Evolution Of Fracture Process Zone Research Articles

Evolution of fracture process zone and variation of crack propagation velocity in sandstone

To solve the safe containment and recovery efficiencies of gas in rock masses, a study on fracture process zone (FPZ) and crack propagation is conducted. By using digital image correlation technology, the displacement of three-point bending specimens was measured. By analyzing the distributions of displacement at different loading stages, a specific region between the pre-crack tip and the loading point was divided into three zones: the intact zone, the crack propagation zone, and the FPZ. The length and the migration velocity of FPZ were determined, and the crack propagation velocity was also measured. The microstructures in FPZ were investigated through optical microscopy, x-ray diffraction analysis, and x-ray photoelectron spectroscopy. The results show that (1) FPZ length slightly varies during crack propagation and the FPZ is fully formed at the peak load; (2) the average value of the bond energy (446.7 eV) in the grains is greater than that (296.7 eV) in the matrix, thus the microdamage appears in the matrix around grain boundaries in FPZ; (3) the mean FPZ length varies from 4.09 to 8.42 mm for all tested specimens during crack propagation; (4) the propagation of the crack and the migration of FPZ proceed simultaneously in the loading process, and both velocities of crack propagation and FPZ migration are almost the same and with the same trend; (5) the peak velocity of crack propagation appears after the peak load, and the crack propagation progress was intermittent due to fracture energy accumulation, fracture energy release, and FPZ's shielding effect.

Experimental study on mechanical properties and evolution of fracture failure of granite considering initial temperature damage and prefabricated fissure length

With the increasing mining depth of deep mineral resources, the influence of high temperature on the fracture failure of surrounding rock with fissures becomes increasingly serious. To investigate the fracture mechanical properties and the evolutionary characteristics of fracture process of fissured rock experiencing initial temperature damage, the three-point bending experiment was conducted on the small sized granite samples with different initial damaging temperatures and prefabricated fissure lengths by applying a μTS mesoscopic testing system. Based on the digital image correlation methods, the evolution of fracture process zone of sample was revealed. Moreover, the macroscopic fracture failure of sample was predicted by the evolution of time-varying acoustic emission b-value. The results show that with the increase of initial damaging temperature and prefabricated fissure length, the peak load of granite sample has a decreasing trend and the fracture characteristics of sample experiencing initial temperature damage gradually transform from brittleness fracture to ductility fracture, resulting in a decrease in the fracture toughness of sample. The crack tip opening displacement, the critical opening displacement and the length of fracture process zone of sample all show an increasing trend. The time interval from the time when time-varying acoustic emission b-value continues to decline to the appearance moment of macroscopic cracks is selected as the warning time of fracture failure of sample, which can conclude that the warning time increases with increasing the initial damaging temperature and prefabricated fissure length, indicating an increase in ductility and a reduction in failure suddenness of sample.

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.

Three-dimensional discrete element model of crack evolution on the crack tip with consideration of random aggregate shape

In this paper, a method for concrete three-dimensional random polyhedral aggregate mesostructure is proposed. Moreover, a concrete discrete element fracture mesoscopic analysis model is established. The mesoscopic destruction mechanism of three-dimensional fracture of concrete three-point bending specimens is investigated. Three-dimensional evolutionary extension morphology of crack tip and fracture process zone (FPZ) of small-size concrete specimens in an indoor laboratory is simulated and analyzed. Furthermore, the entire fracture process of concrete specimens is investigated. The three-dimensional morphology of the crack tip and fracture process zone is analyzed via normal distribution statistics. Consequently, the size effect law of crack extension and fracture process zone evolution is derived. The fracture process of actual large-scale concrete specimens is predicted based on deficiencies of small-scale specimens in indoor tests. The results show that the proposed model is an effective method to characterize the three-dimensional fracture process of concrete and predict mechanical properties of large-scale specimens in actual structures.

