Semi-circular Bend Specimens Research Articles

The use of a two-phase Monte Carlo material model to reflect the dispersion of asphalt concrete fracture parameters

The work covers comprehensive laboratory tests of semi-circular bending (SCB) of asphalt concrete samples. The results of two test series, including four and 32 SCB specimens, indicate a substantial scatter of force–deflection (F-d) histories. The numerical analysis is aimed to reflect the maximum breaking load and fracture energy of the samples, pointing out their random character. The original simulation-based fictitious Monte Carlo material model was introduced. The authors’ algorithm randomly assigns asphalt mortar and coarse aggregate parameters to the finite elements of the numerical model. As a result, sets of random fields are generated to reflect the two-phase material distribution in the samples. The model parameters are numerically adjusted based on laboratory test results of the initial four SCB specimens. In the course of model verification, the 32-sample computations were compared with the laboratory data. The results of FEM simulations are consistent with laboratory test results, including dispersion of fracture parameters. The proposed computational algorithm with a two-phase material model is ready to be implemented in the analysis of actual road pavement constructions and may support the design process.

Fracture studies of 3D-printed continuous glass fiber reinforced composites

Additive Manufacturing (AM), typically known as three-dimensional (3D) printing has paved the way for fabrication of individualized products. Since 3D-printed composites show a superior strength to weight ratio, their applications have significantly increased. In the current study, fracture behavior of 3D-printed fiber-reinforced composites and steel specimens was determined and compared. Particularly, the Fused Filament Fabrication (FFF) process was used to print Semi-Circular Bending (SCB) composite specimens. In this context, nylon and glass fibers were used as matrix and fiber reinforced materials, respectively. Moreover, steel SCB specimens were fabricated and examined for comparison. All specimens were subjected to three-point bending and their mechanical behavior was examined. In this study, Digital Image Correlation (DIC) technique was utilized to measure strain on the surface of the specimen. In addition, a numerical simulation was performed to study fracture load of SCB steel specimens and verify experimental observations. The outcome of this study indicates that structural integrity of SCB specimens increases with fiber volume fraction. The documented results can be used for design, optimization, development, and simulation of 3D-printed continuous glass fiber-reinforced composites.

Effect of printing speed on tensile and fracture behavior of ABS specimens produced by fused deposition modeling

The current paper deals with the influence of printing speed on the tensile and fracture strength of Acrylonitrile Butadiene Styrene (ABS) specimens made by Fused Deposition Modeling (FDM) technique. Four different printing speeds of 10, 30, 50, and 70 mm/s are used to fabricate dog-bone and Semi-Circular Bending (SCB) specimens for examining the mechanical and fracture performance of FDM-ABS parts, respectively. Due to the plastic deformation in the crack tip zone of SCB specimens prior to fracture initiation, the critical value of J-integral is chosen as the fracture characterizing parameter. Therefore, elastic–plastic finite element analyses are performed to calculate the critical values of J-integral (Jc). According to the experimental results, the fabricated specimens with a printing speed of 70 mm/s shows the best performance with the maximum elongation and fracture resistance compared to the other printed specimens with different nozzle speeds. For exploring the failure mechanisms in the tensile specimens Scanning Electron Microscopy (SEM) is utilized and various failure mechanisms have been presented and discussed. These observations are then linked to the tensile and fracture properties of the studied specimens.

Tensile mode fracture toughness experiments on andesite rock using disc and semi-disc bend geometries with varying loading spans

Purpose of this research is to investigate the effect of loading span on mode I fracture toughness for tests conducted by three-point bend geometries. Mode I fracture toughness tests were conducted on Ankara Golbasi Andesite with straight notched disc bending (SNDB) specimens of thicknesses 50 mm and 60 mm. Loading spans were varied in a wide range between 40 mm and 90 mm corresponding to span/radius ratios of S/R = 0.40 to 0.90. Three-point bend tests were conducted with the semi-circular bending (SCB) core specimen geometry for comparison purposes. Mode I fracture toughness results for tests with 60 mm and 50 mm thick SNDB specimens were about 30% greater than the results of SCB tests. It was found that mode I fracture toughness, KIc increases with decreasing the span length for both SNDB and SCB specimens. Mode I fracture toughness values was also increased with increasing the specimen thickness for the SNDB geometry. The differences in KIc results of different specimen geometries were explained by a mechanism employing maximum normal strain criterion. It was demonstrated that despite the dependency of critical stress intensity factor to the geometry and loading conditions of the tested specimen, the critical value of maximum tangential strain (εθθc) at the onset of fracture is a material constant and its value is nearly the same for all disc and semi-disc geometries tested with varying loading spans.

