Semi-circular Bend Specimens Research Articles

Characteristics of mixed-mode Ⅰ-Ⅱ fracture of bedding mud shale based on discrete element method

Mud shale is an abundant unconventional source of oil and gas, with considerable potential for extensive exploration and development. Hydraulic fracturing is a core technology for the harvesting of mud shale resources. Mud shale usually contains developed bedding structures. A mixed-mode Ⅰ-Ⅱ failure occurs when hydraulic fractures meet the bedding layers. Understanding the characteristics of the mixed-mode Ⅰ-Ⅱ fracture of mud shale is of high practical significance. A numerical model for a semi-circular bend (SCB) specimen is built using a flat-joint model (FJM). The macroscopic mechanical parameters of the numerical model are calibrated, including the uniaxial compressive strength, elastic modulus, and Poisson's ratio. The microscopic parameters of the model are constantly adjusted using the trial-and-error method to realize an effective fit between the model and rock parameters. The results show variation characteristics of the stress field, displacement field, and fracture toughness are revealed on a microscopic scale during fracture initiation and propagation. The fracture propagation law under different bedding strengths and initial fracture angles is discussed, and the pattern of fracture interactions under different bedding angles and initial fracture angles is obtained. The results showed that the influence of the fracture toughness as the bedding angle decreased. The fracture arrest and the degree of fracture deflection upon reaching the bedding are more considerably influenced by the strength of the weak plane. The higher the bedding strength of the weak plane, the more likely the fractures were deflected in the bedding. However, fracture penetration of the bedding layer is more greatly influenced by the bedding angle.

Development of maximum tangential strain (MTSN) criterion for prediction of mixed-mode I/III brittle fracture

A number of fracture criteria are available for predicting the cracking behavior under combined contribution of opening-tearing damage mechanism (i.e. mixed-mode I/III). But most of them have some limitations or discrepancies with the experimental results. In this research, a new form of maximum tangential strain criterion called 3D-MTSN is developed for predicting mixed-mode I/III fracture phenomenon. This criterion was used originally for analyzing the mixed-mode I/II fracture but we extended its ability for mixed mode I/III as well. Also, the influence of T-stress in addition to modes I and III stress intensity factors was also considered in driving the fracture toughness and fracture angle formulations of the 3D-MTSN criterion. According to this strain-based criterion it is shown that both sign and magnitude of T-stress can affect the fracture behavior of mixed mode I/III. In general, positive T-stress increases the mixed mode I/III fracture envelope and conversely negative sign of T-stress can decrease it. Meanwhile, the Poisson’s ratio (v) has noticeable influence on the mixed mode I/III fracture envelopes and by increasing v, the mixed mode fracture curve predicted by the generalized MTSN criterion shifts down except for those specimens having positive T-stress values and subjected to dominantly pure mode I loading conditions. The practical ability and validity of 3D-MTSN criterion is examined by predicting different sets of mixed mode I/III experimental results reported in the literature for different brittle and quasi-brittle materials tested with different test samples including edge-notch disc bend (ENDB), inclined single edge notch beam (ISENB) and semi-circular bend (SCB) specimens. A comprehensive comparison with the well-known 3D-MTS (stress-based) criterion was also performed. Compared to the other available energy-based fracture models, the presented 3D-MTSN criterion provided better estimations for the experimental results of different materials and specimens under dominantly mode III conditions.

A novel approach to determine mode II fracture toughness of hot mix asphalt

Fracture behaviors of hot mix asphalt (HMA) are critical to the durability of asphalt pavement, especially at low temperatures. This study proposed a method to test the mode II fracture behaviors of HMA, which is inspired by the mode II test of cement concrete. In this method, compressive tests were conducted on two types of specimens, including the double-edged notch specimen and the cubic specimen. The shear action resulting in the mode II fracture was extracted from the energy difference between the load–displacement curves of the two types of specimens. The stress intensity factor (KII) and fracture energy (GF) were calculated from the theory of energy consumption. On the other hand, the effects of reclaimed asphalt pavement (RAP) and rejuvenator were examined on the mode II fracture performance of HMA. Meanwhile, asymmetric semi-circular bending (SCB) tests were also conducted to obtain the mode II KII and GF, which were used to verify the feasibility of the method proposed in this study. Results indicated that with the increase of RAP, KII and GF both decreased remarkably. When RAP content was 100%, KII and GF were reduced by 42.8% and 55.8%, respectively. When the rejuvenator and 75% RAP were added, the fracture performance was enhanced compared to HMA with 75% RAP only, indicating rejuvenator benefited the mode II fracture resistance. The result comparison between the double-edge notched specimens and the SCB specimens verified the feasibility of the method proposed in this study.

