Crack Growth Analysis Research Articles

Utilizing Spatial Statistical Bounds on Residual Stress Fields From Cold Expansion: Effects on Fatigue Crack Growth Behavior

ABSTRACTThis paper assesses the impact of utilizing statistically defined residual stress fields from cold expansion (Cx) in linear elastic, multi‐point fracture mechanics analyses using the spatial analysis of residual stress (SpARS) methodology. There is significant value and interest in leveraging the increased fatigue life afforded by Cx, but it is imperative to quantify the variability of the residual stress to understand the expected variability in benefit due to Cx. Comparisons of the predicted fatigue lives from SpARS‐produced statistical residual stress fields are made to fatigue test data. Results demonstrated that the less compressive 95% upper bound from the mean residual stress would be a reasonable strategy as it supplies a compromise between safety and inherent material and process variability while still producing a sizable improvement in predicted fatigue life. In this study, using SpARS to incorporate statistically representative residual stress fields in fatigue crack growth analyses demonstrates a methodology to aircraft structural engineers for improved fleet management and allow increased aircraft availability through fewer inspections.

Crack Growth Analytical Model Considering the Crack Growth Resistance Parameter Due to the Unloading Process

Crack growth analysis is essential for probabilistic damage tolerance assessment of aeroengine life-limited parts. Traditional crack growth models directly establish the stress ratio–crack growth rate or crack opening stress relationship and focus less on changes in the crack tip stress field and its influence, so the resolution and accuracy of maneuvering flight load spectral analysis are limited. To improve the accuracy and convenience of analysis, a parameter considering the effect of unloading amount on crack propagation resistance is proposed, and the corresponding analytical model is established. The corresponding process for acquiring the model parameters through the constant amplitude test data of a Ti-6AL-4V compact tension specimen is presented. Six kinds of flight load spectra with inserted load pairs with different stress ratios and repetition times are tested to verify the accuracy of the proposed model. All the deviations between the proposed model and test life results are less than 10%, which demonstrates the superiority of the proposed model over the crack closure and Walker-based models in addressing relevant loading spectra. The proposed analytical model provides new insights for the safety of aeroengine life-limited parts.

Assessment of internal defects in flush ground butt welds in marine structures

In this paper, acceptance criteria of internal planar defects for the highest design S-N curve for surface ground butt welds in fatigue design standards has been assessed based on fatigue tests of tethers containing internal defects. The results from crack growth analysis from defects placed close to the surface are compared with test data from constant amplitude testing of tethers with circumferential welds that includes flaws or small planar defects close to the surface. Floating structures and support structures are subjected to variable loads and the calculated response leads to a long-term stress range distribution with many small stress ranges. This means that if the cracks are small, the resulting stress intensity may be less than the threshold stress intensity factor and the crack does not grow for this stress cycle, or it grows at a reduced crack growth rate in the near threshold region. A methodology to account for this is presented based on a two-parameter Weibull long-term stress range distribution that is representative for load response of floating structures and for support structures for wind turbines. It is shown that the threshold value and the reduced crack growth rate in the near threshold region for small internal defect heights can be used to lift the fatigue test data from constant amplitude testing to be in better correspondence with a higher S-N curve when considering an actual long-term loading.