Crack extension at the concrete–rock interface damaged by high-pressure water environment: DIC research

As a weak link in hydraulic structures such as arch dams, the fracture property of the concrete–rock interface is impacted by various factors, including the material properties of the individual constituents and the fracture process zone (FPZ) at the crack tip. Because the heel area of an extra-high dam has been exposed to a high-pressure water environment, this paper aims to investigate the whole fracture process of the concrete–rock interface after the water pressure effect. In this test, the water pressure was set at 0, 1, 2, and 4 MPa, and the crack deformation of the concrete–rock composite beam under three-point bending (TPB) was monitored in real-time by the digital image correlation (DIC) technique. DIC has been discovered to aid in understanding the damage caused by a high-pressure water environment to material properties. The stable crack extension of TPB composite beams after the high-pressure water exposure was greatly limited, and the corresponding crack length was decreased by up to 35%. The FPZ characteristic length was reduced by 19% when exposed to a high-pressure water environment, resulting in a drop in cohesive toughness on the fictitious crack. KR resistance curves for the concrete–rock interface fracture were constructed to consider the damage to material properties and FPZ evolution by high-pressure water exposure. For a reference for fracture analysis in the dam heel of extra-high dams, the calculation model of critical crack size in elastic fracture and the prediction equation of FPZ characteristic length in nonlinear fracture were constructed for a TPB composite beam.

Effect of carbonation treatment on fracture behavior of low-carbon mortar with recycled sand and recycled powder

This paper presents a systematic experimental study on the fracture behavior of low-carbon mortars with various contents of carbonated recycled sand and recycled powder (CRS and CRP). Three-point bending tests on pre-notched beams were performed to explore the load-induced fracture processes. Based on the strain and displacement fields measured using the digital image correlation technique, the evolution of the fracture process zone (FPZ) was studied qualitatively and quantitatively. Results indicated that the initial cracking toughness (KIcini), unstable fracture toughness (KIcun) and fracture energy (Gf) of mortar reduced gradually with the increasing recycled sand (RS) content but kept relatively steady with the rising recycled powder (RP) dosage except for KIcini. Carbonation treatment could effectively improve the KIcini of mortar with low RP content and Gf with a high proportion of RS but had limited effect on KIcun. A combination of the FPZ evolution characteristics and crack growth resistance curves suggested that the use of RS would increase microcracking in the stable crack growth stage and thus facilitate the connectivity of microcracks in the unstable fracture stage, while the use of RP mainly affected the crack initiation stage of cement paste in the mortar. The improvement of mortar fracture by CO2 treatment of RS or RP also corresponded to these stages. Regarding fracture characteristics and carbon footprint, mortars with CRS and CRP could achieve a synergy of safety and low carbon and thus can be considered as low-carbon cementitious materials compared to normal mortar.

Evolution of the FPZ in steel fiber-reinforced concrete under dynamic mixed-mode loading

This work studies the fracture process zone (FPZ) evolution of steel fiber-reinforced concrete under dynamic mixed-mode loading. We made beams with fiber contents of 0%, 0.4%, and 0.8% in volume and tested them in three-point bending at low displacement rates (2.2 μm/s and 22 mm/s) and impact rates (1.77 m/s and 3.55 m/s). All beams had a notch in the center of the half-span to facilitate a mixed-mode process zone extended from its tip. We recorded the entire crack propagation process in all the tests with a high-speed camera. Using the digital image correlation (DIC) measurements, we locate the FPZ tip from the tensile strain field and determine the stress-free crack tip from the displacement jumps. In this way, we capture the entire process of FPZ evolution. The FPZ stretched with crack propagation until a maximum —full FPZ length— and shortened afterward. The FPZ length at peak load and its maximum value increased with the loading rate. The loading rate and the fiber content have opposite effects on the full FPZ length. The faster the loading rate, the longer the full FPZ length. The more fiber content, the shorter the full FPZ length. In addition, the fiber addition helped to generate multiple FPZs and to cause more distributive damage in the matrix. Under impact loading, the cracked matrix and the steel fibers work in a synergetic way to dissipate the excessive energy input due to impact.

