Crack Propagation Model Research Articles

Dual phase‐field model for immiscible fluid flow through fractured unsaturated porous media

AbstractThe immiscible multiphase fluid flow in intact and fractured porous media is relevant to numerous engineering sectors, including industrial processes, geo‐engineering, and civil engineering. These encompass crucial applications that pose significant challenges in modeling, such as carbon dioxide () storage in underground reservoirs, contaminant transport, and desiccation‐induced hydraulic fracturing in unsaturated soils. In this work, a macroscopic framework is developed to describe the transport of immiscible and multiphase fluids in intact and fractured porous materials. The modeling approach utilizes the embedding of two phase‐field models within the continuum Theory of Porous Media (TPM). The case of negligible capillary pressure in the macroscopic scale is associated with many numerical challenges in solving this nonlinear DAEs system, which forms the major subject of the current work. Hence, the problem of the neglected capillary pressure is defined as a target problem. To deal with this, a thermodynamically consistent modified problem is defined, which incorporates an additional artificial macroscopic capillary pressure based on the Cahn–Hilliard phase‐field approach. To increase the robustness and stability of the numerical solution, the Newton–Raphson method is replaced by a homotopy method that allows a gradual transformation of a simpler, solvable problem into the original target problem that usually converges poorly. The sharp crack topology in the fracture regions is approximated by another phase‐field method, which forms a diffusive transition zone across the crack edges of the deformable porous material. For the solid matrix, we consider a small strain assumption with a heterogeneous distribution of the permeability parameter. The inclusion of heterogeneity allows for a more realistic modeling of crack propagation and fluid‐fluid interaction. For the numerical framework, the coupled DAE system is approximated by the finite element method (FEM), implemented in the open‐source project FEniCSx. Appropriate stabilization techniques are also discussed.

A Modification of the Ostergren Model for Thermomechanical Fatigue Life Prediction of Die-Casting Die Steel

The Ostergren model is simple in form and widely used in engineering practice, also serving as the modeling basis of both the damage differentiation and crack propagation models. However, the shortcomings of the Ostergren model are that the modeling process is affected by thermomechanical fatigue (TMF) test parameters. To establish a TMF life normalized model, a modified Ostergren model based on hysteresis energy damage and TMF data for H13 steel was proposed. The model was successfully applied to TMF life prediction for 4Cr5Mo2V steel. The band of predicted life and test life is basically within the factor of 1.5. In summary, the modified Ostergren model is suitable for the TMF life prediction of Cr-Mo-V-type die-casting die steel.

A Prediction Method for Calculating Fracturing Initiation Pressure Considering the Modification of Rock Mechanical Parameters After CO2 Treatment

The establishment of a more realistic CO2 fracturing model serves to elucidate the intricate mechanisms underlying CO2 fracturing transformation. Additionally, it furnishes a foundational framework for devising comprehensive fracturing construction plans. However, current research has neglected to consider the influence of CO2 on rock properties during CO2 fracturing, resulting in an inability to precisely replicate the alterations in the reservoir post-CO2 injection into the formation. This disparity from the actual conditions poses a substantial limitation to the application and advancement of CO2 fracturing technology. This work integrates variations in the physical parameters of rocks after complete contact and reaction with CO2 into the numerical model of crack propagation. This comprehensive approach fully acknowledges the impact of pre-CO2 exposure on the mechanical parameters of reservoir rocks. Consequently, it authentically restores the reservoir state following CO2 injection, ensuring a more accurate representation of the post-fracturing conditions. In comparison with conventional numerical simulation methods, the approach outlined in this paper yields a reduction in the error associated with predicting fracturing pressure by 9.8%.

Effect of ultrasonic vibration on fatigue life of Inconel 718 machined by high-speed milling: Physics-enhanced machine learning approach

