Development Of Fracture Process Zone Research Articles

Experimental Study of Development of Fracture Process Zone in Rock

By means of digital image correlation (DIC) technology, the displacements and strains on the fracture ligaments of rock specimens were measured during loading. By analyzing the displacement distribution of each fracture ligament at different loading stages, the displacement fluctuation coefficient method was proposed to describe the development of fracture process zone (FPZ). The method can amplify the variation of displacement and clearly show the length of FPZ.The results show that: (1) the initiation of FPZ occurred at 77–89% of the peak load and the fluctuation coefficient of horizontal displacement around the crack tip reached the order of 10–7. (2) The initial length of FPZ was about 1.0–3.1 mm, which is 2 to 6 times the largest grain sizes. As the peak load was approached, the length of FPZ suddenly increased to 4.6–6.1 mm. (3) When a fracture process zone was initiated, the strain at the front end of the FPZ was about 3000–4000 µε. After the load approached the peak value, the strain at the rear end of the FPZ finally reached a peak value of 8000–11000 µε in all specimens.

Experimental study on mode I fracture characteristics of compacted bentonite clay

To explore the pure mode I fracture characteristics of compacted Gaomiaozi bentonite clay, notched semi-circular bend specimens of compacted Gaomiaozi bentonite with different dry densities and moisture contents were prepared by using the self-designed compaction and slitting molds, and then three-point bending tests were carried out, real-time monitoring was also conducted with the help of digital image correlation method. Based on the test results, the effects of dry density (1.5 g·cm−3, 1.6 g·cm−3, 1.7 g·cm−3, 1.8 g·cm−3) and moisture content (6.20%, 9.48%, 13.65%, 16.47%) on the mode I fracture toughness of compacted Gaomiaozi bentonite were analyzed, and the development of fracture process zone (FPZ) was also revealed. The results show that the pure mode I fracture toughness of compacted Gaomiaozi bentonite is in the magnitudes of 30 to 180 kPa·m1/2 within the testing range of dry density and moisture content. The mode I fracture toughness increases with increasing the dry density. At a moisture content of 9.48%, the mode I fracture toughness obtains a peak value, and with the decrease or increase of moisture content, the mode I fracture toughness presents a general decreasing trend. The length of the fully developed fracture process zone and the critical crack tip opening displacement decrease first and then increase with the increase in moisture content, while there is no obvious regularity in the variations of fully developed FPZ length and critical crack tip opening displacement with respect to dry density.

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.

Effects of elevated temperature and water re-curing on fracture process of hybrid fiber reinforced concretes

Hybrid fiber reinforced concrete has been introduced in constructions due to its superior mechanical performance compared to plain and mono fiber reinforced concrete. However, hybrid fiber reinforced concrete mechanical behavior after exposition at elevated temperature is of considerable importance for the safety of concrete structures and need more in-depth understanding. In this study, the effect of the elevated temperatures and water re-curing on the Mode I fracture performance of two hybrid fiber reinforced concretes was investigated. The Mix S exploited long hooked-end and medium hooked-end steel fiber, as well as high strength short wave-shaped steel fiber, for the hybrid reinforcement. Mix P contained polypropylene fibers substituting the high strength short wave-shaped steel fibers. The damage degree (DD) was estimated using the ultrasonic pulse velocity (UPV) method. The fracture process and development of fracture process zone (FPZ) length was studied by three-point bending tests and measuring the full-field displacement and strain on the surface of the specimen by the digital image correlation (DIC) technique. The results indicated an increasing damage degree with the elevated temperature, and a considerable reduction after water re-curing. The elevated temperatures above 200 °C deteriorate: modulus of rupture (MOR), residual strength, and fracture toughness. The dependency of the deterioration coefficient (DC) and the temperature from 20 °C to 800 °C was predicted by a linear / exponential relationship. Branching crack appeared when the elevated temperature exceeded 200 °C. Water re-curing enhanced the flexural performance of thermally damaged hybrid fiber reinforced concrete, reducing the crack branching and recovering the FPZ length. Mix S had a better flexural performance than Mix P at elevated temperature.

