Simulation Of Crack Propagation Research Articles

Crack propagation simulation and overload fatigue life prediction via enhanced physics-informed neural networks

The fatigue crack growth simulation and life prediction of structures are implemented in this paper based on the physics-informed neural networks (PINNs). Firstly, the enhanced PINNs are proposed by introducing the crack tip asymptotic displacement fields, so that the crack tip stress intensity factors can be calculated accurately even when the number of collocation points is small and the distribution grid is regular. The enhanced PINNs essentially transform the solution of elastic body containing crack into the optimization of minimizing the constructed loss functions, and can invert the fracture parameters. Then, an automatic crack propagation simulation method is developed based on the enhanced PINNs. The network architecture and the overall node distribution can be unchanged during the crack propagation process, and only new crack surfaces need to be processed and corresponding loss functions need to be modified. Because the nodal refinement around crack-tip is not required, this simulation method is convenient and can accurately predict the mixed-mode crack propagation path. Finally, the fatigue crack growth life algorithm considering overload is developed, where the effect of each overload can be captured by the cycle-by-cycle method. Based on this algorithm, the retardation behavior can be characterized and the fatigue life of structure under the load spectrum with periodic overloads can be accurately predicted. The sufficient examples are given to verify the feasibility and accuracy of the method proposed in this paper.

Low-cycle fatigue crack growth in brittle materials: Adaptive phase-field modeling with variable-node elements

This work presents an adaptive phase field framework for the simulation of crack nucleation and propagation in brittle materials subject to low-cycle loading. We introduce a fatigue history strain parameter within the phase-field framework to capture the fatigue effect. The resulting coupled differential equations are solved using a staggered iteration scheme. In order to improve the computational efficiency of the phase-field model, an adaptive refinement scheme is introduced. This scheme utilizes an artificial threshold that takes into consideration of both phase-field variables and cumulative fatigue history field variables to determine the elements to be refined. The handling of the hanging nodes resulting from mesh refinement is accomplished through the application of the variable-node element technique, offering a flexible and efficient mesh integration technique. We validate our proposed numerical scheme through five representative numerical examples: single-edge cracked specimen, compact tension specimen, double-edge cracked panel, plate with a hole and plate with multi-cracks and hole. The results demonstrate that the adaptive mesh refinement scheme significantly reduces computational costs without compromising the accuracy of the numerical predictions.

Simulation of Shear and Tensile Fractures Using Ductile Phase Field Modelling with the Calibration of P Wave Velocity Measurement and Moment Tensor Inversion

AbstractThe appropriate understanding and formulation of rock discontinuities via FEM is still challenging for rock engineering, as continuous algorithms cannot handle the discontinuities in rock mass. Also, different failure modes of rock samples, containing tensile and shear failure, need to be computed separately. In this study, a novel double-phase field damage model was introduced with two independent phase field damage variables. The construction of the proposed model follows the thermodynamics framework from the overall Helmholtz free energy, with elastic, plastic and surface damage components. The proposed model is calibrated via traditional damage variables, based on ultrasonic wave velocity measurement and acoustic emission monitoring, and both show great consistency between simulation results and laboratory observations. Then the double-phase field damage model is applied to COMSOL software to simulate microcrack propagation in a pre-fractured rock sample. Both lateral and wing cracks are observed in this study, manifested as shear- and tensile-dominated cracks. We also observed different microcracking mechanisms in the proposed numerical models, such as tensile and shear cracking, the influence of plastic strain and the percolation between tensile and shear microcracks. Overall, this study provides valuable insights into the mechanics of microcracking in rocks, and the proposed model shows promising results in simulating crack propagation.