Three-dimensional numerical study on mode-I local crack propagation of concrete considering boundary effect

A three-dimensional numerical method considering the boundary effect on fracture energy and initial fracture toughness was proposed to simulate the whole propagation process of mode-I local crack in concrete. The initial fracture toughness-based criterion was employed to determine the propagation of local crack surface. The numerical analyses were carried out to obtain the initial cracking load, peak load and load-crack mouth opening displacement curves for a series of concrete beams with a local crack of different sizes. Comparing with the experimental results performed in this study, the numerical results showed good agreements and applicability of the proposed method was verified. After that, the numerical analyses were conducted on the whole fracture process of local crack in concrete. The results indicated the local crack of three-point bending beam always propagated along the thickness direction firstly on the bottom surface of the specimen. The crack front was basically parallel to the upper boundary of specimen after the load decreased to 40%Pmax. For beams with a local crack of different sizes, the variations of the ratio of crack propagation area to ligament area with the ratio of load to peak load were the same so that a function expression was given to predict the increment of crack surface area under different loads. In addition, the fracture process zone evolution during the local crack propagation was discussed.

An experimental study on division of fracture ligament and evolution of fracture process zone in sandstone

Fracture process zone (FPZ) is an irreversible deformation and damage zone in the front of a crack tip in rock. Only a few of them experimentally focused on the size development of FPZ during the loading process. Therefore, the DIC technology was used to monitor the development of FPZ in three-point bending beam rock specimens. The far-field displacements and strains were measured during the whole loading process. By analyzing the strains, the displacements and derivative distributions in the far-field, the fractured ligament is divided into three zones: Intact Zone, Crack Propagation Zone and Fracture Process Zone (FPZ). The FPZ first appears at the 60% pre-peak load, and its initial length is 4-6 mm. The length of the FPZ increases rapidly from the 90% pre-peak load to the 95% pre-peak load, and the increased length at this period occupies 47% of its full length. The length of the FPZ increases slowly near the peak load, and it reaches a maximum (15.5 mm) at the peak load.

A novel methodology for characterizing fracture process zone evolution in Barre granite specimens under mode I loading

Fracturing in quasi-brittle such as rock involves the development of an inelastic zone around the pre-crack tip, also known as the fracture process zone (FPZ). The evolution of FPZ, while influencing the fracture behavior of rocks, is difficult to characterize due to the localized nature of material behavior and microstructural heterogeneities. This study presents a digital image correlation technique (DIC)-based method that consistently describes the FPZ evolution in mode I fracture of Barre granite specimens. The FPZ characteristics were also evaluated using acoustic emission (AE) monitoring. The evolution of the crack tip opening displacement (CTOD) was analyzed to estimate the various fracture parameters, such as threshold values of the elastic and critical opening displacements and the size of the fully developed FPZ. The comparison of DIC-based measurements with the AE-based microcracking activities demonstrated that the displacement approach of the former could be used independently to identify the transition among the three stages of FPZ evolution, namely, (1) elastic stage, (2) formation of FPZ, and (3) macro-crack initiation. Experimental results also indicate a linear relationship between the FPZ length and the inelastic component of the CTOD, along with the quadratic relationship between the local dissipated energy and the FPZ length, which is consistent with the linear softening law for material inside the FPZ.