Size effects on the characteristics of fracture process zone of plain concrete under three-point bending

This paper studies the size effects on the characteristics of fracture process zone (FPZ) of plain concrete, including its physical features and softening behavior. Three-point bending tests were performed on pre-notched beams with similar geometry and different dimensions. Electronic speckle pattern interferometry (ESPI) technique was employed to monitor the crack evolution and full-field deformation of the beams. The development of FPZ was evaluated qualitatively based on the strain fields and quantitatively based on the displacement fields obtained by the ESPI technique. By adopting the incremental displacement collocation method, the tension softening curves (TSCs) of specimens with different sizes were estimated and approximated as bilinear curves. The features identified from the TSCs were correlated to the physical features in the development of FPZ. Finally, an empirical tension softening model and corresponding size-independent parameters were obtained based on the estimated TSCs of different sizes specimens.

Experimental Study on Concrete Fracture Process Zone Using Digital Image Correlation Technique

Abstract The fracture process zone (FPZ) of concrete under three-point bending was extensively investigated using the digital image correlation technique. Surface displacement, strain components, crack opening displacement, effective crack length, and crack tip position were calculated and analyzed. The development of crack and FPZ were obtained through data processing and applied to the analysis of mechanical response. The development of the FPZ, divided into three stages, was found to have strong consistency with the change of the mechanical behavior of concrete. Two characteristic parameters of FPZ were used to study the size effect of concrete. It is found that with the increase of size, the FPZ will develop deeper at peak load. However, the ratio of the maximum length of the FPZ to the initial ligament length does not vary with size, which is about 0.85 in this study.

R-curves determination of ordinary refractory ceramics assisted by digital image correlation method

As a figure-of-merit, the rising ratio of crack propagation resistance to fracture initiation resistance indicates a reduction of the brittleness and enhances the thermal shock resistance of ordinary refractory ceramics. The significant nonlinear fracture behaviour is related to the development of a fracture process zone (FPZ). The universal dimensionless load–displacement diagram method is applied as a promising graphical method for the determination of R-curves for magnesia refractories showing different brittleness. By applying digital image correlation (DIC) together with the graphical method, the problems arisen with accurate determination of the fracture initiation resistance and the crack length are overcome. Meanwhile, the R-curve is subdivided with respect to the fracture processes, viz the fracture initiation, the development of FPZ and the onset of traction free macro-crack. With the simultaneous crack lengths evaluated from DIC, the contribution of each fracture process to the crack propagation resistance at certain loading stage is quantitatively presented.

Development of fracture process zone in full-graded dam concrete under three-point bending by DIC and acoustic emission

In this paper, the fracture process zone (FPZ) of dam concrete under different loading rates is measured, and the formation process of FPZ is studied by applying digital image correlation (DIC) and acoustic emission (AE) technique. The results show that the FPZ development of dam concrete presents the characteristics of stepwise growth. The FPZ has emerged before the peak load, and the rapid growth is basically complete shortly after the peak load. Large aggregate plays an important role in the FPZ development of dam concrete. It can cause the bifurcation and tortuous development path of FPZ, which lead to the enhancement of fracture toughness and fracture energy of dam concrete. The maximum loads of specimens increase accordingly at a higher rate. Meanwhile, the development of FPZ also have the rate effect. Higher loading rate will weaken the effect of aggregate constrained force, resulting in more direct development of FPZ. The damage also seems to be more serious under the same loading stage from AE results.

