Crack Path Prediction Research Articles

Experimental and numerical studies on the propagation paths of gear root cracks

Gear bending fatigue failure has a significant impact on the operational performance of advanced machinery, such as electric vehicles and wind turbines, potentially leading to failures and catastrophic consequences for transmission systems. Several methods are currently used to predict gear crack propagation; however, a comprehensive comparison of their accuracy and efficiency in predicting crack paths is lacking. In this study, the propagation path of root cracks in commonly used automotive gears was investigated using finite element (FE) analysis and experimental testing. Three mixed crack path prediction criteria were integrated to predict the gear root crack propagation using the commercial software ABAQUS by user-defined Python script. The impacts of gear crack parameters, including the gear initial crack length, on gear root crack propagation behaviour were analysed. The simulations were verified by the gear bending fatigue test using a single tooth bending test device. The results indicate that the simulation outcomes align with the experimental tests, demonstrating that all three criteria are effective in predicting gear root crack propagation behaviours.

Accurate prediction of discontinuous crack paths in random porous media via a generative deep learning model

Pore structures provide extra freedoms for the design of porous media, leading to desirable properties, such as high catalytic rate, energy storage efficiency, and specific strength. This unfortunately makes the porous media susceptible to failure. Deep understanding of the failure mechanism in microstructures is a key to customizing high-performance crack-resistant porous media. However, solving the fracture problem of the porous materials is computationally intractable due to the highly complicated configurations of microstructures. To bridge the structural configurations and fracture responses of random porous media, a unique generative deep learning model is developed. A two-step strategy is proposed to deconstruct the fracture process, which sequentially corresponds to elastic deformation and crack propagation. The geometry of microstructure is translated into a scalar of elastic field as an intermediate variable, and then, the crack path is predicted. The neural network precisely characterizes the strong interactions among pore structures, the multiscale behaviors of fracture, and the discontinuous essence of crack propagation. Crack paths in random porous media are accurately predicted by simply inputting the images of targets, without inputting any additional input physical information. The prediction model enjoys an outstanding performance with a prediction accuracy of 90.25% and possesses a robust generalization capability. The accuracy of the present model is a record so far, and the prediction is accomplished within a second. This study opens an avenue to high-throughput evaluation of the fracture behaviors of heterogeneous materials with complex geometries.

A staggered local damage model for fracture analysis in bi-material structures

This article is devoted to extension of the recently developed enhanced local damage model for failure prediction in bi-material structures. Compared to non-local models, the enhanced local model offers lower computational cost while the inherent mesh-dependency issue is treated. By defining equivalent strain based on the bi-energy norm concept and Mazars’s criterion, which considers both tensile and compressive strain components, the model aligns with the behavior of quasi-brittle materials. The state of material point is indicated by a damage parameter, ranging from 0 to 1, to represent the evolution from being fully intact to complete failure. An efficient staggered scheme is introduced, in which the equilibrium equation and the update of damage parameter are decoupled. The proposed model is validated with a series of three-point bending experimental tests on PMMA/Al6061 specimens reported by Lee and Krishnaswamy (2000). Good agreement is observed between the proposed model and experimental data, as well as numerical results from other authors, in crack path prediction.

Evaluation of existing and introduction of new incremental crack propagation approaches in FEM

Full FEM models with incremental crack propagation usually require very small crack propagation increment lengths Δa to accurately predict crack paths. Beside the criterion for the crack propagation direction, the approach to evaluate this propagation direction is important: the driving force of the current crack can either be used directly (explicit approach) or iteratively adapted test cracks can be introduced (implicit approach). Furthermore, the shape of the crack increments can be either straight or curved.Considering two 2D plates with circular holes, the accuracy of the predicted crack paths as a function of Δa is here evaluated for an explicit approach with straight crack increments (explicit approach), an implicit approach with straight crack increments (straight approach), and an implicit approach with curved crack increments (curved approach). It is shown, that the explicit approach and the straight approach react too late and too early, respectively, to spatial changes in the stress field.This work proposes a means of dealing with the changing crack driving force direction within the crack propagation increments for the explicit and straight approaches. All approaches are benchmarked by comparing their efficiency, which is evaluated as the mean deviation from a reference crack path per number of FEM computations required. It is shown that the use of curved crack increments is very efficient in some cases, but less so in one of the cases considered. A significant improvement in efficiency is shown by our adaptation of the explicit and straight approaches.