Ultrasonic assisted high-speed machining (UAHSM) can be served as a thermomechanical surface sever plastic deformation (SSPD), because of the high-frequency impact load exerting to the sample together with thermomechanical loads due to shearing and plowing. Despite existing of few works which studied the impact of ultrasonic vibration on fatigue life assessment of difficult-to-cut material by experimental approach, they couldn’t provide an in-depth analysis to identify the underlying mechanisms of fatigue due time-consuming and costly fatigue life tests. Hence, elucidating the role of ultrasonic vibration in UAHSM on variation of fatigue life needs further studies. In order to do so, in the present work, a hybrid predictive approach based using ANFIS-based machine learning model and micromechanical Navaro-Rios (NR) fatigue crack propagation model has been introduced to directly correlates the UAHSM’s parameters to fatigue life. Here the former correlates feed rate, cutting velocity and vibration amplitude as process inputs, to surface integrity aspects (SIA) viz residual stress, roughness and grain size as output. Then, the modeled SIA are correlated to fatigue life using the former. The introduced hybrid model was then verified through series of UAHSM by examining the fatigue lives of milled Inconel 718 using four-point bending fatigue tests. Upon confirmation of the developed model, a comprehensive study was carried out to find how the process factors impact variation of SIA and subsequently fatigue. It was found from the results of developed models and confirmatory experiments that the role of ultrasonic vibration on improved fatigue life is mainly due to inducing compressive residual stress and more refined microstructure than the roughness.

Modeling Brittle Failure in Rock Slopes Using Semi‐Lagrangian Nonlocal General Particle Dynamics

ABSTRACTThe nonlocal general particle dynamics (NGPD) has been successfully developed to model crack propagation and large deformation problems. In this paper, the semi‐Lagrangian nonlocal general particle dynamics (SL‐NGPD) is proposed to solve brittle failure in rock slopes. In SL‐NGPD, the interaction between particles due to deformation is calculated in the initial configuration, while the friction contact interaction from discontinuities is calculated in the current configuration. The Van der Waals force model is utilized for friction contact. The bond‐level energy‐based failure criterion is developed to predict tensile/compressive‐shear mix‐mode cracks. The artificial viscosity and damage correction are used to enhance the numerical stability and accuracy when modeling brittle failure. The SL‐NGPD paradigm is numerically implemented through adaptive dynamic relaxation and predictor–corrector schemes for stable numerical solutions. The stability and accuracy of SL‐NGPD are verified by simulating compression tests. Thereafter, the crack coalescence patterns of double‐flaw specimens are investigated to understand the triggering failure mechanism of jointed rock slopes. Finally, the progressive failure process of the rock slope with step‐path joints is simulated to demonstrate its validity and robustness in modeling brittle failure in rockslides. The numerical results illustrate that the proposed SL‐NGPD is promising and performant for analyzing brittle failure problems in geotechnical engineering.

Prediction of Rubber Fatigue Life Using an Assimilation‐based Learning Approach and Incremental Crack Propagation Model

ABSTRACTAccurately and efficiently predicting the fatigue life of rubber materials has been a long‐standing challenge due to limited understanding of the fatigue mechanism. In this study, a variational assimilation‐based machine learning method assisted with incremental crack propagation model is proposed to predict the fatigue life of rubber materials. Firstly, according to the fracture mechanics theory, a new rubber fatigue life prediction model based on incremental crack propagation and sparse experimental data is established, which owns higher accuracy than the classical crack energy density model. Further, a rubber fatigue life solver coupled incremental crack propagation model and nonlinear finite element method is introduced to generate a dense fatigue life dataset of rubber materials with high accuracy. Finally, the artificial neural network model is trained, cross‐validated, and tested using the dense dataset, and the three‐dimensional variational assimilation model is employed to merge the predicted values of artificial neural network with experimental data. By comparing against the experimental data, the effectiveness of the proposed method was verified; thereby, we offer an accurate and efficient approach to predict the rubber fatigue life.

Fatigue crack closure assessment by wavelet transform of infrared thermography signals

The occurrence of crack closure significantly impacts the fatigue life of materials and structural components. Whether it is induced by the nature of the loading, the fabrication process or the geometry of the structure, its magnitude and effect should be considered to further improve predictive models of fatigue crack propagation. However, the definition of reliable experimental methods for the observation and assessment of fatigue crack closure, and in particular suited to structure testing, remains a challenge. The present study aims to provide a novel approach for the assessment of fatigue crack closure via the continuous wavelet transform of infrared thermography data. The processing of the temperature signal close to the crack in a coherent time–frequency space allows for the identification of crack closing and opening instants associated with high-frequency components. The method is meant to be suited to any testing configuration (conventional compact tension specimen or full-scale structures) with minimum operator-dependent parameters.