A bi-linear cohesive law-based model for Mode II fracture analysis: Application to ENF test for unidirectional fibrous composites

The complicated toughening mechanism of Mode II cracking in end notch flexure (ENF) test for fibrous composites prevents the existence of clear crack-tip. Hence the concept of equivalent linear crack length was proposed to avoid detecting the crack-tip in ENF test, which assumes that the increase of compliance due to the development of fracture process zone (FPZ) or crack propagation is attributed to the equivalent elastic crack length giving the same compliance as the one of the actual crack with its FPZ; thus the equivalent crack length can be estimated according to the associated compliance obtained from experiment. The objective of the presented work was to develop an analytical model for the analysis of ENF test specimen without need for crack-tip identification and complicated data reduction. Bilinear cohesive law was employed to model the cohesive force across the potential crack interfaces. Analytical solutions for the governing equation were derived. Furthermore, methods to determine the cohesive parameters, the length of fracture process zone (FPZ), and the energy release rate were developed. The critical loads corresponding to the damage and crack onset can also be estimated by the model. Experimental validation was implemented and a good agreement was achieved between the test results and model predictions. It can be concluded that bilinear cohesive law may achieve a good approximation for the tangential traction-separation constitutive relationship in Mode II fracture; the shear strength of the material can be taken as the critical stress of cracking onset; the energy release rate depends on the initial crack length to some extent, and this effect could be reduced as the length of initial crack increases.

Concrete fracture process modeling by combination of extended finite element method and smeared crack approach

This study presents a method that couples the extended finite element method (XFEM) and fixed smeared crack model to simulate fracture process in concrete materials. The Griffith energy criterion is utilized to capture the fracture process zone (FPZ) properties and the distributed microcracks inside the FPZ are modeled using fixed smeared crack concept based on the energy dissipated in the FPZ. Jumping in the displacement gradient field is modeled by incorporating XFEM and fixed smeared crack approach as a new term is added to the stiffness matrix. The model predicts the crack opening as well as the crack sliding displacement so it simulates opening and mixed modes of fracture and, full separation in cracks is taken into account although the smeared approach is utilized. The proposed method captures all phases of concrete nonlinear behavior, which are development of FPZ, distribution of microcracks and formation of macrocracks. It is shown that the model improves the spurious stress transfer although the fixed smeared crack concept is used and the stress-locking phenomenon is overcome. In addition, the model is able to simulate the strain softening behavior in mode I and in mixed mode fracture.

Influence of joint anisotropy on the fracturing behavior of a sedimentary rock

Fracture toughness (FT) and tensile strength (TS) indicate a rock's susceptibility to fracturing. Past studies showed that mechanical properties and FT of homogeneous rocks can be correlated well. In the present study, this capability has been extended to the jointed sedimentary rocks. Sandstone with a wide combination of analogue joints were tested in the laboratory, and the control of joint geometrical properties on the FT, TS, and development of fracture process zone (FPZ) were investigated. A FT prediction model was developed based on the TS of the jointed specimens. Multifractal scaling law (MFSL) was utilized to extend the laboratory results to the field scale. Further, the interaction of propagating crack with the already existing joints were investigated and post-peak behavior were studied. Results show that FT and TS decrease with decreasing joint spacing, but they are more sensitive at higher joint spacing. It is also possible to construct a linear prediction model between the FT and TS of rock. FPZ of jointed rock is less sensitive to joint orientation and more related to joint spacing. A negative correlation between the FPZ size and joint spacing is established in this study. Post-peak behavior of the jointed specimens indicate that crack-joint interaction increases the frictional resistance and dissipated fracture energy of the specimens. Further, comparison of mixed-mode fracture criteria with the experimental results show that Maximum Tangential Stress (MTS) criterion can successfully predict the mixed-mode fracture behavior of jointed sandstone.