Research on the dynamic fracture toughness of reef limestone

The basic properties of reef limestone were measured to explore the dynamic fracture characteristics of reef limestone. The test results show that the physical and mechanical properties of blocky reef limestone are linearly related to the density. Hence, accurate mechanical parameters can be ascribed to standard mechanical specimens. Next, the fracture toughness of the reef limestone was measured using notched semi-circular bend (NSCB) specimens. Meanwhile, fracture energy and characteristics were studied with the help of a high-speed camera and scanning electron microscope. The findings show that the fracture toughness and energy of reef limestone are linearly related to the density with a rate effect. Moreover, the dynamic compressive strength is also linearly correrlated with the dynamic fracture toughness of reef limestone under the same loading rate; the fracture toughness of saturated reef limestone is larger than that of dry reef limestone. Besides, reef limestone has a rough fracture surface for its various crystal shapes and arrangements, with cracks propagating along the interface of varied crystals.

Experimental study on anisotropic fracture characteristics of coal using notched semi-circular bend specimen

To investigate the anisotropic fracture characteristics of coal, physical tests are carried out on semi-circular bend specimens with different pre-crack inclinations and bedding orientations. Regarding the coal as a transversely isotropic body, assigning its elastic properties to the finite element models, the crack geometry factors are calibrated, and stress distributions near the pre-crack tip are analyzed through numerical simulations. Then, the modes I and II critical stress intensity factors are determined based on fracture load. Experimental results show that bedding orientation and pre-crack inclination of coal specimens jointly affect their fracture mode and resistance, and mode I fracture dominates the fracture onset. For straight and inclined pre-cracks, the elliptic function and Fourier series can approximately describe the relationship between effective critical stress intensity factor and bedding angle, respectively. Besides, descriptions of typical propagation paths and their corresponding failure mechanisms are reported in detail. Further, the morphology of fracture surfaces is drawn based on scanning data; afterward, four equidistant cross-sectional profiles in different specimens are extracted and exhibited. Finally, an empirical equation is utilized to calculate the joint roughness coefficients of profiles. Comparing the differences among these coefficients is beneficial to quantitatively characterize anisotropic crack growth in coal.

Determination of dynamic mode I fracture toughness of rock at ambient high temperatures using notched semi-circular bend method

To investigate the influence of loading rate and high temperature on the dynamic fracture toughness of rock, dynamic fracture tests were carried out on notched semi-circular bend specimens under four temperature conditions based on the split Hopkinson pressure bar system. Experimental and analytical methods were applied to investigating the effect of temperature gradient on the stress waves. A high-speed camera was used to check the fracture characteristics of the specimens. The results demonstrate that the temperature gradient on the bars will not significantly distort the shape of the stress wave. The dynamic force balance is achieved even when the specimens are at a temperature of 400 °C. The dynamic fracture toughness linearly develops with the increase of loading rate within the temperature range of 25−400 °C, and high temperature has a strengthening effect on the dynamic fracture toughness.