Effect of shot peening equivalent impact force on fatigue crack growth behavior and fatigue life prediction of train brake discs

Brake discs, vital rail components, are subjected to intense friction and thermal cycling during braking, leading to surface cracking and fatigue failure. To address these issues, a novel equivalent impact force model for shot peening is proposed in this paper, with the aim of measuring the efficacy of shot peening and predicting the fatigue crack propagation life of brake discs with the assistance of an enhanced SSO algorithm. A finite element model of a cast steel brake disc simulated fatigue crack propagation under sinusoidal cyclic loading. The validity of the multiple projectile random impact model was experimentally confirmed by introducing a residual stress field into the disc surface using equivalent impact forces of 0.3, 0.4 and 0.5 MPa. This stress field was incorporated into the cyclic fatigue crack propagation model and compared with the FCGR results. Shot peening produced a compressive residual stress layer which increased in thickness with increasing impact force. The fatigue crack propagation rate was highly sensitive to the equivalent impact force, decreasing between 0.3 and 0.4 MPa and increasing from 0.4 to 0.5 MPa. Optimal crack propagation inhibition was at 0.4 MPa, which increased fatigue life by 457 % compared to non-peened discs. The improved SSO algorithm also achieved a 6 % increase in prediction accuracy.

Efficient BFGS quasi-Newton method for large deformation phase-field modeling of fracture in hyperelastic materials

The prediction of crack propagation in materials is a crucial problem in solid mechanics, with many practical applications ranging from structural integrity assessment to the design of advanced materials. The phase-field method has emerged as a powerful tool for modeling crack propagation in materials, due to its ability to accurately capture the propagation of cracks. However, current phase-field algorithms suffer from the elevated computational cost associated with the so-called staggered solution scheme, which requires extremely small time increments to advance the crack due to its inherent conditional stability. In this paper, we present, for the first time, a quantitative analysis detailing the numerical implementation and comparison of two common solution strategies for the coupled large-deformation solid-mechanics-phase-field problem, namely the quasi-Newton based Broyden–Fletcher–Goldfarb–Shanno algorithm (BFGS) and the full Newton based alternating minimization (or staggered) (AM/staggered) algorithm. We demonstrate that the BFGS algorithm is a more efficient and advantageous alternative to the traditional AM/staggered approach for solving coupled large-deformation solid-mechanics-phase-field problems. Our results highlight the potential of the quasi-Newton BFGS algorithm to significantly reduce the computational cost of predicting crack propagation in hyperelastic materials while maintaining the accuracy and robustness of the phase-field method.

The crack propagation behaviors, microstructure and mechanical properties of T-welded joints for TIGW with crystal plasticity model and XFEM

In view of the significant impact of welding defects on the fracture behaviors involving the strength, stress concentration and bearing capacity of welded joint, etc., the propagation behaviors and mechanical properties of welded joints with porosity and micro crack are deeply investigated using a multiscale method. In this work, a crack nucleation and propagation model based on crystal plasticity theory, combined with the extended finite element method (XFEM), is established for the T-welded joint. The maximum slip on the predominant slip system method is applied to predict the crack propagation path of pores and micro cracks in the weld zone (WZ), and the effect of crystal orientation on crack growth is explored. Then, a continuous model is used to analyze the micro and macro fracture behaviors near the weld under tensile load, combined with the maximum principal stress method. The WZ and heat affected zone (HAZ) are observed using electron backscatter diffraction (EBSD) to study the microstructure evolution. Considering grain boundaries, the image information of crystal morphology is processed through binary image analysis for FE modeling. The local mechanical properties testing is carried out using micro-specimens of HAZ and WZ to calibrate the crystal plastic parameters. The results show that the resolved shear stress of the predominant slip system of crack initiation and propagation elements is increased by pore and crack defects. The fracture positions of tensile specimens through numerical simulation are in good agreement with the macroscopic experimental results. It will provide an analysis basis for preventing fracture failure and improving the service performance of thin-walled structures in future.

On the importance of the cracking process description for dynamic crack initiation simulation

A dynamic implementation of the coupled criterion under quasi-static loading, based only on the mean velocity during crack initiation, is proposed. It relies on a simultaneous node release method. It consists of computing the dynamic incremental energy release rate by simultaneously opening a crack of a finite length during a given time increment rather than progressively opening smaller crack increments following a velocity profile as in the progressive node release method. Both methods result in significantly different kinetic energy variations as a function of the crack length, and thus different incremental energy release rates for large enough crack velocities, for which the kinetic energy magnitude is similar to the elastic strain energy magnitude. Both simultaneous node release method and progressive node release method can however be equivalently used for small enough crack velocities since similar incremental energy release rates are obtained with both methods. Inverse identification of fracture properties based on dynamic crack initiation at a hole in Brazilian disk specimens yields critical energy release rates in the same order of magnitude as the one obtained based on dynamic crack propagation modeling.

