Size Of Fracture Process Zone Research Articles

Employing Williams’ series for the identification of fracture mechanics parameters from phase-field simulations

Fracture mechanics and damage mechanics are two theories that describe the degradation of the bearing capacity of structures. Fracture mechanics is based on a discontinuous description of cracking, while damage mechanics proposes a continuous description of material degradation. These two approaches are often opposed in the literature, from both theoretical and numerical points of view. This work suggests correlating the two approaches by applying Williams’ series, usually dedicated to experimental results, to phase-field computations. Williams’ series are employed to extract equivalent fracture mechanics parameters as a post-processing step. The proposed analysis based on a fracture mechanics description excludes the fracture process zone. Typical fracture mechanics parameters such as energy release rate, stress intensity factors, fracture process zone size, and crack tip position are determined from the phase-field computations. The approach is illustrated on a two-dimensional structure representing a beam whose notch opening displacement is controlled. The dependence on the choice of the internal length of the phase-field model is studied. Similarities and differences between both modeling routes are discussed.

Effect of size and anisotropy on fracture process zone of coal: An experiment and numerical simulation

The size and properties of the fracture process zone (FPZ) have a significant impact on the fracture toughness of materials. Researching and understanding the characteristics of FPZ contribute to optimizing material performance and enhancing the reliability of engineering structures. In this study, the newly proposed modified semi circular bending (SCB) test method was used to carry out the pure mode I fracture test of coal samples with four sizes and four bedding angles, the development process of FPZ was obtained by using digital image correlation method, and the cohesive zone model considering the bedding plane was established. The influence of size and anisotropy on the development and size of FPZ was studied, and the influence mechanism of FPZ on the size effect and anisotropy of fracture toughness was revealed. The results show that the FPZ length of coal has obvious size effect and anisotropy. The FPZ length increases with the increasing specimen size, and increases first and then decreases with the increasing bedding angle. The FPZ relative length decreases with increasing specimen size, indicating that as the specimen size increases, the influence of specimen boundaries on PFZ gradually decreases, and the size effect of fracture toughness also gradually weakens. The competition between microcrack development driven by principal stress and microcrack development driven by bedding plane results in anisotropy in the development process of FPZ. The anisotropy of FPZ development process results in the anisotropy of FPZ length, fracture toughness and crack propagation path. The research findings can provide valuable guidance for the design of hydraulic fracturing in coal seams.

Improved size effect law (SEL) considering size-dependent fracture process zone (FPZ) for quasi-brittle materials

Establishing a mechanistic model to simultaneously capture the descending size effect (DSE) and the change from DSE to the ascending size effect (ASE) remains a challenging issue for quasi-brittle materials. A size-dependent fracture process zone (FPZ) model is proposed and verified by experimental and simulative results. Subsequently, the size effect law (SEL) of unnotched specimens is improved by considering the size-dependent FPZ model, which is termed the improved SEL in this paper. Parametric studies are conducted for a better understanding of the improved SEL. It is found that the underlying mechanism of the DSE and the change from DSE to ASE is the competition between the relative rates of FPZ and specimen size change with respect to specimen size. The ASE is obtained when the relative rate of FPZ change is higher than that of specimen size. Conversely, the DSE is observed. No size effect exists when the relative rate of FPZ change is equal to that of specimen size. Experimental and simulative results are adopted to validate the improved SEL of unnotched specimens. The validation of the improved SEL indicates that the improved SEL not only accurately predicts the DSE, but also correctly captures the change from DSE to ASE. In addition, the size effect of nominal strength with different maximum aggregate size is well captured by the improved SEL. The fitting parameters of the improved SEL lie in the given interval. By comparing the determination coefficients R2 of the SEL, unified size effect law (USEL), and improved SEL, it is found that the R2 of the improved SEL is higher than that of the SEL for the DSE and is close to that of the IUSEL for the change from DSE to ASE. Therefore, it is recommended that engineers and researchers use the improved SEL to describe the DSE and the change from DSE to ASE of unnotched specimens.