Mixed-mode I/II fracture properties of selectively laser sintered polyamide

Additive manufacturing (AM) is a topical field today and has received the attention of many researchers. However, further research is needed to overcome the many challenges facing AM, especially in the mixed-mode fracture. The results presented in this paper are framing the experimental data obtained for mixed-mode I/II fracture properties of laser sintered polyamide. The experiment was carried out on Semi-Circular Bend (SCB) specimens manufactured from polyamide PA2200 using EOS Formiga P100 laser sintering machine. To achieve the full range of fracture toughness values, from pure mode I to pure mode II, five crack orientations of the SCB specimens (0, 15, 30, 45 and 54°) were considered. Further, crack initiation angle and crack paths of SCB specimens have been assessed in order to identify the fracture phenomena (interlayer and/or intralayer fracture). The main fracture properties (fracture toughness, crack initiation angles and crack paths) were compared with the theoretical predictions of three mixed-mode fracture criteria (Maximum Tensile Stress-MTS, Maximum Energy Release Rate-Gmax and Equivalent Stress Intensity Factor-ESIF). The results underline differences between theoretical approaches and experimental data, especially due to the interlayer fracture phenomenon. However, it was obtained that the Gmax and ESIF criteria show the best match with the experimental data.

Fracture toughness and cracking behavior of frozen sandstone at different freezing temperatures

Fracture toughness and crack behavior of frozen rocks have an important guiding significance for engineering in cold regions, where the freezing temperature is one of the main factors that affect the mechanical properties of frozen rocks. Therefore, both mechanical properties (fracture toughness, compressive strength, and tensile strength) and pore phase composition of water-saturated sandstone at different freezing temperatures (0 °C, −2 °C, −4 °C, −6 °C, −8 °C, −10 °C, −12 °C, −15 °C, −20 °C) were tested in this paper. High-speed photography was used to capture the crack propagation process of the semi-circular bending (SCB) specimen. Also, morphological characteristics of the fracture surface under different freezing temperatures were analyzed. The results show the following: (1) The fracture toughness of saturated sandstone increases exponentially with the decrease of freezing temperature, reaching an increase of 402 % at −20 °C. (2) When the freezing temperature decreases from 0 °C to −8 °C, the crack growth rate increases rapidly. (3) The fracture surface roughness coefficient (Rs) of the SCB specimen shows a two-stage decreasing trend: a rapid decrease (0 °C to −8 °C), and a slow decrease (−8 °C to −20 °C). (4) The change of phase composition with freezing displayed two distinct stages: the unfrozen water content decreases rapidly and the ice content increases rapidly (0 °C to −4 °C) and then the unfrozen water content decreases slowly and the ice content increases slowly (−4 °C to −20 °C). Based on the above test results, we suggest that: (1) With the decrease of the freezing temperature, the pore phase composition changes significantly, resulting in enhanced mechanical properties of the rock. (2) The cementation and filling effect of pore ice reduce the dissipative energy in the process of crack expansion, increasing the brittleness index, so the crack growth rate of the SCB specimens increases rapidly.

Use of DIC and AE for investigating fracture behaviors of cold recycled asphalt emulsion mixtures with 100% RAP

Cracking damage have great influence on the service life of cold recycled asphalt emulsion mixtures (CRAEM). As non-destructive methods, digital image correlation (DIC) and acoustic emission (AE) techniques can diagnose and visualize various distresses efficiently. The objective of this research was to explore and characterize the fracture behaviors of CRAEM with DIC and AE. Firstly, the semi-circular bending (SCB) tests, accompanied with DIC and AE monitoring were conducted on CRAEM with different cement contents. Secondly, the fracture energy examined by DIC as well as the tracked cracking path were analyzed to correlate with the fracture characteristics of CRAEM. Then, the variation of AE parameters (i.e., AE energy, AE amplitude) were investigated to identify the damage stages of SCB specimens. Finally, the box-counting dimension and the AE b-value were established based on cumulative AE energy and AE amplitude separately to quantitatively assess the transition of damage state. The results indicate that the cement content would significantly affect the cracking resistance performance of CRAEM, and CRAEM with a moderate content could have the benefits of more alternative energy release paths in the process of crack initiation and propagation. The fracture failure process of CRAEM could be divided into four stages through the simultaneous mutations of cumulative AE energy and AE amplitude. The difference of fracture surface morphologies of CRAEM with different cement contents obtained by the digital microscope could provide a reliable explanation for the fracture behaviors of the whole damage evolution process of CRAEM. The transition of the value of box-counting dimension from the maximum to the minimum could reflect the formation of macrocracks of CRAEM. The inflection point of the AE b-value curve arriving at the minimum value could be regarded as a precursor information to predict the complete fracture of CRAEM.

