Non-planar Crack Growth Research Articles

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.

Scaled fatigue cracks under service loads

Scaled experimentation is a powerful engineering tool yet its application to fatigue is limited by significant changes in behaviour with scale. The recent discovery of new similitude rules however opens new possibilities that are explored in this work through numerical experimentation for industrially representative fatigue-crack growth scenarios. It is shown for the first time, how the geometric size effects present in mixed mode fatigue tests are eliminated by performing two appropriately designed scaled experiments. The first order finite similitude theory is applied to mixed mode (modes I and II) fatigue crack growth in three case studies, viz., compact tension shear (CTS) specimen, wing fuselage attachment lug, and a T-joint with an inclined semi elliptical crack. Both planar and non-planar crack growth feature, along with surface and through thickness cracks. Low and high cycle fatigue (up to circa 60,000 cycles) is examined for three different materials (Al-6061 T6 alloy, structural steel, and AISI 316 stainless steel) under a variety of load ratios. The new rules return near exact crack-path predictions whereas lifecycle predictions have errors ranging between 1 % and 9 %. Paris law constants C and m are predicted with up to 99.9 % accuracy supporting the theory that Paris law is a first order similitude rule. Geometric size effects afflicting industrial type scaled-fatigue studies employing a damage tolerant design approach are confirmed to be eliminated on combination of information from two appropriately designed scaled models.

Three-dimensional non-planar crack growth analysis using enriched finite elements

The paper presents computational mixed mode non-planar fatigue crack growth analyses using Fracture and Crack Propagation Analysis System (FCPAS), which employs enriched crack tip finite elements to calculate the mixed mode stress intensity factors (SIFs) and utilizes from other sub-modules to predict the evolving crack growth trajectories and the resulting fatigue crack growth lives. Numerical applications on different problems selected from the literature; a hollow shaft, an H-shaped specimen and cylindrical rods containing cracks with different initial orientations and sizes and subjected to different fatigue loading types are presented. Comparisons of results from the numerical analyses with the corresponding data from the literature agree well in terms of computed SIFs, predicted evolving crack paths and crack propagation lives.

Three-dimensional modeling of non-planar fatigue crack growth in spur gear tooth using tetrahedral finite elements

In this paper, a numerical methodology for prediction of crack growth path and life of structures containing cracks and its application to three different case studies on spur gear tooth are presented. Three-dimensional non-planar fatigue crack propagation analyses are carried out using FRAC3D, which is part of Fracture and Crack Propagation Analysis System (FCPAS), employing fully unstructured tetrahedral elements along the crack front and in the whole model. Fatigue crack growth path predictions are performed using recently developed crack growth criteria that combine different equations used to predict crack deflection angle and to determine equivalent stress intensity factor. Comparisons of obtained results from numerical simulations with available data from the literature in terms of crack growth trajectories show very close agreement. Therefore, it is concluded that FCPAS is capable of performing three-dimensional non-planar crack growth modeling using fully tetrahedral elements in the whole finite element model, which requires less user intervention, time and effort for modeling. Moreover, the presented methodology and the recently developed crack growth criteria can be used for three-dimensional crack growth analysis.

Rapid Uncertainty Propagation for High-Fidelity Prognostics Using SROMPy and Python

This work introduces a practical approach for accelerating probabilistic, high-fidelity prognostics using the stochastic reduced order model (SROM) method and its availability in the open-source Python package, SROMPy. SROMs are used as an efficient Monte Carlo simulation (MCS) method, providing low-dimensional representations of random model inputs enabling rapid and non-intrusive uncertainty propagation. This study represents the first application of the SROM approach in the field of prognostics and health management and serves as a tutorial demonstration of the SROMPy software package. The relative ease of applying SROMs with SROMPy for uncertainty propagation is demonstrated on an example of probabilistic, non-planar crack growth simulation. Results show that the SROM approach agrees well with results from MCS while providing orders of magnitude computational speedup. The complete source code and input data required to reproduce the results in this paper are available online to facilitate further evaluation and adoption of the SROM method by researchers in the field.

Probabilistic Prognosis of Non-Planar Fatigue Crack Growth

Quantifying the uncertainty in model parameters for the purpose of damage prognosis can be accomplished utilizing Bayesian inference and damage diagnosis techniques such as non-destructive evaluation or structural health monitoring. The number of samples required to solve the Bayesian inverse problem through common sampling techniques (e.g., Markov chain Monte Carlo) renders high-fidelity finite element-baseddamage growth models unusable due to prohibitive computation times. However, these types of models are often the only option when attempting to model complex damage growth in real-world structures. Here, a recently developed highfidelity fatigue crack growth model is used which, when compared to finite element-based modeling, has demonstrated reductions in computation times of three orders of magnitude through the use of surrogate models and machine learning. A probabilistic prognosis framework incorporating this model is developed and demonstrated for non-planar crack growth in a modified edge-notched aluminum tensile specimen. Predictions of remaining useful life are made over time for fiveupdates of the damage diagnosis data, and prognostic metrics are utilized to evaluate the performance of the prognostic framework. Challenges specific to the probabilistic prognosis of non-planar fatigue crack growth are highlighted and discussed in the context of the experimental results.