The effect of fracture growth rate on the fracture process zone of salt rock after heat treatment

The importance of rate on the mechanical properties of rocks has been widely acknowledged by numerous scholars. Currently, most researchers mainly focus on investigating the influence of loading rate, while there is limited research on the effects of fracture growth rate on mechanical properties such as fracture process zone (FPZ) and fracture toughness of rocks. In order to explore the impact of fracture growth rate on the mechanical properties of rocks, this study conducted three-point bending pure I-mode fracture experiments on salt rocks at temperatures ranging from ambient to 700 °C using different quasi-static loading rates (0.02–2 mm/min). Meanwhile, digital image correlation (DIC) technology was employed to monitor displacement and strain variations, identify and calculate the fracture growth rate and FPZ size, and subsequently compute the corrected fracture toughness. The study discussed the effects of temperature and fracture growth rate on the FPZ and fracture toughness of rocks. The following main conclusions are drawn based on the analyzed results: (1) Temperature and loading rate have a great influence on the onset of FPZ in salt rocks. The higher the temperature and loading rate, the earlier the onset of FPZ. (2) With the increase of the average fracture growth rate, the FPZ length at the peak load of rock salt and the modified fracture toughness increased continuously, and was divided into two stages, in the stage of the crack extension rate generated by the loading rate of 0.02 mm/min-1 mm/min grew faster, and the growth of the crack extension rate generated by the loading rate of more than 1 mm/min became slower. (3) The effect of temperature on the fracture parameters of rock salt is significant, the peak load moment FPZ length and fracture toughness first increase and then slowly decrease with increasing temperature from room temperature to 700℃. The inflection point is at 500℃, where the fracture toughness and FPZ length reach the maximum value. (4) As the loading rate increases the proportion of transgranular fracture in the rock salt fracture surface gradually rises, and the crack extension path becomes smoother and smoother.

Biomimicry and topology optimization for adhesive toughness design in bonded heterogeneous films

Heterogeneous films have recently been extensively studied due to their superior material properties compared to homogeneous films. However, studies focusing on the design of heterogeneous films, especially with multi-material phases and structures, have been relatively scarce. This paper presents a bioinspired design methodology aimed at optimizing the mechanical properties of heterogeneous films through the strategic arrangement of stiff and soft material blocks. The heterogeneous film is represented as a composite beam and the interfacial failure process is simulated by a cohesive zone model. Then an optimization algorithm is employed to adjust the distribution of stiff materials within the soft film patch in the heterogeneous film. The results show that a nearly twofold increase in adhesive toughness for the optimized film compared to the original. Further discussions shed light on the energy distribution and variations in the fracture process zone size, providing insights into the observed enhancements. In terms of efficiency, the proposed optimization method distinctly outperforms the greedy method, demonstrating the potential for a more effective and efficient design of heterogeneous films with improved mechanical properties.

Thermal treatment effects on rock fracture behaviour under three loading modes: A comparative analysis of granite and mudstone

Temperature and thermal damage have a major impact on the behaviour of fractures in the earth’s crust. For deep earth engineering such as underground coal gasification, geothermal energy extraction, and nuclear waste repositories, developing fracture criteria governing the propagation of fractures under thermal effect is crucial. As a result, the ability of stress, energy, and strain-based fracture criteria to predict rock fracture behavior both before and after thermal treatment is assessed in this paper considering two rock types; granite, and mudstone, which are very different from one another in terms of their mineralogical composition and mechanical properties. The overall findings showed that the energy-based criterion was more effective in predicting fracture parameters both before and after thermal treatment than the stress and strain-based criteria. Specifically, after thermal treatment at 500 °C for the granite, and at any temperature for the mudstone, the strain-based criterion was no longer valid. It was found that the temperature and loading mode have a significant impact on the granite’s transition from brittle to ductile, where this transition can occur at an approximated temperature of 460 °C. Meanwhile, an increase in brittleness with rising temperature was noted in mudstone. Moreover, the Fracture Process Zone (FPZ) size was predicted by the energy-based criterion to be greater than that predicted by stress and strain-based criteria. It was found that the FPZ size is proportional to the brittleness degree of the two rock types, which is considerably impacted by thermal treatment. In addition, this study discusses several critical areas in rock fracture mechanics in the presence of thermal effects including fracture envelopes under mixed mode loading I/II, fracture stress, and initial crack extension angle. All of these are of high importance in assessing the safety and stability of rock structures in the presence of thermal effects.