Experimental investigation of fracture process zone of rock in dynamic mode I fracturing and its effect on dynamic crack initiation toughness

Fracture process zone (FPZ) is critical to the applicability of linear fracture mechanics (LEFM) in rock fracturing, but little attention has been given to quantify the FPZ under dynamic loading condition in previous studies. This study presents the experimental results of notched semi-circular bending (NSCB) tests undertaken by split Hopkinson pressure bar (SHPB) to investigate the FPZ evolution for red sandstone under dynamic mode I fracturing and its effect on dynamic crack initiation toughness. A hybrid displacement–strain calibration method was proposed to characterize the FPZ with high-speed digital image correlation (DIC) technique. Results show that the FPZ initiation in dynamic fracturing is much earlier than that in quasi-static cases, and the FPZ length fully develops when crack initiation taking place at the pre-peak stage. The FPZ in dynamic fracturing is of a semi-elliptical shape with a width independent from the loading rate. The opening displacement exhibits a nonlinear decreasing trend along the FPZ boundary. LEFM theory underestimates the inherent dynamic crack initiation toughness, and the corrected dynamic crack initiation toughness was approximately 1.6 ∼ 2.1 times the uncorrected one within the loading rate ranging from 8.5 ∼ 78.2 GPa•m1/2/s in present study. The FPZ length in dynamic mode I fracturing lies in between the values predicted by Schmidt model and Irwin model, which indicates a non-linear cohesive stress with higher gradient near the FPZ tip is distributed along the FPZ.

Fracture properties of steel fiber reinforced concrete: Size effect study via mesoscale modelling approach

Steel fiber reinforced concrete (SFRC) can exhibit superior performances of high strength and toughness due to the enhancing effect of discontinuous steel fibers randomly distributed in concrete matrix. For better understanding the size effect on the fracture properties of SFRC structural elements, we developed a three-dimensional (3D) two-phase mesoscale model considering the random distribution and orientation of steel fibers in concrete, to investigate the quasi-static flexural responses of the notched SFRC beams with different beam depths, i.e., 30 mm, 60 mm, 90 mm, 120 mm and 150 mm. A new coupling method was employed to describe the interfacial relationship between steel fibers and concrete matrix in the present simulations. The fracture behaviors of SFRC beam were numerically studied in terms of the load versus cracking mouth opening displacement curve, the evolution of fracture process zone, the nominal flexural strength and the fracture failure patterns. Through the analysis and comparison between the present numerical results and the available test data, it was found that there is negligible size effect on the fracture patterns of SFRC beam. The size effect on the nominal flexural strength of SFRC beam can be well characterized and analyzed using the Bažant’s size effect law. Further, the numerical results of SFRC beams showed a favorable agreement with the corresponding test results, demonstrating the great feasibility and potential of the developed mesoscale modelling approach in simulating and investigating the mechanical behaviors of SFRC.

Experimental Study of Evolution of Fracture Process Zone in Dam Concrete under Cyclic Loading Using Digital Image Correlation

In this paper, three-point bending tests were carried out o investigate the post-peak cyclic loading behavior of dam concrete under two loading rates. The fracture parameters, residual load capacity, cyclic modulus, dissipated energy, and deformation recovery were presented and analyzed. The analysis was made to understand the evolution of fracture process zone (FPZ) under post-peak cyclic loading for dam concrete by utilizing digital image correlation (DIC) technique. The results showed while the dam concrete under a higher loading rate showed an increase in maximum load, it is not necessarily the same for post-peak bearing capacity. The specimens with higher post-peak bearing capacity had higher residual stiffness, higher dissipation energy, and higher Crack Mouth Opening Displacement (CMOD) reversibility under cyclic loading. The FPZ development was investigated quantitatively, and the extension and retraction of its tip were observed. Moreover, it was found that the FPZ in specimens with higher residual stiffness developed more slowly, and FPZ had a more significant retraction rate during unloading for the specimens with higher residual bearing capacity.