Crack propagation in anisotropic brittle materials: From a phase-field model to a shape optimization approach

The phase-field method is based on the energy minimization principle which is a geometric method for modeling diffusive cracks that are popularly implemented with irreversibility based on Griffith’s criterion. This method requires a length-scale parameter that smooths the sharp discontinuity, which influences the diffuse band and results in mesh-dependent fracture propagation results. Recently, a novel approach based on the optimization on Riemannian shape spaces has been proposed, where the crack path is realized by techniques from shape optimization. This approach requires the shape derivative, which is derived in a continuous sense and used for a gradient-based algorithm to minimize the energy of the system. In this paper, the novel approach based on shape optimization is presented, followed by an assessment of the predicted crack path in both isotropic and anisotropic brittle material using numerical calculations from a phase-field model.

Phase field approach to predict mixed-mode delamination and delamination migration in composites

In this work, we present a mixed-mode phase field approach to model delamination progression and its migration. The proposed model includes the volumetric and deviatoric effects that occur during the mixed-mode delamination and migration. The volumetric–deviatoric split is combined with a power law criterion of delamination to capture the mixed-mode effects. An anisotropic tensor is used in the crack surface density function for capturing the anisotropic fracture. Two history parameters are introduced to ensure the irreversibility of the damage field throughout the evolution process of delamination and to consider the maximum value of the strain energy. A staggered approach is implemented for solving the equilibrium and evolution equations. The algorithm enables to obtain stable numerical solutions with faster convergence. Several examples of mode I and mode II as per standard tests have been incorporated to demonstrate the working of the proposed method. The numerical examples are validated by comparison with experimental results from the literature. It is observed that the proposed model can predict crack paths and angles closer to the experimental results. Examples of multiple delamination and delamination migration are also studied to understand the kinking in the delamination scenario. It is observed that the delamination migration is governed by the ratio of notch length a to the distance of the load from the edge L, and by the stress state in front of the crack tip. In the case of laminates with multiple interphases, the event of delamination impinging and kinking at interphase depends on the fracture toughness ratio of the bulk and the interphase. The example of the single-edge notched composite lamina and open-hole tension test with different fiber orientations has been validated with the literature and experiments.

The displacement mechanism of the cracked rock – a seismic design and prediction study using XFEM and ANNs

Materials with sufficient strength and stiffness can transfer nonlinear design loads without damage. The present study compares crack propagation speed and shape in rock-like material and sandstone when subjected to seismic acceleration. The nonlinear extended finite element method (NXFEM) has been used in numerical simulation. It assumes the model has a pre-existing crack at 0° from the horizontal. The mechanical properties of the model, crack propagation shape, and crack speed were selected as the main parameters. The nonlinear stress and strain along the crack have been compared in two simulated models. NXFEM and Artificial Neural Networks (ANNs) were used to predict the displacement. The simulation results illustrate that the materials’ crack propagation mechanism and mechanical properties control the stress, strain, and displacement at the selected points in the model. In addition, crack propagation in materials is related to elastic-plastic stresses and strains along the crack path. The speed and shape of the crack are associated with the mechanical properties of the materials. The prediction of crack paths helps to understand failure patterns. Comparison of the seismic response of the rock-like material with sandstone helps to assess the stress, strain, and displacement levels during cracking. This study’s findings agree with the literature report and field observations.