Predictive Analysis of Crack Growth in Bearings via Neural Networks

Machine learning (ML) and artificial intelligence (AI) have emerged as the most advanced technologies today for solving issues as well as assessing and forecasting occurrences. The use of AI and ML in various organizations seeks to capitalize on the benefits of vast amounts of data based on scientific approaches, notably machine learning, which may identify patterns of decision-making and minimize the need for human intervention. The purpose of this research work is to develop a suitable neural network model, which is a component of AI and ML, to assess and forecast crack propagation in a bearing with a seeded crack. The bearing was continually run for many hours, and data were retrieved at time intervals that might be utilized to forecast crack growth. The variables root mean square (RMS), crest factor, signal-to-noise ratio (SNR), skewness, kurtosis, and Shannon entropy were collected from the continuously running bearing and utilized as input parameters, with the total crack area and crack width regarded as output parameters. Finally, utilizing several methodologies of the Neural Network tool in MATLAB, a realistic ANN model was trained to predict the crack area and crack width. It was observed that the ANN model performed admirably in predicting data with a better degree of accuracy. Through analysis, it was observed that the SNR was the most relevant parameter in anticipating data in bearing crack propagation, with an accuracy rate of 99.2% when evaluated as a single parameter, whereas in multiple parameter analysis, a combination of kurtosis and Shannon entropy gave a 99.39% accuracy rate.

Analysis of creep crack growth in bonded joints based on a Paris' law-like approach

Creep crack growth is one of the factors that could affect the durability of a bonded joint and compromise the safety of structures over long periods of time. However, numerical tools and test methods relating to creep crack growth in bonded joints are not widely available yet. In this work, a Creep Crack Growth Model (CCGM) is proposed for adhesively bonded joints. The model describes the relation between the crack growth rate and the energy release rate. The CCGM is fitted with results from Roller Wedge Driven creep crack growth (RWDC) tests and validated against the results obtained from tapered double cantilever beam (TDCB) tests with a constant load applied. Additionally, it is demonstrated that the proposed model can be introduced in a fatigue tool commercially available from the finite element method (FEM) code Abaqus to predict creep crack growth. The FEM results show that the phenomenological expression fitted from experimental tests results, which is used as input for the FEM tool, is reproduced with accuracy. Moreover, it is shown that the CCGM is capable of predicting creep crack growth rates when a different specimen geometry is used, thus demonstrating that the model correctly captures the physics of the problem.

Reliability Analysis of Fatigue Crack Growth in Plain Concrete

Civil engineers know that fatigue indicates themajority of structural failures. In plain and reinforced concrete structures, fatigue might account for excessivedeformation, excessive of crack widths, de-bonding ofreinforcement and rupture of the reinforcement, all of thesecan lead to structural collapse. Fatigue crack propagation can be a method to predict a remaining life of structures.Herein some works that have been done will be shown inorder to analyse the fatigue crack growth for plain concretespecimens. The goals of this study are to estimate the criticalcrack length and remaining life of a plain concrete specimen, determine the state of the specimen either havingfailed or being safe using first order reliability method(FORM) and assess which parameter has most influence onthe reliability index

First and second law analysis of crack propagation in canvas painting

The knowledge of how the craquelures happen and their pattern on historical objects, especially paintings, is interested in the field of cultural heritage. Entropy generation and thermal analysis of crack growth are calculated numerically for the canvas painting. The painting is modeled as a three-layer composite with isotropic material properties. An in-house code is developed to model the plane strain elasto-static structural mechanics with hybrid-Trefftz finite element formulation. The results are benchmarked with numerical and analytical solutions. Entropy generation and temperature fields are simulated throughout stacking in mode I of a delamination process. The parameter study shows that the parameter of entropy has a great influence on the process of expectation of break proliferation in fast and low areas. It is likewise demonstrated that the use of the corruption entropy age hypothesis gives a technique for assessing the steady in the law of crack growth regarding the rate of entropy production.

Reliability analysis of fatigue crack growth in shallow shell structures using the Dual Boundary Element Method