An ultrafast time-resolution method based on picosecond pulsed laser for determining rock fracture toughness at multipoint during the crack propagation

An innovative ultrafast time-resolution method based on a picosecond pulsed laser was employed to investigate the mode-I crack propagation characteristics of fractured rock. Its time resolution is as fast as the degree of 45 picoseconds. Then, a series of three-point compressive loading tests with this method were conducted on tuff semi-circular bend (SCB) specimens. Based on this method, we found that the mode-I fracture process of the tuff specimens were composed of repeated crack initiation, arrest, and re-initiation. In addition, the experimental results showed that the fracture rates of the tuff specimens in the initial 10 μs were 636 m/s, 663.9 m/s, and 578 m/s. In comparison, the fracture rates of the specimens were 11.19 m/s, 19.23 m/s, 26.79 m/s during the whole fracture process. As a typical heterogeneous material with primary defects, rock has different fracture toughness at different locations. Therefore, we proposed a new method for determining rock fracture toughness at multipoint during the crack propagation. This new method emphasizes the effect of fracture toughness on crack propagation, which enables to determine the fracture toughness at multipoint and is closer to the original definition of fracture toughness.

U-notch fracture in additively manufactured ABS specimens under symmetric three-point bending

This paper aims to investigate the fracture behavior of U-notched semi-circular bend (USCB) specimens fabricated from the Acrylonitrile Butadiene Styrene (ABS) using the fused deposition modelling (FDM) method under opening-mode loading. The notched specimens are manufactured with different notch tip radii and various unidirectional layup configurations for which the fracture loads are experimentally acquired by conducting fracture tests under symmetric three-point bending. Some additional tests are also performed on cracked and plain tensile specimens to obtain the fracture toughness and tensile properties of the ABS material. With the goal of estimating the fracture loads theoretically, the recently proposed virtual isotropic material concept (VIMC) is linked to three different brittle fracture models, namely the point-stress (PS), mean-stress (MS), and averaged strain energy density (ASED) criteria. Comparing with the experimental results, it is shown that the VIMC-MS criterion is generally the best model among the three ones, while VIMC-PS criterion gives fair results and VIMC-ASED criterion is excellent only for larger notch tip radii. The crack growth path of the mentioned samples as well as their type of failure is also evaluated. It is revealed that the unidirectional USCB samples with 0, 30, and 45 degrees layup configurations experience inter/cross-laminar fracture, while those with 60 and 90 degrees layups experience inter-laminar fracture.

Fracture Toughness Determination on an SCB Specimen by Meshless Methods

This work investigates fracture characteristics of a marble semi-circular bend (SCB) specimen with a pre-defined crack under a compressive loading condition. It aims at evaluating how the fracture toughness can be affected by the crack and span length variation. Numerically, the model is solved using meshless methods, extended to the linear elastic fracture mechanics (LEFM), resorting to radial point interpolation method (RPIM) and its natural neighbor versions (NNRPIMv1 and NNRPIMv2). Alternatively, to validate the meshless method results, the problem is resolved following the finite element method (FEM) model based on the standard 2D constant strain triangle elements. As a result, fracture toughness and the critical strain energy release rate are characterized following the testing method on the cracked straight through semi-circular bend specimen (CSTSCB). A comparison is drawn amongst the theoretical, meshless methods and FEM results to evaluate the capability of advanced numerical methods. Encouraging results have been accomplished leading to validate the supporting numerical methodologies.