Marginal integrity in minimally invasive molar resin composite restorations: Impact of polymerization shrinkage

ObjectivesThis study utilized non-linear finite element (FE) models to explore polymerization shrinkage and its impact on marginal integrity in molars following both selective caries removal (SCR) and conventional treatment. Specifically, we performed 2D in silico simulations to study residual stresses post-resin polymerization shrinkage and their influence on the marginal integrity of various restoration types. MethodsInitially, FE models were developed based on a cohesive zone framework to simulate crack propagation along the bonded interfaces between restoration and tooth structure in SCR-treated molars with class I and class II restorations. The modeled resin composite restorations first underwent polymerization shrinkage and were then subjected to various occlusal loading conditions. Stress magnitudes and distributions were identified to evaluate the margin integrity and predict the mechanism and location of interfacial failure. Results and discussionThe FE models computed polymerization shrinkage stresses of less than 1 MPa, exerting a minor influence on the composite/tooth interface. Occlusal loading, however, significantly impacted the load-bearing capacity of the composite/tooth (c/t) interface, potentially jeopardizing the restoration integrity. Especially under bi-axial occlusal loading, interfacial debonding occurred in the vertical cavity walls of the class I restorations, increasing the risk of failure. Notably, SCR-treated teeth exhibited better margin integrity than restored teeth after complete caries removal (NCR).These findings provide valuable insights into the mechanical behavior of SCR-treated teeth under different loading conditions and highlight the importance of considering the load scenarios that may lead to failure at the c/t interface. By investigating the factors influencing crack initiation and delamination, this novel research contributes to the optimization of restorative treatments and aids in the design of more resilient dental restorations.

Investigation of ice wedge bearing capacity based on an anisotropic beam analogy

Ships and offshore structures operating in ice-covered waters need to be able to break ice. The hulls of ships and offshore structures are often designed to be inclined so that an out-of-plane force can be incurred to initiate flexural failure. During this process, an in-plane force co-exists as the result of the hull inclination, which can affect the bending process and alter the magnitude of interaction force. Additionally, the loading process can be rapid and incur dynamic effect within the ice sheet, resulting in higher peak loads compared to the scenario of quasi-static loading. The effect of in-plane force and loading speed, however, are often neglected in the modelling of the icebreaking process in order to enable simplified solutions of analytical form, which leads to deviations in the estimation of ice loads. This paper aims to investigate the effects of in-plane force and loading speed on the ice bearing capacity during the icebreaking process. This is conducted via the Finite Element Analysis (FEA) with the Cohesive Element Method (CEM). An anisotropic beam analogy concept is proposed to model a 3D ice wedge with a 2D beam which has varying properties along the axial direction. The analogy enables fast and stable simulation of ice crack propagation through its thickness direction, while maintaining properties of the ice wedge in 3D. The analogy is verified with Nevel's closed-form solution for a narrow wedge resting on an elastic foundation. After that, the beam is loaded with a rigid wall with different inclination angles and loading speeds. The results reveal that the in-plane force and loading speed have significant influence on the icebreaking process, resulting in different bearing capacity and overall energy consumption. Based on the numerical results, a regression study is conducted to derive a correction coefficient accounting for the joint effect of in-plane force and loading speed on the bearing capacity, which can be incorporated into ice-structure interaction simulation models.

Effects of fissure length and angle on the fracture modes of 3D printed teeth model: Insights from DIC-based fracture tests and meshless numerical simulations

To investigate the influences of teeth fissure properties on their failure modes, 3D Printing technology is used to prepare the teeth models. The strain distributions of the teeth model surfaces at each moment of the loading processes are obtained by the DIC technique. And the progressive failure processes as well as the stress distributions of the teeth models are simulated by the improved Smoothed Particle Hydrodynamics (SPH) Method. Experimental results show that under the action of the steel ball, the teeth models mainly produce two types of cracks: The tensile cracks along the pre-existing fissures and the shear cracks along both sides of the teeth model. The existence of prefabricated fissures greatly reduces the peak strength of the teeth models. Compared with the circumstances containing no pre-existing fissures, the peak strength of d = 1 cm, d = 2 cm and d = 3 cm decreases by 22.33%, 31.79% and 18.94%, respectively, and the peak strength of θ = 30°, θ = 45°, θ = 60° decreases by 10.78%, 44.01% and 34.3%, respectively. Numerical results show that the initiations of tensile cracks are induced by the high tensile stress concentrations at the pre-existing fissure tips, while the shear cracks are caused by the high tensile stress concentrations in the low tensile stress concentration areas after the initiation of tensile cracks. The research results can provide some references for the understandings of teeth failure mechanisms as well as the applications of SPH method into teeth crack propagation simulations.