This work presents a novel methodology for fatigue life reliability analysis using a newly developed Dual Boundary Element Method-based Implicit Differentiation Method (DBEM-IDM) in shallow shell structures. The proposed DBEM formulations evaluate stress intensity factors and fatigue life sensitivities in shallow shells considering geometrical variables and curvature. The IDM formulations, obtained through direct differentiation of the shallow shell DBEM formulations, uses the First-Order Reliability Method (FORM) to assess the reliability index and probability of failure of shallow shell structures with multiple cracks. Two numerical examples were simulated to illustrate the effectiveness of the proposed methodology. The first example examines a shallow shell with a centre hole and cracks subjected to various loads. The critical crack length required to ensure structural reliability and inspectability is determined. Fatigue reliability assessment is performed for the same example, employing limit state functions expressed in terms of fatigue life. FORM results are compared with the results of Monte Carlo Simulations (MCS), and provided a maximum difference of 3.67%. Parametric analyses are conducted to identify significant variables that affect reliability, and it was found that precise determination of design parameters is necessary to reduce the probability of failure, particularly for the Paris law constants. The second example, featuring more complex geometry, involved assessing fatigue reliability in a cylindrical shallow shell structure with multiple cracks. The results of this example indicate a 3.49% maximum difference between FORM and MCS. The results exhibit a low error compared to the MCS, and the inherent efficiency of the IDM-based FORM underscores its suitability for addressing uncertainty in reliability analysis.

Mixed mode fatigue crack growth and fatigue threshold analysis in polyurethane adhesives at elevated temperatures

The paper investigates mixed-mode fatigue crack growth in ductile polyurethane adhesives, emphasizing mode decoupling to distinguish the impact of each loading mode component on crack propagation. It also explores the temperature sensitivity of fatigue crack growth rates for each loading mode. Individual scrutiny of the role of each loading mode in tests is accompanied by an analysis of fatigue fracture surfaces to clarify failure mechanisms. The findings indicate differential sensitivity to ambient temperature between the mode I and mode II components in a mixed mode fatigue test. Notably, the fatigue response of the mode I component exhibited higher sensitivity to temperature than the mode II component in mixed mode fatigue fracture of the tested polyurethanes. The polyurethane adhesives' composition, particularly the hard segment ratio, emerged as a pivotal factor influencing their sensitivity to fatigue loading at elevated temperatures. Temperature effects led to a significant reduction (63%) in the mode I component of mixed mode fatigue for one of the tested adhesives, while the other exhibited a noteworthy increase (154%). This trend which was attributed to the hard segment ratio of the adhesives was also persisted in the shear mode of the mixed mode fatigue results.

A combined ALE-cohesive fracture approach for the arbitrary crack growth analysis

This work introduces an advanced numerical model, based on a cohesive zone approach and the moving mesh technique, for simulating fracture propagation in quasi-brittle materials. The proposed procedure involves two stages: first, a mesh boundary representing the crack is selected and aligned with the crack growth direction by using the Arbitrary Lagrangian-Eulerian (ALE) methodology; next, a zero-thickness interface cohesive element, equipped with a traction-separation law, is adaptively inserted along the previously selected mesh boundary, in order to describe the nonlinear fracture process. The proposed model allows for multiple crack onset and propagation without requiring mesh-updated procedures and sensibly reduces the well-known mesh dependency issues of the standard discrete fracture approaches. Numerical analyses of mixed-mode fracture in concrete specimens are performed and suitable comparisons with experiments show the effectiveness and reliability of the proposed model in predicting arbitrary crack growth.

Fatigue crack growth and microstructural analysis of rail steel specimens under periodic overloads

The present paper aims to study the effects of periodic overloads on the fatigue crack growth and microstructure of railway rail specimens. Numerical analysis and experimental tests were exploited to examine the crack path in specimens. A three-dimensional nonlinear boundary element model was used to predict the crack path in specimens. The effect of several parameters on the fatigue life of the rail steel specimens were evaluated using numerical model and experimental tests. The numerical and experimental test results revealed that the fatigue life curve had an optimal overload ratio at which the fatigue life was maximized. The number of fixed cycles was kept fixed between the overloads, measuring the effect of the overload ratio on the fatigue crack growth. Also, the fractographic analysis showed that by increasing the stretching speed of the rail steel specimens, the amount of plastic deformation is reduced and the brittleness of the material is increased.

