Fracture Process Zone Research Articles

Non-constant evolution of mixed mode fracture process zone in heat-treated salt rock during the whole loading

Exploring the evolution of the fracture process zone (FPZ) in mixed fracture within salt rock is vital for enhancing our comprehension of salt rock fracture properties and assessing the long-term stability of energy reservoirs. Prior research has identified the existence of constant evolution within the FPZ, a topic that has sparked debate. For this purpose, we acquired data on the evolution of the FPZ during the whole loading process of mixed fracture in salt rock at different temperatures by employing Digital Image Correlation (DIC) technology. After the experiments, we employed the computerized tomography (CT) scanning technique to analyze the pore structure within the mixed-mode salt rock fracture. This analysis aims to provide further insights into the impact of temperature on the evolution of the FPZ. The findings demonstrate that the evolution of the FPZ in mixed mode salt rock fracture exhibits non-constant behavior, involving intricate evolutionary processes. When the specimen was subjected to a temperature of 700 °C and an angle of 10°, the length of the FPZ increased from 0.4 mm to 10.7 mm, before decreasing to 9.2 mm. Moreover, during the whole loading process, the non-constant evolution of the FPZ is notably influenced by temperature. Notable variations in the evolution of the FPZ emerged during the whole loading process, especially when the temperature was below 400 °C, as opposed to when it exceeded 500 °C. When the temperature exceeded 500 °C, the FPZ emerged at an earlier stage. At a temperature of 700 °C, the FPZ emerged in the 30 % pre-peak stage of the process. Additionally, during the post-peak stage, a more complex and non-constant evolution was observed. A bilinear relationship between the length of the FPZ and temperature at the peak load stage was observed.

Digital image correlation and cracked hinge model applied to notched beams reinforced with GFRP bars

In this study, three-point bending fracture tests of notched beams reinforced with a glass fiber-reinforced polymer bar are conducted. Plain concrete beams are also tested for comparison. Two different widths are considered for the beams. Digital image correlation (DIC) is used on the lateral surface of the beam to study the fracture process zone (FPZ) and neutral axis depths at different load stages. A non-linear analytical model named cracked hinge model and cross-sectional analysis are used to obtain the force in the bar and the interfacial slip between bar and concrete, which are compared to the results from pull-out tests.

Study on the Effect of Bedding Plane and Loading Style on Fracture Process Zone in Coal

Study on the Effect of Bedding Plane and Loading Style on Fracture Process Zone in Coal

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.

Effect of grouting on damage and fracture characteristics of fractured rocks under mode I loading

Grouting is widely used to improve the mechanical properties of fractured rocks, but its impact on the fracture behavior of fractured rocks remains incompletely understood. This research aims to investigate the effects of grouting on the damage and fracture characteristics of fractured rocks under mode I loading. We used epoxy resin and ultrafine cement to grout granite and sandstone centre-cracked Brazilian disc specimens. We conducted Brazilian splitting tests on intact specimens, as well as specimens with and without grouting under mode I loading. Acoustic emission (AE) and digital image correlation (DIC) techniques were utilized to study the effect of grouting on rock fracture behavior. Furthermore, we employed an improved fracture toughness calculation method to evaluate the anti-fracture capacity of grouted specimens. The results show that grouting positively reinforces fractured rocks by increasing the shear crack ratio, mitigating the stress concentration effect at the crack tip, and fostering a more complete and stable development of the fracture process zone (FPZ). Materials with superior strength and bonding properties can effectively improve the mechanical performance of fractured rocks. Notably, epoxy resin significantly boosts the strength, deformation adaptability, and anti-fracture capacity of the specimens, outperforming ultrafine cement in terms of grouting effect. The entropy change of AE energy during the loading process indicates that the rock system undergoes three stages of order-to-disorder-to-order. The second stage and the abrupt changes in entropy value can serve as precursors to rock damage and fracture. This research enriches our understanding of how grouting influences the damage and fracture behavior of fractured rocks, providing valuable insights for risk assessment and disaster prediction in geotechnical grouting engineering.

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.