Initiation and growth of fatigue cracks in sheets with U-shaped notches in the first and mixed modes of fracture

This study presents the effects of the geometry of the notches on the fatigue life, crack initiation, and growth in mixed mode and first mode of the fracture. For this purpose, some samples were tested with U-shaped notches with different radii and depths and various orientations with respect to the loading directions under fatigue loads. Using the fatigue crack growth rates, the Paris law coefficients were obtained for the used material in different conditions. It was shown that these coefficients are independent of the geometry of the samples. Fatigue crack growth behaviors in the mixed mode tests were also in good agreement with the result of the numerical simulations. Predictions of the maximum tangential stress criterion and numerical simulation for the position of the crack initiation on the notch root were compared with the tested observations, which showed good agreement. 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An adaptive finite element method for coupled fretting wear and fatigue crack propagation simulation

Fretting wear and fatigue crack propagation often occur at the same time in the service of mechanically connected structures. In order to analyze the effect of fretting wear on the process of fatigue crack propagation, a finite element simulation method for fatigue crack propagation considering fretting wear is proposed. In this method, the Archard model is used to predict the wear process, and the conventional Paris equation is modified based on the wear rate. In order to improve the accuracy of crack propagation prediction, a crack-tip super singular element (CSSE) is used to calculate the singular stress field and fracture control parameters of the crack tip. An adaptive meshing technique that automatically adjusts the mesh density according to the simulation process is designed to ensure the computational efficiency of the algorithm and the accuracy of the numerical results. The smoothing technique used in wear simulation can alleviate the influence of contact stress fluctuation on wear profile prediction. The usage of the new simulation method is introduced through benchmark examples. It is proved that the numerical results of crack propagation obtained by the adaptive finite element method (FEM) have high precision, good convergence and high computational efficiency. It is found that wear reduces the crack growth rate compared with the simulation results without considering wear. This method has a promising application in the coupling analysis of fretting wear and fatigue crack propagation of mechanically connected structures.

Three-Dimensional Probabilistic Semi-Explicit Cracking Model for Concrete Structures

This paper introduces a three-dimensional (3D) semi-explicit probabilistic numerical model for simulating crack propagation within the framework of the finite element method. The model specifically addresses macrocrack propagation using linear volume elements. The criteria governing the macrocrack propagation is based on the softening behavior observed in concrete under uniaxial tension. This softening behavior corresponds to a dissipated cracking energy that is equal to the mode I critical fracture energy (GIC) used in the Linear Elastic Fracture Mechanics theory (LEFM). The probabilistic nature of this model revolves around the random distribution of two mechanical properties: tensile strength (ft) and fracture energy, which varies based on the volume of finite elements. The scattering of the fracture energy increases as the volume of finite elements decreases in order to consider the strong heterogeneity of the material. This work primarily aims to estimate the relationship between the standard deviation of GIC and the volume of finite elements through the development of the numerical model. For this purpose, an inverse analysis is conducted based on a fracture mechanical test simulation. This test involves macrocrack propagation in a large Double Cantilever Beam (DCB) specimen with a crack length exceeding two meters. The proposed inverse analysis procedure yields highly significant results, indicating that the numerical model effectively evaluates both crack length and crack opening during propagation.