Application of Asymmetric Notched Semi-Circular Bending Specimen to Evaluate Mixed-Mode I-II Fracture Behaviors of Sandstone

In this paper, to investigate mixed-mode I-II fracture behaviors, three different asymmetric notched semi-circular bending specimens (ANSCB) were designed by adjusting the angle and the distance between supporting rollers to conduct asymmetric three-point bending tests. Several aid technologies, including acoustic emission (AE), digital image correlation (DIC), crack propagation gauge (CPG), and scanning electron microscopy (SEM), was utilized to monitor and assess the fracture characteristic. Meanwhile, the fractal dimension of the fracture surface was assessed based on the reconstructed digital fracture surface. The results show that mixed-mode I-II ANSCB three-point bending fracture is a brittle failure with the characteristics of the main crack being rapidly transfixed and the bearing capacity decreasing sharply. Based on the DIC method, the whole fracture process consists of a nonlinear elastic stage, fracture process zone, crack initiation stage and crack propagation stage. The crack initiation is mainly caused by the tension-shear strain concentration at the pre-existing crack tip. At the microscale, the crack propagation path is always along the grain boundary where the resultant stress is weakest. According to the monitoring of the AE, it can be found that micro-tensile cracks are mainly responsible for the asymmetric three-point bending fracture. The data obtained by CPG suggest that the subcritical crack growth rate is positively correlated to the ultimate load. In addition, asymmetric loading leads to a coarser fracture surface, and thus a higher fractal dimension of the fracture surface. The current study can provide a better understanding of the mixed-mode I-II fracture behaviors of rock.

Study on mode I fracture toughness of rocks using flat-joint model and moment tensor

The semi-circular bend specimens with straight and chevron notches have been widely used to determine the fracture toughness owing to their simplicity and convenience of testing. The notch shape, model size and heterogeneity affect the cracking mechanism and the accuracy and feasibility of the mode I fracture toughness, which typically leads to deviations from different methods. In this paper, the flat-joint model is used to calibrate Kowloon granite with uniaxial compressive strength, indirect tensile strength, Young’s modulus and mode I fracture toughness (semi-circular bend (SCB) test) of approximately 180 MPa, 5.6 MPa, 20 GPa and 1.24 MPa·m0.5. The moment tensor is used to quantitatively investigate fracture process of SCB and the cracked chevron notched semicircular bend (CCNSCB) specimens of Kowloon granite with a loading rate of 0.0084 m/s. During modelling, the failure model and microcracking mechanism are quantified and compared in detail against laboratory data in the literature. The results indicate that the chevron notch is more likely to cause ideal mode I fracture due to its higher proportion of tensile source and larger average value of k. Size effect analysis is used to verify the ISRM-suggested size for the SCB specimen and provide some size recommendations of the CCNSCB specimen. Three typical classification methods are used to quantitatively study the effect of heterogeneity on cracking mechanisms suggesting that for the fully-developed fracture process zone (FD-FPZ), the nature of the source and energy characteristics are associated with heterogeneity. These results shed some light on the microcracking mechanism of the SCB and CCNSCB tests.

Extended finite element modeling of hot mix asphalt based on the semi-circular bending test

Semi-circular bending (SCB) test is widely used to characterize the fracture behaviors of asphalt mixtures. In this study, heterogeneous models of SCB specimens were prepared with the difference in aggregate shape. Asphalt concrete was composed of coarse aggregate and fine aggregate matrix (FAM). Extended finite element modeling (XFEM) was utilized to capture the fracture behaviors of asphalt mixtures under −10 and 20 °C. The initiation and propagation of cracks under different temperatures were observed. Local cracking was mainly initiated around the aggregates or on the aggregates. Statistical analysis of the failure loads and the displacements corresponding to the peak loads were obtained, and comparison was made with the laboratory test results. SCB tests with the round particles presented the greatest failure load, followed by convex, ellipse and concave particles. The effect of aggregate shape on dissipated fracture energy was the same as the effect of particle shape on failure load. Laboratory results were consistent with the simulation results, proving the reliability of the numerical model.