Evolution of the mixed mode FPZ and fracture roughness of Beishan granite after coupled thermo-hydro-mechanical treatment

Deep surrounding rocks contain a network of longitudinally intersecting fissures. Exploration of their fracture process zone (FPZ) size evolution during mixed loading and fracture surface roughness after failure has always been a hot topic, especially for coupled thermo–hydro–mechanical (THM) treatment. This study takes Beishan granite as the research object. The fracture surface roughness and FPZ length were obtained using Grasselli statistical and mixed strain–displacement methods. Finally, an electron microscope was employed to observe the fracture surface after failure at different temperatures and loading angles. Results reveal a notable temperature and load dependence of the fracture surface roughness and FPZ length evolution. In the low-temperature stage (25°C–300°C), the mineral primarily exhibited transgranular fractures and the average fracture surface roughness showed a slightly decrease with increasing temperature. In the high-temperature stage (500℃–650℃), the degree of internal damage to the prepared specimens substantially increased, with intergranular fractures being the dominant fracture mode, and rapid roughness growth occurred. Under the same temperature condition, the roughness value was in the order of mode I > mixed mode > mode II. The FPZ length increased, stabilized, and decreased as the load increased. In the low-temperature stage, the FPZ length reached its maximum value at the maximum load, whereas in the high-temperature stage, the FPZ length was fully developed before the peak load. Under the same loading angle condition, the FPZ lengths corresponding to the three loading modes followed the order of mode I < mixed mode < mode II.

Numerical implementation of a modified cohesive zone model for HCF behavior of adhesively bonded composite laminates under mixed mode loading

In this paper, the cohesive zone model for high-cycle fatigue (HCF) behavior of adhesively bonded composite laminates subjected to mixed mode loading is implemented in Abaqus/Standard 6.14. The cyclic cohesive zone model takes into account mode-dependent penalty stiffness and fracture process zone size in adhesively bonded orthotropic composite laminates. Unlike earlier cyclic cohesive-based models, the developed UEL/UMAT is made available to the readers and end users for their specific needs. The model is validated extensively against the available experimental results in both load as well as displacement control. The model exhibited superior accuracy, positioning it as a valuable research tool. Furthermore, a novel parametric study was conducted to investigate the impact of fracture toughness and strength on HCF behavior. Finally, numerical simulation on a single fiber composite system is performed to explore micro-scale debonding using the developed model.

Experimental study on effects of cyclic loading paths on cracking behavior and fracture characteristics of granite

To investigate the impact of cyclic loading paths on the Mode I fracture characteristics of granite, a series of fracture tests were conducted on semi-circular bend (SCB) specimens using acoustic emission (AE), digital image correlation (DIC) and 3D scanning. The tests included monotonic loading, variable amplitude (VA) cyclic loading, and tiered constant amplitude (TCA) cyclic loading. The results demonstrated that VA cyclic loading leads to an average enhancement of 5.6% in fracture toughness, whereas TCA cyclic loading results in an average reduction of 3.7% in fracture toughness. During cyclic loading and unloading, the TCA loading path exhibits a higher rate of cumulative plastic deformation growth and greater magnitude cumulative plastic deformation compared to the VA loading path. Additionally, detailed observations from 3D scanning revealed that under cyclic loading, the fracture trajectories and surface morphology exhibit more tortuosity and roughness compared to monotonic loading, particularly in the case of TCA cyclic loading. Furthermore, according to the AE and DIC analysis, the proportion of microcrack initiation and stable propagation stage, cumulative AE counts and fracture process zone (FPZ) size generated under VA cyclic loading are greater than those generated under TCA cyclic loading, displaying a consistent variation pattern with fracture toughness. The changes of fracture properties can be attributed to a competition between the compaction-induced hardening effect and the cracking-induced damage effect. A higher cyclic upper limit and incomplete unloading are more likely to accelerate the growth of the irreversible crack damage and rapid crack extension, resulting in weakened rock fracture properties. These findings provide important references for rock instability control in underground rock engineering.

