Crack Propagation Model Research Articles

Effect of grain structure on fatigue crack propagation behavior of 2024 aluminum alloy under different stress ratios

The fatigue load that a material experiences and its microstructure are important factors influencing fatigue crack propagation behavior. This study employed laser scanning microscopy and electron backscatter diffraction (EBSD) technology, along with fatigue crack propagation experiments, to investigate the fatigue crack propagation behavior of 2024 aluminum alloy under varying stress ratios (R). The results showed that the stress amplitude (σp) was the main factor controlling the fatigue crack propagation life (N). Additionally, detailed characterization of the fatigue crack propagation path was conducted using crystal models and EBSD. A fatigue crack propagation model for 2024 aluminum alloy under different R-values was established based on the grain twist angle and Schmid factor. Finally, the impact of R on the crack tip shielding (Ks) was systematically analyzed, elucidating the intrinsic mapping relationship between R, microstructure, and crack propagation characteristics.

2D numerical modeling of crack propagation using SFEMD method of a LEHI material

Numerical methods today play a useful and important role in solving various problems related to fracture mechanics including modeling crack propagation, fretting fatigue and cohesion... Furthermore, these methods have been widely used to solve problems in linear and nonlinear fracture mechanics in cases of elastic, plastic fracture problems. The evaluation of stress intensity factor in 2D and 3D geometries, thus these techniques widely used for non-standard crack configurations. The objective of this work is study the effects of the crack length and the number of structural elements on the two crack parameters such as the stress intensity factor KI and KII and the contour integral (J). As well as presenting a numerical modeling of crack propagation, for a LEHIM (Linear Elastic Homogeneous Isotopic Material) with mechanical characteristics by the method SFEMD (Stretching Finite Element Method Developed), the model chosen with quadratic elements with 4 nodes (CPE4). However, this method is based on the effect of the number of contours and the number of elements around the crack tip on the variation of the stress intensity factors. In addition, the crack propagation criterion (MCSC) was used, a computer program was created in FORTRAN language to develop and evaluate the stress intensity factors and the contour integral (J). Several examples of crack lengths a = 0.7, 1.4, 2.1, 2.8 and 3.5 mm were used. Additionally, the number of items has been changed several times. The stress intensity factors of modes I and II and direction angles (α) are calculated to solve the problem using the ABAQUS finite element code. The results obtained by the SFEMD method and the results of the analytical method are very close.

Bedding effect on progressive crack propagation in layered sandstone grotto roof

Roof failure significantly threatens the safety and stability of grottoes. For the layered roof of sandstone grottoes, the failure process is closely related to bedding effects of crack propagation. Taking the Yuanjue Cave as an example, the progressive failure process of the layered roof was summarized. The mechanisms of crack propagation in the roof were analyzed theoretically, and bedding effects together with influencing factors of crack propagation were explored. Results showed that the instability process of the layered roof in sandstone grottoes can be summarized into four stages: tensile fracture of the roof, vertical expansion of cracks, horizontal deflection of cracks, and instability collapse of blocks. The development and propagation of cracks constituted the intrinsic cause of the instability of layered roofs. A fracture mechanics model for crack propagation in layered roofs was established considering the bedding effect, and the criteria for vertical expansion of cracks in grotto roofs was derived. Moreover, the fracture criterion of crack competition was modified in combination with the bedding effect, revealing that an increase in interlaminar cohesion inhibited the crack deflection mode. The crack deflection mode in grotto roofs was jointly determined by the stress at the crack-tip (σfxx and σfyy), the strength of the rock layers and bedding plane (σ't, μ and c). To control the crack propagation in roofs, the engineering reinforcement of grotto roofs can be achieved by weakening bedding effects and indirectly reducing the roof span. This study is of great significance for revealing the progressive failure process and optimizing the reinforcement scheme of layered roofs in grottoes.

Effectiveness of the Concrete Equivalent Mortar Method for the Prediction of Fresh and Hardened Properties of Concrete

