Fracture Parameters Research Articles

Modeling and evaluation of the fracture resistance of alkali-resistant glass fibre reinforced concrete under different loading rates

Alkali-resistant glass fibre reinforced concrete (AR-GFRC) has garnered significant interest due to its economic and environmental friendliness. Given the critical importance of evaluating the crack resistance of AR-GFRC under dynamic loading conditions and the size effect inherent in determined fracture parameters using traditional methods, this study aims to propose an analytical approach based on the boundary effect model. The goal is to predict the realistic dynamic tensile strength (ft) and fracture toughness (KIC) while elucidating the rate sensitivity of fracture resistance. Three-point bending tests were conducted on AR-GFRC with three different fibre volumes to investigate dynamic fracture behaviors under varying loading rates. By introducing discrete parameter and the microstructure characteristic parameter that account for material discontinuity and heterogeneity, the realistic dynamic ft and KIC of AR-GFRC can be directly obtained as closed-form solutions upon determining the maximum fracture load from the tests. The results revealed a substantial increase in ft and KIC with an improvement in the loading rate. However, due to relatively weakened fibre activities, the enhancement of dynamic fracture resistance decreases with the increase in fibre content and loading rate.

A higher-order asymptotic solution for 3D sharp V-notch front tip fields in creeping solids

As one of the most important topics studied in creep fracture mechanics, mechanics fields at 3D sharp V-notch front tip in creeping solids have drawn remarkable attention at present. In this paper, the higher-order asymptotic analysis is carried out for 3D sharp V-notch front tip fields in creeping solids subjected to mode Ⅰ loading, and a 3D higher-order term solution is theoretically proposed by introducing the out-of-plane stress factor Tz to establish the 3D nonlinear governing equations of front tip fields. The present higher-order asymptotic solution for 3D sharp V-notch can naturally be degenerated to that for 3D crack. It is found that the stress exponents and angular distribution functions of higher-order terms for 3D notch and crack are highly related to Tz. The proposed 3D higher-order term solution overall shows better agreement with the FEA results than the existing 3D leading-term solution and 2D higher-order term solutions available in the literature, especially for smaller notch angle and shorter ligament lengths. Based on the 3D higher-order asymptotic solution, a new fracture parameter A2T is given and combined with Tz to characterize 3D constraint effect. It is noted that the effects of A2T and Tz on 3D constraint are highly interlinked rather than simply separated into in-plane and out-of-plane parts. The present 3D higher-order asymptotic solution can promote the understanding and characterization of 3D constraint effect and is of great significance in the evaluation of 3D fracture behavior and structural failure assessment under creep conditions.

Multifractal detrended fluctuation analysis on the fracture surface of polycarbonate and acrylonitrile-butadiene-styrene alloy

Multifractal detrended fluctuation analysis (MF-DFA) has been carried out to evaluate the multifractal properties of the fracture morphology for Polycarbonate (PC) and Acrylonitrile-butadiene-styrene (ABS) alloy, and the relationship between the long-range correlation parameter of the samples fracture - Hurst exponent and fractal dimension was explored and analyzed. The results suggest that the existence of multifractal properties within the micrometer scale domain we investigated for the fracture surface of PC/ABS alloy samples. The Hurst exponent and fractal dimension can both be used to measure and characterize the fracture surface morphology of the PC/ABS alloys. As the content of compatibilizer PP-g-MAH increased, the tensile strength of PC/ABS alloy decreased, the fracture surface peaks tend to dominate, the Hurst exponent increased, the fractal dimension decreased, and its strength retention rate increases, displaying persistence.