Crack propagation characteristics and fracture toughness analysis of rock-based layered material with pre-existing crack under semi-circular bending

Fracture initiation, fracture propagation, and their interactions with the interlayer interface in rock-based layered material are important in assessing the stability of rock-based structures such as lined tunnels. A numerical model based on the inserted cohesive zone model (CZM) method is established, and further verified against the semi-circular bending (SCB) test to simulate the complex crack initiation and propagation behavior in a rock-based layered semi-circular disk with pre-existing rock crack at different angles. From the results, three typical crack propagation modes are identified: interface fracture, wing fracture from crack tip and wing fracture not from crack tip. At a small crack inclination angle, interfacial crack is formed, while at a larger crack inclination angle, wing crack which initiates deviating from the crack tip appears. It is found that the crack propagation mode is also controlled by the interface strength, and the interface crack is always formed in SCB specimens with lower interface strength. By increasing the interface strength, the length of interface crack gradually decreases and wing crack presents. When the pre-existing rock crack inclines greater than 45° and the interface strength is larger, the wing crack initiating far away from the crack tip merges with the interface crack to be connected propagating path, and the initiation position of wing crack gradually moves toward the crack tip with the further increasing of interface strength. Moreover, it is also found that the crack length ratio and the support span ratio are important influencing factors for crack propagation mode. Increasing the crack length ratio can suppress the formation of interfacial crack. When the crack inclination angle is more than 45°, the wing crack tends to originate at the tip of pre-existing crack as the support span ratio increases. In addition, the effects of crack length ratio, support span ratio, crack inclination angle and Young’s modulus ratio on the fracture toughness of layered SCB specimen under different loading modes are also investigated and the corresponding results indicate that these factors remarkably control the fracture mode and fracture resistance of rock-based layered material.

Characterization of crack resistance mechanism of fiber modified emulsified asphalt cold recycling mixture based on acoustic emission parameters

In the present study, to solve the problem of poor early strength and crack resistance of emulsified asphalt cold recycled mixture, the enhancement and fracture mechanism of fiber on emulsified asphalt cold recycled mixture were studied from multi-scale. The effect of fiber on the macroscopic mechanical properties of emulsified asphalt cold recycled mixture was studied by early and molding strength, dry-wet splitting ratio test and fracture energy index of semi-circular bending specimen. Optimum fiber types and dosages for emulsified asphalt cold recycled mixes have been selected. The relationship between crack evolution and acoustic emission parameters activity of fiber emulsified asphalt cold recycled mixture is studied, which reflects the microscopic failure mechanism of the material. The microstructure and morphology of fibers in the mixture were observed by scanning electron microscopy (SEM). The results show that both fibers can improve the strength and crack resistance of emulsified asphalt cold recycled mixture. Basalt fiber has better adsorption and anchoring effect on asphalt due to its high modulus and rough surface texture. The optimum dosage is 0.3 % of the mixture quality. Fracture characteristics of fiber emulsified asphalt cold recycled mixture are reflected by acoustic emission parameters. At the optimum fiber content, the acoustic emission parameters showed that the time from micro-cracks to macro-cracks in the fiber-emulsified asphalt cold recycled mixture was 122.22% longer than that in the control group. Basalt fiber plays the role of reinforcing crack resistance and anchorage in emulsified asphalt mixture, delaying the expansion of micro cracks.

Effect of friction at the supports of semi-circular bending tests on fracture mode of loading

This paper aims to provide an investigation of the impact of supports on fracture mode of loading using semi-circular bending (SCB) specimen. A crack with an angle of α is assumed within the SCB specimen, and extensive finite element analyses are performed by altering some important parameters namely crack angle, crack length, span and friction coefficient at the supports. According to the numerical results, all these parameters can influence the values of geometry factors YI and YII. Interestingly, it is found that the friction coefficient (or support type) can significantly change the mode of loading at the crack tip. To verify this issue, some experiments on a rock material are also carried out under different fracture modes using three various types of supports called type I, type II and type III. Based on the results of finite element and tests, in order to produce the same mode of loading using the mentioned support types, the crack angle should be changed. In other words, the crack angles of 29, 25 and 23° should be respectively used for the support types of I, II and III to produce the same mixed mode of loading with Me = 0.5. Likewise, they should be regarded as 41, 37 and 36° for the support types of I, II and III to produce the pure mode II loading. Furthermore, the friction coefficients for the mentioned support types are computed.

