Fracture Process Research Articles

The length of fracture process zone deciphers variations of rock tensile strength

Tensile strength is one of the most critical design factors in many rock engineering projects. However, despite many available testing techniques, an accurate estimation of the true tensile strength of quasi-brittle rock-like materials is yet a controversial problem since it can vary by the shape and size of a test specimen, the adopted test method, and applied loading conditions. Different studies have tried to address this issue by providing (mainly empirical) laws for determining variations of rock tensile strength as a function of a particular test parameter such as specimen size. In this study, however, a new general approach is presented that can decipher the tensile strength variations of rock under various testing conditions. Using coupled Finite Fracture Mechanics (FFM), it is first proved that the length of the Fracture Process Zone (FPZ) can be determined with accuracy and ease using the energy criterion of coupled FFM. Then, the length of FPZ is used in the stress criterion of coupled FFM to determine rock tensile strength. The failure stress of a material is then proved to be mainly a function of the FPZ length following a power law originated from the Linear Elastic Fracture Mechanics (LEFM). The results assist in deciphering variations of rock tensile strength related to the sample size and test method.

Enhancing flexible electronics: Unveiling the role of strain rate in the performance of molybdenum-coated PET films

This work analyzes the mechanical and electrical properties of molybdenum (Mo) thin films at 100 and 200 nm thicknesses under different strain and strain rate circumstances. The study examines Mo film deposition by RF magnetron sputtering on PET substrates and their mechanical stress behavior. The investigation reveals distinct patterns of crack initiation and propagation, where primary cracks predominantly appear perpendicular to the direction of applied strain, and secondary cracks develop due to stress redistribution, displaying a complex interplay between film thickness, strain rate, and crack morphology. A key finding of this study is the observation of more advanced and irregular crack patterns in thicker films (200 nm) subjected to higher strain rates (1000 mm/min), suggesting a heightened sensitivity to mechanical stress and a more chaotic fracture process compared to thinner films or those under lower strain rates. Additionally, instances of film edge delamination, particularly under high strain conditions, highlight the challenges in maintaining film-substrate adhesion and integrity under extreme mechanical deformation. The research provides critical insights into the mechanical robustness and electrical performance of Mo thin films, emphasizing the influence of microstructural properties, deposition parameters, and external stressors on their applicability in high-tech industries. The findings underscore the importance of optimizing deposition techniques and understanding material behavior under stress to enhance the durability and reliability of Mo thin films in practical applications, ranging from semiconductor devices to photovoltaic systems.

Fracture properties and acoustic emission characteristics of manufactured sand recycled fine aggregate concrete

To promote the application of recycled fine aggregates, fracture characteristics of concrete beams containing manufactured sand (MS) and recycled fine aggregate (RFA) were investigated. The fracture properties and acoustic emission (AE) characteristics of manufactured sand recycled fine aggregate concrete (MSRFAC) with 0 %, 25 %, 50 %, 75 % and 100 % RFA replacement rates were evaluated by three-point bending test of single-sided notched beams. The fracture mechanisms of MSRFAC beams were explored using AE and digital image correlation (DIC) techniques, and fracture process zone (FPZ) was qualitatively and quantitatively analyzed. The results indicated that the critical nominal stiffness, initial fracture toughness, fracture energy and characteristic length of MSRFAC decreased significantly with the increase of RFA replacement rate, up to 20.2 %, 37.7 %, 22.8 %, and 26.6 %, respectively, while the unstable fracture toughness was insensitive to the variation of RFA. Moreover, the AE activity, the tensile crack, large-scale crack, high amplitude, and high peak frequency in MSRFAC increased with increasing RFA replacement rate. According to the FPZ characteristics of MSRFAC, its FPZ length increased with the increase of RFA replacement rate, while the FPZ width decreased with the increase of RFA replacement rate. The critical FPZ lengths of MSRFAC with different RFA replacement rates were about 20.2–30.0 mm, and the maximum FPZ widths were about 26.0–36.7 mm. The RFA weakened the friction mechanism and interlocking effect between aggregates of MSRFAC, resulting in a faster FPZ propagation rate and smaller damage width of MSRFAC than normal manufactured sand concrete.