Influence of heterogeneity due to toughness variations on weakest-link modeling for brittle failure

The effect of heterogeneous microstructures on the macroscopic probability of failure is studied by use of weakest-link modeling. Heterogeneity is here associated with a local variation of toughness, where a size scale characteristic of this variation defines a length parameter. The ratio between this length parameter and the size of the active fracture process zone, defined as the heterogeneity ratio, is key to evaluating the impact of a heterogeneous microstructure. Two extremes are identified; small-scale heterogeneity (SSH) and large-scale heterogeneity (LSH). For these cases, it is possible to formulate analytical expressions based on the weakest-link concept, and references are made to existing models in the literature. Typically, heterogeneity along the crack front, where gradients of the mechanical fields are small, falls under the category of SSH. On the other hand, the effect of heterogeneity in a plane perpendicular to the crack front depends strongly on the heterogeneity ratio. Cases that can neither be identified with SSH nor LSH must be addressed with care. How this can be done is discussed, and examples are given for four different microstructure configurations of interest. The investigation is carried out by numerical analysis of a modified boundary layer model. The cumulative probability of failure by cleavage fracture is evaluated in a post-processing step, where two different statistical models are examined; the Beremin model and the Kroon–Faleskog model. Both models render the same conclusion about the alteration of the overall failure probability distributions caused by heterogeneity.

Fatigue fracture quantification in brittle cementitious materials using acoustic emission testing and digital image correlation

Fatigue loading in brittle materials introduces damage at the micro-scale. These micro-fractures can accumulate and cause a significant reduction in material stiffness or even lead to structural failure. Deformation-based monitoring techniques can be inadequate when detecting damage at the micro-level. Hence, here is where advanced non-destructive testing (NDT) methods such as acoustic emission testing (AET) and digital image correlation (DIC) can provide a significant improvement in quantifying fatigue damage. The paper aims to combine AET and DIC for advanced fatigue damage analysis on brittle cementitious mortars. Cylindrical samples with three different sizes are subjected to fatigue loading in a Brazilian splitting test. The damage advancement quantified from cumulative AE event count and energy analysis showed a good correlation with the tensile deformation measurement of the DIC. It was observed that for low cycle loading, the slowly progressing damage evolution may not always occur, instead abrupt failure similar to monotonic loading can occur even after passing several load cycles. The size of the fracture process zone (FPZ) was measured using several AE-based and DIC-based methods. The comparison of the approaches indicated that the AE energy-based method is the most suitable to quantify the FPZ size during fatigue damage progress. From AE-based FPZ analysis of the experimental results, it was concluded that for low-cycle loadings, the lack of a well-developed FPZ can be a cause of the sudden brittle failure.

Comparative analysis of fracture characteristics between rock and rock-like materials