Mechanical and fracture characteristics in center cracked circular discs of coal specimens with different sizes: An experimental investigation

The propagation of cracks on a small scale can result in dynamic disasters, such as rock bursts induced by large-scale fractures in coal seams. To gain insights into the mechanism of fracture-induced disasters in deep coal seams, this study investigates the micro-process and size effect of crack propagation in coal specimens featuring different sizes of center-crack circular discs (CCCD). We conducted Brazilian splitting tests on coal samples with varying dimensions and employed acoustic emission (AE) and digital image correlation (DIC) techniques to quantitatively describe the crack propagation process. Additionally, coal specimens of different diameters were compared for the size effect characteristics of different fracture parameters during the tensile failure process. The results show that as the specimen size increases, quasi-brittle failure characteristics become pronounced, tensile strength gradually decreases and stabilizes, while fracture toughness and fracture process zone length gradually increase and tend to stabilize. The macroscopic cracks in the coal specimens generally extend from the centre of the specimen to both ends along the precracks. Large energy events are mainly concentrated at the lower end of the precracks. As coal specimen size increases, the number of AE events decreases, while the proportion of large energy events gradually increases, and the critical crack opening quantity exhibits a linear increase with specimen size. By conducting the fracture size effect experiment on coal specimens, we extend the relevant mechanical parameters from laboratory-scale tests to field engineering scales. This provides fundamental parameters for the analysis of large-scale fracture process of in-situ coal based on fracture mechanics.

Estimating crack tip position in adhesively bonded joints subjected to mode II quasi‐static loading

AbstractThis study aimed at estimating crack tip position in adhesive bonded joints under mode II quasi‐static loading using experimental and numerical approaches. Experimental techniques were utilized and compared, including optical backscatter reflectometry, visual testing, and a novel strategy based on digital image correlation. Additionally, a finite element analysis was employed to identify the numerical crack tip position and the extent of damage within the bondline. This analysis revealed that a significant portion of the crack propagation region in the adhesive is occupied by the fracture process zone. Moreover, optical backscatter reflectometry shows the potential to detect this process zone within the adhesive that the other methods may not detect. This capability is particularly beneficial for detecting damage at early stages.

Effect of accelerated carbonation of fully recycled aggregates on fracture behaviour of concrete

Accelerated carbonation of recycled aggregates (RAs) enables fast carbon sequestration while improving engineering properties of prepared concrete. This paper presents a systematic experimental study on the fracture behaviour of concrete with carbonated recycled coarse and fine aggregates (RCA and RFA), in terms of fracture parameters and fracture process zone (FPZ). The relevant influencing mechanism was investigated by relating the macroscopic fracture responses to microstructural features. Results indicate that carbonated RFA mainly enhanced the initial fracture toughness of concrete, while carbonated RCA primarily increased its unstable fracture toughness. The enhancement of fracture energy was closely associated with carbonated RCA and RFA. The utilization of RFA resulted in the looseness and higher porosity of mortar matrix, which reduced the crack initiation resistance of concrete, mainly affecting its initial cracking stage. The incorporation of RCA reduced crack bifurcation and deflection of concrete, leading to a smaller width of FPZ, which made the initial descending segment of the tension softening curve (TSC) steeper and its tail segment shorter. The carbonation treatment of RAs improved the densification of the adhered old mortar and reduced the porosity of prepared concrete, rising the cracking resistance and inducing a wider FPZ. As a result, the initial descending segment of TSC became flatter and its tail segment tended to be longer.

Review of Fracture Properties and Research Methods of Fiber Recycled Concrete

Aiming at the background of the application of fracture mechanics in fiber recycled concrete as well as the shortcomings of the current research, the relevant results and progress are summarized from three aspects, namely, the basic theory of fracture mechanics of fiber recycled concrete and the research progress of the fracture properties of fiber recycled concrete as well as the testing methods of the fracture of fiber recycled concrete, respectively. The development history of the application of fracture mechanics in concrete is described, three fracture forms, fracture process zones and three softening curve models of concrete are introduced, and it is proposed to combine the bilinear softening curve and the virtual crack zone model to construct the ontological relationship of the whole process of concrete cracking. The current research status of recycled brick aggregate concrete and polypropylene coarse fiber concrete is introduced. The incorporation of recycled brick aggregate adversely affects the workability, basic mechanical properties and fracture properties of concrete. The reinforcing effect of polypropylene fibers on concrete can effectively improve the adverse effects of brick aggregate on concrete, which opens up the research prospect of green concrete and has high research value. The applications of three-point bending test, four-point bending test and DIC technique in the study of concrete fracture characteristics are introduced.