Experimental and numerical evaluation of semi‐circular bending specimen for mixed mode I/III and pure mode III fracture tests

AbstractThis paper suggests a simple loading configuration for conducting the SCB (semi‐circular bend) tests on brittle materials to produce mixed mode I/III loadings. In the suggested test setup, the SCB specimen containing an inclined crack is loaded using a conventional three‐point bending fixture, but the bottom supports touches nearly half of the specimen thickness rather than the entire thickness. It is found that various mixed mode I/III loadings can be provided by rotating the crack, and especially the SCB specimen experiences pure mode III when the crack angle is set to be 90°. Different values of the crack length, span and crack angle are then considered in the numerical analyses to further study the proposed SCB test setup. Finally, several experiments are successfully conducted on the rock samples under various mixed mode I/III and pure mode III loadings to evaluate the SCB test setup in practical point of view.

Determination of mode I fracture toughness of rocks with field fitting and J-integral methods

Static fracture testing was performed on ISRM-suggested semi-circular bend (SCB) specimens with a constant CMOD increment rate of 0.0002 mm·s−1, and the digital image correlation (DIC) technique, as a practical and effective non-contact tool, was adopted for full-field deformation measurement and fracture process zone (FPZ) size determination. Two displacement-based methods, i.e. field fitting method and J-integral method, were employed to measure the fracture toughness of three types of rocks, i.e. red sandstone, marble, and granite. The effectiveness and robustness of two displacement-based methods were verified with synthetic images containing a mode I crack. Moreover, the sensitivity of the affecting factors in displacement-based methods, such as crack tip location, area for field fitting, the number of solution terms, and the integral paths were studied for more reliable fracture toughness of SCB specimens. Both displacement-based methods give the effective fracture toughness inherently considering the existence of the FPZ above the notch tip, without knowledge of the geometry of the specimen and applied loads. Experimental results indicated that the crack tip location estimated by the field fitting method is close to the merged point of the opening displacement contours, i.e. the tip of the FPZ. Both displacement-based methods generate comparable fracture toughness of three rocks, and an increase of 20%∼35% in fracture toughness is observed compared to the standard load-based method. Moreover, the effectiveness and applicability of the modified load-based method that takes the FPZ length into account are also verified with the two displacement-based methods.

Application of asymmetric semi-circular bend test for determining mixed mode I + II fracture toughness of compacted soil material

Soil is a common material for constructing the sub-grade layer in multi-layer pavement systems, buried pipelines and embankment dams. Failure and fracture of this material may result in undesired deformation and bad effect on the long-term performance of such structures. So far a number of testing methods and data are available for tensile type fracture (or mode I fracture) of soil materials. However, soil materials can experience mixed mode tensile-shear deformations in real situations due to external applied loads. Hence, a suitable testing method called asymmetric semi-circular bend (ASCB) specimen was proposed and utilized in this paper for characterizing the mixed mode tensile-shear cracking behavior of compacted soil materials. Full mode mixities ranging from pure mode I to pure mode II were tested on a clay soil material using the ASCB specimen. Depending on the mode mixity, the soil fracture toughness value was varied between 0.025 and 0.035 MPa.m0.5. The lowest fracture toughness was obtained at mixed mode I/II with nearly the same contribution of tensile and shear deformations. In this loading situation the effective fracture toughness (Keff) was approximately 30% less than KIc and KIIc (i.e. pure modes I and II fracture toughness values, respectively). The fracture toughness values under pure mode I and pure mode II were almost equal. The maximum tangential stress criterion was also able to predict well the experimental mixed mode I/II soil fracture toughness results.

The mode I fracture toughness alternation and crack propagation behavior evolution due to long-term Sc-CO2 saturation

