Flattened Disc Research Articles

Dynamic splitting tensile behaviours of distilled-water and river-water ice using a modified SHPB setup

The tensile strength of ice subjected to dynamic loading constitutes many ice engineering applications such as ice blasting and hail-aircraft impact. In this study, the dynamic tensile behaviours of distilled-water and river-water ice were firstly investigated using the flattened Brazilian disc method with a modified split Hopkinson pressure bar system. Columnar freshwater ice samples were tested at strain rates ranging from 20 to 135 s−1 and temperatures ranging from −5 to −45 °C. The effects of impact velocity, loading rate, and ice sample thickness on the dynamic splitting tensile strength were also explored. Distilled-water ice specimens exhibited a higher indirect tensile strength than their river-water counterparts. The lower the temperature, the greater is the tensile strength, particularly in the case of distilled-water ice in the strain rate range of 89–135 s−1. The temperature had less effect on the dynamic tensile strength of distilled-water ice compared to the loading rate, and the specimen thickness had little effect on the dynamic indirect tensile strength. A large number of non-penetrating cracks were observed on the disc surface, indicating the inhomogeneous distribution of the tensile stress interpreted based on the 3D Brazilian disc theory. The closer the two end faces in the central cross section, the greater the tensile stress. The presence of single and multiple strip cracks on the splitting surface were discovered, possibly because of the instant expansion of the ice specimen and subsequent formation of mode-I cracks in the thickness direction.

Characterization of the glycans involved in sea urchin Paracentrotus lividus reversible adhesion

Sea urchins have hundreds of specialized adhesive organs, the tube feet, which play a key role in locomotion, substrate attachment and food capture. Tube feet are composed by two functional units: a proximal cylindrical stem that is mobile and flexible, attached to a distal flattened disc that produces adhesive secretions. Oral tube feet discs possess a specialized duo-glandular epidermis that produces adhesive and de-adhesive secretions, enabling strong but reversible adhesion to the substrate. Due to the growing interest in biomimetic adhesives, several studies have been carried out to characterize sea urchin adhesives, and up to date, it has been shown that it is composed by proteins and glycans. The protein fraction has been the subject of several studies, that pin-pointed several adhesion-related candidates. Contrastingly, little is known about the glycans that compose sea urchin adhesives. This study aims at contributing to this topic by focusing on the characterization of the glycosidic fraction of the adhesive secreted by the sea urchin Paracentrotus lividus (Lamarck, 1816), using a battery of 22 lectins, applied to 3 complementary techniques. Our results show that five lectins label exclusively the disc adhesive epidermis and simultaneously the secreted adhesive, being, therefore, most likely relevant for sea urchin adhesion. In addition, it was possible to determine that the glycosidic fraction of the adhesive is composed by a high molecular weight glycoprotein containing N-acetylglucosamine oligomers.

Dynamic tensile behavior of rocks under static pre-tension using the flattened Brazilian disc method

Rocks in underground engineering projects, are likely to be subjected to static pre-stress and dynamic loading simultaneously. To measure the tensile strength of brittle rocks under coupled static-dynamic loads, a coupled static-dynamic flattened Brazilian disc (FBD) testing method is proposed in this study via a modified split Hopkinson pressure bar (SHPB) system. Our method has unique advantages on coupled static-dynamic tests using SHPB, because under different static pre-loads, the contact area between the loading platens and the specimen remain nearly constant, contributing to maintaining a consistent contact condition. Using the method, we experimentally and numerically investigate the tensile response of sandstone subjected to different static pre-tensions and different dynamic loading rates. By careful pulse shaping, the dynamic force equilibrium on both loading ends of FBD specimens can be satisfied. Detailed progressive fracture processes of tested specimens are captured via a high-speed camera, and the central crack initiation is observed in all our coupled static-dynamic tests. The dynamic tensile strength of sandstone decreases with the increase of the pre-tension, while the total tensile strength features an increase, and both the dynamic tensile strength and total tensile strength show the obvious rate dependence. The numerical simulation reveals that under a higher pre-tension ratio, more microcracks are observed at the static pre-tension stage, suggesting that more damage is induced in the rock. Our method is feasible to indirectly measure the tensile strength of rocks under coupled static-dynamic loads.