Introducing a novel LLD-CMOD equivalence fracture model for quasi-brittle materials exposed to three-point bending

Effective crack models have been preferred in the fracture of concrete thanks to their analytical solution for equivalent effective crack length. Nevertheless, the main hypothesis in the effective crack models, the Load-LLD or Load-CMOD equivalence between a real cohesive material and a corresponding virtual specimen, is controversial. The present study aims to offer a distinct perspective on the effective crack approach. To this end, the Load-LLD or the Load-CMOD equivalence was replaced by the LLD-CMOD equivalence in the proposed fracture model for the notched beams under three-point bending. In the proposed LLD-CMOD equivalence fracture model, three fracture toughness parameters are used, two of them depend on the evolution of the fracture process zone (FPZ) and the other is for the peak load measured. That is, KICin and KICde define the limit of the nonexistent FPZ and the fully developed FPZ, respectively, but KICun corresponds to the peak load only. The test results of the notched beams revealed that KICin and KICun show size independence, but this was not the case for KICde. The proposed fracture model was also compared with the Double-K model through the experimental results from the literature. Accordingly, a good agreement between both models was achieved in terms of the effective crack length and fracture toughness at the peak load.

Enhancing toughness through geometric control of the process zone

Material architecture provides an opportunity to alter and control the fracture process zone shape and volume by redistributing the local stresses at a crack tip. Properly designed structures can enlarge the plastic zone and enhance the effective toughness. Here, we use a pillar array as a model structure to demonstrate how variations in geometry at a crack tip control the size and shape of the plastic zone and can be used to engineer the effective toughness. Elastic–plastic finite element simulations are used to quantify how the pillar width, spacing, and height can be varied to tailor the size and shape of the plastic zone. A set of analytical mechanics models that accurately estimate the shape, volume, and resulting toughness as a function of the base material properties and geometry are also presented. A case study extends the analysis to sets of non-regular pillar arrays to illustrate how architecture can be used to alter toughness along the crack path.

Numerical investigation of two-dimensional Mode-II delamination in composite laminates

Existing standards for delamination tests on composite materials typically employ one-dimensional (1D) beam specimens. However, such specimens may not represent real delamination scenarios in composite structures, where cracks tend to propagate in two dimensions. To address this limitation and compare the delamination behavior under both 1D and two-dimensional (2D) Mode-II fracture conditions, a numerical investigation was carried out based on previous experiments. A novel cohesive zone model, considering both microcracking and fiber bridging within the fracture process zone, was developed using a semi-experimental approach and incorporated in three-dimensional finite element simulations. According to the numerical results, the investigated laminates exhibited similar maximum strain energy release rates in both 1D and 2D delamination; however, different traction-separation responses were obtained. Practical methods of locating the tip of an embedded crack were proposed based on curvature and strain measurements on the laminate surface, demonstrating potential for application in structures with irregular crack shapes.

Trans-layer and inter-layer fracture behavior of extrusion-based 3D printed concrete under three-point bending

This paper presents a systematic study on the effect of layer-by-layer printing process on the fracture behavior of hardened extrusion-based 3D printed concrete (3DPC). Based on three-point bending tests on center-notched beams, the fracture response of printed specimens with two fracture patterns including crack propagation across layers (trans-layer fracture) and crack propagation along layers (inter-layer fracture) was compared with that of cast specimens. The fracture mechanism of 3DPC was explored using the fracture parameters and fracture process zone (FPZ) characteristics. Experimental phenomena can be explained by the additional interlaminar cracking in FPZ of concrete introduced by the layer-by-layer stacking process. It could produce a toughening effect if cracks propagate through layers, as it is beneficial to reduce stress concentration and improve deformability. In the printing process design of 3DPC, such feature can be rationally utilized to transform the process-induced weak interfaces from inherent defects to toughening means.

Cutting soft matter: scaling relations controlled by toughness, friction, and wear.