Modern concrete mix design is a complex process involving superplasticisers, fine powders, and fibres, requiring time and energy due to the high number of trial tests needed to achieve rheological properties in the fresh state. Concrete batching involves the extensive use of materials, time, and the testing of chemical admixtures, with various methodologies proposed. Therefore, in some instances, the required design properties (physical and mechanical) are not achieved, leading to the loss of resources. The concrete equivalent mortar (CEM) method was introduced to anticipate concrete behaviour at fresh and hardened states. Moreover, the CEM method saves time and costs by replacing coarse aggregates with an equivalent sand mass, resulting in an equivalent specific surface area at the mortar scale. This study aims to evaluate the performance of fibre in CEM and concrete and determine the relationships between the CEM and the concrete in fresh and hardened states. Steel and polypropylene fibres were used to design three series of mixtures (CEM and concrete): normal-strength concrete (NSC), high-strength concrete (HSC), high-strength concrete with fly ash (HSCFA), and equivalent normal-strength mortar (NSM), high-strength mortar (HSM), and high-strength mortar with fly ash (HSMFA). This study used three-point bending tests and digital image correlation to evaluate load and crack mouth opening displacement (CMOD) curves. An analytical mode I crack propagation model was developed using a tri-linear stress–crack opening relationship. Post-cracking parameters were optimised using inverse analysis and compared to actual MC2010 characteristic values. The concrete slump is approximately half of the CEM flow; its compressive strength ranges between 78% and 82% of CEM strength, while its flexural strength is 60% of CEM strength. The post-cracking behaviour showed a significant difference attributed to the presence of aggregates in concrete. The fracture energy of concrete is 28.6% of the CEM fracture energy, while the critical crack opening of the concrete is 60% of that of the CEM.

Dipole‐based BEM formulation for three‐dimensional cohesive crack propagation modelling

AbstractThis study presents an alternative boundary element method (BEM) formulation for the cohesive crack propagation modelling in three‐dimensional structures. The proposed formulation utilises an initial stress field for representing the mechanical behaviour along the fracture process zone, which leads to a set of self‐equilibrated forces named as dipole. Cohesive laws govern the material nonlinear behaviour along the fracture process zone. The proposed dipole‐based formulation demonstrates some advantages in comparison to classical BEM approaches in this field. Among them, it is worth citing the requirement of solely three integral equations per collocation point positioned at the fracture process zone. The effectiveness of the dipole‐based formulation has been demonstrated by four applications. The results have been compared to numerical, experimental and analytical solutions available in the literature, in which excellent performance has been observed.

Modeling of the Complexity Propagation of Crack in a Ductile Material Under Complex Solicitation in Crack Tip: Introduction of a Matrix of Stress Intensity Factors of Bifurcation

In fracture and damage mechanics, modeling of crack propagation has always been a source of difficulties. Numerous works have been carried out on this case at the crack tip, introducing new parameters: the Stress Intensity Factor (K); which is the local Irwin parameter, and also the Rice integral (J), the Griffith's energizing method, in which J and G are the global parameters around the crack tip. The problem of the crack remains very complex and difficult problem to be solved. Several methods are used to investigate the crack problem, namely the method of gradient, the numerical methods by finite elements, as well as the thermodynamic approach and the classical methods of Irwin, Griffith or Rice, according to the Intensity Stress Factor. This study adds to the work already carried out. Using the analytical analysis method of equations, we manage to show that the Stress Intensity Factor has a matrix of rank 3 at the crack tip, which is a better form since it includes complex combination cases of crack mode and bifurcation. Furthermore, when the material is subjected to complex stress, after analysis we emerge from a new singularity in (r) which is different from the classical mode. Finally, we are shown the new form of singularity, which is frequency dependent. This work can explain many situations, for example, the case of certain structural disasters showing the presence of cracks for complex or uncontrollable stress.

Study on the impact of ultrasonic vibration-assisted grinding of glass-ceramics on surface/subsurface damage mechanism

PurposeAn investigation was conducted into the impact of various process parameters on the surface and subsurface quality of glass-ceramic materials, as well as the mechanism of material removal and crack formation, through the use of ultrasonic-assisted grinding.Design/methodology/approachA mathematical model of crack propagation in ultrasonic-assisted grinding was established, and the mechanism of crack formation was described through the model. A series of simulations and experiments were conducted to investigate the impact of process parameters on crack depth, surface roughness, and surface topography during ultrasonic-assisted surface and axial grinding. Additionally, the mechanism of crack formation was explored.FindingsDuring ultrasonic-assisted grinding, the average grinding forces are between 0.4–1.0 N, which is much smaller than that of ordinary grinding (1.0–3.5 N). In surface grinding, the maximum surface stresses between the workpiece and the tool gradually decrease with the tool speed. The surface stresses of the workpiece increase with the grinding depth, and the depth of subsurface cracks increases with the grinding depth. With the increase of the axial grinding speed, the subsurface damage depth increases. The roughness increases from 0.780um/1.433um.Originality/valueA mathematical model of crack propagation in ultrasonic-assisted grinding was established, and the mechanism of crack formation was described through the model. The deformation involved in the grinding process is large, and the FEM-SPH modeling method is used to solve the problem that the results of the traditional finite element method are not convergent and the calculation efficiency is low.

