Tensile strength and failure behavior of rock-mortar interfaces: Direct and indirect measurements

The tensile strength at the rock-concrete interface is one of the crucial factors controlling the failure mechanisms of structures,such as concrete gravity dams.Despite the critical importance of the failure mechanism and tensile strength of rock-concrete interfaces,understanding of these factors remains very limited.This study investigated the tensile strength and fracturing processes at rock-mortar interfaces subjected to direct and indirect tensile loadings.Digital image correlation(DIC)and acoustic emission(AE)techniques were used to monitor the failure mechanisms of specimens subjected to direct tension and indirect loading(Brazilian tests).The results indicated that the direct tensile strength of the rock-mortar specimens was lower than their indirect tensile strength,with a direct/indirect tensile strength ratio of 65%.DIC strain field data and moment tensor inversions(MTI)of AE events indicated that a significant number of shear microcracks occurred in the specimens subjected to the Brazilian test.The presence of these shear microcracks,which require more energy to break,resulted in a higher tensile strength during the Brazilian tests.In contrast,microcracks were predominantly tensile in specimens subjected to direct tension,leading to a lower tensile strength.Spatiotemporal monitoring of the cracking processes in the rock-mortar interfaces revealed that they show AE precursors before failure under the Brazilian test,whereas they show a minimal number of AE events before failure under direct tension.Due to different microcracking mechanisms,specimens tested under Brazilian tests showed lower roughness with flatter fracture surfaces than those tested under direct tension with jagged and rough fracture surfaces.The results of this study shed light on better understanding the micromechanics of damage in the rock-concrete interfaces for a safer design of engineering structures.

Static and dynamic tensile failure characteristics of rock based on splitting test of circular ring

Static and dynamic splitting tests were conducted on ring marble specimens with different internal diameters to study the tensile strength and failure modes with the change of the ratio of internal radius to external radius （ρ） under different loading rates. The results show that the dynamic tensile strength of disc rock specimen is approximately five times its static tensile strength. The failure modes of ring specimens are related to the dimension of the internal hole and loading rate. Under static loading tests, when the ratio of internal radius to external radius of the rock ring is small enough （ρ〈0.3）, specimens mostly split along the diametral loading line. With the increase of the ratio, the secondary cracks are formed in the direction perpendicular to the loading line. Under dynamic loading tests, specimens usually break up into four pieces. When the ratio ρreaches 0.5, the secondary cracks are formed near the input bar. The tensile strength calculated by Hobbs’ formula is greater than the Brazilian splitting strength. The peak load and the radius ratio show a negative exponential relationship under static test. Using ring specimen to determine tensile strength of rock material is more like a test indicator rather than the material properties.

Study on mechanical properties of composite materials by in-situ tensile test

The mechanical properties of the SiC fiber-reinforced Mg-Al metal matrix composite materials have been studied on internal microstructure by (scanning electron microscopy) SEM in-situ tensile test. The emergence and propagation of the crack, and the fracture behavior in materials have been observed and studied. It is found that in the case of the tensile test, the crack emerged in SiC fiber initially. In the case of the strong cohesion of the fiber-metal interface, the crack propagated in the fiber, meanwhile the fibers in the neighborhood of the cracked fiber began to crack and the Mg-Al metal deformed plastically, and at last the material fractured. Otherwise the toughness of the materials grows in the case of the lower cohesion of the fiber-metal matrix interface.

Correction of dynamic Brazilian disc tensile strength of rocks under preloading conditions considering the overload phenomenon and invoking the Griffith criterion

Dynamic tensile failure is a common phenomenon in deep rock practices,and thus accurately evaluating the dynamic tensile responses of rocks under triaxial pressures is of great significance.The Brazilian disc(BD)test is the suggested method by the International Society for Rock Mechanics and Rock Engineering(ISRM)for measuring both the static and dynamic tensile strengths of rock-like materials.However,due to the overload phenomenon and the complex preloading conditions,the dynamic tensile strengths of rocks measured by the BD tests tend to be overestimated.To address this issue,the dynamic BD tensile strength(BTS)of Fangshan marble(FM)under different preloading conditions were measured through a triaxial split Hopkinson pressure bar(SHPB).The fracture onset in BD specimen was captured through a strain gage around the disc center.The discrepancy between the traditional tensile strength(TTS,determined by the peak load P_(f) of the BD specimen)and the nominal tensile strength(NTS,obtained from the load P_(i) when the diametral fracture commences in the tested BD specimen)was applied to quantitatively evaluating the overload phenomenon.The Griffith criterion was used to rectify the calculation of the tensile stress at the disc center under triaxial stress states.The results demonstrate that the overload ratio(s)increases with the loading rate(σ)and decreases with the hydrostatic pressure(σ_(s)).The TTS corrected by the Griffith criterion is independent of theσ_(s)due to the overload phenomenon,while the NTS corrected by the Griffith criterion is sensitive to both the andσ.Therefore,it is essential to modify the tensile stress in dynamic confined BD tests using both the overload correction and the Griffith criterion rectification to obtain the accurate dynamic BTS of rocks.