Compact-tension-shear specimen for orthotropic materials in fracture toughness testing

Conducting Compact-Tension-Shear (CTS) tests emerges as a promising research methodology to determine the fracture toughness of orthotropic materials in mixed-mode I&II. However, the absence of pertinent fracture parameter solutions incorporating material orthotropy impedes the further application and standardization of CTS testing. Therefore, this study performed a systematic two-dimensional finite element analysis (FEA) on orthotropic CTS specimens to evaluate critical fracture parameters, including the normalized stress intensity factors (YI, YII) and compliance (u). First, the impacts of three commonly cited boundary conditions (BCs) of CTS models were investigated, revealing that the simplified or equivalent methods developed for isotropic CTS models are no longer applicable. Subsequently, the suitable CTS models were used to analysis the coupling effects of material orthotropy (λ, ρ), crack length ratios (a/W), and loading angles (β). Findings indicated that YI or u no longer exhibit a monotonic relationship with respect to a/W or β under strong orthotropy. The impact of λ and ρ on fracture parameters is equally significant across different geometries and loading conditions. Further, the impact of orthotropy on YII is relatively small, while the more affected YI may have a difference compared to isotropic results of over 80%. Finally, CTS tests were carried out on the unidirectional carbon fiber-reinforced epoxy resin composite measuring the fracture toughness in mixed-modes I&II. The obtained fracture parameter solutions were applied and validated during the process. The acquired results are poised to contribute to the advancement of fracture toughness testing standardization for orthotropic materials under mixed-mode loading.

Experimental study on the updated optimization method for particle size distribution of lost circulation materials

The use of laboratory methods to simulate the process of plugging slurry sealing the fracture is an efficient and convenient method for Lost Circulation Materials (LCMs) selection and formula design. However, commonly used plugging evaluation devices have defects such as small-scale fractures and low reproducibility. To address these shortcomings, we applied a wellbore-fracture coupling plugging experimental device to simulate the process of plugging slurry extrusion. We processed a large-scale visualized fracture using Plexiglas based on the geometric parameters of the formation fracture, reproduced the undulation characteristics of the fracture surface using laser etching technology, and characterized the three-dimensional morphology characteristics of commonly used calcite, walnut shells, and flake polybutyl ester at the wellsite to carry out experiments on the transportation of LCMs under wellbore-fracture coupling conditions. The results indicate that the discrepancy between laboratory evaluation outcomes and field application practices, as well as the low success rate of single-attempt on-site plugging, can be primarily attributed to mouth sealing. The migration behavior of the LCMs is dictated by its morphological characteristics. A larger disparity among the three-axis diameters leads to increased irregularity in the LCM. Characterization of irregularity yielded the following results: walnut shell exhibits the highest irregularity, followed by flaky polybutene and calcite. Increased irregularity in the LCM corresponds to a heightened risk of mouth sealing. Entry into the fracture can only be guaranteed when the D90/Wf ratios for calcite, flaky polybutene, and walnut shell are less than or equal to 0.56, 0.42, and 0.39, respectively. The methods and findings presented in this study provide a scientific basis for selecting LCMs in fractured formations and explain the reasons for poor loss control and significant repetitive loss in wellsite practice.

Moving EMPS model for semipermeable two equal collinear interface cracks in dissimilar magneto-electro-elastic materials

The moving electric-magnetic polarization saturation (EMPS) model is studied for two equal collinear interface cracks in mode-III dissimilar magneto-electro-elastic (MEE) bimaterial under semipermeable crack face conditions. The closed-form solutions of all three possible cases of the proposed EMPS model are derived using the distributed dislocation technique (DDT) and singular integral method. An iterative scheme and explicit expressions of fracture parameters are used to implement the semipermeable crack-face conditions. The study of local energy release rate based on constant electric and magnetic breakdown strength-based saturated conditions concludes that increasing the mismatch of the MEE bimaterial can improve its fracture toughness.

Experimental and Numerical Investigation of the Fracture Behavior of Extruded Wood-Plastic Composites under Bending.