The mode I fracture toughness is a critical parameter which defines the rock’s resistance to crack propagation, especially in hydraulic fracturing. Recently, Supercritical carbon dioxide (Sc-CO2) has been proposed as a fracturing fluid candidate in hydraulic fracturing stimulations of shale reservoirs. However, its effects on fracture toughness transition and crack propagation behaviors have not been understood well. In this study, we performed a series of semicircular bend specimens (SCB) before the Longmaxi shale specimens’ saturation. Three-point bending tests along divider orientation showed that after Sc-CO2 saturation, mode I fracture toughness (KIC), elastic modulus (E) and absorbed energy (Ue) of shale were decreased by 22.1%, 24.5% and 44.3%, respectively. High speed camera images indicated that after Sc-CO2 saturation, mode I crack directly propagated straight along artificial pre-crack direction, decreasing the degree of crack deviation as in KIC. The results of Cronos high-precision 3D scanning system and scanning electron microscopy (SEM) revealed complicated fracture mechanisms (transgranular, intergranular and mutual coupling crack mechanisms) of shale after Sc-CO2 saturation, which reduced the roughness and area of fracture crack surface. The generation of pore and cracks was the main reason for the decrease of shale resistance to fracture. Furthermore, Sc-CO2 saturated shale specimens only needed to absorb less energy to more rapidly cause the initiation and propagation of mode I cracks with the main fracture mode being transgranular cracks.

Mixed modes crack paths in SCB specimens obtained via SLS

The paper presents experimental results of the crack path in Semi-Circular Bend (SCB) specimens obtained through additive manufacturing using Selective Laser Sintering (SLS) process. Determination of fracture parameters for components obtained via Additive manufacturing is a challenging topic, due to the influence of manufacturing parameters on the mechanical properties. Several researches provided the fracture toughness of SLS components, however there are not yet available results regarding the crack paths in such materials. The SCB specimens were designed with different crack orientations (0°, 15°, 30°, 45°, and 54°) and manufactured using EOS Formiga – SLS equipment (energy density 0.066 J/mm2, chamber temperature 169.5 °C, layer thickness 0.1 mm) using PA2200 material. The specimens were tested in symmetric three point bending configuration, creating 6 mode mixity from mode I (0° – crack orientation) to pure mode II (54° – crack orientation). Tests were performed at room temperature using 2 mm/min loading speed in a Zwick ProLine Z005 testing machine. For each crack orientation five specimens were tested. Crack initiation angle and crack propagation were measured by image digitization after the mechanical testing and presented in accordance to the initial orientation of the crack. Also, numerical simulation of crack path was conducted in the same way like the experiment and results were compared to the measured one.

Size effect in PLA and PETG specimens obtained using FDM

The Semi Circular Bend Specimens loaded in symmetric three point bending were considered to investigate the size effect in PLA and PETG specimens obtained using FDM technology. Four specimen sizes were manufactured with radius R = 10, 20, 30 and 40 mm, with thickness of 6 mm and tested. A strong size effect for PLA and PETG materials obtained through additive manufacturing is experimentally demonstrated, representing the transition between strength of materials approach (with no size effect) and asymptotic case of linear elastic fracture mechanics. This agrees well with the size effect law proposed by Bažant (2002) and Zdenek et al. (2003).

Evaluation of the fatigue properties for the long-term service asphalt pavement using the semi-circular bending tests and stereo digital image correlation technique

Reliable assessment of the fatigue resistance of asphalt pavement with a long-term service is critically crucial for the rational formulation of original pavement utilization strategies in reconstruction and expansion projects. Currently, the pavement performance evaluation indicators are mainly used to guide pavement preventive maintenance, and its applicability in reconstruction and expansion projects of the freeway is limited. This paper aims to propose an evaluation method of fatigue resistance of asphalt concrete utilizing semi-circular bending (SCB) tests and stereo digital image correlation (stereo-DIC) techniques. A total of 27 asphalt concrete cores were drilled from the three freeways (K84, K124, and K165) with a service life of more than 20 years, and the SCB specimens were produced to conduct the SCB fracture and fatigue tests. During the SCB test, the stereo-DIC technique was employed to monitor the evolution process of the strain distribution and crack length for the specimens. K-dimension tree neighbor-searching algorithm (K-d tree algorithm) was used to effectively measure the change of crack length corresponding to each fatigue load cycle. Meanwhile, the strain threshold of asphalt concrete crack initiation was determined by the bilinear softening cohesive zone model (CZM) to ensure the accuracy of the crack length calculated by the K-d tree algorithm. Furthermore, the relationship between crack growth rate and stress intensity, which was used to fit the Paris law parameters, was determined. The CZM and DIC results indicated that the strain threshold of asphalt concrete crack should be set as 2000 με when using the K-d tree algorithm to determine the crack length. With the stress ratio increase, the Paris law parameter A increased wavily, and the parameter n decreased steadily, while the threshold of the stress intensity factor increased steadily. The Paris law master curves could characterize the fatigue performance of various road sections at a wide load range. The residual fatigue life of K84, K124, K165 the road sections were 2.13E + 08, 3.57E + 08, and 1.02E + 07, respectively.