In order to investigate the characteristics of rock and rock-like materials during the fracture process, notched semi-circular bending (SCB) experiments of 3 rocks and 2 rock-like materials were conducted in this paper. The process of the crack mouth opening was measured with a clip gauge. Acoustic emission was used to analyze the damage and failure mode of the specimens. Meanwhile, the fracture process zone (FPZ) was analyzed with the digital image correlation (DIC). Finally, the differences in the fracture process between rocks and rock-like materials were observed with a polarized microscope, and the formation mechanism of FPZ was discussed. The results indicate that the sequence from brittleness to plasticity is gypsum, marble, granite, concrete and fine sandstone. The crack opening velocity of gypsum, marble, and granite reaches 0.02–0.025 mm/s, far exceeding that of sandstone and concrete at 0.003 mm/s and 0.005 mm/s. The stronger the brittleness of geomaterials, the less significant their acoustic emission effect. Only a few acoustic emissions occur during the fracture process of gypsum with 8 hits. Its fracture occurs instantaneously rather than through a process of damage to fracture and the failure mode is tensile failure. Sandstone has the strongest plasticity, with a large count of acoustic emissions before and after fracture, with a hit number of 5062, which is 630 times of pure gypsum. The fracture is a process of damage accumulation with 94% of sandstone, 89% of concrete, 80% of granite, and 60% of marble showing a tensile and shear failure mode except gypsum. In addition, the stronger the brittleness of geomaterials, the smaller their FPZ size. The FPZ of gypsum is only about 3 mm, which can be considered as lacking, while other materials are about 6–11 mm. The formation of FPZ depends on whether an interlocking structure can be formed inside the material, which is related to the base material and crystalline or aggregate particle size.

A methodology for performing and evaluating miniaturized wedge splitting tests accompanied by digital image correlation

This methodology study investigated the application of a miniaturized wedge splitting test (WST) accompanied by digital image correlation (DIC) for the novel analysis of fracture mechanisms occurring during fracture of quasi-brittle refractories. Results from representative miniaturized WST were compared to standard WST results. Accuracy was improved by excluding experiments where unstable crack growth occurred or when the crack propagated perpendicular to the notch direction. Besides a sample size effect, a limitation of the fracture process zone (FPZ) size occurred. This FPZ limitation reduced the specific fracture energy G‘F from 112.4 N/m for the standard WST to 55.4 N/m for the miniaturized WST. Due to the sample size effect, the brittleness number was 0.194 and lower than for the standard WST with 0.414. The miniaturized WST enabled a more detailed evaluation of the acting mechanisms by analyzing the load–displacement curves together with the DIC. Grain bridging, microcracking, crack deflection/branching mechanisms and friction effects were evaluable. The analysis of the miniaturized WST could prove the supposed mechanisms acting during the standard WST. However, not all observed mechanisms also occurred in the standard WST due to the difference in the samples' brittleness.

An improved understanding of the influence of w/c ratio and interfacial transition zone on fracture mechanisms in concrete

The interfacial transition zone (ITZ) is significantly influenced by the water/cementitious materials (w/cm) ratio and governs the overall strength and fracture properties of concrete. Even though an ample number of studies on this topic are available in the literature, there is a lack of unified conclusions pertaining to the influence of w/cm ratios on various fracture characteristics and the underlying mechanisms. In this study, an attempt was made to investigate fracture characteristics (such as the size of the fracture process zone (FPZ), fracture energy, traction-free cracks (TFCs), toughening mechanisms) for varying ITZ properties and water/cement (w/c) ratios. Plain concrete beams of size 700 × 150 × 80 mm (l × d × b) with varying w/c ratios were tested under centre-point loading by controlling the crack mouth opening displacement. The acoustic emission (AE) technique was used to assess the internal damage parameters. A novel method was developed for identifying the TFC tip and the FPZ size using AE event location data at different stages of loading. The role of the ITZ on the fracture mechanisms of different types of concrete was also assessed. Evaluation of the fracture energy revealed that its relation with the w/c ratio is affected by the type of concrete.

Size-effect testing: Nano-alumina enhances fracture toughness of epoxy resins

Epoxy resins are widely used as matrix in fiber-reinforced composites. We investigate how adding nano-alumina affects the mechanical strength of epoxy resins. Size-effect testing is used to determine the fracture toughness of epoxy resin samples with 0.1%, 0.2%, 0.3%, 0.4%, and 0.5% weight fraction. For each weight fraction, the measured strengths follow type-II energetic strength scaling law. With increasing weight fraction, the fracture toughness rose monotonically from 1.48 MPam to 2.43 MPam, a 64% increase. The fracture process zone size(FPZ) also increased monotonically from 0.28 mm to 0.93 mm. Larger FPZ at higher weight fractions is associated with more distributed cracking and higher energy dissipation. These results show the toughening effect of the nano-alumina on epoxy resins. Field Emission Scanning Electron Microscope (FESEM) images of failed specimens showed formation of nano-alumina agglomerates at higher weight fractions. However, these agglomerates have no adverse effect on strength for the weight fractions considered.