Permeability evolution of granite under cyclic hydraulic fracturing and its deterioration during in-situ stress retention in geothermal engineering

Hot Dry Rock (HDR) geothermal resources are a promising source of renewable energy with significant exploitation potential. HDR is typically exist at depths exceeding 2500 m, which presents challenges in terms of high in-situ stress and low permeability of the rock. To overcome these challenges and reduce the risk of fracking induced earthquakes, a scheme for cycling fluid injection has been proposed. In addition, the influence of geo-stress on the re-closure of rock fractures, as well as its effect on granite permeability, are important considerations in HDR exploitation. To study this, the GCTS triaxial testing system has been modified to simulate the hydraulic fracturing process of the deep hot rock reservoir, and permeability tests were conducted simultaneously. A protocol-cyclic fluid injection has been applied to fracture granite specimens under various fluid pressures. The results of the experiments showed that the permeability of the rock was significantly improved after fracturing, with an increase of 1–2 orders of magnitude compared to before. Cyclic hydraulic fracturing techniques can significantly reduce the granite breakthrough pressure and create more complex fracture networks. The permeability of the specimens displayed a decreasing trend during stress retention and tended to stabilize at around 1000 min. The maximum decrease was 90 %, which highlights the importance of considering the impact of stress aging on permeability in engineering. Additionally, the axial and radial strains of the specimens also decreased during stress retention. The mechanism for the change in rock permeability was attributed to the closure of newly formed fractures from hydraulic fracturing. Moreover, the experiments also showed that the smaller the injection fluid pressure, the faster the permeability of the specimens stabilized after fracturing. These findings can provide a theoretical basis for the effect of stress aging on granite permeability and offer reference for secondary fracturing time intervals in practical engineering applications.

Study on crack propagation behaviors of three-point bending concrete beams with small span-depth ratios

Three-point bending (TPB) beams with small span-depth ratios, i.e. TPB beams with the same span of 400 mm but various depths (100 mm, 150 mm and 200 mm), were tested to study the crack propagation behaviors of concrete. The evaluations of crack extension resistance curve (KR-curve), fracture process zone (FPZ) length, lFPZ, and crack tip opening displacement (CTOD) were studied. The digital image correlation (DIC) technique was utilized to monitor the entire loading process. Moreover, the effects of strain rates (10−5/s, 10−4/s, 10−3/s and 10−2/s) on the fracture process of TPB beams with small span-depth ratios (2, 2.5 and 3) were discussed based on findings in literature. The results shown that (1) with the increase of specimen depth from 100 mm to 200 mm, the obtained KR-curves and initial fracture toughness were not influenced by the small span-depth ratios, while different increase trends were observed for the unstable fracture toughness, the average maximum value of lFPZ and the value of CTOD. (2) With the loading rate increasing from 10−5/s to 10−2/s, the obtained KR-curve and the maximum length of FPZ increased slightly, while the evolution of CTOD was not affected by the loading rate.

Influence of processing parameters on the fracture behaviour of 316L SS printed by laser powder bed fusion

This study explored the relationship between process parameters and fracture behavior in 316L stainless steel printed by laser powder bed fusion. Fracture testing was conducted according to ASTM E1820 for single edge notch bending, and elastic mechanical properties were determined using ultrasonic surface wave analysis. Five test sets were considered in a vertical building configuration using five different volumetric energies belonging to conduction mode. The critical fracture toughness was calculated and discussed along with the plastic deformations at the crack tip. The study found that local plastic deformation for single edge notch bending was influenced by powder bed fusion process parameters. A correlation was observed between energy density, fracture toughness, and the dimensions of the fracture process zone. The R-curves showed different fracture behaviors depending on the energy density. The energy required to grow a crack was associated with larger plastic zones, resulting in fracture toughness values ranging from 43 (43 J mm−3) to 427 kJ/m2 (68 J mm−3). Results are discussed in terms of porosity and strain hardening capacity depending on the manufacturing conditions.