An adaptive multi-patch isogeometric phase-field model for fatigue fracture

Fatigue fracture is one of the main causes of structural failure under cyclic loading, so accurate evaluation of fatigue fracture is very important for the design of structures subjected to cyclic loading. In this work, we propose an adaptive fatigue phase-field model within the framework of multi-patch isogeometric analysis to simulate crack nucleation and propagation in brittle materials under cyclic loading. Multiple non-uniform rational B-splines (NURBS) patches are used to exactly represent complex structures, and the Nitsche’s method is adopted to enforce the compatibility of the displacements, stresses and phase-field variables between two patches. The coupled governing equations of fatigue phase-field model are established based on the Nitsche’s method, and the selection of Nitsche’s parameters are determined from numerical experiments. A refinement-correction adaptive approach based on locally refined non-uniform rational B-splines (LR NURBS) structured mesh refinement strategy is developed to alleviate the computational burden caused by the requirement of small element size around crack surface and the large number of fatigue loading. The proposed multi-patch isogeometric phase-field model can deal with the coupling between equal/unequal length interfaces, thus the fatigue crack propagation simulation in arbitrary complex structure can be implemented. Several numerical examples are investigated to verify the practicality of the multi-patch isogeometric phase-field model and the effectiveness of the adaptive scheme.

The effect of inclusions and pores on creep crack propagation of linear friction welded joints of GH4169 superalloy

Superalloy has become the key material in components of blisks for aero-engines produced by linear friction welding. However, during the long-term service of the blisks, stress rupture occurs on the blisk under long-term creep. In this study, the linear friction welded joints of GH4169 superalloy were studied with experiments and numerical simulation. The Sin-Hyperbolic creep-damage constitutive model was established. Based on the compact tension specimen model, the numerical simulation of crack propagation was carried out, analyzing the effect of defects in linear friction welded joints such as cracks, inclusions, and pores on creep crack propagation. Results show that inclusions have an impact on the deflection and promotion of creep crack propagation. The maximum values of crack propagation rate can be observed when radius is 0.03 mm for circular inclusions and length-to-diameter ratio is 3 for elliptical inclusions, respectively. When the transverse distance between the center of the pore and the crack tip is 0.6 mm, the effect on crack propagation is the most significant, with the crack deflecting and expanding towards the direction of the pore. The effect of elliptical pores on creep crack propagation is more significant than that of circular pores. When the length-to-diameter ratio is 3, cracks have initiated firstly on both sides of elliptical pores. When the angle between the pore and the prefabricated crack is 0°, the elliptical pore has the greatest deflection effect on the creep crack. Overall, the effect of pores on creep crack propagation is stronger than that of inclusions.

3D crack propagation study of a railway component using XFEM method

This work develops a methodology to study the crack propagation through ABAQUS simulation. This simulation study uses the service condition of the mechanical component and the complex geometry of a manufacturing defect obtained by microtomography. It was concluded that the XFEM method is an essential tool in predicting crack propagation of a railway component. Furthermore, the type of criteria used in the XFEM method allowed the analysis of the propensity of the manufacturing defect to initiate crack propagation. The C3D4 elements were essential in realising the crack propagation simulation, considering a manufacturing defect. Having the pore’s complex geometry was crucial to developing the methodology presented in this study. The static analysis results indicated that the maximum stress concentration value in the pore is in a zone that can be identified as a hot spot. In addition, the pore showed a higher concentration of Von-Mises stresses than in the static simulation performed without a pore and of the material’s ultimate strength. In conclusion, the methodology presented in this work shows that developing a more realistic simulation study is possible. For a complete structural integrity study, the mechanical design simulation studies must include some complex geometries of intrinsic manufacturing defects.

A coupled hydro-thermo-mechanical model based on TLF-SPH for simulating crack propagation in fractured rock mass

In this paper, a hydro-thermo-mechanical coupling model based on the smoothed particle hydrodynamics with total Lagrangian formula (HTM-TLF-SPH) is proposed to simulate the crack propagation and instability process of fractured rock mass. TLF-SPH uses the Lagrangian kernel approximation, that is, the kernel function and its gradient need only be calculated once in the initial configuration, which is much more efficient than the smoothed particle hydrodynamics (SPH) based on the Euler kernel approximation. In TLF-SPH, particles interact with each other through virtual link, and the crack propagation path of rock mass is tracked dynamically by capturing the fracture of virtual link. Firstly, the accuracy and robustness of the HTM-TLF-SPH coupling model are verified by a reference example of drilling cold shock, and the simulation results agree well with the analytical solutions. Then, the crack propagation law of surrounding rock and the evolution characteristics of physical fields (displacement, seepage and temperature fields) after excavation and unloading of deep roadway under the coupling condition of hydro-thermo-mechanical are investigated. In addition, the seepage and heat transfer processes of the surrounding rock of Daqiang coal mine under different coupling conditions are successfully simulated. Meanwhile, the effect of the boundary water pressure difference on the temperature and seepage fields under the hydro-thermal coupling condition is quantitatively analyzed.