Investigations on fracture properties and analytical solutions of fracture parameters at rock-concrete interface

To investigate fracture properties and find analytical solutions of fracture parameters at rock-concrete interface, three-point bending tests were performed on the composite rock-concrete specimens with different degrees of interface roughness. Numerical simulations were conducted to analyse the crack propagation and the fracture process zone evolution at rock-concrete interface. For convenient applications in practice, a series of analytical solutions were derived or curve-fitted to calculate the fracture parameters of rock-concrete interface. The results indicate that the roughness degree has significant effects on the fracture properties of rock-concrete interface. With the increase of the roughness degree, the fracture energy, the critical crack length and the double-K fracture parameters exhibit obvious increasing tendencies. Meanwhile, the ratio of the unstable fracture toughness of rock-concrete interface to concrete is much less than that of the initial fracture toughness, indicating the much weaker cohesive effect of rock-concrete interface compared with concrete. In addition, with the increase of the roughness degree, the length of the fully formed FPZ and the corresponding ratio of the crack propagation length to the ligament length decrease. The characteristic length of rock-concrete interface is proved to decrease with the increase of the roughness degree, indicating larger brittle behaviour with the increase of the roughness degree. Finally, a series of analytical expressions were curve-fitted or derived to calculate the fracture parameters of rock-concrete interface under three-point bending loading, including the mode-I stress intensity factor, the critical crack length and the characteristic length of rock-concrete interface.

Mesoscale modelling of size effect on the evolution of fracture process zone in concrete

A comprehensive mesoscopic investigation has been conducted to examine the evolution of the fracture process zone (FPZ), using notched plain concrete beams subjected to three-point bending as a generic representation. The concrete beams are modelled as random heterogeneous materials containing three components, namely coarse aggregates, mortar and the interface transition zone (ITZ). To better represent the fracture process in concrete, a coupled cohesive-contact interface approach is employed to model the crack initiation, crack propagation and the friction mechanismsduring the fracture process. Thus,the FPZ is naturally captured in the simulation as the zone composed by microcracks along the ITZ or through the mortar matrix in the mesoscale model. The macroscopic response of load-deformation curves as well as the shapes and sizes of FPZ calculated from numerical results are validated against experimental observationsand good agreement is achieved. Subsequent modelling results demonstrate that the FPZ tend to exhibit a main crack and multiple secondary microcracks. During the growth of the main crack, new microcracks initiate while some microcracks formed earlier stop growing and even close. The evolution path of the FPZ is strongly irregular due to the random spatial distribution of the aggregate particles with weak ITZs. The influence of the size effect on the FPZ is also investigated from the numerical simulation. Results show that the width of the FPZ is insensitive to the beam size but the length of the FPZ is strongly dependent on the beam size, and such characteristics of the FPZ are deemed to be intrinsic reasons for the overall size effect phenomenon in concrete structures.

Size effect analysis of quasi-brittle fracture with localizing gradient damage model

The size effect of a quasi-brittle fracture is associated with the size of fracture process zone relative to the structural characteristic length. In numerical simulations using damage models, the nonlocal enhancement is commonly adopted to regularize the softening response. However, the conventional nonlocal enhancement, both integral and gradient approaches, induces a spurious spreading of damage zone. Since the evolution of fracture process zone cannot be captured well, the conventional nonlocal enhancement cannot predict the size effect phenomenon accurately. In this paper, the localizing gradient enhancement is adopted to avoid the spurious spreading of damage. Considering the three-point bend test of concrete beams, it is demonstrated that the dissipation profiles obtained with the localizing gradient enhancement compare well with those of reference meso-scale lattice models. With the correct damage evolution process, the localizing gradient enhancement is shown to capture the size effect phenomenon accurately for a series of geometrically similar concrete beams, using only a single set of material parameters.

Microcracking behavior transition in thermally treated granite under mode I loading