A Comparative Analysis of 3D Software for Modeling Fatigue Crack Growth: A Review

Fatigue crack growth modeling is critical for assessing structural integrity in various engineering applications. Researchers and engineers rely on 3D software tools to predict crack propagation accurately. However, choosing the right software can be challenging due to the plethora of available options. This study aimed to systematically compare and evaluate the suitability of seven prominent 3D modeling software packages for fatigue crack growth analysis in specific applications. The selected software tools, namely ABAQUS, FRANC3D, ZENCRACK, LYNX, FEMFAT, COMSOL Multiphysics, and ANSYS, were subjected to a comprehensive analysis to assess their effectiveness in accurately predicting crack propagation. Additionally, this study aimed to highlight the distinctive features and limitations associated with each software package. By conducting this systematic comparison, researchers and engineers can gain valuable insights into the strengths and weaknesses of these software tools, enabling them to make informed decisions when choosing the most appropriate software for their fatigue crack growth analysis needs. Such evaluations contribute to advancing the field by enhancing the understanding and utilization of these 3D modeling software packages, ultimately improving the accuracy and reliability of structural integrity assessments in relevant applications.

High-cycle and low-cycle fatigue life prediction under random multiaxial loadings without cycle counting

A novel fatigue life prediction method under random multiaxial loadings is proposed in this paper. One unique benefit of the proposed method is that it is based on the time-derivative fatigue crack growth formulation and does not need cycle counting under arbitrary loadings. First, a brief review of subcycle fatigue crack growth (FCG) analysis and the equivalent initial flaw size (EIFS) concept for life prediction is introduced. Next, the existing subcycle fatigue crack growth model is extended to near-threshold conditions. An intrinsic fatigue threshold of the material is introduced, and a hypothesis is proposed that the crack only grows when the local stress intensity factor is beyond the intrinsic threshold. Following this, the analogy of stress intensity factor and strain intensity factor is used to extend the fatigue life prediction model to strain-based fatigue analysis. Correction for large plastic deformation is included to handle low-cycle fatigue life prediction. The novelties of this model are that it considers the FCG at the threshold and near-threshold region and it is able to predict both HCF and LCF conditions using FCG-based life prediction. Following this, extensive in-house and literature data for AL-7075-T6 under uniaxial and multiaxial, constant, and random loadings are used for model validation. Discussions for the effect of model parameters are provided based on parametric analysis. Conclusions and future work are mentioned. Code and data are released in public cloud service for interested readers.

Fatigue Crack Growth on Several Materials under Single-Spike Overloads and Aircraft Spectra during Constraint-Loss Behavior

Abstract The phenomenon of flat-to-slant crack growth has been studied by many in the fracture mechanics community. At low stress-intensity factors, a fatigue-crack surface is flat (tensile mode) and the crack-front region is under plane-strain conditions (high constraint). As the crack grows with higher stress-intensity factors, a 45° shear lip occurs through the thickness of the sheet or plate. This behavior is the shear mode, which is under low constraint or plane-stress conditions. In 1966, Schijve found that the transition from flat-to-slant crack growth on a 2024-T3 Alclad aluminum alloy over a wide range in stress ratios (R) occurred at a “constant” crack-growth rate. Also, Newman and Hudson showed the same behavior on 7075-Temper-6 and Ti–8Al–1Mo–1V alloys, validating Schijve’s observation that crack-growth rate was the key parameter for flat-to-slant crack-growth behavior. The materials considered herein are 2024-T3, 7075-T6, and 9310 steel. Crack-growth behavior during single-spike overloads and simulated aircraft spectrum loading are presented. The fatigue structural analysis (FASTRAN) crack-closure based life-prediction code was used to correlate the constant-amplitude (CA) crack-growth-rate data over a wide range in stress ratios (R = Smin/Smax) and rates from threshold to near fracture, and to calculate or predict the crack-growth behavior on single-spike overload tests. Crack-closure behavior is strongly dependent upon the level of constraint. The main objective was to see if the constraint-loss region is the primary reason for crack-growth delays after single-spike overloads. Also, crack-growth analyses are presented on tests that were conducted by Wanhill on 2024-T3 Alclad aluminum alloy under the transport wing standard (TWIST) spectrum. Crack-growth analyses using crack-closure theory without constraint loss was “unable” to predict crack growth under spike overloads or simulated aircraft spectra. However, predicted crack length against cycles with constraint-loss behavior compared reasonably well with all tests.