Mathematical formulation of an analytic approach to the stress field in a flattened Brazilian disc

Although more than fifteen years have passed since the flattened Brazilian disc test was introduced, analytic studies on the respective stress field are scarce, mainly due to difficulties related to the shape of its boundary. In this context, an alternative mathematical formulation, providing a full-field solution for the distribution of stresses in the flattened Brazilian disc, is here proposed, based on the configuration of an intact circular disc, under a large number of equal point forces, arranged at equal distances along two symmetric parallel chords of the disc. Considering each point force as the resultant of stresses acting on an eliminated hole, a great number of such forces implies the introduction of a large number of small holes, dividing the uniform disc into three distinct parts; the one between the two chords is to stand as the flattened disc under uniform compression. This particular problem for the uniform disc is here solved with the aid of Muskhelishvili’s complex potential technique, providing a closed-form, full-field solution for the stresses on the as above “truncated” disc, and thus, in a first approximation, on the flattened Brazilian disc. The analysis, apart from highlighting the advantage of the flattened against the classical intact Brazilian disc (regarding the reduction of stress concentration along the disc-loading platen contact region), revealed, also, that the pressure on the flat edges of the flattened disc should be non-uniform in order to better approximate the experimental reality. In this direction, a numerical model was developed, indicating the proper non-uniform distribution of pressure that should be applied along the flat edges of the flattened Brazilian disc, in order for these edges to remain plane after deformation, in accordance to the laboratory implementation of the experiment.

Type I Fracture Toughness Test of Rock‐like Materials Based on the Particle Flow Method

In order to investigate the feasibility and reliability of the three‐dimensional particle flow method in simulating the type I fracture toughness test, four types of numerical samples were established by particle flow code PFC3D: straight crack three‐point bending (SC3PB), edge cracked flattened semicircular disc (ECFSD), cracked chevron notched Brazilian disc (CCNBD), and edge cracked flattened ring (ECFR). Three models with different strength parameters (group A, group B, and group C) were established for each type, in which group A parameters are obtained from the concrete model, group B parameters are applied for simulating marble, and group C parameters are for granite. The type I fracture toughness and the failure form of each model are obtained by conducting the numerical test, and the curves of load versus displacement of loading point are recorded. The numerical test results show that, with the same strength parameter, the maximum difference in test results of each specimen type is 0.39 MPa·m1/2. The KIC of ECFR specimen is 0.13–0.28 MPa·m1/2 smaller than that of CCNBD specimen, and the KIC of ECFSD specimen is slightly higher than that of CCNBD sample. The KIC of SC3PB specimen is 0.06–0.21 MPa·m1/2 smaller than that of the CCNBD sample. When the loading rate is less than 0.01 m/s, the effect of loading rate on fracture toughness can be reduced to less than 0.1 MPa·m1/2.

Three-dimensional dynamic numerical simulation of a Brazilian disc of concrete with variation of dip angle of parallel double slits

In order to study the influence of the change of the inclination angle of parallel double slits on concrete disk under dynamic load, we establish a three-dimensional dynamic numerical model of the flattened Brazilian disc by using finite element method. Non-uniform distribution of concrete materials has been realized in the model by adopting Weibull statistical theory. Moreover, we study the effect of variation of dip angle of parallel double slits on crack propagation pattern under stress wave, and obtain both diagrams of the complete failure process and acoustic emission of crack initiation, propagation and penetration. The results show that the failure of the specimen is cleavage and the direction of new crack growth is consistent with that of the dynamic load, the acoustic emission activity decreases with the increase of the dip angle of the prefabricated slits; the bigger the dip angle of prefabricated parallel double slits is, the bigger the peak load is, and the less the accumulated energy of acoustic emission is, the less likely the specimen is to be damaged.

Constitutive modelling of the TiB2–B4C composite by experiments, simulation and neutral network

The JH-2 constitutive relations of the TiB2–B4C composite were studied by the experiments, simulations and feedforward neural network. The flattened Brazilian disc experiments were designed to obtain the strength model of intact ceramic. The strength and strain rates sensitivity of the TiB2–B4C composite were studied by the static and dynamic tests. The Hugoniot elastic limit and equation of state of the composite were analyzed by the plate impact tests and Doppler pins test system. The confined compression tests for ceramic particles were designed to model the normalized fracture strength relations. Then the feedforward neural network model was established to train samples and analyze the damage constants of the TiB2–B4C composite. The samples of the input layer and output layer were derived from the experiments and simulation of the ceramic/metal composite armor impacted by high speed ball projectile. The Bayesian regularization algorithm was used to avoid converging on local minimum value in the neural network. Lastly, the constitutive model of the TiB2–B4C composite was verified by the comparison between the experimental and simulation results which were the depth of penetration, radial and circular crack of ceramic plate.