Non-planar crack growth analyses of multiple cracks in thin-walled structures

Non-planar crack propagation analyses for thin-walled structures containing multiple cracks are performed using Fracture and Crack Propagation Analysis System (FCPAS) finite element software. Numerical results from FCPAS, which employs three-dimensional enriched finite elements and is applied first time to multiple non-planar cracks, agree well with numerical and experimental data from the literature. In order to validate FCPAS crack growth results for non-planar multiple cracks in thin-walled structures, three different problems are solved and the corresponding results are compared with available data. Comparisons of obtained results show very close agreement with the available numerical and experimental data in terms of crack paths and stress intensity factors (SIF) under Linear Elastic Fracture Mechanics (LEFM) conditions. Therefore, it is concluded that FCPAS is capable of predicting non-planar multiple crack growth behavior in thin-walled structures.

Multiple and non-planar crack propagation analyses in thin structures using FCPAS

In this study, multiple and non-planar crack propagation analyses are performed using Fracture and Crack Propagation Analysis System (FCPAS). In an effort to apply and validate FCPAS procedures for multiple and non-planar crack propagation analyses, various problems are solved and the results are compared with data available in the literature. The method makes use of finite elements, specifically three-dimensional enriched elements to compute stress intensity factors (SIFs) without special meshing requirements. A fatigue crack propagation criterion, such as Paris-Erdo?an equation, is also used along with stress intensity factors to conduct the simulation. Finite element models are generated within ANSYS™ software, converted into and solved in FRAC3D program, which employs enriched crack tip elements. Having computed the SIFs for a given crack growth increment and using a growth criterion, the next incremental crack path is predicted and the fracture model is updated to reflect the non-planar crack growth. This procedure is repeated until cracks reach a desired length or when SIFs exceed the fracture toughness of the material. It is shown that FCPAS results are in good agreement with literature data in terms of SIFs, crack paths and crack growth life of the structure. Thus, accuracy and reliability of FCPAS software for multiple and non-planar crack propagation in thin structures is proven.

Modelling 3D crack propagation in ageing graphite bricks of Advanced Gas-cooled Reactor power plant

In this paper, crack propagation in Advanced Gas-cooled Reactor (AGR) graphite bricks with ageing properties is studied using the eXtended Finite Element Method (X-FEM). A parametric study for crack propagation, including the influence of different initial crack shapes and propagation criteria, is conducted. The results obtained in the benchmark study show that the crack paths from X-FEM are similar to the experimental ones. The accuracy of the strain energy release rate computation in a heterogeneous material is also evaluated using a finite difference approach. Planar and non-planar 3D crack growth simulations are presented to demonstrate the robustness and the versatility of the method utilized. Finally, this work contributes to the better understanding of crack propagation behaviour in AGR graphite bricks and so contributes to the extension of the AGR plants’ lifetimes in the UK by reducing uncertainties.

An improved atomistic simulation based mixed-mode cohesive zone law considering non-planar crack growth

A novel and improved atomistic simulation based cohesive zone law characterizing interfacial debonding is developed which explicitly accounts for the non-planarity of the crack propagation. Group of atoms in the simulation constituting cohesive zones which are used to obtain local stress and crack opening displacement data are determined dynamically during the non-planar crack growth as they cannot be determined apriori. The methodology is used to study the debonding of Σ5 (210)/[001] symmetric tilt grain boundary interface in a Cu bicrystal under several mixed mode loading conditions. Simulations show that such bicrystalline specimen exhibits three types of energy dissipative mechanisms – shear coupled GB migration (SCM) away from the crack-tips, change in spacial orientation of GB structural units rendering highly disordered grain boundary near the crack tips and brittle intergranular fracture. Which combination of these three deformation mechanism will be active influencing the degree of non-planarity of the crack propagation at various stages of loading depends on the loading mode-mixity. As the ratio of shear component of the loading parallel to the GB plane and normal to the tilt axis with respect to the normal loading increases (thereby increasing the mode-mixity), overall strain-to-failure also increases and SCM tends to become the dominant deformation mechanism. Through this framework, analytical functional forms and parameters describing cohesive laws for both normal and shear traction as a function of the mode-mixity of the loading and crack opening displacement are predicted.