A nonlinear elastic-plastic model describing the bending and fracture behavior of Caragana korshinskii Kom. branch wood

ABSTRACT Caragana korshinskii Kom. branch (CKB), a vital biomass source in northwest China, has not been thoroughly studied in terms of its bending fracture mechanics. This research aims to establish a nonlinear constitutive model that clarifies the fracture behavior of CKB when subjected to bending loads. The nonlinear bending fracture process of CKB was characterized through a three-point bending test, revealing stages of elastic deformation, elastic-plastic transition, and plastic fracture. A power-enhanced elastic-plastic model combined with continuous damage mechanics theory was used to develop an intrinsic bending fracture model, from which the equations governing bending damage evolution were derived. The model's accuracy was validated with simulations in Abaqus/Explicit, showing that CKB from various growth sites demonstrated distinct nonlinear bending behaviors. At the critical damage strain, cumulative damage led to a reduction in the effective elastic modulus, with the bending fracture curve exhibiting a power function trend. The parameters of the nonlinear elastic-plastic constitutive model were derived through curve fitting, yielding coefficients of determination (R²) exceeding 0.99. The consistency between the trends observed in actual tests and simulations, along with a peak bending force error of 7.7%, validated the finite element model's reliability and confirmed the intrinsic model's accuracy.

Comprehensive research on the correlation between microstructure and mechanical properties of polyacrylonitrile‐based precursor fibers prepared by wet‐spinning

AbstractPolyacrylonitrile (PAN)‐based precursor fibers with different mechanical properties prepared by wet‐spinning and its correlation with microstructure was researched, the primary structural factors that affecting its properties were analyzed. The tensile strength and modulus of precursor fibers increased from 4.63 cN/dtex to 9.16 cN/dtex and 99.09 cN/dtex to 168.92 cN/dtex, respectively, with the increase in crystallinity from 69.29% to 87.84% and orientation degree increased from 83.95% to 93.81%, high performance precursor fibers could be achieved by decrease in the crystallite size and interlayer spacing, these aggregation structure plays a decisive role to the mechanical properties of fibers. The integrality of aggregation structure and properties could reflected by boiling water shrinkage behavior and glass transition temperature from the side. The fracture morphology of fibers with different properties were studied by scanning electron microscope (SEM) and three fracture characteristics were observed, PF1 and PF3 presented the radial extended fracture without microfibril pull out, radial cluster fracture with the pull out of microfibril for PF2, PF4–PF6, together with the axial splitting pattern in PF6, which was revealed by microfibrils/fibrils in longitudinal and transverse combined with solution etching. Precursor fibers with less voids, without serious skin‐core, continuous arrangement, tightly stacked, well‐developed and complete oriented microfibrils/fibrils, exhibited excellent mechanical properties. Possible fracture process was given from the perspective of aggregation structure and microfibrils/fibrils, which become dominant factors determining properties of precursor fibers. Improve the performance could be achieved by regulating surface structure and cross‐sectional shape. As one of the main structural factors that determining properties, by reducing diameter could minimize the numbers and sizes of defects.

Study on crack initiation mechanism of notched TC4 titanium alloy plate based on acoustic emission information entropy

ABSTRACT Titanium alloys are widely used in high-end manufacturing fields such as aerospace and nuclear energy due to their excellent mechanical properties and corrosion resistance, but it is prone to cracking under load, seriously affecting its performance and safety. Therefore, studying the crack initiation process of titanium alloys is of great significance for improving their service life and safety. In this study, TC4 titanium alloy material is taken as the research object, and the crack emergence mechanism during its tensile fracture process is investigated by combining tensile test and AE test. The experiments were carried out under displacement-controlled conditions, and crack emergence detection was carried out by two methods: AE characterisation parameters and AE information entropy, and SEM was used to observe and analyse the specimen fracture. The results indicate that the AE characteristic parameters of different notched specimens have the same evolution pattern, and this method can be used to predict crack initiation, but there is a certain degree of uncertainty. Compared with the former, the information entropy theory can more accurately predict crack initiation. Therefore, the analysis of the entropy of AE information can be used as a highly practical real-time condition detection method to provide effective detection means for engineering applications.