Research on Integrated Control Strategy for Wind Turbine Blade Life.

Wind turbine blades bear the maximum cyclic load and varying self-weights in turbulent wind environments, which accelerate the propagation of cracks that ultimately progress from minor faults, resulting in blade failure and significant maintenance and shutdown costs. To address this issue, this paper proposes an adaptive control strategy for the blade's useful life. The control system is divided into the inner control loop and the outer control loop. The outer loop is based on the Paris crack propagation model combined with a particle filtering algorithm and calculates the degradation of the blade life under the crack threshold conditions provided by the operation and maintenance strategy to determine the parameter settings of the inner-loop load-shedding controller. The control strategy we propose can balance the load-shedding capability of the controller with the fatigue load of the pitch actuator while considering the predefined remaining useful blade life in the operation and maintenance strategy, avoiding unplanned downtime and reducing maintenance costs.

Parametric characterization of the Christopher–James–Patterson model for crack propagation in welded zone of A7N01 Aluminum alloys

AbstractAluminum alloy is a widely used material in railway vehicle structures. In order to accurately analyze the crack propagation mechanism of Aluminum alloy welding structures and predict their crack propagation life, this study focuses on the A7N01 Aluminum alloy and proposes a full‐field strain solution method based on the least‐squares method. For the first time, digital image correlation (DIC) experimental measurements are combined with the finite element analysis method to determine the shape and size of the plastic zone at the crack tip of the compact tension (CT) specimen. And it also calculates the crack propagation driving force parameters of the Christopher–James–Patterson (CJP) model using traditional crack propagation driving parameters. The research results revealed that the plastic zone at the crack tip captured by DIC experiments is in good agreement with the finite element simulation results. Additionally, the crack growth rate curve of the A7N01 Aluminum alloy, fitted based on the CJP model, is insensitive to the stress ratio. The results offer an effective approach to utilizing the da/dN‐∆KCJP curve in analyzing A7N01 Aluminum alloy and welded structural failures, broadening the scope of engineering applications for the CJP model.

Experimental and numerical investigations on rate-dependent fracture behavior of concrete-rock interface

To ensure the safety and stability of the concrete gravity dams built in the seismic regions, this study investigated the rate-dependent fracture behavior of the concrete-rock interfaces with different roughness degrees. Firstly, direct tensile tests and three-point bending tests were conducted to measure the mechanical and fracture properties of the concrete-rock interface with three roughness degrees, i.e. the 4 × 4 interface, natural interface, and 7 × 7 interface, and under four strain rates, i.e. 10-5/s, 10-4/s, 10-3/s, and 10-2/s. By employing the fictitious crack model and initial fracture toughness-based crack propagation criterion, numerical simulations were conducted to analyze the crack propagation processes of the concrete-rock interfaces under different strain rates. The results indicated that the tensile strength and initial fracture toughness exhibited an obvious increasing tendency with the increase of the strain rates, and they showed a nearly linear relationship with the logarithms of the strain rates. Prediction models were proposed to calculate the tensile strength and initial fracture toughness of the concrete-rock interface under different strain rates. In addition, the initial fracture toughness-based crack propagation criterion was proved to be applicable to analyze the crack propagation processes of the concrete-rock interfaces under both quasi-static and seismic strain rates. It was found that the fully-formed fracture process zone lengths and the corresponding crack length decreased obviously with the increase of the strain rates, indicating that the boundary effect of the concrete became stronger under the higher strain rates, which approached to the fracture behaviors of the large-size specimens.

Fatigue analysis of selective laser melting Inconel 718 and the mechanism of ductile–brittle continuous alternating steps during fatigue process

In this paper, Inconel 718 powber fabricated by selective laser melting were studied to explore the mechanical characteristics and microstructures. The results of microstructure show that the material exhibits the columnar, honeycomb, and mixed crystal structures. The microhardness is very uniform, with a average value of 317 HV. Tensile test shows the ultimate tensile strength of 785Mpa, elongation of 4.93%, which is high stress brittle fracture. The fatigue strength of 180 MPa was obtained from the fatigue test. The fatigue life was sensitive to the effect of stress. In the scanning electron microscope observation, small crack propagation was found in the fracture, and a large number of step-like fracture characteristics of repeated transformation of toughness and brittleness were found. The mechanism analysis of the step-like ductile–brittle fracture is carried out, which is divided into four stages. Mathematically analyzing the tough-brittle fracture of the step type, where the crack is subjected to both the stress field around the pore and the stress field at the crack tip on the way to extension, a stress field model for crack propagation around the pore and a fracture toughness formula for transverse and longitudinal propagation of tough-brittle steps applicable to this paper are proposed.