Propeller blade structural reliability analysis considering mixed-mode fatigue crack growth

Legacy propeller blades made of aluminum alloy are susceptible to fatigue cracking. Once the crack nucleated, it propagates rapidly because of the high rotational speed of the blade. This study uses mixed-mode fatigue crack analysis to understand the out-of-plane interaction of intergranular crack (IGC) and fatigue crack revealed in a U.S. Marine Corp. C-130 crash in 2017. The cracking mechanism is sequential: IGC followed by fatigue cracking, which eventually causes the liberation of the blade. A finite-element-method-based stress analysis elucidates the transition from IGC to fatigue crack. The result showed that the IGC provided enough driving force for the fatigue crack nucleation. A Monte-Carlo-simulation-based risk analysis is performed using the stress and crack growth analyses. The critical plane approach is utilized to determine the equivalent stress intensity factor for the crack growth analysis. The risk analysis results support the rapid liberation of the blade with consideration of large variation in initial crack size. The results also clearly show the necessity of structural risk analysis for planning inspection and maintenance.

A general DBEM for mixed-mode cohesive crack problems

This work proposes a general dual boundary element method (DBEM) for cohesive mixed-mode crack problems. Local cohesive stiffnesses are defined to yield the boundary element nonlinear equations for any mixed-mode cohesive model in a direct way. The main novelty resides on the fact that the formulation can take into account all possible cohesive surface conditions: (i) contact, (ii) softening, (iii) unloading/reloading and (iv) complete failure, which may occur independently of the chosen cohesive model. Besides, the well-established Park–Paulino–Roesler (PPR) model was incorporated into DBEM methods. The tangent matrix of the discrete model is explicitly derived and the solution is sought by a proper degree-of-freedom (DOF) control method. The proposed formulation is validated reproducing mode I and mode II patch-tests. Some other relevant problems, including a mixed-mode fracture test, are also presented to demonstrate that the above conditions are essential to reproduce complex mixed-mode cohesive fractures. The results also shown that the control of a monotonically increasing DOF yields reliable solutions in problems with snap-back instabilities. In order to facilitate the validation of the method, predefined crack paths were assumed in the examples. Further developments may include incorporating arbitrary crack growth and damage-based cohesive models for fatigue crack growth analysis.

Damage Tolerance Behaviour of Stiffened Crown Panel of a Transport Aircraft Fuselage

Ever since the introduction of damage tolerance requirements in the aviation regulations, efforts continue to be made to prevent catastrophic failures due to damages present in the structure. It has also been realized that damage detection is the weakest link in the whole process of damage tolerance design to maintain continued airworthiness. The major components of the aircraft structure consist of both integral and riveted panels of sheets and stringers which are employed in fuselage skin panels, spar webs and stiffeners. In spite of all precautions, cracks or damages may arise in many of these primary structural members. These cracks cause stiffness degradation and reduce the total load-carrying capacity of the structure. In this paper, the damage tolerance behaviour of fuselage crown panel both integral and riveted stiffened panel configurations of Aluminium alloy 2024-T351 are studied using finite element based tools using crack growth analysis methods. The crack growth behaviour of both integral and riveted stiffened panels of aircraft fuselage having same geometrical configuration and subjected to uniformly distributed tensile loads is investigated. For this, a metallic stiffened panel with eight stringers, representative of crown panel of a transport aircraft fuselage is analysed with a centre skin crack propagating through the stringers. Stress intensity factors and fatigue crack propagation rates at the progressive crack tip of both types of the stiffened panels are computed by using Modified Virtual Crack Closure Integral (MVCCI) method. The stiffened panels fatigue crack growth rate was computed by using Paris law under constant amplitude fatigue loads. The analysis results show that integral stiffened panel causes higher stress intensity factor and less load bearing capability than riveted stiffened panel which has better damage tolerant capability in comparison to the integrally stiffened panel.