Scratch-induced micro-fracture behaviour and translational failure of glass: An experimental and numerical study

The structural safety of aged glass members shows significant sensitivity to surface scratches. The distribution and geometrical features of scratch impacts the glass fracturing. In this study, the fracture behaviour of scratched thin glass pane was investigated by the ordinary state-based peridynamic (OSB-PD) theory. Coaxial double ring test was first conducted to identify the mechanical and fracture behaviour of scratched glass plates that serve as the benchmark. The applicability of simplifying and reconstructing the actual scratches in numerical models was then examined. The refined three-dimensional fracture process from micro-crack coalescence to macro-propagation of featured cracks can be well described by the developed PD model. The propagation of in-plane radial cracks was found prior to median cracks along the thickness for scratched glass. Crack branch was observed due to shallow scratch depth and the primary crack branching point lies near the edge of the scratch. The transition from scratch-induced failure to strength-induced failure due to particular scratch spatial location was also tackled, which benefits the accurate performance assessment of scratched glass.

Understanding Toughening Mechanisms and Damage Behavior in Hybrid-Fiber-Modified Mixtures Using Digital Imaging

Pavement cracking is a primary cause of early damage in asphalt pavements, and fiber-reinforcement technology is an effective method for enhancing the anti-cracking performance of pavement mixtures. However, due to the multi-scale dispersed structure of pavement mixtures, it is challenging to address cracking and damage with a single fiber type or fibers of the same scale. To investigate the toughening mechanisms and damage behavior of hybrid-fiber-modified mixtures, we analyzed the fracture process and damage behavior of these mixtures using a combination of basalt fiber and calcium sulfate whisker hybrid fiber modification, along with semicircular bending tests. Additionally, digital imaging was employed to examine the fracture interface characteristics, revealing the toughening mechanisms at play. The results demonstrated that basalt fibers effectively broaden the toughness range of the modified mixture at the same temperature, reduce mixture stiffness, increase residual load at the same displacement, and improve crack resistance in the mixture matrix. While calcium sulfate whiskers enhanced the peak load of the mixture, their high stiffness modulus was found to be detrimental to the mixture’s crack toughness. The fracture interface analysis indicated that the three-dimensionally distributed fibers form a spatial network within the mixture, restricting the relative movement of cement and aggregate, delaying crack propagation, and significantly improving the overall crack resistance of the mixture.

A 3D coupled numerical simulation of energised fracturing with CO2: Impact of CO2 phase on fracturing process

Engineered fractures play a critical role in enhancing energy extraction efficiency. In this study, energised fracturing with CO2, as an alternative approach to conventional water-based hydraulic fracturing, is investigated via numerical simulations. We validated the CO2 finite element-based fracturing model against analytical as well as CO2-fracturing laboratory experiments, then utilised the model to investigate the effects of pressure-temperature dependent properties of CO2 on energised fracturing process. To account for the temperatures expected in a real field, four cases with injection temperatures of CO2 varying between 250 K and 350K, under both isothermal and adiabatic conditions have been considered. In the adiabatic conditions, the temperature variation during compression of CO2 is captured using the Joule-Thompson coefficient, assuming no thermal exchange between the CO2 and the surrounding medium. The results highlight the significant influence of CO2 phase on the fracturing process, during the pressurisation stage, as well as post-breakdown, the speed of fracture growth after the breakdown and subsequent depressurisation and associated cooling of CO2. In the designed cases, the phase-change from gas to liquid or supercritical occurs during the pressurisation and prior to breakdown, while the phase remains unchanged post breakdown and during fracture propagation. Liquid CO2 presents a fast-pressurising process while gaseous CO2 undergoes a lengthy compression stage. Supercritical CO2 is the best performing as the pressurisation is not too lengthy, while the instantaneous post breakdown fracturing is significant. Results show that higher temperature of supercritical CO2 is causing larger instantaneous fracture propagation as it has lower viscosity for the given in situ stresses (>10 MPa).