An explicit improved meshless numerical manifold method for dynamic crack propagation

Accurately simulating the dynamic propagation of cracks is critical to investigating the mechanisms of rock fracture under dynamic loading. The meshless numerical manifold method, characterized by its node-based interpolation approximation akin to the meshless method and the dual-cover of numerical manifold method, is particularly suitable for crack analysis and has been successfully applied to quasi-static crack propagation. This paper aims to extend its application to the simulation of dynamic crack propagation. Initially, the meshless numerical manifold method's nodal arrangement and numerical integration scheme are enhanced to address dynamic problems more effectively, referred to as the Improved Meshless Numerical Manifold Method (iMNMM). Subsequently, we introduce a novel mass lumping method grounded in rigorous mathematical principles, an energy-conserving extended degrees of freedom inheritance strategy and a crack propagation criterion based on dynamic stress intensity factors. Additionally, the viscous artificial boundaries and the “large mass” acceleration method are incorporated to impose the acceleration and zero-displacement boundary conditions. Further, the improved explicit meshless numerical manifold method based on the central difference method is established for dynamic crack propagation. Finally, for verification, iMNMM is tested on several numerical examples. Numerical results manifest that iMNMM can enable the simulation of dynamic crack propagation with larger, constant time steps.

Numerical Simulation of Crack Propagation and Branching Behaviors in Heterogeneous Rock-like Materials

The characterization and understanding of crack evolution in non-uniform geological structures are crucial for predicting the mechanical response of rock-like materials or structures under varying loading conditions. In this study, an improved Peridynamic model with a degree of heterogeneity characterized by random pre-breaking “bonds” coefficients is introduced to capture the intricacies of crack initiation, propagation, and branching behaviors in heterogeneous rock-like materials. MATLAB discrete programs for heterogeneous material models and PD simulation programs based on the FORTRAN language were developed. The effectiveness of the heterogeneous PD model in simulating crack propagation and branching patterns in heterogeneous materials has been verified through dynamic and static (quasi-static) loading cases with pre-notch. The different levels of heterogeneity not only affect the direction of crack propagation but also determine the crack deflection direction and branching patterns. The crack propagation path appears to possess obvious asymmetry in the crack propagation direction. As the load applied continues to increase, the asymmetric multi-crack branching phenomenon will occur. The higher the level of heterogeneity, the more complex the behaviors of crack propagation and branching become. This research provides valuable insights into the interplay of material heterogeneity and crack evolution, offering a foundation for improved numerical simulations and contributing to the broader field of geomechanics.

Methodology for numerical evaluation of fracture resistance under pinch loading of spent nuclear fuel cladding containing reoriented hydrides

It is important to maintain cladding integrity in spent nuclear fuel management. This study proposes a numerical analysis method to evaluate the fracture resistance of irradiated zirconium alloy cladding under pinch load known to cause Mode-III failure. The mechanical behavior and fracture of the cladding under pinch loading can be evaluated by a Ring Compression Test (RCT). To simulate the fracture of hydride precipitates, zirconium matrix, and Zr/hydride interfaces under the stress field generated by RCT, a micro-structure crack propagation simulation method based on Continuum Damage Mechanics (CDM) has been proposed. Our RCT simulation model was constructed from microscopic images of irradiated cladding. In this study, we developed an automated process to generate a pixel-based finite element model by separating the hydride precipitates, zirconium matrix, and interfaces using an image segmentation method. The appropriate element size was selected to ensure the efficiency and accuracy of a crack propagation simulation. The load-displacement curves and strain energies from RCT were compared and analyzed with the simulation results of different element sizes. The finalized RCT simulation model can be used to establish the failure criterion of fuel rods under pinch loading. The advantages and limitations of the proposed method are fully discussed here.

