical crack propagation rates correlate well with existing experimental data, in material with uniform strength and strength gradient, showing the ability of the model to account for strength variation at the crack path.

An analytical model for the coupled-field dynamic fatigue crack growth in a metallic beam under chaotic excitations

Dynamic fatigue crack growth (FCG) under chaotic excitations has not yet received due attentions. The current paper presents an analytical model for predicting the FCG in a metallic notched beam subject to external chaotic excitations. The proposed stand-alone analytical model only requires the physical properties of the cracked beam; initial crack conditions; the material constants for the Paris power law; and the time series of the external chaotic excitation. The validity of the analytical model proposed is verified using relevant experimental results from other researchers.The validated model is employed to conduct parametric studies on the coupled field FCG in a notched metallic beam vibrating under external chaotic excitations. The fatigue lives obtained under a group of statistically similar chaotic excitations significantly disperse. The ratio between the maximum and minimum fatigue lives is around 5.2. The ratio remains as high as 2.4, even when only the initial conditions in the chaotic excitations vary.The common practice Palmgren-Miner rule is also used to estimate the fatigue life under chaotic excitations. These predictions differ, by several times, from those provided by the current validated analytical model. Similar shortcomings were noticed in a previous experimental study, where the Palmgren-Miner rule, reportedly, considerably overestimated the fatigue damage under chaotic excitations. In the current study, both under and over-predictions are noted.

An interaction integral retardation model for predicting fatigue life under multi-step loading

This paper proposes an interaction integral retardation (IIR) model to predict fatigue life accurately for components subjected to multi-step loading (MSL) conditions. The IIR model is based on the cyclic interaction integral that considers the effect of elasticity and plasticity simultaneously at the crack tip. Elasto-plastic numerical simulations were carried out based on FEM to compute the cyclic interaction integral. The IIR model was verified against the experiments under different loading conditions including constant amplitude loadings, single tensile overloads, and MSL for different steel strengths. The fatigue lives calculated by the IIR model exhibit a very good agreement with those obtained by the experiments for the applied loading conditions and steels. The efficiency of the IIR model was manifested by comparing the calculated fatigue lives against those computed by different traditional and well-established fatigue crack growth (FCG) models. For the MSL condition, fatigue lives obtained by the IIR model revealed a better agreement against the experiment compared to those given by the traditional FCG models. The crack-tip driving force represented by the elasto-plastic cyclic interaction integral could explain the mechanics of crack growth retardation and acceleration due to the change in the applied loading. Further, the local material behavior ahead of the crack tip was examined rigorously for different crack lengths under variable cyclic loadings. It was found that the local material behavior has a significant influence on the state of crack growth (retardation/acceleration) which results in accelerating or retarding the crack growth rate.

Uncertainty Modeling of Fatigue Crack Growth and Probabilistic Life Prediction for Welded Joints of Nuclear Stainless Steel.

Welded joints are widely used in the pipeline connection of nuclear power plants. Defects in these joints are an important factor leading to the failure of welded joints. It is critical to study the fatigue crack growth and life prediction methods for the welded joints with defects, to reduce their likelihood. In this paper, we present our study of the uncertainty of fatigue crack propagation and probabilistic life prediction for welded joints of nuclear stainless steel. The standard compact tension (CT) specimens were fabricated according to the American Society for Testing and Materials (ASTM) standard. Fatigue crack propagation tests with different stress ratios were performed on CT specimens, using the Mei Te Si (MTS) fatigue test system. A fatigue crack propagation rate model considering the uncertainty of material parameters, and based on the Paris formula and crack propagation experimental data, was established. A probabilistic life prediction method based on Monte Carlo simulation was developed. The fatigue crack propagation prediction result of a CT specimen was compared with the actual tested result, to verify the effectiveness of the proposed method. Finally, the method was applied to an embedded elliptical crack in welded joints of nuclear stainless steel, to predict the fatigue crack growth life and evaluate the reliability.