Experimental study on evaluating fracture processes of different rocks using multiple physical parameters

To improve the accuracy of rock fracture evaluation, three types of rocks with different lithologies, namely, granite, coal, and sandstone, were processed into cuboid samples with unilateral notches for three-point bending tests. Real-time data were obtained via load, resistance, and acoustic emission (AE) monitoring. Various fracture patterns of the fractured rocks were collected, and the correlations between multiple physical parameters were determined. The results indicated that granite had the highest fracture toughness and initial fracture energy required for macroscopic fracturing, followed by sandstone, which had the lowest fracture toughness and initial fracture energy. The primary crack participated in the fracture process of coal and produced the most complex crack morphology, exhibiting the characteristics of “Progressive fracture” different from the “Instantaneous fracture” of granite and sandstone. The crack length reached 90.5 mm, which was much longer than that of sandstone. The temporal characteristics obtained from multiple physical quantities were synchronized with the fracture behavior. The resistivity increased gradually with the fracture, and the resistivity fluctuation caused by crack propagation increased. The resistivity change rate of granite was the highest when macrofractures occurred, whereas that of coal after complete fracture was the highest. Rock fracture produced a large number of AE events with small amplitude and low peak frequency, concentrated in the 100 ± 50 kHz band. The AE count corresponded to the crack propagation process, and the AE location indicated the crack complexity. The peak change rate of the resistivity was used to evaluate the fracture performance and exhibited a significant linear relationship with the peak load, fracture toughness, and initial fracture energy. The relationship between the accumulated AE energy and the fracture length was a quadratic function, which was used to evaluate the fracture complexity. The multiple physical quantity monitoring method is promising for predicting the fracture behavior of rocks.

Simulation Analysis of Three-Point Bending Fracture Process of Yellow River Ice

During the ice flood period of the Yellow River, the fracture and destruction of river ice can easily lead to the formation of ice jams and ice dams in the curved and narrow reaches. However, the occurrence and development mechanism of river ice fracture remain incompletely understood in the Yellow River. Therefore, based on the three-point bending physical test of the Yellow River ice, a three-point bending fracture numerical model of the Yellow River ice was constructed. The fracture failure process of the Yellow River ice under three-point bending was simulated, and the effects of the crack-to-height ratio and ice grain size on the fracture properties of the river ice were analyzed. By comparing the results with those of physical tests on river ice, it is evident that the fracture model can effectively simulate the cracking process of river ice. Within the confines of the simulated sample size spectrum, as the crack-to-height ratio varies from 0.2 to 0.8, the fracture toughness value of the Yellow River ice spans a range from 115.01 to 143.37 KPa·m1/2. Correspondingly, within the simulated calculation values ranging from 5.38 mm to 24.07 mm for ice crystal size, the fracture toughness value of the Yellow River ice exhibits a range from 116.89 to 143.37 KPa·m1/2. The findings reveal that an increase in the crack-to-depth ratio leads to a decrement in the fracture toughness of river ice. Within the scale range encompassed by the model calculations, as the average size of the ice crystal grains augments, the fracture toughness of the river ice exhibits a gradual ascending trend. The research results provide a parameter basis for studying the fracture performance of the Yellow River ice using a numerical simulation method and lays a foundation for investigating the cracking process of river ice from macro and micro multi-scales.

Mechanical response and failure mechanism of circular inclusion embedded in brittle materials under dynamic impact