Study on the Interaction Propagation Mechanism of Inter-Cluster Fractures under Different Fracturing Sequences

Horizontal-well multi-cluster fracturing is one of the most important techniques for increasing the recovery rate in unconventional oil and gas reservoir development. However, under the influence of complex induced stress fields, the mechanism of interaction and propagation of fractures within each segment remains unclear. In this study, based on rock fracture criteria, combined with the boundary element displacement discontinuity method, a two-dimensional numerical simulation model of hydraulic fracturing crack propagation in a planar plane was established. Using this model, the interaction and propagation process of inter-cluster fractures under different fracturing sequences within horizontal well segments and the mechanism of induced stress field effects were analyzed. The influence mechanism of cluster spacing, fracture design length, and fracture internal pressure on the propagation morphology of inter-cluster fractures was also investigated. The research results indicate that, when using the alternating fracturing method, it is advisable to appropriately increase the cluster spacing to weaken the inhibitory effect of induced stress around the fractures created by prior fracturing on subsequent fracturing. Compared to the alternating fracturing method, the propagation morphology of fractures under the symmetrical fracturing method is more complex. At smaller cluster spacing, fractures created by prior fracturing are more susceptible to being captured by fractures from subsequent fracturing. The findings of this study provide reliable theoretical support for the optimization design of fracturing sequences and fracturing processes in horizontal well segments.

Voronoi-based 3D phase field model and numerical simulations of granite crack propagation

The distribution of mineral grains within underground rocks and materials is crucial for understanding geological processes and the stability of engineering structures. However, numerical simulation methods that consider 3D mineral particles are still immature. This study presents a 3D phase-field fracture model of mineral grains based on Voronoi polygons, making some beneficial attempts in this regard. The phase-field method does not rely on mesh reconstruction or crack path tracking and can simulate complex crack propagation behavior. Meanwhile, the Voronoi polygon can better describe the microscopic structure of rock with grain boundaries. Rooted in Voronoi polygons, this model efficiently captures the complex geometric shapes of mineral grains and accurately characterizes their positions, shapes, and sizes. Therefore, this study combines Voronoi polygons to establish a 3D phase-field model. Through two numerical simulation cases, the model demonstrates its effectiveness in simulating the impact of three-dimensional mineral grains on crack propagation behavior, showing that cracks tend to propagate at the boundaries or inside softer mineral grains. The modeling approach proposed in this paper has good reference value for numerical simulation studies considering the microscopic structure of rocks.

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

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

A hybridized DDA-DDM for modeling jointed rock masses

The complexity of geo-materials’ behaviors surpass the capabilities of conventional numerical methods alone, particularly when realistically modeling rock structures. Coupling methods can enhance the realism of numerical modeling. Discontinuous deformation analysis (DDA) and displacement discontinuity method (DDM) are combined to model block displacement and crack propagation mechanisms in a blocky rock mass. DDA calculates stresses, strains, rotations, and displacements of the blocks, while DDM predicts crack propagation paths based on specified boundary conditions. The displacements result from DDA are transformed into stresses, followed by investigating crack propagation mechanisms within each block using Kelvin's solution. Boundary stresses are adjusted as cracks propagate, updating stress boundary conditions in DDA. This iterative process continues until crack propagation halts or a new block emerges. In this paper, the complete failure process of a rock slab with one pre-existing non-persistent joint located on the crest of a rock slope and compression test on the rock-like specimen with a single random crack with a 45° slope angle is simulated using the proposed numerical approach. The proposed numerical solution is compared with existing numerical results. This comparison confirms the accuracy and effectiveness of the proposed procedure, as the predicted crack propagation paths from the coupled numerical method align well with the corresponding numerical results from the rock-like samples.

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

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

Phase field modeling of crack propagation in three-dimensional quasi-brittle materials under thermal shock

Quasi-brittle materials create intricate crack patterns on their surface and internal three-dimensional crack networks when exposed to thermal shock conditions. Their cracking behavior is notably impacted by their quenching temperature and size. In this paper, a coupled three-dimensional phase field-cohesive zone model that accounts for thermoelastic fracture is developed to reproduce the quenching and cracking experiments of ceramic balls. The accuracy of the phase field model is demonstrated by simulating the phase field of a single-element cooling process and comparing it with the analytical solution. The quench fracture process of the 3D ceramic ball is then simulated. The phase field simulations show that the surface crack morphology during the quenching process is somewhat random. Still, the crack distribution density is determined by the quenching temperature difference and ceramic ball size. Furthermore, a threshold size is present during the quenching process. When the ceramic ball's radius falls below this threshold, the surface crack pattern no longer appears during quenching. Consequently, the phase-field-cohesive zone model represents an effective means of predicting three-dimensional fracture processes in quasi-brittle materials subjected to thermodynamically coupled loading.