Origin of misalignments: protostellar jet, outflow, circumstellar disc, and magnetic field

Recent observations uncover various phenomena around the protostar such as misalignment between the outflow and magnetic field, precession of the jet, and time variability of the ejected clumps, whose origins are under debate. We perform a three-dimensional resistive magnetohydrodynamics simulation of the protostar formation in a star-forming core whose rotation axis is tilted at an angle $45^\circ$ with respect to the initial magnetic field, in which the protostar is resolved with a spatial resolution of $0.01\,$au. In low-dense outer region, the prestellar core contracts along the magnetic field lines due to the flux freezing. In high-dense inner region, on the other hand, the magnetic dissipation becomes efficient and weakens the magnetic effects when the gas number density exceeds about $10^{11}\,{\rm cm^{-3}}$. Then, the normal direction of the flattened disc is aligned with the angular momentum vector. The outflow, jet, and protostellar ejection are driven from different scales of the circumstellar disc and spout in different directions normal to the warped disc. These axes do not coincide with the global magnetic field direction and vary with time. This study demonstrates that a couple of misalignment natures reported by observations can be simultaneously reproduced only by assuming the star-forming core rotating around a different direction from the magnetic field.

Morphology and molecular analysis of Paratylenchus chongqingensis n. sp. (Nematoda: Paratylenchinae) from soil associated with Ophiopogon japonicus in China

Paratylenchus chongqingensis n. sp. extracted from the soil associated with Ophiopogon japonicus in China is described and illustrated. The new species is characterized by having the female with a body length of 243–274.5 μm, stylet 21–24.5 μm long, lip region distinctly set off forming a flattened labial disc, lateral field with three lines, lateral vulval flaps distinct, tail with a beak-like and subacute terminus; male with a 224.5–246.5 μm long body, spicules 13–14.5 μm long, stylet lacking and pharynx degenerate, tail tapering gradually, and then becoming narrow abruptly near the terminus, forming a short pointed filiform tail tip. The internal transcribed spacer sequences of the ribosomal RNA (ITS rRNA) gene of the new species were amplified and sequenced. The phylogenetic relationships of this new species with other Paratylenchus spp. using the ITS rRNA gene is given in this study.

Detection of Degenerative Changes in the Articular Disc of the Temporomandibular Joint Using Delayed Gadolinium- Enhanced MRI at 3 Tesla – A Case Report

The delayed Gadolinium-Enhanced Magnetic Resonance Imaging of Cartilage (dGEMRIC) is a useful tool for the evaluation of a repair tissue status after cartilage transplantation. A previous study showed the feasibility of dGEMRIC at 3 Tesla in TMJ. This case report describes the application of dGEMRIC to a TMD patient. A 27 years old female patient reported TMJ (VAS 87) with increasing intensity. The examination according to RDC/TMD showed myofacial pain (group I) and arthralgia of the right and left joint (IIIa). The graded chronical pain score showed grade III. The conventional MRI showed no sign of discus dislocation. T2 mapping showed a significant signal in homogeneity in both disci, as well as an increased amount of fluid in both compartments and a flattened disc in the lateral area. The application of dGEMRIC with patients suffering from temporomandibular disorders could be very well suited for early detection of onset pathological change in fibrocartilage.

Experimental study on dynamic split tensile properties of rubber concrete

Static and dynamic split tensile tests were conducted on rubber concrete with varied volume fractions of rubber particles that replaced fine aggregate (10%, 20%, 30%, 40%, and 50%, named as RC10, RC20, RC30, RC40, and RC50, respectively). The flattened Brazilian disc specimens were applied to determine the tensile properties and energy absorption capabilities under high strain rate by an SHPB (Split Hopkinson Pressure Bar) and medium strain rate by a drop-hammer testing machine. With a high-speed camera, the crack growth of specimens in the SHPB and drop-hammer impacting tests was observed and validated. The experimental result of five rubber concretes and one normal concrete without rubber particles was obtained, and the strain-rate effect on tensile strength of rubber concretes and normal concrete was confirmed. For high strain rate, RC10, RC20 and RC30 were sensitive to strain rate dependence, but rate dependence of RC40 and RC50 was lower than normal concrete. RC30 exhibited the most sensitivity and excellent energy absorption capability in static and dynamic tests. Excessive rubber content did not continually increase the toughness of the concrete under dynamic loadings.