Two-stage planar approximation of non-planar crack growth

Mechanical components subject to multiaxial variable amplitude loading may experience non-planar crack growth, which usually requires three dimensional finite element analyses for high fidelity simulation of non-planar fatigue crack growth. This is computationally expensive and prohibits recurrent use of high fidelity models in further probabilistic life prediction analysis. This paper presents an efficient and accurate two-stage approach for planar approximation of non-planar crack growth that reduces the computational effort. In this method, the non-planar crack is first approximated using an equivalent planar crack. Then, using the equivalent representation, planar crack growth analyses designed to account for uncertainty in crack growth are conducted. The proposed methodology employs two surrogate models: the first surrogate model is trained using 3-D simulations of non-planar fatigue crack growth to capture the relationship between the applied load history and equivalent planar crack orientation. The second surrogate model is trained using planar crack growth simulation to calculate the stress intensity factor as a function of crack size, crack orientation, and load magnitude for use in planar crack growth analysis. Individual predictions of the two surrogate models, as well as their combined predictions are verified for accuracy using full 3-D finite element simulations. The verified two-stage approach is then demonstrated in an illustrative example of uncertainty quantification in 3-D crack growth prediction in a mechanical component similar to a rotorcraft mast.

Surrogate modeling of 3D crack growth

This paper presents the development of a surrogate modeling technique for efficient non-planar fatigue crack growth analysis in mechanical components under multi-axial loading. Non-planar crack fronts are freely deformable space curves and require a high-dimensional representation. The large number of Cartesian co-ordinate variables involved in crack front representation makes it prohibitively expensive to train surrogate models for crack growth. Therefore, in our previous work, the crack shape was approximated using a planar parametrized representation. However, the parametrized representation limits the choice of crack shapes that can be considered. This paper presents the development of a non-parametric crack shape representation that allows for construction of a surrogate model for non-planar crack growth with complex crack shapes. The surrogate model is trained using a few runs of high-fidelity 3D simulations and predicts the evolution of a non-planar crack front under a given multi-axial, variable amplitude load history. We first parametrize the crack fronts as 3D spline curves with a fixed number of nodes. Instead of modeling the crack growth in this high dimensional data space, we project the data to a lower dimensional space using Principal Component Analysis (PCA) and then model the crack growth in this lower dimensional space. Finally, the predicted crack fronts are recovered using PCA back to the original data space. The proposed crack representation, growth modeling and recovery are illustrated using training points gathered from high-fidelity 3-D finite element simulations of non-planar crack growth in a cylindrical component similar to a rotorcraft mast, and the ability of the surrogate model to accurately predict the evolution of the crack growth over entire load histories is demonstrated.

Experimental and numerical investigation of fatigue of thin tensile specimen

This paper presents the results of experimental and numerical investigation on fatigue of thin 304 stainless steel tensile specimens. In order to achieve the experimental aspects of this investigation a Micro Fatigue Test Rig (MFTR) was designed and developed to evaluate fatigue life and failure mechanism of tensile specimen. A 3D finite element model was also developed to investigate the fatigue damage of thin tensile specimen and to account for the effects of topological randomness of material microstructure on fatigue lives. The topology of the material grain structure was modeled using randomly generated 3D Voronoi tessellations corresponding to the measured grain size. Continuum damage mechanics was used to model the progressive material degradation. The damage parameters were obtained from the experimentally obtained S–N curve. A 3D mesh partitioning procedure was developed to consider both crack initiation and propagation stages considering the predominant transgranular, non-planar crack growth observed in the experiments. The stress–life results obtained from the fatigue damage model are in good agreement with the experimental data. The progression of damage and the proportion of life spent in crack initiation obtained from the model are consistent with empirical observations. The fatigue damage model was used to assess the influence of microstructure randomness accompanied by material inhomogeneity and internal voids on fatigue life dispersion.

Three-dimensional cohesive fracture modeling of non-planar crack growth using adaptive FE technique

In this paper, the three-dimensional adaptive finite element modeling is presented for cohesive fracture analysis of non-planer crack growth. The technique is performed based on the Zienkiewicz–Zhu error estimator by employing the modified superconvergent patch recovery procedure for the stress recovery. The Espinosa–Zavattieri bilinear constitutive equation is used to describe the cohesive tractions and displacement jumps. The 3D cohesive fracture element is employed to simulate the crack growth in a non-planar curved pattern. The crack growth criterion is proposed in terms of the principal stress and its direction. Finally, several numerical examples are analyzed to demonstrate the validity and capability of proposed computational algorithm. The predicted crack growth simulation and corresponding load-displacement curves are compared with the experimental and other numerical results reported in literature.