Research on the influence of rock fracture toughness of layered formations on the hydraulic fracture propagation at the initial stage

Deep underground rocks exhibit significant layered heterogeneity due to geological evolution and sedimentation. Rock fracture toughness, as one of the important indicators of hydraulic crack propagation, also exhibits heterogeneous distribution. In order to investigate the influence of non-uniform fracture toughness of layered rocks on hydraulic crack propagation, this paper establishes a planar three-dimensional hydraulic crack propagation model. The model is numerically solved using the 3D displacement discontinuity method (3D-DDM) and the finite difference method. The calculation results indicate that when the distribution of the fracture toughness of layered rocks changes from uniform to non-uniform, the fracture morphology develops from a standard circular crack to an elliptical crack. When the difference of the rock fracture toughness between adjacent rock layers and the middle rock layer (pay zone) is large enough, the fracture morphology will develop towards a rectangular shape. In addition, when the fracture toughness of rock layers is non-uniformly distributed, the hydraulic crack not only rapidly expand in the softening layer (rock layer with lower fracture toughness), but also slowly propagate in the strong layer (rock layer with higher fracture toughness). However, the propagation speed in the softening layer is much faster than that in the strong layer. The results indicate that the heterogeneity of rock fracture toughness has an important impact on the morphology, propagation speed, and direction of hydraulic fractures.

XFEM based study on fatigue performance of rib-to-diaphragm welded joints considering initial defects

Orthotropic steel bridge decks (OSBDs) have been widely used in the field of bridges. However, their service life is significantly limited by fatigue issues. This study presents an analysis of the fatigue performance at the structural details of the rib-to-diaphragm joint, taking into account the impact of initial defects. A numerical segment model employing shell-solid coupling is established to determine the influence surface range and the most unfavorable working condition of the fatigue details, using fatigue standard vehicle loading. The accuracy of the local full-scale model is validated. A local model test of the rib-to-deck welded joint is carried out to deduce the parameter selection for the numerical simulation, based on the test results. Additionally, the crack propagation process in rib-to-diaphragm joints is simulated using XFEM. The simulation results of crack propagation demonstrate good agreement with the actual bridge crack path and shape. The crack propagation model can effectively evaluate the fatigue life, crack development stage, and shape of fatigue details. The study determines the effects of crack depth, crack length, and crack angle on fatigue performance. This study provides a basis for studying the residual fatigue life and crack propagation behavior of rib-to-diaphragm welded joints with initial defects. It is of great significance for understanding the crack propagation mechanism, formulating repair measures, and determining repair time.

Coupled crystal plasticity and damage model for micro crack propagation in polycrystalline microstructures

Coupled crystal plasticity and damage model for micro crack propagation in polycrystalline microstructures

Effect of additive content on texture evolution and mechanical properties of Si3N4 ceramics prepared by hot pressing

The purpose of this research is to investigate influence of additive content on sintering behavior, texture evolution and mechanical properties of Si3N4 ceramics systematically. Si3N4 ceramics with different additive contents are prepared by hot pressing at 1750 °C for 1h. XRD analysis confirms that the densification process is dominated by particle rearrangement instead of phase transformation. Grain morphology characterization demonstrates that additive content affects relative amount between textured β-Si3N4 grains and β-Si3N4 nuclei during initial sintering. During subsequent sintering, β-Si3N4 nuclei surrounded by residual liquid phase elongated randomly, and then weaken texture degree of Si3N4 ceramics. The texture degree of Si3N4 ceramics decreases first and then increases as additives increase steadily. Based on the CTE misfit model and the stochastic model of crack propagation, texture degree, residual stress and grain size have a synergistic effect on crack propagation behavior of β-Si3N4 ceramics. The outstanding flexural strength (1096 MPa) and fracture toughness (10.61 MPa ∙ m1/2) is achieved in hot pressed SN21 with a relatively high texture degree (fL = 0.213).

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

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

Modelling of crack propagation in miniaturized and normal SENB specimens based on local failure criterion

The use of miniaturized specimen testing methods is a promising way to solve the problem of limited materials in RPV monitoring programs. The use of miniature specimens allows the evaluation of fracture toughness from other specimen materials used. In particular, the small-size compact tensile test specimen (0.16T CT) is promising for the determination of fracture toughness, as it can be produced from the standard size Charpy specimen that has already been tested. However, if we have only 0.16T CT test, we cannot investigate the dimensional response and also have only one restricted deformation state, which may pose problems in verifying geometry independence and determining local parameters for state-of-the-art analyses. It is therefore recommended to prepare at least two tests with two different restricted deformation specimens. Therefore, the testing of mini single edge notched bending (SENB) is also required and can be worked out from the Charpy specimens. The paper presents the determination of fracture toughness for these miniaturized specimens by modifying the virtual crack closure technique (VCCT) simulation method using GTN parameters instead of energy release as the driving force. This allows the calculation of the J-integral to proceed in parallel with the crack propagation.

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

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