Cyclic flattened Brazilian disc tests for measuring the tensile fatigue properties of brittle rocks.

We propose a cyclic flattened Brazilian disc (FBD) testing method to measure the tensile fatigue properties of brittle rocks. Our method has obvious merits in its specimen preparation and experimental operation. Two parallel flattens are introduced in the disc specimen, which facilitate easily and uniformly loading the specimen without special loading devices required. Moreover, the contact regions between two flattens and loading planes barely change during the entire loading and unloading process, ensuring a consistent contact condition. With certain appropriate loading angles, this method guarantees that the very first breakage of the specimen occurs at the center of the disc, which is the prerequisite of the Brazilian-type indirect tensile tests. To demonstrate our new method, nine cyclic FBD tensile tests are conducted. The fatigue load-deformation characteristics of FBD specimens are revealed. The tensile fatigue lives of tested specimens are observed to increase with the increase in cyclic loading frequency. Our proposed method provides a convenient and reliable approach to indirectly measure the fatigue tensile properties of brittle rocks and other brittle solids subjected to cyclic tensile loadings.

Breaking pharmaceutical tablets with a hole: Reevaluation of the stress concentration factor and influence of the hole size

Mechanical strength is an important property for pharmaceutical tablets. Its study using the theory of linear elastic fracture mechanics has been introduced in the pharmaceutical field through the Brittle Fracture Index (BFI). This index is based on the stress concentration factor (SCF) and contradictory results have been published in the pharmaceutical literature about the value of the SCF during the diametral compression of a disc with a hole.In this work, thanks to the use of numerical simulations (FEM) and analytical results, the value of the SCF was proved to be equal to 6. The result was also applicable for the case of the flattened disc geometry that was introduced in a previous work. The value of the SCF is found to be nearly independent of the hole size if the ratio between the hole and the tablet diameters was lower than 0.1. Nevertheless, experimental results presented in this paper show that the load needed to break a compact varies with the hole size. This influence is due to the change in the stress distribution around the hole when the hole size is changing. Criteria such as the average stress criterion, which takes into account the stress distribution, made it possible to explain the influence of the hole on the breaking load.

Reevaluation of the diametral compression test for tablets using the flattened disc geometry

Mechanical strength is an important critical quality attribute for tablets. It is classically measured, in the pharmaceutical field, using the diametral compression test. Nevertheless, due to small contact area between the tablet and the platens, some authors suggested that during the test, the failure could occur in tension away from the center which would invalidate the test and the calculation of the tensile strength. In this study, the flattened disc geometry was used as an alternative to avoid contact problems. The diametral compression on both flattened and standard geometries was first studied using finite element method (FEM) simulation. It was found that, for the flattened geometry, both maximum tensile strain and stress were located at the center of the tablet, which was not the case for the standard geometry. Experimental observations using digital image correlation (DIC) confirmed the numerical results. The experimental tensile strength obtained using both geometries were compared and it was found that the standard geometry always gave lower tensile strength than the flattened geometry. Finally, high-speed video capture of the test made it possible to detect that for the standard geometry the crack initiation was always away from the center of the tablet.

English

In this study, effect of loading angle on location of crack initiation in flattened Brazilian disc (FBD) specimens was studied by both numerical and experimental methods. FBD tests were conducted on disc samples with various loading angles and tests were simulated by finite element method (FEM). The results showed that probability of crack initiation at flattened ends of samples where jaws and sample are connected should be considered along with central crack initiation which is a usual prerequisite to have a valid FBD test. In addition, experimental analysis was performed on FBD samples which is rarely observed in literature. Moreover, the loading angle of 30° was determined as an appropriate angle for FBD test that guarantees the occurrence of central crack and avoids crack initiation at flattened ends of samples. Key words: Fracture toughness, FBD method, loading angle, central crack, experimental method, numerical method.