Acoustic emission activity in directly tensile test on marble specimens and its tensile damage constitutive model

For understanding acoustic emission （AE） activity and accumulation of micro-damage inside rock under pure tensile state, the AE signals has been monitored on the test of directly tension on two kinds of marble specimens. A tensile constitutive model was proposed with the damage factor calculated by AE energy rate. The tensile strength of marble was discrete obviously and was sensitive to the inside microdefects and grain composition. With increasing of loading, the tensile stress-strain curve obviously showed nonlinear with the tensile tangent modulus decreasing. In repeated loading cycle, the tensile elastic modulus was less than that in the previous loading cycle because of the generation of micro damage during the prior loading. It means the linear weakening occurring in the specimens. The AE activity was corresponding with occurrence of nonlinear deformation. In the initial loading stage which only elastic deformation happened on the specimens, there were few AE events occurred; while when the nonlinear deformation happened with increasing of loading, lots of AE events were generated. The quantity and energy of AE events were proportionally related to the variation of tensile tangent modulus. The Kaiser effect of AE activity could be clearly observed in tensile cycle loading. Based on the theory of damage mechanics, the damage factor was defined by AE energy rate and the tensile damage constitutive model was proposed which only needed two property constants. The theoretical stress-strain curve was well fitted with the curve plotted with tested datum and the two property constants were easily gotten by the laboratory testing.

Brazilian disc test study on tensile strength-weakening effect of high pre-loaded red sandstone under dynamic disturbance

Tensile failure(spalling or slabbing)often occurs on the sidewall of deep tunnel,which is closely related to the coupled stress state of deep rock mass under high pre-static load and dynamic disturbance.To reveal the mechanism of rock tensile failure caused by this coupled stress mode,the Brazilian disc tests were carried on red sandstone under high pre-static load induced by dynamic disturbance.Based on the pure static tensile fracture load of red sandstone specimen,two static load levels(80%and 90%of the pure static tensile fracture load)were selected as the initial high pre-static loading state,and then the dynamic disturbance load was applied until the rock specimen was destroyed.The dynamic disturbance loading mode adopted a sinusoidal wave(sine-wave)load,and the loading wave amplitude was 20%and 10%of the pure static tensile fracture load,respectively.The dynamic disturbance frequencies were set to 1,10,20,30,40,and 50 Hz.The results show that the tensile failure strength and peak displacement of red sandstone specimens under coupled load actions are lower than those under pure static tensile load,and both parameters decrease significantly with the increase of dynamic disturbance frequency.With the increase of dynamic disturbance frequency,the decrease range of tensile strength of red sandstone increased from 3.3%to 9.4%when the pre-static load level is 80%.While when the pre-static load level is 90%,the decrease range will increase from 7.4%to 11.6%.This weakening effect of tensile strength shows that the deep surrounding rock is more likely to fail under the coupled load actions of pre-static load and dynamic disturbance.In this tensile failure mechanism of the deep surrounding rock,the stress environment of deep sidewall rock determines that the failure mode of rock is a tensile failure,the pre-static load level dominates the tensile failure strength of surrounding rock,and dynamic disturbance promotes the strength-weakening effect and affects the weakening range.

Stress-deformed state of cylindrical specimens during indirect tensile strength testing

In this study, the interaction between cylindrical specimen made ofhomogeneous, isotropic, and linearlyelastic material and loading jaws of any curvature is considered in the Brazilian test. It is assumed thatthe specimen is diametrically compressed by elliptic normal contact stresses. The frictional contactstresses between the specimen and platens are neglected. The analytical solution starts from the contactproblem of the loading jaws of any curvature and cylindrical specimen. The contact width, correspondingloading angle （2 ^0）, and elliptical stresses obtained through solution of the contact problems are used asboundary conditions for a cylindrical specimen. The problem of the theory of elasticity for a cylinder issolved using Muskhelishvili＇s method. In this method, the displacements and stresses are represented interms of two analytical functions of a complex variable. In the main approaches, the nonlinear interactionbetween the loading bearing blocks and the specimen as well as the curvature of their surfacesand the elastic parameters of their materials are taken into account. Numerical examples are solved usingMATLAB to demonstrate the influence of deformability, curvature of the specimen and platens on thedistribution of the normal contact stresses as well as on the tensile and compressive stresses actingacross the loaded diameter. Derived equations also allow calculating the modulus of elasticity, totaldeformation modulus and creep parameters of the specimen material based on the experimental data ofradial contraction of the specimen.