Inclusions are prevalent in both natural and synthetic materials. Gaining a comprehensive understanding of their dynamic response and interaction with the surrounding matrix is essential in fundamental mechanics and engineering applications. This study aims to achieve such understanding through theoretical analysis, experimental investigations, and numerical simulations, focusing on the dynamic destruction of inclusions and the underlying mechanisms. Firstly, the circumferential, radial, and shear stresses around elastic heterogeneous inclusions were derived by the wave function expansion and Duhamel integration methods. Subsequently, a set of experiments on sandstone specimens containing three types of inclusions (plaster, epoxy resin, cement) were conducted utilizing the Split Hopkinson Pressure Bar (SHPB) system in conjunction with high-speed photography and Digital Image Correlation (DIC) techniques to obtain the surface deformation of inclusion specimens. Eventually, a series of Finite Element Method (FEM) numerical simulations adopted suitable materials were also carried out to investigate the fracture process of inclusion and matrix under dynamic impact. The results demonstrate that the stress distributions and fracture mode of matrix and inclusion are highly dependent on the physical and mechanical properties of the inclusions and the surrounding matrix, specifically, density ρ, elastic modulus E, Poisson's ratio v, and strength. With an increase in the E and v, there is a reduction in the concentration of circumferential stress, while the radial and shear stresses experience an increase. The experimental and numerical results corroborated the theoretical findings and indicated that the localized dynamic stress concentrations induced by wave scattering around the inclusions directly dominated both local and overall specimen failure. Due to the dissimilarities in elastic parameters and strength between the inclusion and the matrix, the stress state of the inclusion and the interface is not homogeneous. Under dynamic loading, the weaker inclusion experiences tensile cracking at both ends of the loading, and as the mechanical properties (ρ, E, v, and strength) of the inclusion rise, a transition from tensile- hybrid-shear failure occurs within the inclusion. The findings of this study help us understand the dynamic failure mechanisms of dissimilar inclusions in brittle material.

Mitigation of Fracturing Fluid Leak-Off and Subsequent Formation Damage Caused by Coal Fine Invasion in Fractures: An Experimental Study

During the hydraulic fracturing process of coalbed methane (CBM) reservoirs, significant amounts of secondary coal fines are generated due to proppant grinding and crack propagation, which migrate with the fracturing fluid into surrounding fracture systems. To investigate whether coal fines can form plugs to reduce fluid leak-off during the hydraulic fracturing stage, we conducted physical simulation experiments on coal seam plugging and unplugging to demonstrate that coal fines indeed contribute to reducing fluid leak-off during hydraulic fracturing. We also explored the plugging mechanisms of coal fines under different concentrations and particle sizes in fracturing fluids, and revealed the damage law of coal fines of temporary plugging on reservoir permeability. Research results indicate the leak-off volume of fracturing fluids containing coal fines is lower than an order without coal fines, demonstrating a significant effect of coal fines in decreasing fluid leak-off. The temporary plugging rate of coal fines increases with higher concentrations and decreases with larger particle sizes, achieving rates exceeding 90%. The high temporary plugging effect of coal fines results from the superposition of internal and external filter cakes. Under conditions of small particle size and high concentration, the damage to fractures during the fine return process is minimized. Considering the potential damage of coal fines to propping fractures and wellbore, the concentration of coal fines in fracturing fluids should be kept relatively low while ensuring a high temporary plugging effect. Overall, these findings provide crucial insights into optimizing the temporary plugging performance of coal fines during the hydraulic fracturing stage and controlling their behavior during the fracturing fluid flow-back stage, thereby enhancing reservoir fracturing effectiveness and improving CBM production rates.

Cracking Behavior of Environmental Barrier Coatings/CMC System Using Acoustic Emission and Digital Image Correlation

Abstract An investigation into the cracking behavior of advanced environmental barrier coating / woven SiC/SiC ceramic matrix composite (CMC) system under uniaxial tension testing was performed in this study. The effect of substrate (CMC) condition on the coating behavior was also studied. Acoustic emission (AE) and digital image correlation (DIC) were implemented as health monitoring techniques to gain detailed insights into the fracture process of the coating and to identify the origin and location of the fracture events. Fluorescent penetrant inspection was used in-situ in some cases to help identify cracks. Post-test microscopy was performed to correlate the results with DIC and AE. It was evident that for the as-produced woven substrate, the EBC coating cracked prior to substrate cracking; however, for the altered surface substrate, the CMC substrate formed matrix cracks prior to the EBC coating.