Quantitative analysis of three‐dimensional fatigue crack path selection in Mg alloy WE43 using high‐energy X‐ray diffraction microscopy

AbstractFatigue short‐cracks in Mg alloys display complex growth behavior due to high plastic anisotropy and crack path dependence on local microstructural features. In this study, the three‐dimensional crystallography of short‐crack paths in Mg alloy WE43 was characterized by mapping near‐field high‐energy X‐ray diffraction microscopy (HEDM) reconstructed grain maps to high‐resolution X‐ray CT reconstructions of the fracture surfaces in the crack initiation and short‐crack growth regions of six ultrasonic fatigue specimens. Crack–grain–boundary intersections were analyzed at 81 locations across the six crack paths. The basal intragranular, non‐basal intragranular, or intergranular character of short‐crack growth following each boundary intersection was correlated to crystallographic and geometric parameters of the trailing and leading grains, three‐dimensional grain boundary plane, and advancing crack front. The results indicate that crack paths are dependent on the combined crystallographic and geometric character of the local microstructure, and crack path prediction can be improved by use of dimensionality reduction on subsets of high‐linear‐correlation microstructural parameters.

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.

Fretting fatigue crack propagation under out-of-phase loading conditions using extended maximum tangential stress criterion

In this paper, a numerical crack growth analysis is conducted by using the Maximum Tangential Stress (MTS) criterion and its extension, which considers the contact stress between the crack surfaces. Moreover, fretting fatigue is a multiaxial non-proportional loading problem, and most components are subjected to asynchronous loads. Therefore, this paper mostly focuses on the influence of loading phase difference (Φ) on the crack propagation behavior. Meanwhile, for the fretting fatigue problem, as there is a relationship between the crack initiation and propagation, the effect of initiation characteristics, including crack initiation position and direction is studied under different loading phase differences using Linear Elastic Fracture Mechanics (LEFM) theory. It is observed that the predicted crack path and lifetime by using the extended MTS criterion and Paris’ law is in good agreement with the experimental results in the literature. It is found that the phase difference has a strong effect on the crack propagation behavior. Furthermore, we found that the crack initiation position has a greater influence on crack propagation behavior than the crack initiation direction.

Convergence study of stabilized non-ordinary state-based peridynamics for elastic and fracture problems

Non-ordinary state-based peridynamics simulates crack propagation while avoiding the imposition of additional criteria to describe the responses at discontinuities. However, an incomplete coverage by the sphere of a horizon near the boundaries and crack surfaces could cause the boundary effect. In this study, the boundary effects occurring in the stress concentration region are investigated in δ- and m-convergence tests for elastic deformation and crack propagation. Three types of boundary imposition methods are investigated in m-convergence and the method showing the fastest convergence is applied to fracture problems. The weighted average stress estimation is proposed for the damage criterion to reduce the variation in the crack paths in the convergence test, and the weight function is defined as a parameter that can change the shape of the function into three different forms: linear, bilinear, and constant. The fracture simulation is performed in an L-shaped panel with varying geometrical parameters. As a result, the bilinear weighted average stress estimation reduces the variation in the crack path compared to the conventional arithmetic average estimation method. Therefore, the proposed weighted average stress estimation method increases the accuracy of the crack path prediction and will enlarge the application area for fracture simulation using peridynamics.

A coupled peridynamics–smoothed particle hydrodynamics model for fracture analysis of fluid–structure interactions

In this paper, a numerical model that couples peridynamics (PD) with smoothed particle hydrodynamics (SPH) is presented for fracture modeling in fluid–structure interaction (FSI) problems. PD was employed to simulate the solid structure fracture because of its ability to deal with discontinuity problems. SPH was applied to simulate the fluid behavior because of its advantages in modeling free-surface flows. A virtual particle layer was established in the fluid–structure interfacial region to ensure the force and deformation transfer between the fluid and solid phases. Validation was performed qualitatively and quantitatively through simulations of classical benchmark tests. The SPH model of the free-surface flow, the PD model of the solid structure, and the coupled PD-SPH model of the FSI were carefully verified. It was demonstrated that the results matched the experimental observations well, with a maximum error of less than 10%. The hydraulic fracture of a gravity dam and the impact of dam-break flow on a baffle were simulated as applications of the coupled PD-SPH model. The predicted crack path in the gravity dam agreed closely with the experimental observations, with a Pearson correlation coefficient of 0.9983. A preliminary extension of the proposed PD-SPH model to three dimensions is also presented, and its performance was evaluated. The results indicate that the coupled model is accurate in modeling the solid fracture process in FSI problems.