The ability of wood-plastic composites (WPCs) to withstand various loads and resist plastic failure is attracting more and more interest due to the global increase in demand for WPCs by over 6 million tons per year. Among the most important and innovative research methods are those based on fracture mechanics-their results enable material designers to optimize the structures of these hybrid polymer composites at the nano, micro and macro levels, and they allow engineers to more accurately evaluate and select functional, sustainable, long-lasting and safe product designs. In this study, standard single-edge notched bending (SENB) tests were used to analyze the fracture toughness of two different extruded WPCs along the longitudinal (L) and transverse (T) directions of extrusion. In addition to their resistance to crack propagation, critical fracture criteria, initial contact stiffness, fracture parameters and fracture surfaces, the mechanical properties of these composites were also investigated. The results showed that WPC-A coded composites withstood higher loads until failure in both directions compared to WPC-B. Despite the larger data spread, both types of composites were more resistant to crack propagation in the T direction. Mode II of crack propagation was clearly visible, while mode III was not as pronounced. The experimental results and the numerical finite element (FE) model developed up to 58% of the maximum load correlated well, and the obtained deformation curves were best approximated using cubic equations (R2 > 0.99). The shear stress zone and its location, as well as the distribution of the equivalent stresses, had a major influence on crack propagation in the fracture process zone (FZP).

Study on the Mechanism and Regulation Method of Longitudinal Penetration of Hydraulic Fractures in Multilayered Shale

Summary Shale reservoirs have longitudinally developed multilayered weak surfaces. The strong geological discontinuity and the stress heterogeneity caused by it lead to the complicated morphology of hydraulic fracture propagation, and the longitudinal propagation mechanism of the hydraulic fracture is still unclear. The extended finite element 3D numerical model of the single-cluster fracture and multicluster fracture extension has been established. The effects of vertical stress difference, bonding strength of bedding plane, fracturing fluid displacement, fracturing fluid viscosity, and cluster spacing on fracture propagation morphology are analyzed by numerical examples. The results show that as the vertical stress difference and the bonding strength of the bedding plane increase, the bedding plane becomes more difficult to activate, and the fractures are more likely to realize the longitudinal penetration. As the cluster spacing decreases, the interfracture interference becomes stronger, and the hydraulic fractures are more likely to activate the bedding plane and form the orthogonal network fracture. At a high injection rate, the fracture passes easily through the layer and activates the bedding plane. Low-viscosity fracturing fluid is conducive to the activation of the bedding plane, and high-viscosity fracturing fluid can better achieve fracture penetration. Based on the research results, the fracturing parameters of Well X-1 are optimized, and the fracture monitoring results are in good agreement with the design objectives. This study reveals the longitudinal penetration mechanism of multilayered shale hydraulic fractures and provides a reference for the optimization of hydraulic fracturing parameters of multilayered shale.

Geomechanical Response Characteristics of Different Sedimentary Hydrodynamic Cycles—Exampled by Xujiahe Formation of Upper Triassic, Western Sichuan Basin

This study delves into the geomechanical responses of different sedimentary hydrodynamic cycles in deep tight sandstone formations. Employing core observation and thin section analysis, we quantitatively identified and characterized bedding planes, sedimentary microfacies, and tectonic fractures. Then, the intricate relationships between various architectural interfaces and geomechanical parameters were elucidated. Subsequently, utilizing finite element numerical simulation software, in situ stress and fracture parameters were derived. By identifying a fracture facies zone correlated with the sedimentary hydrodynamic cycle and production data, our findings unveil several key insights: (1) Geomechanical parameters (Young’s modulus, Poisson’s ratio, brittleness index) exhibited noteworthy variations within the T3x2−5 sand group, indicative of weak elasticity and robust plasticity. (2) The effective distance, influenced by diverse reservoir architecture interfaces, displayed variability, with each transition between peak-valley-peak or valley-peak-valley pinpointed as a distinct sedimentary hydrodynamic cycle. (3) In environments characterized by strong sedimentary hydrodynamics (between two level 3 architecture interfaces), fractures with larger strike angles and lower dip angles were observed to be more prevalent. (4) Three significant fracture faces—level I, level II, and level III—were discerned within the study area. Notably, reservoirs associated with level III exhibited characteristics suggestive of medium porosity and permeability, indicative of a gas layer. By thoroughly understanding the geomechanical response characteristics of formations such as the Xujiahe Formation, it is possible to guide the exploration and development of energy resources such as oil and natural gas. This helps to improve the efficiency and safety of resource extraction, promoting the sustainable utilization of energy.