Life Prediction for Complex Structures

The surface integral method, an indirect boundary element method that represents a crack as a distribution of force dipoles, has been developed to model three-dimensional nonplanar crack growth in complex structures. The finite body was effectively modeled by superposition of stress influence functions for a half-space. As a result of this strategy, only the fracture has to be discretized. Crack propagation was modeled using the maximum circumferential stress theory to predict crack direction and the Forman fatigue equation, modified with an equivalent stress intensity solution for mixed-mode, to predict extension. Comparisons with benchmark solutions and field data verified the computational methodology and defined the limits of its applicability.

Torsional Crack Growth Test to Simulate Belt Edge Deformation

Abstract The study of fatigue crack growth resistance for tire belt compounds is motivated by the high deformation cycles inherent in the belt edge region of radial tires. To improve the understanding of fatigue in this region, a test has been developed to simulate crack growth in shear (mode III). A rubber disk with a circumferential pre-crack is tested in cyclic torsion to simulate belt edge interlaminar shear cycles. Theoretical, numerical [finite element analysis (FEA)] and experimental methods have been employed to investigate and quantify the response. A recent improvement to the analysis considers nonlinear elastic material behavior which is characteristic of carbon black-filled tire compounds. The best agreement between torsional test results and results from typical thin sheet geometries was found for lightly reinforced compounds; crack branching often complicates results for more highly reinforced compounds. Fracture surfaces are examined for evidence of non-planar crack growth to help interpret the results.

Nonplanar Crack Growth Using the Surface Integral Method

A surface integral formulation, based on representing a crack as a distribution of force dipoles, has been developed for modeling the propagation of a three-dimensional nonplanar fracture. The minimum strain energy density and maximum circumferential stress theories were used to determine the direction of crack growth. The extension of the fracture surface was based on the Paris law for fatigue. Remeshing of the fracture during growth was accomplished by adding a ring of elements to the existing mesh at the conclusion of each increment of crack growth. This promoted the efficiency of the algorithm by eliminating the need to recalculate the entire coefficient matrix. Use of the surface integral method, coupled with growth criteria, has yielded an accurate model for three-dimensional nonplanar crack growth under mixed mode loading conditions. The study of several penny-shaped precracks under mixed-mode loading conditions produced the expected growth trajectory, and compared favorably to existing two-dimensional, three-dimensional, and experimental results found in the literature.

Three-dimensional crack growth simulation using BEM

In this paper an application of dual boundary element method to the analysis of three-dimensional mixed-mode crack growth is presented. The crack growth processes are simulated numerically with an incremental crack-extension analysis based on the minimum strain energy density criterion and a fatigue crack growth law. For each crack extension, the size of the increment (crack growth) and direction of crack growth is evaluated along the crack front. The dual boundary element analysis is applied to perform a single-region analysis and the stress intensity factors are evaluated using a displacement-based method. The crack extension is modelled with the introduction of new boundary elements, removing the requirement of interior remeshing, an intrinsic feature of the dual boundary element method. Results of analysis are presented for several geometries, including planar and non-planar crack growth.

An analysis of non-planar crack growth under mixed mode loading

A method is presented for calculating stress intensity factors at the tip of a slightly wavy three-dimensional crack. The solution is used to calculate the direction of propagation of an initially planar semi-infinite crack, which is subjected to uniform remote loading. In particular, the combinations of remote load which cause the crack to deviate from its original plane are found. For the particular case of a two-dimensional crack subjected to combined mode I and mode II loading, we recover the results of Cotterell and Rice [1980, Int. J. Fract.16(2), 155]. For a crack loaded by combined mode I and mode III loading, it is shown that there is a critical ratio of KIII/KI which causes the crack to deviate from its original plane. The influence of T-stresses, which act parallel to the crack plane, is also investigated. Finally, the predictions of the perturbation theory are compared with full-field numerical simulations which predict the path of a crack propagating under mixed mode remote loading.

Tilting cracks: the evolution of fracture surface topology in brittle solids

For a growing crack the conventional definitions of tilting and twisting are inadequate. New definitions are proposed, based on differential geometry, and it is shown that, in homogeneous, isotropic, brittle solids, non-planar crack growth must occur entirely by tilting movements. Examples are given of the growth of cracks on curved surfaces which illustrate that the no-twist condition produces significant constraints on the path of fracture. The development of fracture surfaces when cracks are subject to mixed-mode loading conditions are described with particular reference to the influence of mode III, twisting conditions. It is shown that the requirement that only tilting can occur leads to many characteristic fractographic features.