A microstructure-sensitive analytical solution for short fatigue crack growth rate in metallic materials

Short fatigue crack growth in engineering alloys is among the most prominent challenges in mechanics of materials. Owing to its microstructural sensitivity, advanced and computationally expensive numerical methods are required to solve for crack growth rate. A novel mechanistic analytical model is presented, which adopts a stored energy density fracture criterion. Full-field implementation of the model in polycrystalline materials is achieved using a crystallographic crack-path prediction method based on a local stress intensity factor term. The model is applied to a range of Zircaloy-4 microstructures and demonstrates strong agreement with experimental rates and crack paths. Growth rate fluctuations across individual grains and substantial texture sensitivity are captured using the model. More broadly, this work demonstrates the benefits of mechanistic analytical modelling over conventional fracture mechanics and recent numerical approaches for accurate material performance predictions and design. Additionally, it offers a significant computer processing time reduction compared with state-of-the-art numerical methods.

Numerical modelling of microstructure inhomogeneity to reproduce experimentally observed scatter in fretting fatigue lifetimes

Experimental fretting fatigue lives exhibit large degree of scatter. One of the aspects behind this is the microstructural inhomogeneity which affects the stresses in the material. Variance in stress values can greatly impact crack initiation speed, leading to changes in fretting fatigue lifetimes, as well as the crack propagation behaviour. This research aims to study this issue in more detail and recreate the experimentally observed scatter using numerical modelling. In this work, Voronoi tessellation is used to simulate microstructural topologies of low carbon steel, where each grain is assigned elasto-plastic properties at random, from a predetermined range. In total, 60 finite element models are created and the effect of microstructural inhomogeneity on fretting fatigue lifetime dispersion is evaluated using a Continuum Damage Mechanics approach. Additionally, crack propagation is studied with XFEM combined with Smith-Watson-Topper fatigue parameter to determine crack path under multiaxial, non-proportional loading conditions. For both crack initiation and propagation investigation, the Theory of Critical Distances is applied to overcome the effect of high stress gradients. Simulation results show that microstructural inhomogeneity has significant impact on the contact stress distributions and subsurface stress and strain fields. Scatter observed in the predicted lifetimes matches well with that observed in practical experiments and is used to propose a design curve for the studied material. The applied crack path prediction approach captures the variance in crack paths originating from microstructural inhomogeneity and shows good correlation with reference experimental results at low bulk stress levels.

An FFT-based crystal plasticity phase-field model for micromechanical fatigue cracking based on the stored energy density

A novel FFT-based phase-field fracture framework for modelling fatigue crack initiation and propagation at the microscale is presented. A damage driving force is defined based on the stored energy and dislocation density, relating phase-field fracture with microstructural fatigue damage. The formulation is numerically implemented using FFT methods to enable modelling of sufficiently large, representative 3D microstructural regions. The early stages of fatigue cracking are simulated, predicting crack paths, growth rates and sensitivity to relevant microstructural features. Crack propagation through crystallographic planes is shown in single crystals, while the analysis of polycrystalline solids reveals transgranular crack initiation and crystallographic crack growth.

Physics-Informed Neural Network Integrating PointNet-Based Adaptive Refinement for Investigating Crack Propagation in Industrial Applications

Crack is one of the critical factors that degrade the performance of machinery manufacturing equipment. Recently, physics-informed neural networks (PINNs) have received attention due to their strong potential in solving physical problems. For fracture problems, PINNs have been used to predict crack paths by minimizing the variational energy of discrete domains where refined meshes are necessary. To obtain refined meshes, posteriori adaptive refinement techniques are commonly used to perform local refinement of the mesh based on errors in the intermediate calculation process; thus, they require pretest calculations. However, it is computationally expensive to precalculate complex problems, especially crack propagation. To solve this problem, we propose a PointNet-based adaptive refinement method to avoid precalculation when constructing the discrete domain. The proposed method is applied to simulate crack propagation using a PINN. Results show that the proposed method can be used to obtain reliable results efficiently when using the PINN framework.