An in-depth understanding of the thermomechanical properties of rocks is fundamentally important in many fields of geotechnical engineering. However, the microcracking mechanisms of thermally treated granite under mode I loading are very complex. To investigate the effect of thermal treatment on the microcracking behavior, we perform mode I three-point bending tests on a set of pre-notched semi-circular specimens. The specimens are pre-heated to different target temperatures (i.e. 50 °C, 100 °C, 150 °C, 200 °C, 400 °C, and 600 °C), which are then naturally cooled down to room temperature. Acoustic emissions are monitored during the loading tests to provide clues on the microcracking processes. The fracture process zone (FPZ) development features before the initiation of macrofracture are interpreted through analysis of the spatial-temporal evolution of AE events. Based on the AE signatures, we identify the microcracking behavior transition phenomenon as the thermal treatment temperature increases from 150 °C to 200 °C, which is related to the development of thermal microfractures. As the transition occurs, we observe (1) relatively lower load levels at the beginning of the rapid FPZ development phase; (2) longer rapid FPZ development duration; (3) larger size and maximum event density for fully-developed FPZs. Taking the microscopic observation into consideration, we propose an extended conceptual model to describe the FPZ evolution before the unstable fracture propagation in crystalline rocks. The present findings provide useful insights into the microcracking behavior in geoengineering practices where the host rocks are subjected to temperature changes.

Experimental Study on Crack Propagation of Concrete Under Various Loading Rates with Digital Image Correlation Method

The quantificational exploration of the propagation law of fracture process zone (FPZ) is of great importance to the research on concrete fracture. This paper performed fracture experiments on pre-cracked concrete beams under various loading rates. Digital image correlation (DIC) method was applied to obtain the whole field displacement of concrete in the fracture test. The crack opening displacement (COD) and the evolution of FPZ were determined based on the whole field displacement. The results show that the length of FPZ first increases and then decreases with the development of the effective crack length and the maximum length of FPZ is about 60 mm. It can be found that the length of FPZ corresponding to the peak load decreases with the increase of loading rates. Based on the fictitious crack model, a bilinear softening model was established. According to the proposed model, the mechanical behavior and the propagation law of FPZ were analyzed. The bilinear softening model can reflect the microcrack development and the aggregate interlocking in the FPZ.

An experimental investigation on FPZ evolution of concrete at different low temperatures by means of 3D-DIC

The three-point bending tests of concrete specimens at different temperature levels (20 ℃, 0 ℃, −20 ℃, and −40 ℃) were performed using a low-temperature fracture test system. The 3D digital image correlation (3D-DIC) technique was employed to measure the surface deformations of the beams during fracture process. Combined with the displacement fields obtained from 3D-DIC, the crack propagation lengths and crack widths at different loading points were determined, providing information for the fracture process zone (FPZ) evolution in concrete at different temperatures. The results revealed that temperature has significant effect on the crack propagation, i.e. the average FPZ length in the later stage of unloading and the critical crack length ac decrease with decreasing temperature. In addition, the FPZ length for specimens at 0 ℃, −20 ℃ and −40 ℃ decreases slowly in the initial stage and then decreases significantly when the crack extends to the specimen boundary.

Analytical method for crack propagation process of lightly reinforced concrete beams considering bond-slip behaviour

Characterization of crack extension process is crucial for evaluating the fracture behaviour of reinforced concrete (RC) structures. Although extensive research has shown that cracking in RC members is generally influenced by the bond-slip behaviour between steel bars and the surrounding concrete, little attention has been paid to the crack growth process. Based on the principles of fracture mechanics, this paper presents an analytical method for predicting the crack extension process of lightly RC three-point bending beams with bond-slip behaviour. A closed-form solution is derived, with which the mode I crack growth process in concrete and the interfacial debonding evolution induced by the bond-slip between steel bars and concrete can be evaluated. The validity of the presented method is demonstrated through comparison with experimental data obtained from the literature. The effects of the bond-slip behaviour on the crack growth resistance curve and the evolution of fracture process zone (FPZ) length are examined with the method. The results show that the bond-slip behaviour exhibits a significant impact on the crack extension properties. At the initial loading stage, the crack growth resistance is primarily provided by the cohesive stress on the FPZ. When the crack approaches the beam top, the bridging force of steel bars is significantly strengthened and plays a dominant role against crack propagation. Since the tensile softening of concrete, the steel-concrete bond, and the yielding of steel have been taken into account, the presented method can be utilized as a simple tool to investigate the mechanical behaviour of lightly RC structures.