Cutting mechanics of soft solids is gaining rapid attention thanks to its promising benefits in material characterization and other applications. However, a full understanding of the physical phenomena is still missing, and several questions remain outstanding. E.g.: How can we directly and reliably measure toughness from cutting experiments? What is the role of blade sharpness? In this paper, we explore the simple problem of wire cutting, where blade sharpness is only defined by the wire radius. Through finite element analysis, we obtain a simple scaling relation between the wire radius and the steady-state cutting force per unit sample thickness. The cutting force is independent of the wire radius if the latter is below a transition length, while larger radii produce a linear force-radius correlation. The minimum cutting force, for small radii, is given by cleavage toughness, i.e., the surface energy required to break covalent bonds in the crack plane. The force-radius slope is instead given by the wear shear strength in the material. Via cutting experiments on polyacrylamide gels, we find that the magnitude of shear strength is close to the work of fracture of the material, i.e., the critical strain energy density required to break a pristine sample in uniaxial tension. The work of fracture characterizes the toughening contribution from the fracture process zone (FPZ), which adds to cleavage toughness. Our study provides two important messages, that answer the above questions: toughness can be estimated from wire-cutting experiments from the intercept of the force-radius linear correlation, as previously explored. However, as we discovered, this only estimates cleavage toughness. Additionally, the force-radius slope is correlated with the work of fracture, giving an estimation of the dissipative contributions from the FPZ.

Fracture Process Zone in Cracked Nonlinear Orthotropic Body

Fracture Process Zone in Cracked Nonlinear Orthotropic Body

Shear response and fracture processes of hybrid steel fiber reinforced concrete

Ten hybrid steel fiber reinforced concrete mixtures are designed to analyze the influence of the hybridization of three different steel fibers (long hooked-end, medium hooked-end, short wave) on the shear performance by Z push-off shear tests. The presence of steel fibers improves the shear strength and toughness of the concrete, which increase with the volume fraction of hybrid fibers. The hybrid steel fiber reinforcement affects the fracture processes. Micro cracks propagation, cracks onset, cracks propagation and cracks post-peak propagation are the four main fracture stages. The volume fraction above 1.0% changes the evolution trend of fracture process zone length. The hybridization of the long hooked-end steel fiber with the other steel fibers produces a synergistic effect on inhibiting the propagation of the fracture process zone (FPZ) compared with the long hooked-end steel fiber reinforced concrete. The hooked-end steel fiber produces a better effect on slowing down the damage degree factor than short wave shaped steel fiber. The damage degree factor at the same loading level is reduced with the increase of the volume fraction of hybrid steel fiber.

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.

Effects of adhesive layer thickness on the fracture properties of a concrete-epoxy resin interface

Adhesive layer thickness is a crucial factor that affects the performance of interfaces in cement-based composite structures. However, the influence of adhesive layer thickness on the fracture properties of concrete–epoxy resin remains unclear. In this study, a two-parameter fracture model of a concrete-epoxy resin interface from the perspective of fracture mechanics. Digital image correlation (DIC) technique was used to investigate the evolution of the fracture process zone (FPZ) of nine specimens with adhesive layer thicknesses of 2 mm, 5 mm, and 8 mm, respectively. The interfacial fracture toughness parameters of the concrete-epoxy resin interface were determined based on the four-point bending (FPB) tests. The test results indicated that increasing the adhesive layer thickness changed the failure mode of the interface from approximate-brittle to quasi-brittle. The load-carrying capacity and interfacial stiffness of the concrete-epoxy resin interface decreased by approximately 13.8 % and 61.1 % with an adhesive layer thickness from 2 mm to 8 mm, respectively. The deflection across the specimen increased by approximately 37.2 % with an increase in adhesive layer thickness due to the lower elastic modulus of epoxy resin compare to the concrete. Furthermore, the FPZ for the adhesive layer thickness of 5 mm was the longest; it was approximately 18.7 % longer than that for the test specimen with an adhesive layer thickness of 2 mm. In terms of structural load-bearing capacity and fracture toughness, the concrete-epoxy resin interface exhibited the best working performance when the thickness of the adhesive layer was 5 mm.

A smooth Crack-Band Model for anisotropic materials: Continuum theory and computations with the RKPM meshfree method

A smooth Crack Band Model (sCBM) is developed for anisotropic materials with both high and low magnitude of anisotropy. sCBM is primarily used as a regularization mechanism to enable capturing the correct size and shape of the fracture process zone (FPZ) as well as the smooth distribution of strain inside the zone. The versatility of the proposed sCBM formulation is demonstrated by its adaptability to any material law of choice. A Reproducing Kernel Particle Method (RKPM) is employed to discretize such formulation, the benefit of which is its ability to compute the Hessian of the displacement field (i.e., the sprain tensor), a key quantity in the sCBM theory, using only the nodal displacements as the problem unknowns. This makes the resulting formulation accurate and efficient, which is shown by the validations against size-effect and radial crushing experiments, illustrating the power of the proposed methodology for practical applications.