Comparative study on modes I and II fracture characteristics of bituminous coal using asymmetric semi-circular bend specimen

Modes I and II fractures of coal play an important role in coal mining and have a serious impact on coal production and the control of mining hazards. Therefore, asymmetric semi-circular bend (ASCB) specimens with different notch depths were used to carry out modes I and II loading tests. The differences in the modes I and II fracture characteristics of coal specimens were studied. The internal damage characteristics, surface displacement characteristics, failure mode and microscopic damage mechanism of bituminous coal specimens were analysed by acoustic emission (AE) and digital image correlation (DIC) methods. The results show that the fracture toughness of coal under mode II loading is 1.02 times greater than that under mode I loading. The crack initiates along the centreline of the specimen and propagates in a roughly linear form under mode I loading. Under mode II loading, the curved crack mainly initiates from the upper left of the ASCB specimens. The notch length has a significant impact on peak load and fracture toughness, but it has a slight influence on crack propagation path. Larger notch depths are more suitable for modes I and II ASCB fracture tests. In this study, a method based on AE parameters is proposed to determine the real-time microscopic failure mechanism of coal. Combined with AE and DIC methods, it is revealed that the coal specimens experience tensile fracture (mode I) initiation under both mode I and mode II loading, and no specimen can be initiated with mode II shear fracture under pure mode II loading. Mode II loading and mode II fracture are not equivalent.

Experimental evaluation of the transient propagation fracture properties of rocks under dynamic mode I loading: An insight from digital image correlation

Accurate measurement of dynamic fracture properties is crucial for the safety and stability of the engineering applications. In this study, the dynamic mode I fracture tests are conducted on the notched semi-circular bend (NSCB) specimens with the split Hopkinson pressure bar (SHPB) loading system. By virtue of digital image correlation (DIC) technique combined with high-speed photography, the velocity fields of specimen are revealed, and thus an improved method is proposed to accurately calculate the transient kinetic energy and transient propagation fracture toughness of NSCB specimens under dynamic mode I loading. Our method has obvious merits in its specimen preparation and calculation accuracy since no specific assumptions are required. In addition, the crack propagation gauge (CPG) system is also applied into the tests to capture the transient crack propagation velocity and verify the testing results obtained by DIC technique. The results show that the transient propagation velocity of rocks continues to decrease with a three-stage evolution during the process of rock fracture, while the transient fracture energy of rock gradually increases. Moreover, the transient propagation fracture toughness is inversely proportional to the transient crack propagation velocity. Furthermore, the initiation fracrture toughness, propagation fracture toughness, propagation velocity and fracture energy all feature significant loading rate dependence.

Mixture optimization of epoxy base concrete for achieving highest fracture toughness and fracture energy values using Taguchi method

Manufacturing polymer concrete (PC) with suitable performance against cracking is an important issue for using these composite materials in practical applications. Fracture toughness and fracture energy of such randomly distributed aggregates inside the matrix of polymeric resin is affected by the mix design and percentages of PC ingredients. In this research, the optimum composition of epoxy base PC mixture made of four ingredients (epoxy resin, fine and coarse silica aggregate and E-glass fiber) was obtained using a L32 Taguchi design of experiment method. Some fracture toughness tests under mode I were conducted on symmetric semi-circular bend specimen according to design of experiment suggested by Taguchi method. The initial range for each PC ingredient was selected as: 0–2% fiber, 20–35% fine aggregate, 13–28% epoxy resin, and 41–56% coarse aggregate, and it was found that the mixture containing maximum resin (25–28%), moderate fine filler (28–31%), minimum percentages of fiber and coarse aggregate can provide the highest fracture energy and fracture toughness values.