Mixed mode I/II fracture behavior and surface morphology of hard rock under dynamic loading

To investigate the dynamic mixed mode I/II fracture properties of hard rock, split-Hopkinson pressure bar (SHPB) was utilized to conduct dynamic fracture tests on cracked straight through Brazilian disc (CSTBD) diorite specimens with different mode mixities. The dynamic fracture load and fracture toughness for different crack angles or mode mixities were determined. The dynamic fracture process and crack mouth opening displacement (CMOD) of CSTBD specimens were monitored by high-speed camera and digital image correlation (DIC) technique, and the fractal and morphology characteristics of fracture surfaces were further analyzed using laser 3D scanner and scanning electron microscope (SEM). The test results indicate that the dynamic CMOD behavior is interrelated closely to the force acting on the crack surface, and the allowable CMOD corresponding to the dynamic peak load decreases with increasing crack angle. In addition, the stress-based and strain-based fracture criteria were introduced to analyze the mixed mode fracture mechanism of diorite. It is found that the GMTS criterion with small fracture process zone (FPZ) size and the EMTSN criterion have the best prediction effect for fracture toughness and crack initiation angle respectively. Observation results show that the macro fracture trajectories of primary cracks and secondary cracks are controlled by the prefabricated crack angle, while the variation in mode mixity has little impact on the meso-roughness and micro-morphology of the fracture surface. The fracture surface of CSTBD diorite specimen under dynamic load exhibits the SEM morphology features of mixed tensile-shear cracks.

Size effect of fracture characteristics for anisotropic quasi-brittle geomaterials

Understanding the size effect exhibited by the fracture mechanism of anisotropic geomaterials is important for engineering practice. In this study, the anisotropic features of the nominal strength, apparent fracture toughness, effective fracture energy and fracture process zone (FPZ) size of geomaterials were first analyzed by systematic size effect fracture experiments. The results showed that the nominal strength and the apparent fracture toughness decreased with increasing bedding plane inclination angle. The larger the specimen size was, the smaller the nominal strength and the larger the apparent fracture toughness was. When the bedding inclination angle increased from 0° to 90°, the effective fracture energy and the effective FPZ size both first decreased and then increased within two complex variation stages that were bounded by the 45° bedding angle. Regardless of the inherent anisotropy of geomaterials, the nominal strength and apparent fracture toughness can be predicted by the energy-based size effect law, which demonstrates that geomaterials have obvious quasi-brittle characteristics. Theoretical analysis indicated that the true fracture toughness and energy dissipation can be calculated by linear elastic fracture mechanics only when the brittleness number is higher than 10; otherwise, size effect tests should be adopted to determine the fracture parameters.