The role of mix design and short glass fiber content on mode-I cracking characteristics of polymer concrete

Suitable resistance against fracture and cracking is a primary requirement for using polymeric concrete materials in practical applications. The main aim of this research is to investigate the effect of mix-design on mode I cracking behavior. A total number of 72 different Polymer Concrete (PC) mix-designs made of four ingredients (epoxy resin, coarse silica aggregate, fine sand filler and chopped strand E-glass fibers) were considered for conducting fracture experiments using the Semi-Circular Bend (SCB) specimen. The weight percentages of the ingredients were varied in the following range: 17–25% resin, 75–81% fine and coarse aggregates and 0–2% glass fibers. The investigated mix-designs were categorized into six groups (ultra-high, high, medium-high, medium-low, low and ultra-low) in terms of the adhesive agent content (i.e. the ratio of resin plus fiber content to the weight of the whole mixture). The experiments showed the noticeable dependency of both fracture toughness and fracture energy values (KIf and GIf) on the PC mix-design. In addition, the effect of substituting 1 and 2% of resin content with glass fiber was investigated. It was found that adding the fiber cannot necessarily enhance the performance of PC mixture against cracking and for some mix-designs; the addition of fiber can even reduce both KIf and GIf values.

Investigating the effect of printing speed and mode mixity on the fracture behavior of FDM-ABS specimens

The majority of engineering components are subjected to a multiaxial state of stress. This multiaxiality can be induced by a complex loading or complex geometry of the part. Therefore, investigating the mixed-mode fracture behavior would be an essential task to have an assessment of the fracture resistance in the mechanical components. Additive Manufacturing (AM) as one of the latest fabrication techniques has shown great benefits for design and fabrication of complex components. Among AM techniques, Fused Deposition Modelling (FDM) is one of the favorite processes that is currently used not only for prototyping but also for fabrication of complex structural components. Therefore, this research aims to evaluate mixed mode I/II fracture behavior of the FDM Acrylonitrile Butadiene Styrene (ABS) specimens with special focus on the effects of printing speed and mode mixity on fracture resistance. Four different printing speeds of 30, 50, 70, and 90 mm/s were used for fabricating the test specimens. Aside from these speeds, four different crack angles of 0, 15, 30, and 40° were used to investigate mixed-mode fracture behavior using Semi-Circular Bending (SCB) specimens. The fracture loads of the tested specimens were then predicted by employing the Equivalent Material Concept (EMC) method combined with the J-integral approach and the accuracy of the predictions were studied for various cases. Ultimately, Scanning Electron Microscopy (SEM) was used to investigate the failure mechanisms in fractured SCB specimens and link the fracture features to the fracture resistance of the FDM specimens.

Influence of bedding anisotropy on the dynamic fracture behavior of layered phyllite

Layered phyllite, a typical anisotropic rock caused by the existence of beddings, is common in rock engineering. To evaluate the influence of beddings and loading rates on the dynamic fracture behavior of layered phyllite, notched semicircular bending (NSCB) specimens were measured using a split-Hopkinson pressure bar (SHPB) system. Static fracture testing using a servo-controlled material testing system was also conducted for comparison. The results of this study indicate that three typical fracture paths can be found for NSCB specimens under both static loading and dynamic loading. The fracture path evidently exhibits dependence on the loading rate. For specimens under static loading, dominated fractures are more likely to propagate along the bedding planes while the dominated fractures tend to ignore bedding planes as the loading velocity increases. Consequently, the fracture length ratio along the bedding plane is considerably lower under dynamic loading than under static loading. Anisotropic effects on static and dynamic fracture toughness are evident; however, the anisotropy of fracture toughness decreases as impact velocity increases. The results of this study confirm that a reduced fracture length ratio along the bedding plane induced by an increase in loading rate weakens the dependence of dynamic fracture toughness on anisotropy.