The influence of temperatures on the mechanical properties and fracture behavior of rocks under mixed mode I/II loading

A comprehensive understanding of the fracture behavior of pre-heated rocks under to mixed mode I/II loading is crucial for deep underground engineering. The effect of high temperature on the fracture process zone (FPZ) and fracture toughness of rocks was experimentally investigated using semi-circular bend (SCB) samples. Surface displacement and associated strain field under loading were captured using digital image correlation. The results showed that the mechanical properties of SCB samples gradually decreased with increasing temperature. Rocks exposed at temperature exceeding 600 °C demonstrated a significant reduction in peak load, generalized stiffness, fracture toughness, and absorbed energy. Moreover, the load–displacement curves and macroscopic fracture characteristics of pre-heated SCB samples revealed a transition from brittleness to ductility with increasing temperature under mixed mode I/II loading. Both the length and width, as well as the crack tip opening displacement of the FPZ, increased with rising temperature. At lower temperatures (25 ∼ 400 °C), the ratio of FPZ length to width typically ranged between 2 and 3. While, at elevated temperature (600 ∼ 1000 °C), this ratio expanded to between 3 and 4. The initiation of thermally induced cracks in rocks will accelerate damage evolution under mixed mode I/II loading, as indicated by the development of the maximum principal strain with displacement. Scanning electron microscopy and polarization microscopy images of the microscopic fracture morphology in pre-heated rocks illustrated isolated and dispersed microcracks appeared at lower temperatures, whereas at elevated temperatures, intricate microcrack networks and broken grains were observed.

Numerical study of the influence of the parameters of statistical distribution of the structural elements’ ultimate strength on deformable bodies’ fracture processes

This work is dedicated to the numerical study of the influence of the parameters of statistical distribution of the structural elements’ ultimate strength on fracture processes of deformable bodies with stress concentrators. The loading diagrams, the macro level behavior and the damaging process kinetics have been studied using various probability distribution laws and their standard deviations. The main types of the damage accumulation process have been identified. The approach basing on the analysis of the solutions of the boundary value problems within the elasticity theory has been proposed in order to predict the fracture process kinetics, the corresponding parameters have been introduced. Advantages, limitations and potential practical use of the proposed methodology have been discussed. It has been concluded that the statistical distribution of the structural elements’ strength properties should be taken into account in the numerical modeling of the fracture processes to ensure the reliability and safety of critical structures.

Fracture Evolution during CO2 Fracturing in Unconventional Formations: A Simulation Study Using the Phase Field Method

With the introduction of China’s “dual carbon” goals, CO2 is increasingly valued as a resource and is being utilized in unconventional oil and gas development. Its application in fracturing operations shows promising prospects, enabling efficient extraction of oil and gas while facilitating carbon sequestration. The process of reservoir stimulation using CO2 fracturing is complex, involving coupled phenomena such as temperature variations, fluid behavior, and rock mechanics. Currently, numerous scholars have conducted fracturing experiments to explore the mechanisms of supercritical CO2 (SC-CO2)-induced fractures in relatively deep formations. However, there is relatively limited numerical simulation research on the coupling processes involved in CO2 fracturing. Some simulation studies have simplified reservoir and operational parameters, indicating a need for further exploration into the multi-field coupling mechanisms of CO2 fracturing. In this study, a coupled thermo-hydro-mechanical fracturing model considering the CO2 properties and heat transfer characteristics was developed using the phase field method. The multi-field coupling characteristics of hydraulic fracturing with water and SC-CO2 are compared, and the effects of different geological parameters (such as in situ stress) and engineering parameters (such as the injection rate) on fracturing performance in tight reservoirs were investigated. The simulation results validate the conclusion that CO2, especially in its supercritical state, effectively reduces reservoir breakdown pressures and induces relatively complex fractures compared with water fracturing. During CO2 injection, heat transfer between the fluid and rock creates a thermal transition zone near the wellbore, beyond which the reservoir temperature remains relatively unchanged. Larger temperature differentials between the injected CO2 fluid and the formation result in more complicated fracture patterns due to thermal stress effects. With a CO2 injection, the displacement field of the formation deviated asymmetrically and changed abruptly when the fracture formed. As the in situ stress difference increased, the morphology of the SC-CO2-induced fractures tended to become simpler, and conversely, the fracture presented a complicated distribution. Furthermore, with an increasing injection rate of CO2, the fractures exhibited a greater width and extended over longer distances, which are more conducive to reservoir volumetric enhancement. The findings of this study validate the authenticity of previous experimental results, and it analyzed fracture evolution through the multi-field coupling process of CO2 fracturing, thereby enhancing theoretical understanding and laying a foundational basis for the application of this technology.