Molecular dynamics simulation of crack propagation in very small grain size nanocopper with different grain size gradients.

In this paper, we use molecular dynamics to simulate the crack propagation behavior of gradient nano-grained (GNG) copper models with different grain size gradients, compare the crack propagation rates of different models, and analyze the microstructural changes and the mechanism of crack propagation. The simulation results show that the increase of the grain size gradient of the GNG copper model can improve the fracture resistance of the material, and the crack propagation mode undergoes a transition from brittle propagation along the grain boundaries to the formation of pores at the grain boundaries, and then to ductile fracture along the inclined plastic shear zone. The number of dislocations increases with the grain size gradient, while the crack passivation is more serious, indicating that a larger grain size gradient is more effective in inhibiting crack propagation. The introduction of gradient grain size promotes crack propagation and weakens the plasticity of the material relative to the nano-grained (NG) copper model.

Stress-strain characteristics of autoclaved aerated concrete masonry under varying displacement rates

Comprehending the impact of displacement rate on the mechanical properties of autoclaved aerated concrete (AAC) masonry is critical for predicting the response of structures to seismic and other natural dynamic loads. This study investigates the effect of varying displacement rates (0.1 mm/min, 1 mm/min, and 10 mm/min) on the mechanical properties of AAC masonry under uniaxial compression through systematic laboratory tests. Results indicate a substantial increase in elastic modulus (100 %) and compressive strength (200 %) as displacement rates rise from 0.1 mm/min to 10 mm/min. Finite element analysis using a micro-modelling strategy in Abaqus corroborates experimental findings, simulating crack propagation and identifying stress and strain distribution. The outcomes of this study would facilitate the accurate design and analysis of framed buildings infilled with AAC block masonry, especially under dynamic loading. These findings are expected to significantly contribute to the enhancement of structural engineering practices, enhancing the reliability and effectiveness of AAC block masonry for constructing resilient buildings.

Re-Distribution of Welding Residual Stress in Fatigue Crack Propagation Considering Elastic–Plastic Behavior

The welding residual stress re-distribution behavior during fatigue crack propagation in butt-welded high-strength steel plates for ship construction is investigated based on experimental test results and numerical analyses. The specimens’ initial welding residual stresses are obtained from X-ray for middle tensile (MT) specimens cut from butt-welded high-strength steel plates. Then, fatigue crack propagation experiments on MT specimens are conducted, and a strain gauge is used to measure the residual stress re-distribution field around cracks. A practical fatigue crack propagation simulation procedure is developed with a dynamic update of in-situ welding residual stress, where the residual stress intensity factor Kres of the MT specimen is deduced. The stress ratio effect on Kres during fatigue crack propagation is analyzed and a good agreement between experimental and numerical results is achieved.

Multi scale simulation of crack propagation in polycrystalline SiC

Silicon carbide (SiC) is considered one of the most promising emerging materials in the fields of refractory materials and semiconductors. In this paper, a multi-scale numerical simulation method is proposed to investigate crack propagation in SiC at different scales, using a combination of cohesive zone model and molecular dynamics (MD). The microstructure of the material is represented by Voronoi subdivision, and bilinear treatment is applied at the grain boundaries. Firstly, MD models with different microscopic defects were established to obtain the corresponding traction separation curves. Then, the element parameters, obtained by fitting the traction separation law, were inserted into the cohesive elements located at the grain boundary and within the grain. Finally, the finite element models were simulated by the failure criterion. The fracture toughness of the material is predicted, and the influence of microscopic defects and grain distribution on macroscopic fracture toughness is explored. The results indicate that the grain distribution and the type of micro defect have an impact on the crack growth path and macro fracture toughness. The simulation results are consistent with published experimental results, which demonstrates the viability of employing this multi-scale analysis method for examining and replicating the micro-, meso-, and macro-scale crack propagation characteristics of SiC.