Numerical analysis of bending property of bi-modulus materials and a new method for measurement of tensile elastic modulus

In nature,there are widely distributed bi-modulus materials with different deformation characteristics under compressive and tensile stress states,such as concrete,rock and ceramics.Due to the lack of constitutive model that could reasonably consider the bi-modulus property of materials,and the lack of simple and reliable measurement methods for the tensile elastic parameters of materials,scientists and engineers always neglect the effect of the bi-modulus property of materials in engineering design and numerical simulation.To solve this problem,this study utilizes the uncoupled strain-driven constitutive model proposed by Latorre and Montáns(2020)to systematically study the distributions and magnitudes of stresses and strains of bi-modulus materials in the three-point bending test through the numerical method.Furthermore,a new method to synchronously measure the tensile and compressive elastic moduli of materials through the four-point bending test is proposed.The numerical results show that the bi-modulus property of materials has a significant effect on the stress,strain and displacement in the specimen utilized in the three-point and four-point bending tests.Meanwhile,the results from the numerical tests,in which the elastic constitutive model proposed by Latorre and Montáns(2020)is utilized,also indicate that the newly proposed measurement method has a good reliability.Although the new measurement method proposed in this study can synchronously and effectively measure the tensile and compressive elastic moduli,it cannot measure the tensile and compressive Poisson’s ratios.

Non-Contact Stress Measurement during Tensile Testing Using an Emat for SH₀-Plate Wave and Lamb Wave

The stress on a test specimen during tensile testing is generally measured by a strain gauge. This method has some problems in that it would influence the measurement conditions of the tensile test and can evaluate only the position at which the strain gauge is attached. The acoustoelastic method is proposed as a method replacing the strain gauge method. However, an ultrasonic sensor with a piezoelectric oscillator requires a coupling medium to inject an ultrasonic wave into a solid material. This condition, due to the error factor of the stress measurement, makes it difficult for the ultrasonic sensor to move on the specimen. We then tried to develop a non-contact stress measurement system during tensile testing using an electromagnetic acoustic transducer (EMAT) with an SH0-plate wave and S0-Lamb wave. The EMAT can measure the propagation time in which the ultrasonic wave travels between a receiver and a transmitter without a coupling medium during the tensile testing and can move easily. The interval between the transmitter and the receiver is 10mm and can be moved along the parallel direction or the vertical direction of the tensile load. The transit time was measured by a cross-correlation method and converted into the stress on the test specimen using the acoustoelastic method. We confirmed that the stress measurement using an SH0-plate wave was superior to that with an S0-Lamb wave.

3-D distribution of tensile stress in rock specimens for the Brazilian test

It is claimed that the formula used for calculating the tensile strength of a disk-shaped rock specimen in the Brazilian test is not accurate, because the formula is based on the 2-dimensional elastic theory and only suitable for very long or very short cylinders. The Matlab software was used to obtain the 2-dimensional distribution of stress in the rock specimen for Brazilian test. Then the 2-dimensional stress distribution in Brazilian disk was analyzed by the Marc FEM software. It can be found that the results obtained by the two software packages can verify each other. Finally, the 3-dimensional elastic stress in the specimen was calculated. The results demonstrate that the distribution of stress on the cross section of the specimen is similar to that in 2-dimension. However, the value of the stress on the cross section varies along the thickness of the specimen and the stress is bigger when getting closer to the end of the specimen. For the specimen with a height-to-diameter ratio of 1 and a Poisson＇s ratio of 0.25, the tensile strength calculated with the classical 2-D formula is 23.3% smaller than the real strength. Therefore, the classical 2-D formula is too conservative.

Analysis on the deformation and fracture behavior of carbon steel by in situ tensile test

The deformation and fracture behaviors of low-carbon steel, medium-carbon steel, and high-carbon steel were studied on internal microstructure using the scanning electron microscopy in situ tensile test. The microstructure mechanism of their deformation and fracture behavior was analyzed. The results show that the deformation and fracture behavior of low-carbon steel depends on the grain size of ferrite, the deformation and fracture behavior of medium-carbon steel depends on the size of ferrite grain and pearlite lump, and the deformation and fracture behavior of high-carbon steel depends on the size of pearlite lump and the pearlitic interlamellar spacing.