Numerical Analysis of Flattened Brazilian Disc Test Based on the Cusp Catastrophe Theory

The Brazilian disc test is a simple and useful technique to determine the tensile strength of rock materials. By using FLAC3D, 63 numerical simulations in total were performed when flattened Brazilian disc coefficient and Poisson’s ratio were different. Based on Griffith theory, the corresponding FISH language was compiled to record the Griffith equivalent stress. Through analysis of numerical simulation results, it is indicated that fracture plane was not the plane going through center of the Brazilian disc, which was in good agreement with the references. In addition, the flattened Brazilian disc coefficients had greater influence on tensile strength than Poisson’s ratio. Based on cusp catastrophe theory, the flattened Brazilian disc coefficient should not exceed 0.035 for the flattened Brazilian disc tests. Consequently, a tensile strength empirical formula considering flattened Brazilian disc coefficient by utilizing the flattened Brazilian disc test was established, which wasσt=0.9993 exp (-11.65ε)2p/πDt,ε≤0.035.

Experimental study on tensile behavior of cement paste, mortar and concrete under high strain rates

Effects of the strain rate on cement paste, mortar and concrete were studied. A modified SHPB testing technique with flattened Brazilian disc (FBD) specimen was developed to measure the dynamic tensile stress-strain curve of materials. A pulse-shaped split Hopkinson pressure bar (SHPB) was employed to determine the dynamic tensile mechanical responses and failure behavior of materials under valid dynamic testing conditions. Quasi-static experiments were conducted to study material strain rate sensitivity. Strain rate sensitivity of the materials was measured in terms of the stress-strain curve, elastic modulus, tensile strength and critical strain at peak stress. Empirical relations between dynamic increase factor (DIF) and the material properties were derived and presented.

Determination of elastic modulus, tensile strength and fracture toughness of bioceramics using the flattened Brazilian disc specimen: analytical and numerical results

Ceramics and bioceramic composites are materials characterized with strong but quite low crack-resistance properties. Indeed, their application is hindered by their brittleness and low ability to deform, and the accurate measurement of their fracture toughness can often be challenging. This measurement along with that of tensile strength and elastic modulus were conducted using a novel configuration of the Brazilian test. The flattened Brazilian specimens, which are in the shape of discs having parallel flat ends, are subjected to compression for the determination of opening mode I fracture toughness KIC. The experiments were conducted using tricalcium phosphate–fluorapatite composites which were tested by compressive loading on the parallel flat ends. The loading angle corresponding to the flat end width is about 2α=20° to guarantee crack initiation at the specimen center according to the Griffith criteria. Finite element program, called ABAQUS, is used for the numerical modeling for finding stress intensity factors. The effects of fluorapatite additives and fracture toughness were studied. The fracture toughness values of tricalcium phosphate–fluorapatite composites were found to increase with the increase in fluorapatite addition until an appropriate value. It is shown that there is a good agreement between the experimental, analytical and numerical results.

Sequential determination of dynamic initiation and propagation toughness of rock using an experimental–numerical–analytical method

We propose the use of an experimental–numerical–analytical method to determine the dynamic initiation and propagation toughness of rock. The specimen adopted is the cracked straight-through flattened Brazilian disc diametrically impacted by a split Hopkinson pressure bar. The crack initiation moment and crack propagation velocity were sequentially measured with a crack propagation gauge glued in front of the specimen’s crack tip. Dynamic stress intensity factor histories were obtained by finite element analysis, with inputs of the dynamic loading histories recorded in the experiment. In determining the dynamic propagation toughness, the effect of the crack propagation velocity on the dynamic stress intensity factor was taken into account analytically, by applying the universal function (Freund, 1990).

圆孔内单边（或双边）裂纹平台巴西圆盘应力强度因子的全面标定

虽然径向压缩含内单边裂纹的圆环型试样已有学者进行了分析,但在该试样上增加有益于加载的平台,就形成了新的试样——圆孔内单边裂纹平台巴西圆盘（holed single cracked flattened Brazilian disc,HSCFBD）,并对其进行了研究.此外,对圆孔内（双边）裂纹平台巴西圆盘（holed cracked flattened Brazilian disc,HCFBD）做了进一步研究.通过有限元分析,对含有不同内外半径比、无量纲裂纹长度、平台角的HSCFBD和HCFBD的无量纲应力强度因子Y进行了全面标定,给出Y的曲线和拟合公式,拟合公式计算结果与数值标定结果相对误差在±1.39%以内.分析了试件形状参数对应力强度因子的影响：内外半径比越大,平台角越小,无量纲应力强度因子越大.根据应力强度因子的变化规律,推荐了适合测试Ⅰ型断裂韧度的HSCFBD和HCFBD的参数.进行了HCFBD的初步试验,还用国际岩石力学学会建议的人字形切槽巴西圆盘做了对比试验.