Research on the effect of thermal treatment on the crack resistance curve of marble using notched semi-circular bend specimen

The crack resistance curve is widely used to describe the complete fracture process of quasi-brittle materials. In the paper, the crack resistance curves of thermally treated marble were tested through the notched semi-circular bend specimens. The acoustic emission (AE) and digital image correlation (DIC) techniques were used to monitor the fracture behaviors of the specimens during the test. The AE results indicated that the crack will initiate from the notch when the axial load is less than the peak load. And, when the axial load reaches the peak load, the DIC results demonstrated that there exists a large fracture process zone (FPZ) in front of the crack notch. The effect crack length was calculated by the compliance method, which is coincided with the DIC results. The amplitude of the crack resistance curves decreases with the increase of treatment temperature, which suggested that the fracture resistance of the specimen declines due to thermal treatment. Based on the K-resistance curves, the initial fracture toughness, unstable fracture toughness, and fracture toughness when FPZ is fully formed have been determined for the thermally treated specimens. The results showed that these parameters both decrease in the increase of treatment temperature. Moreover, The FPZ length first increases and then decreases with the increase of normalized crack length and the critical and maximum non-dimensional FPZ length tends to increase with the increase in treatment temperature.

Experimental investigation on Mode I crack growth and damage mechanism of sandstone subjected to cyclic loading

To further investigate the Mode I crack growth and damage mechanism, compression tests were performed on notched semi-circular bending (NSCB) specimens at different cycle amplitudes. The crack propagation gauge and digital image correlation (DIC) recorded the entire process of crack growth. The real-time crack growth rate and evolution of the horizontal strain field during crack growth were obtained. Based on the crack growth rate, the crack growth process can be divided into three stages: the cracking latent period (primary stage), stable crack growth stage (secondary stage), and accelerated crack growth stage (tertiary stage). The cracking latent period accounts for a large proportion of the entire crack growth. The stable crack (i.e., steady subcritical crack growth) expanded slowly to a certain extent after initiation, and then the accelerated crack growth led to failure. With the increase in the cyclic amplitude, the cracking latent period is shortened and the crack growth rate is accelerated. The crack growth rate is positively correlated with the stress intensity factor. Moreover, scanning electron microscopy (SEM) was used to analyse the development of the fracture process zone (FPZ) and the subcritical crack damage mechanism. The SEM images showed two damage phenomena: (1) intergranular cracks caused by grain debonding (primary mechanism) and (2) transgranular cracks (secondary mechanism).

Extending application of asymmetric semi-circular bend specimen to investigate mixed mode I/II fracture behavior of granite

Extending application of asymmetric semi-circular bend specimen to investigate mixed mode I/II fracture behavior of granite

Size effect in true mode [formula omitted] fracturing of rocks: Theory and experiment

The influence of specimen size on the measured values of true mode II fracture toughness (KIIc) of rocks have been investigated both experimentally and theoretically. In the experimental study, the double-edge notched Brazilian disk (DNBD) test is utilised to perform fracture toughness experiments with various specimen radii ranging from 27 to 101 mm. Test results demonstrate a significant increase of KIIc with the specimen size. The reason for this trend is explained by a novel mathematical model developed based on the fracture process zone and the energy release rate (ERR) concepts. Comparing the predictions of the theoretical model with the experimental data reveals that the proposed theory can accurately predict the size effect phenomenon in the DNBD test data. To compare the results of KIIc with KIc, similar experimental and theoretical analyses are also performed for mode I fracture toughness tests using the semi-circular bend specimens. Lastly, we present a set of correction factors as functions of specimen size, whereby making it possible to estimate the size independent value of KIIc from the test results obtained from laboratory size DNBD specimens.

Translaminar notch fracture toughness expressions for composite laminates

First, two different test specimens, namely the rectangular tension (RT) and semi-circular bend (SCB) specimens, weakened by U-notches of various notch tip radii and made of E-glass/epoxy composite laminates of different lay-up configurations, are considered for measuring experimentally the translaminar notch fracture toughness (TLNFT) of the composite material under pure mode I loading conditions. Then, two new closed-form expressions are proposed for the TLNFT, by taking advantages of the maximum tangential stress (MTS) and the mean stress (MS) criteria, as well as the recently proposed virtual isotropic material concept (VIMC), with the goal to estimate the experimental results. It is found that both criteria can well estimate the test results that locate always between the predictions of MTS and MS criteria. Taking into account that MTS criterion is more conservative and simpler than MS criterion, it is preferred in mechanical design of notched E-glass/epoxy composite structures.