Characterization of microstructure and strain response in Ti-6Al-4V plasma welding deposited material by combined EBSD and in-situ tensile test

Additive layer manufacturing （ALM） of aerospace grade titanium components shows great promise in supplying a cost-effective alternative to the conventional production routes. Complex microstructures comprised of columnar remnants of directionally solidifiedβ-grains, with interior inhabited by colonies of finerα-plate structures, were found in samples produced by layered plasma welding of Ti-6Al-4V alloy. The application of in-situ tensile tests combined with rapid offline electron backscatter diffraction （EBSD） analysis provides a powerful tool for understanding and drawing qualitative correlations between microstructural features and deformation characteristics. Non-uniform deformation occurs due to a strong variation in strain response between colonies and across columnar grain boundaries. Prismatic and basal slip systems are active, with the prismatic systems contributing to the most severe deformation through coarse and widely spaced slip lines. Certain colonies behave as microstructural units, with easy slip transmission across the entire colony. Other regions exhibit significant deformation mismatch, with local build-up of strain gradients and stress concentration. The segmentation occurs due to the growth morphology and variant constraints imposed by the columnar solidification structures through orientation relationships, interface alignment and preferred growth directions. Tensile tests perpendicular to columnar structures reveal deformation localization at columnar grain boundaries. In this work connections are made between the theoretical macro- and microstructural growth mechanisms and the observed microstructure of the Ti-6Al-4V alloy, which in turn is linked to observations during in-situ tensile tests.

TENSILE TEST AND PHYSICAL MODEL OF NiTi SHAPE MEMORY ALLOY

The tensile stress-strain curves of NiTi wires are obtained by tensile experiments under different heat treatments. A phenomenological physical model based on hysteresis element method is developed to describe the experimentally determined stress-strain curves of shape memory alloy (SMA) wires. Numerical simulations are made. Simulation results show that：(1) a series of unusual changes on physical and mechanical properties of SMA wires occur when martensitic, especially R (rhombohedral) phase transformation emerge. The stress-strain relation of SMA wires is highly non-linear; (2) there are no notable yielding phenomena before NiTi wires are broken; (3) numerical results obtained by the physical model are in good agreement with experimental data.

Microstructural Changes of Graphene/PLA/PBC Nanofibers by Electrospinning during Tensile Tests

This study focuses on the nanostructure and nanostructural changes of novel graphene/poly（lactic acid） （PLA）/ poly（butylene carbonate） （PBC） nanofibers via electrospinning, which are characterized by differential scanning calorimetry （DSC）, scanning electron microscopy （SEM）, tensile test and in situ small angle x-ray scattering. DSC indicates that the endothermic peak at 295℃ of pure PLA/PBC nanofibers shifted from 317℃ to lower 290℃ with the increasing graphene content. SEM observations reveal a fine dispersion of graphene in the nanofiber matrices. The graphene/PLA/PBC nanofiSers exhibit good improvements in mechanical property. The tensile strength of nanofibers increases with the addition of 0.01 g graphene but reduces with further addition of 0.04g graphene. The scattering intensities increase dramatically when the strain levels are higher than the yield point due to the nucleation and growth of nanovoids or crystals. However, the increasing content of graphene in the PLA/PBC matrix provokes a strong restriction to the deformation-induced crystals.

Tensile strength of sea ice using splitting tests based on the digital image correlation method

The splitting test is a competitive alternative method to study the tensile strength of sea ice owing to its suitability for sampling.However,the approach was questioned to the neglect of local plastic deformation during the tests.In this study,splitting tests were performed on sea ice,with 32 samples subjected to the regular procedure and 8 samples subjected to the digital image correlation method.The salinity,density,and temperature were measured to determine the total porosity.With the advantage of the digital image correlation method,the full-field deformation of the ice samples could be determined.In the loading direction,the samples mainly deformed at the ice-platen contact area.In the direction vertical to the loading,deformation appears along the central line where the splitting crack occurs.Based on the distribution of the sample deformation,a modified solution was derived to calculate the tensile strength with the maximum load.Based on the modified solution,the tensile strength was further calculated together with the splitting test results.The results show that the tensile strength has a negative correlation with the total porosity,which agrees with previous studies based on uniaxial tension tests.