Study on two-dimensional mixed-mode fatigue crack growth employing ordinary state-based peridynamics

Mixed-mode fatigue crack propagation analysis is studied using ordinary state-based peridynamics. By introducing the concept of “remaining life”, the fatigue crack nucleation and propagation can be simulated in the PD framework. The PD fatigue modelling and the crack path prediction is carefully investigated. For the comparison purpose, the maximum circumferential stress criterion is introduced. The interaction integral and the peridynamic differential operator is employed to evaluate the fracture mechanics parameters. Two pre-cracked structures under mixed-mode loading conditions are provided with the validations from reference solutions.

A probabilistic model for fast-to-evaluate 2D crack path prediction in heterogeneous materials

This paper is devoted to the construction of a new fast-to-evaluate model for the prediction of 2D crack paths in concrete-like microstructures. The model generates piecewise linear cracks paths with segmentation points selected using a Markov chain model. The Markov chain kernel involves local indicators of mechanical interest and its parameters are learnt from numerical full-field 2D simulations of cracking using a cohesive-volumetric finite element solver called XPER. This model does not include any mechanical elements. It is the database, derived from the XPER crack, that contains the mechanical information and optimizes the probabilistic model. The resulting model exhibits a drastic improvement of CPU time in comparison to simulations from XPER.

Crack path predictions in heterogeneous media by machine learning

The interaction between stress fields at the crack-tip and nearby microstructural heterogeneities influences the crack path, and in turn, the effective fracture toughness of a material. In this paper, we assess the ability of artificial neural networks (ANNs) for machine learning to predict the crack paths from given initial void defect distributions in the material, and to provide insights into the underlying crack growth mechanics. Our ANN accurately captures the process zone size, crack growth sequence, and resulting crack patterns in the simplistic case where the proximity of voids to the crack-tip forms the criterion for crack advance. In a ductile medium, pre-existing voids grow with deformation and link up with the primary crack either contiguously or through the formation of multiple unconnected damage zones. The complex crack patterns for both these ductile fracture processes are successfully captured by an ANN, trained on the cracking sequences in a micromechanics-based ductile fracture model containing two size-scales of voids. In addition, the ANN architecture is capable of predicting stochastic crack growth, by providing a multiplicity of possible crack paths, along with a quantified likelihood of each path. Results further demonstrate the utility of autonomous crack path predictions in enabling fracture-by-design.

Identification of microscale fracture models for mortar with in-situ tests

The microscale fracture modeling of concrete requires explicit descriptions of the microstructure and the fracture properties of its constituents. The identification of fracture properties of mortar was carried out by numerical analyses of two in situ (via X-ray tomography) mesoflexural tests on small-scale specimens. Realistic meshes were created for mechanical simulations to be run. The experimental kinematic fields were measured by processing the reconstructed volumes via Digital Volume Correlation. The measured displacements were used as kinematic boundary conditions to simulate three-point flexural tests. The full dataset consisting of realistic geometry and experimental boundary conditions, allowed for full simulations of the performed tests. A phase-field model for brittle materials was selected to describe damage of the cement paste, and debonding at the matrix-aggregate interfaces was modeled with a cohesive zone model. The fracture paths and ultimate forces simulated with the phase-field model were consistent with the experiment thanks to representative microstructure and boundary conditions. In both tests, the predicted crack path changed because of interface debonding. The introduction of cohesive interface elements did not significantly improve the faithfulness of the path prediction. This study demonstrates the potential of microscale simulations of in situ tests for model identification, validation and development at the microscale of mortar.