Toughening by interpenetrating lattices

•Separate lattices can be interwoven to significantly increase their toughness •The sub-lattice properties can be tuned via topology and optimized for toughness •The toughening effect can be explained using a crack-bridging model As structural lattice metamaterials become more accessible through 3D printing, there is a need to better understand their fracture behavior, which sets practical limits for engineered structures. Lattices face a problem of decreasing toughness as their density and cell size decrease. Recently discovered interpenetrating lattices, made by weaving two or more physically separate lattices through the same volume, offer a potential path to significantly improve fracture toughness by increasing the fracture process zone size and inducing unique contact and friction toughening mechanisms. Interpenetrating lattices possess a steeply rising resistance-curve behavior, with the final toughness associated with catastrophic fracture an order of magnitude greater than the initiation toughness needed to begin advancing a crack. Remarkably, the interpenetrating lattice’s toughness in certain topologies can be five times greater than its corresponding, fully dense solid base material, and the toughening effect can be tailored by controlling the mechanical mismatch of the constituent sub-lattices. As structural lattice metamaterials become more accessible through 3D printing, there is a need to better understand their fracture behavior, which sets practical limits for engineered structures. Lattices face a problem of decreasing toughness as their density and cell size decrease. Recently discovered interpenetrating lattices, made by weaving two or more physically separate lattices through the same volume, offer a potential path to significantly improve fracture toughness by increasing the fracture process zone size and inducing unique contact and friction toughening mechanisms. Interpenetrating lattices possess a steeply rising resistance-curve behavior, with the final toughness associated with catastrophic fracture an order of magnitude greater than the initiation toughness needed to begin advancing a crack. Remarkably, the interpenetrating lattice’s toughness in certain topologies can be five times greater than its corresponding, fully dense solid base material, and the toughening effect can be tailored by controlling the mechanical mismatch of the constituent sub-lattices.

Characteristics of the Fracture Process Zone for Reservoir Rock with Various Heterogeneity

Hydraulic fracturing for oil-gas and geothermal reservoir stimulation is closely related to the propagation of Mode I crack. Nonlinear deformation due to rock heterogeneity occurs at such crack tips, which causes the fracture process zone (FPZ) to form before the crack propagates unsteadily. However, the relationship between the FPZ characteristics and rock heterogeneity still remains elusive. We used three rock types common in reservoirs for experimental investigation, and each of them includes two subtypes with different heterogeneity due to grain size or microstructural characteristics. Drawing on the experiment results, we calculated the FPZ size (represented by the radius of an assumed circular FPZ) in each cracked chevron-notched Brazilian disk, and we reproduced the formation process of the FPZ in marble using the discrete element method. We showed that strong heterogeneity is favorable to large FPZ size, can enhance the ability of crack generation and make crack morphology complex. Coupling the Weibull distribution with fracture mechanics, the dependence of the FPZ size on heterogeneity degree can be theoretically explained, which suggests that the inherent heterogeneity of rocks sets the physical foundation for formation of FPZs. These findings can improve our recognition of propagation mechanisms of Mode I cracking and provide useful guidelines for evaluating reservoir fracability.

A Review of the Hydraulic Fracturing in Ductile Reservoirs: Theory, Simulation, and Experiment

The bottom-hole pressure of hydraulic fracturing in ductile reservoirs is much higher than that of the hydraulic fracturing simulation, and the fracture toughness inferred from the field data is 1–3 orders of magnitude higher than that measured in the laboratory. The rock apparent fracture toughness increases with the increase in the confining pressure. Excluding the influence of the fluid viscosity and the fluid lag on the apparent fracture toughness, the fracture process zone (FPZ) at the fracture tip can explain the orders of magnitude of difference in the apparent fracture toughness between the laboratory and the field. The fracture tip is passivated by plastic deformation, forming a wide and short hydraulic fracture. However, the size of the FPZ obtained in the laboratory is in the order of centimeters to decimeters, while an FPZ of 10 m magnitude is speculated in the field. The FPZ size is affected by the rock property, grain size, pore fluid, temperature, loading rate, and loading configuration. It is found that the FPZ has a size effect that tends to disappear when the rock specimen size reaches the scale of meters. However, this cannot fully explain the experience of hydraulic fracturing practice. The hydraulic fracturing behavior is also affected by the relation between the fracture toughness and the fracture length. The fracture behavior of type II and mixed type for the ductile rock is poorly understood. At present, the apparent fracture toughness model and the cohesive zone model (CZM) are the most suitable criteria for the fracture propagation in ductile reservoirs, but they cannot fully characterize the influence of the rock plastic deformation on the hydraulic fracturing. The elastic-plastic constitutive model needs to be used to characterize the stress–strain behavior in the hydraulic fracturing simulation, and the fracture propagation criteria suitable for ductile reservoirs also need to be developed.