Axial Tensile Testing of Single Fibres

The mechanical and damage properties of single fibres used in fibrous composite have gained tremendous importance in recent years. These properties are used in determination of effective properties of composites by micromechanics. These are also used in the micromechanical damage modeling. Further, these properties are used as an indicator of the excellence of product by manufacturers. In the present study the axial tensile modulus, ultimate strength and failure strain of single fibres are determined for carbon and glass fibres. ASTM D3379-75 standard is followed and a number of fibers are tested for statistical analysis. The axial tensile moduli measured are 246.7 GPa and 93.3 GPa, respectively and strength are 3031.6 MPa and 2035.9 MPa, respectively for carbon and glass fibres. Further, the respective axial tensile failure strains are 0.0137 and 0.0224. The error in the measurement of axial modulus is below 8% while for axial tensile strength is below 1%.

Mechanical Characterization of Electroplated Ni Films by Micro-tensile Testing

Mechanical properties of structural materials are particularly important for design, performance realization and reliability analysis of microelectromechanical systems （MEMS）. Furthermore, accurate database of mechanical properties at the micro scale can provide indispensable reference for establishing MEMS standard. Electroplated nickel film is one of the most favored structural materials used in MEMS, thus its mechanical properties has been studied for many years. However, the measured values show large scatter in Yotmg＇s modulus of nickel film. Young＇s modulus and yield stress of electroplated nickel film are measured by using a micro-tensile testing instrument. The tensile load applied on the specimen is measured by a load cell with accuracy 0.25 mN directly, without additional friction. Through measuring the axial stiffness coefficient of the tensile instnunent in situ, the tensile strain of the specimen is obtained by using two-serial spring model. The electroplated nickel films were fabricated from sulfarnate baths, and the gauge section is 500μm long and 10μm wide nominally, and thickness range between 25 μm and 50μm. The obtained Young＇s modulus from tensile testing is 83＋6 GPa for nickel specimens electroplated at current density of 20 mA/cm2 and it increases to 124＋5 GPa as current density is decreased to 10 mA/cm2. The phenomena are interpreted in terms of porosity of microstructure. The higher current density produced rnicrostucture with low density and high volume fraction of pores, and the microstructure of high porosity corresponds to a lower modulus. The measured values of Young＇s modulus are consistent with those of calculated from the exponential empirical formula between Young＇s modulus and porosity. The micro-tensile testing instrument can also be used for mechanical measurement of other MEMS films.

TENSILE TESTING OF C/C COMPOSITES AT HIGH TEMPERATURES

The tensile properties of three different carbonfiberreinforced carbon composites (C/C), mat C/C, 2D laminate and 4D C/C, were investigated under the combined influence of temperature and loading rate. From the experiments the following could be concluded: loading rate between 10-1-10 mm/min was valid; the fracture stress of the three kinds of C/C composites increased with increasing temperature in the range from room temperature to 1900, and the initial modulus of 2D laminate C/C composites increased with the increase of temperature up to 2000.

A METHOD TO QUANTIFY CRAZING DEFORMATION BY TENSILE TESTS FOR POLYSTYRENE/POLYOLEFIN ELASTOMER IMMISCIBLE BLENDS

A method to quantify crazing deformations by tensile tests for polystyrene （PS） and polyolefin elastomer （POE） blends was investigated. The toughness of PS/POE blends, reflected by the Charpy impact strength, increased with the content of POE. SEM micrographs showed the poor compatibility between PS and POE. In simple tensile tests, it is very easy to achieve the ratio of crazing deformation, i.e. K by measuring the size changes of samples. The K values decreased with increasing the content of POE, and the deformations of PS/POE blends were dominated by crazing. The plots of the change of volume （△V） against longitudinal variation （△I） showed a linear relationship, and the slope of lines decreased with the content of POE. Measuring samples at the tensile velocities of 5 mm/min, 50 mm/min, and 500 mm/min respectively, the K values kept unchanged for each PS/POE blends.

Design and Development of Grip for Circular Test Piece Inuniversal Tensile Testing Machine

The design and development of jaw grip for circular tensile test samples in a universal mechanical tester were undertaken in this work. In developing economies, the cost of acquiring laboratory testing equipment and accessories is huge, thereby depriving most of the supposedly advanced laboratories of most of this necessary research equipment. Where the equipment is available, they are either non-functional due to inadequate maintenance know-how or non-availability of necessary accessories. The developed grip in this work is part of an effort at providing accessories as their need arises. Advanced design and manufacturing tools were deployed to develop the jaw grip by using austenitic stainless steel. The developed jaw grip was used on the test equipment to conduct tensile tests on steel samples and the results were found to conform to international standard. Consequently, replacement of worn-out accessories has been carried out in resent time, which eventually saves idle time of equipment or otherwise importation for replacement.