Mixed-mode crack growth analysis using a cyclic plasticity model

The effects of two singularity fields, namely, the HRR solution and modified form of the nonlinear kinematic hardening (NKH) solution, on the pure mode I and mixed mode I/II fatigue crack propagation were investigated. Experiments and computations were performed on compact tension shear (CTS) specimens of P2M steel, aluminium 7050, and Ti-6Al-4V with different monotonic and cyclic elastic–plastic properties. The analysis of the experimental data on the crack growth rate for all tested materials is given in terms of plastic stress intensity factors (SIFs) according to the HRR and NKH models. The elastic–plastic crack tip fields were obtained by FE computation as a function of the position along the curvilinear crack path for the monotonic condition and the first several cycles of fatigue deformation considering the Bauschinger effect. As a complement to the FE modelling, digital image correlation (DIC) measurements of the displacement and strain fields around the crack tip in the CTS specimens were performed. This study aimed to obtain more detailed information on the local cyclic strain ahead of the mixed mode crack tip by using DIC. From the sensitivity analysis, it was established that the DIC value depended significantly on the location along the crack direction of the pair of points selected before and behind the crack tip. In this study, acceleration or retardation of the crack growth rate in terms of the NKH plastic SIF with respect to the HRR model was observed because of the coupling effect of the mode mixity and cyclic plastic properties of the tested P2M steel, aluminium 7050, and Ti-6Al-4V.

B-Spline Surface-Based Reduced-Order Modeling of Nonplanar Crack Growth in Structural Digital Twins

Nonplanar crack growth holds a critical role in aeronautical structures, necessitating effective analysis under mixed fatigue loading to assess structural integrity. This study introduces a reduced-order modeling (ROM) method for predicting nonplanar crack growth in structural digital twins. The method’s advantage lies in its representation of the entire crack surface morphology using a B-spline surface, which better captures its impact on crack growth. The symmetric Galerkin boundary element method–finite element method coupling method is adopted as a full-order method to generate the crack database. Isoparametric coordinates of the crack surface and stress intensity factor serve as input and output, respectively, for training the ROM, which integrates -means clustering, principal component analysis, and Gaussian process regression. The proposed approach is demonstrated using a rotorcraft-mast-like component. Results reveal superior fracture mechanics parameter prediction compared to the crack-front-based ROM. Furthermore, the method boasts three orders of magnitude greater efficiency than full-order simulation, enabling its coupling with approaches like Monte Carlo for probabilistic crack growth analysis. Future work entails integrating our method into the probabilistic framework of digital twins.

A finite crack growth energy release rate for elastic-plastic fracture

The concept of energy release rate proposed by Griffith originally used for elastic brittle material was extended for ductile material by Irwin and Orowan using the sum of the surface energy and the work of plastic dissipation as fracture resistance. This fracture resistance, however, depends on the load type and specimen geometry, which hinders its wide application. In contrast, in this paper, a finite crack growth energy release rate is proposed by assuming a finite crack growth, which is conveniently applicable to finite element analysis. The effect of the plastic dissipation on the crack growth is considered in the driving force. Elastic-plastic finite element analysis is used to apply the present energy release rate. Compared to the experiment results, it is shown that for a fixed finite crack growth, a constant critical energy release rate can well predict the stable crack growths and residual strengths of sheets with single and various collinear cracks subjected to different types of loads. The present finite crack growth energy release rate is conceptually simple, has a solid physical foundation, and would be appealing for ductile crack growth analysis.