Simulation of Key Influencing Factors of Hydraulic Fracturing Fracture Propagation in a Shale Reservoir Based on the Displacement Discontinuity Method (DDM)

In the process of the large-scale hydraulic fracturing of a shale gas field in the Weiyuan area of Sichuan province, the quantitative description and evaluation of hydraulic fracture expansion morphology and the three-dimensional distribution law are the key points of evaluation of block fracturing transformation effect. Many scholars have used the finite element method, discrete element method, grid-free method and other numerical simulation methods to quantitatively characterize hydraulic fractures, but there are often the problems that the indoor physical simulation results are much different from the actual results and the accuracy of most quantitative studies is poor. Considering rock mechanics parameters and based on the displacement discontinuity method (DDM), a single-stage multi-cluster fracture propagation model of horizontal well was established. The effects of Young’s modulus, Poisson’s ratio, the in situ stress difference, the approximation angle, the perforation cluster number and the perforation spacing on the formation of complex fracture networks and on the geometrical parameters of hydraulic fractures were simulated. The research results can provide theoretical reference and practical guidance for the optimization of large-scale fracturing parameters and the quantitative post-fracturing evaluation of horizontal wells in unconventional reservoirs such as shale gas reservoirs.

Modelling the Charpy Impact Ductile-Brittle Transition of a Ship Plate Steel with CAFE Modelling

In the present work, a cellular automata finite element model (CAFE) was developed to model the ductile-brittle transition of a Grade A ship plate steel. Therefore, ductile and brittle cellular automata (CA) arrays of cells were created in the model to integrate material data at microstructural level, along with the ductile and brittle fracture processes. Microstructural data was analysed with Weibull distributions and incorporated in CAFE model using random number generators, along with ductile and brittle fracture parameters. Ductile fracture was modelled with Rousselier damage model; hence damage model parameters were calibrated with experimental data. Brittle fracture was modelled with Beremin model, and four different cleavage particles, found in a Grade A ship plate steel, were incorporated in CAFE model in order to model a competition of particles nucleating microcracks of critical size in the damage regions of Impact Charpy tests and four-point double-notch bend tests performed at low temperature. The mechanical properties the plate steel was measured in the transition region and incorporated in CAFE model, along with ductile-brittle transition rules. The present CAFE model was able to simulate distributions of microcracks in the notch region of four-point double-notch bend models (in the transition region), which correlated with experimental data. CAFE model was also able to simulate microvoids in the notch region of Charpy specimens along with the load-displacement Charpy curve for room test temperature, with very good agreement with experimental data. Once CAFE model was validated at micro and structural level, it was applied to model the typical scatter of impact Charpy energy values in the transition region of Grade A ship plate steel with good agreement with the measured ductile-brittle transition curved of the plate steel. Keywords: cellular automata, finite element modelling, ductile-brittle transition, damage modelling.

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.

Influences of clean fracturing fluid viscosity and horizontal in-situ stress difference on hydraulic fracture propagation and morphology in coal seam

The viscosity of fracturing fluid and in-situ stress difference are the two important factors that affect the hydraulic fracturing pressure and propagation morphology. In this study, raw coal was used to prepare coal samples for experiments, and clean fracturing fluid samples were prepared using CTAB surfactant. A series of hydraulic fracturing tests were conducted with an in-house developed triaxial hydraulic fracturing simulator and the fracturing process was monitored with an acoustic emission instrument to analyze the influences of fracturing fluid viscosity and horizontal in-situ stress difference on coal fracture propagation. The results show that the number of branched fractures decreased, the fracture pattern became simpler, the fractures width increased obviously, and the distribution of AE event points was concentrated with the increase of the fracturing fluid viscosity or the horizontal in-situ stress difference. The acoustic emission energy decreases with the increase of fracturing fluid viscosity and increases with the increase of horizontal in situ stress difference. The low viscosity clean fracturing fluid has strong elasticity and is easy to be compressed into the tip of fractures, resulting in complex fractures. The high viscosity clean fracturing fluids are the opposite. Our experimental results provide a reference and scientific basis for the design and optimization of field hydraulic fracturing parameters.