Microstructural investigation of subcritical crack propagation and Fracture Process Zone (FPZ) by the reduction of rock fracture toughness under cyclic loading

This study presents the results of laboratory diametrical compression tests performed on Brisbane tuff disc specimens to develop much-needed understanding of the micro-mechanical and micro-structural dynamics of sub-critical crack propagation. The strength variation in rocks under mechanical loading without corrosive chemical environment was investigated by investigating the mode-I (tensile) fracture toughness (KIC) response to static and cyclic loading. In some cases, cracks can grow at a lower load level compared to the static case. This phenomenon is called subcritical crack propagation and depends on the behaviour of the Fracture Process Zone (FPZ). The KIC response to cyclic loading was found to be different from that under static loading in terms of the ultimate load and the damage mechanisms in front of the chevron crack. A maximum reduction of the static KIC of 43% was obtained for the highest amplitude increasing cyclic loading test. Detailed Scanning Electron Microscope (SEM) examinations were performed on the surfaces of the tips of the chevron notch cracks, revealing that both loading methods cause fatigue in the disc rock specimens. When compared with static rupture, the main difference with the cyclically loaded specimens was that intergranular cracks were formed due to particle failure under cyclic loading, while smooth and bright cracks along cleavage planes were formed under static loading. It is believed in this study that the rock texture characteristics such as interlocked and cemented grains, cement volume, cement mineralogy play very important role on damage behaviour of rocks and development of FPZ and subcritical cracking.

Experimental and Numerical Studies on Development of Fracture Process Zone (FPZ) in Rocks under Cyclic and Static Loadings

The development of fracture process zones (FPZ) in the Cracked Chevron Notched Brazilian Disc (CCNBD) monsonite and Brisbane tuff specimens was investigated to evaluate the mechanical behaviour of brittle rocks under static and various cyclic loadings. An FPZ is a region that involves different types of damage around the pre-existing and/or stress-induced crack tips in engineering materials. This highly damaged area includes micro- and meso-cracks, which emerge prior to the main fracture growth or extension and ultimately coalescence to macrofractures, leading to the failure. The experiments and numerical simulations were designed for this study to investigate the following features of FPZ in rocks: (1) ligament connections and (2) microcracking and its coalescence in FPZ. A Computed Tomography (CT) scan technique was also used to investigate the FPZ behaviour in selected rock specimens. The CT scan results showed that the fracturing velocity is entirely dependent on the appropriate amount of fracture energy absorbed in rock specimens due to the change of frequency and amplitudes of the dynamic loading. Extended Finite Element Method (XFEM) was used to compute the displacements, tensile stress distribution and plastic energy dissipation around the propagating crack tip in FPZ. One of the most important observations, the shape of FPZ and its extension around the crack tip, was made using numerical and experimental results, which supported the CT scan results. When the static rupture and the cyclic rupture were compared, the main differences are twofold: (1) the number of fragments produced is much greater under cyclic loading than under static loading, and (2) intergranular cracks are formed due to particle breakage under cyclic loading compared with smooth and bright cracks along cleavage planes under static loading.

Variation of Fracture Energy Dissipation along Evolving Fracture Process Zones in Concrete

This paper examines the fracture energy properties over ligament length for crack propagation process accompanied by fracture process zone (FPZ) advancement. Local fracture energy as well as its average value along the crack path is investigated by considering the influence of specimen boundaries on the development of FPZ. To address the specimen boundary affected region over which local fracture energy generally spreads in a non-uniform manner, two concepts are introduced: Back boundary affected length and overall boundary affected length. Tests were conducted on wedge splitting concrete specimens to identify the variation of fracture energy dissipation when FPZ evolves toward the specimen back surface. Results included here reveal that the back boundary affected length is decreasing approximately in a linear way along with crack evolution. The overall boundary affected length, however, proves to be increasing at early stages of crack growth and then decreasing in a way similar to the back boundary affected length. Local fracture energy over crack extension decreases before FPZ gains its full development. For the case of a full-developed FPZ, it can be described by two different forms: one is in the form of a horizontal line, the other part shows to be decreasing but with a constant average value. The average value of local fracture energy, however, is predicted to increase along with the evolution of FPZ.