Phase field modeling of crack propagation in structures under tensile stress

Phase field modeling of crack propagation in structures under tensile stress

Modeling the effect of material heterogeneity on the thermo-mechanical behavior of concrete using mesoscale and stochastic field approaches

The adverse impact of high temperatures on concrete is a well-recognized issue that can lead to significant mechanical deterioration and structural integrity loss. Factors such as aggregate type, cement composition, temperature, duration of exposure, and moisture content can substantially influence the fire resistance of concrete. To simulate and better understand the effects arising from the heterogeneity of concrete in a fire situation, a mesoscale approach is proposed, using the Mesh Fragmentation Technique (MFT) to assess the complex thermo-mechanical behavior of concrete. The MFT introduces high aspect ratio interface elements to model crack propagation and interfacial transition zones by means of an appropriated tensile damage constitutive law. In this extended framework, a fully-coupled thermo-mechanical model is proposed. The modeling approach includes considerations of both macroscopic and mesoscopic scales, in which the coarse aggregate, mortar matrix and interfacial transition zones are represented. Besides, a stochastic distribution is assumed for the material properties to account for the lower scale heterogeneity. The main novelty proposed in this study consists in the synergy of mesoscale and stochastic approaches that are herein combined to model the effect of heterogeneity on the concurrent macro-mesoscale thermo-mechanical behavior of concrete. To validate the numerical model’s capabilities in capturing thermally induced cracks, benchmark cases and a simulation of a bending beam exposed to elevated temperatures are presented. The results demonstrate the potential of the proposed approach in predicting the behavior of concrete subjected to thermal loading and the role played by heterogeneity in the thermally induced cracking.

Hygrothermal effect of bio-inspired helicoid laminate plate for strengthening damaged RC beam

This study investigates the influence of moisture and Thermo-hygroscopic influence on bio-inspired helicoidally laminated composite plates (BHLC) for strengthening damaged reinforced concrete (RC) beams. Borrowing inspiration from nature’s design principles, BHLC plates represent a novel approach to rehabilitation. An analytical approach based on deformation compatibility is employed, assuming constant shear and normal stresses across the adhesive layer within the framework of linear elasticity. BHLC plates are implemented to restrict crack propagation within the RC beam. The analytical methodology considers equilibrium and deformation compatibility across all components: the concrete beam, BHLC plate, and adhesive layer. A parametric study explores the sensitivity of interfacial stresses to parameters such as laminate and adhesive stiffness, plate thickness, and helicoidal layup configuration. The results reveal a significant influence of these factors on the magnitude of maximum interfacial shear and normal stresses. This study establishes a foundation for future analyses of damaged RC beams strengthened with BHLC plates, potentially leading to advancements in rehabilitation methodologies and improved crack propagation modeling in RC beams.

A Revised Abaqus® Procedure for Fracture Path Simulation Based on the Material Effort Criterion.

This paper presents the results of computer simulations of fracture in three laboratory tests: the three-point bending of a notched beam cut from sandstone, the pull-out test of a self-undercutting anchor fixed in sandstone, and the pull-out test of a bar embedded in concrete. Five material failure criteria were used: Rankine, Coulomb-Mohr, Drucker-Prager, Ottosen-Podgórski, and Hoek-Brown. These criteria were implemented in the Abaqus® FEA system to work with the crack propagation modeling method-extended finite element method (X-FEM). All criteria yielded similar force-displacement relationships and similar crack path shapes. The improved procedure gives significantly better, close-to-real crack propagation paths than can be obtained using the standard subroutines built into the Abaqus® system.

A computational approach for phase-field model of quasi-brittle fracture under dynamic loading

AbstractA computational model is formulated for studying dynamic crack propagation in quasi-brittle materials exposed to time-dependent loading conditions. Under such conditions, inertial effects of structural components play an important role in modelling crack propagation problems. The computational model is proposed within the theory of regularised cracks which uses a damage-like internal variable. Here, fracture considers phase-field damage which gives rise to a material degradation in a narrow material strip defining the regularised crack. Based on the energy formulation using the Lagrangian of the system, the proposed computational approach introduces a staggered scheme adopted to solve the coupled system and providing it in a variational form within the time stepping procedure. The numerical data are obtained by quadratic programming algorithms implemented together with a finite element code.