Interaction between microcapsules and crack using XFEM and data-driven fracture toughness predictive model

The interaction mechanism between microstructures of materials, including microcrack, inclusion and interface defect, is crucial for studying the microscopic damage of materials. The interaction between microcapsules and cracks in self-healing material is examined using a combination of the extended finite element method (XFEM) and the interaction integral method, which is implemented by a program written in Fortran language. The non-dimensional stress intensity factors (SIFs) of a crack with a single microcapsule, a pair of microcapsules and a cluster of microcapsules are investigated. Moreover, the data-driven fracture toughness predictive model using a genetic programming-based symbolic regression (SR) technique is proposed by training the data from the XFEM program. Results reveal that the non-dimensional SIFs are related to the mechanical property, geometry and interface defect of microcapsule. The influence of microcapsule on the SIF is limited within a distance of five times the microcapsule radius. The predictive model quantifies the contribution of microscopic structures on the macroscopic fracture parameter, highlighting the potential of machine learning in guiding the quantitative design and discovery of high-performance smart materials.

Novel semi-analytical model for solving the C*-integral of specimens with mode-I crack under various constraints

The energy rate line integral C* is an essential fracture parameter that characterizes the stress and strain rate field intensity at a crack tip for materials undergoing creep deformation, and is also a crucial parameter describing the creep crack growth rate. This study proposes a method for determining the characteristic parameters of the creep displacement rate model for specimens with mode-I crack under various constraints. Based on the displacement rate model, a semi-analytical model of the C*-integral related to the displacement rate, load, specimen sizes, and Norton's law parameters of materials is proposed. Furthermore, finite element analysis (FEA) models were established for compact tension (CT), single-edged notched bending (SEB), C-shaped tension (CST), and single-edge notched tension (SET) specimens, and the proposed models were verified using FEA results and those predicted by the ASTM method. The explicit correlation between the creep displacement rate and crack length a in the model can contribute to developing novel testing methods for real-time crack length and creep crack growth rate.

Strip electro-mechanical yield model for three equal straight collinear cracks in piezoelectric materials

This paper is devoted to the development of a model to study three straight collinear cracks in piezoelectric materials under the influence of combined electrical and mechanical loading conditions. Mathematical relationships for the size of yield zones with mechanical yielding conditions and the saturation zone sizes to applied electrical field has been established. To make this plausible, two different cases are considered: first when the electrical saturation zones are bigger than the mechanical yield zones while other case in which situation is just opposite. Closed-form analytic expressions are derived for various fracture parameters with the help of well known complex variable method. Numerical results are presented to study the multiple cracks in different piezoelectric materials. Results obtained are reported graphically, analyzed and concluded.

A Practical probabilistic history matching framework for characterizing fracture network parameters of shale gas reservoirs

Simulating fluid flow in complex fracture systems encountered in subsurface systems, such as those encountered in tight or shale gas reservoirs, presents considerable challenges. Sophisticated numerical techniques and characterization approaches are required to integrate static and dynamic data from multiple sources to account for the intricate interplay between fractures and the surrounding rock matrix. A novel workflow using an indicator-based probability perturbation method (PPM) is applied to characterize uncertain discrete fracture network parameters. The posterior probability distributions of primary and secondary fracture transmissivity, aperture, length, height, and intensity of the secondary fracture are estimated according to the production (flow) histories. A case study based on the Horn River shale gas reservoir is presented. A pilot point scheme is formulated to update the distributions of P32L. The forward modelling entails upscaling each fracture model into a dual-porosity dual-permeability model and performing multiphase flow simulation. This approach produces an ensemble of history-matched discrete fracture and upscaled models by incorporating static and dynamic data. The results demonstrate the utility of the developed method for estimating secondary fracture parameters, which are not inferrable from other static information alone. The inference of both primary and secondary fractures offers a more comprehensive characterization of the fracture networks in tight or shale gas reservoirs. Integrating a pilot point parameterization technique and a sequential simulation approach into the PPM framework presents significant novelties in contributing to a comprehensive and effective method of simulating fluid flow in complex fracture systems, addressing the challenges associated with non-linear relationships between fracture model parameters and the corresponding flow response.

Investigating the influence of various three-point bending specimen configurations on rock fracture parameters testing: an experimental study

The fracture parameters of rocks, including fracture toughness and fracture energy, represent their resistance to crack propagation under external stress. These parameters play a critical role in engineering design, construction safety, geological mechanics research, and rock material assessment. This study determined the fracture parameters of granite under Mode I loading conditions using notched semicircular bend (NSCB) and single-edge notched beam (SENB) specimens. Although there was little difference between the initial and unstable fracture toughness values of the two specimen configurations, significant differences were observed in the fracture process and other fracture parameters. For example, the NSCB specimen exhibits a higher elastic modulus, and it witnessed rapid failure after reaching the peak load, whereas the SENB specimen displayed a more gradual failure process with a distinct post-peak stage. This may be one of the reasons for the higher fracture energy in the NSCB specimen than in the SENB specimen. Based on finite element analysis and the extraction of the tangential stress at the crack tip region, the application of the maximum tangential stress fracture criterion provided a robust explanation for the coherence observed in the unstable fracture toughness test results between the two specimen configurations.

The microscopic fracture model for determining the fracture behavior of self-compacting lightweight concrete

The fracture toughness (KIC) and tensile strength (ft) of concrete are critical parameters governing crack resistance. Concrete usually exhibits brittleness under flexure and tension, so this brittle fracture first occurs at the micro level. Many researchers have studied its fracture properties at the micro level. However, the theoretical model and calculation formulae do not reflect the influence of micro-material parameters on the corresponding fracture properties. In this paper, the microscopic fracture model of self-compacting lightweight aggregate concrete (SCLC) was developed, considering the parameters of micro-nano silica materials. First, the characteristic parameters, such as particle size, specific surface area, and unit weight of micro silica (MS) and colloidal nano-silica (CNS), were considered, and the calculation equation for fictitious crack growth length was proposed. Then, the micro-fracture model was developed, which was further used to calculate the fracture parameters KIC and ft of SCLC incorporated with micro-nano silica. The results are found to be consistent with the fracture parameters determined by the size effect model. In addition, the failure curves of different structural fracture modes of SCLC were established through the fracture parameters KIC and ft obtained from the microscopic fracture model, and the fracture modes of SCLC incorporated with MS and CNS were identified. The peak load of the minimum specimen size satisfying linear elastic fracture was also predicted. This research provides a new perspective for evaluating concrete fracture parameters, realizes the progressive prediction of concrete fracture performance from macro to micro, and fills in the research gaps in the existing knowledge base on the synergistic effect of MS and CNS to enhance the fracture performance of SCLC.

Ductile fracture of tubular specimens under non-proportional loading condition

The ductile fracture behaviours of two tubular specimens, a AA6260-T4 macrotube (60 mm diameter and 2 mm thickness), and a SS-304L microtube (2.38 mm diameter and 0.15 mm thickness) under non-proportional loading condition are studied using a combined experimental-numerical approach. The experiments are conducted by loading the tubes under axial force and internal pressure along various non-proportional (i.e., corner) paths until failure by controlling the force/pressure ratio. The plastic behaviours of the tubes are characterized using the non-quadratic anisotropic yield criteria Yld2000-2D and Yld2004-3D. The material models are employed in the finite element (FE) simulation of the tube experiments using Abaqus/Standard (implicit). The FE models, which include thickness imperfection to capture the failure modes observed in the experiments, are then used to probe the fracture parameters inside the tube wall where fracture is likely to initiate. It is observed that the fracture strains from the non-proportional loading results are noticeably different when introduced to the proportional fracture strains, revealing the path-dependence fracture behaviour in tubular specimens.