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.

Effect of brazing temperature on microstructure and tensile strength ofγ-TiAl joint vacuum brazed with micro-nano Ti−Cu−Ni−Nb−Al−Hf filler

A novel micro-nano Ti−10Cu−10Ni−8Al−8Nb−4Zr−1.5Hf filler was used to vacuum braze Ti−47Al−2Nb−2Cr−0.15B alloy at 1160−1220℃ for 30 min.The interfacial microstructure and formation mechanism of TiAl joints and the relationships among brazing temperature,interfacial microstructure and joint strength were emphatically investigated.Results show that the TiAl joints brazed at 1160 and 1180℃ possess three interfacial layers and mainly consist of α_(2)-Ti_(3)Al,τ_(3)-Al_(3)NiTi_(2) and Ti_(2)Ni,but the brazing seams are no longer layered and Ti_(2)Ni is completely replaced by the uniformly distributed τ_(3)-Al_(3)NiTi_(2) at 1200 and 1220℃ due to the destruction of α_(2)-Ti_(3)Al barrier layer.This transformation at 1200℃ obviously improves the tensile strength of the joint and obtains a maximum of 343 MPa.Notably,the outward diffusion of Al atoms from the dissolution of TiAl substrate dominates the microstructure evolution and tensile strength of the TiAl joint at different brazing temperatures.

Effect of the mineral spatial distribution heterogeneity on the tensile strength of granite:Insights from PFC3D-GBM numerical analysis

The mechanical characteristics of crystalline rocks are affected by the heterogeneity of the spatial distribution of minerals.In this paper,a novel three-dimensional(3D)grain-based model(GBM)based on particle flow code(PFC),i.e.PFC3D-GBM,is proposed.This model can accomplish the grouping of mineral grains at the 3D scale and then filling them.Then,the effect of the position distribution,geometric size,and volume composite of mineral grains on the cracking behaviour and macroscopic properties of granite are examined by conducting Brazilian splitting tests.The numerical results show that when an external load is applied to a sample,force chains will form around each contact,and the orientation distribution of the force chains is uniform,which is independent of the external load level.Furthermore,the number of high-strength force chains is proportional to the external load level,and the main orientation distribution is consistent with the external loading direction.The main orientation of the cracks is vertical to that of the high-strength force chains.The geometric size of the mineral grains controls the mechanical behaviours.As the average grain size increases,the number of transgranular contacts with higher bonding strength in the region connecting both loading points increases.The number of high-strength force chains increases,leading to an increase in the stress concentration value required for the macroscopic failure of the sample.Due to the highest bonding strength,the generation of transgranular cracks in quartz requires a higher concentrated stress value.With increasing volume composition of quartz,the number of transgranular cracks in quartz distributed in the region connecting both loading points increases,which requires many high-strength force chains.The load level rises,leading to an increase in the tensile strength of the numerical sample.

Size effects on the tensile strength and fracture toughness of granitic rock in different tests

This study investigates the tensile failure mechanisms in granitic rock samples at different scales by means of different types of tests.To do that,we have selected a granitic rock type and obtained samples of different sizes with the diameter ranging from 30 mm to 84 mm.The samples have been subjected to direct tensile strength(DTS)tests,indirect Brazilian tensile strength(BTS)tests and to two fracture toughness testing approaches.Whereas DTS and fracture toughness were found to consistently grow with sample size,this trend was not clearly identified for BTS,where after an initial grow,a plateau of results was observed.This is a rather complete database of tensile related properties of a single rock type.Even if similar databases are rare,the obtained trends are generally consistent with previous scatter and partial experimental programs.However,different observations apply to different types of rocks and experimental approaches.The differences in variability and mean values of the measured parameters at different scales are critically analysed based on the heterogeneity,granular structure and fracture mechanics approaches.Some potential relations between parameters are revised and an indication is given on potential sample sizes for obtaining reliable results.Extending this database with different types of rocks is thought to be convenient to advance towards a better understanding of the tensile strength of rock materials.

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.

A Fuzzy Logic Approach to Predict Tensile Strength in TIG Mild Steel Welds

Welding defects influence the desired properties of welded joints giving fabrication experts a common problem of not being able to produce weld structures with optimal strength and quality. In this study, the fuzzy logic system was employed to predict welding tensile strength. 30 sets of welding experiments were conducted and tensile strength data was collected which were converted from crisp variables into fuzzy sets. The result showed that the fuzzy logic tool is a highly effective tool for predicting tensile strength present in TIG mild steel weld having a coefficient of determination value of 99%.

Springback and tensile strength of 2A97 aluminum alloy during age forming

The analysis of variance(ANOVA), multiple quadratic regression and radial basis function artificial neural network(RBFANN) methods were used to study the springback and tensile strength in age forming of 2A97 aluminum alloy based on orthogonal array. The ANOVA analysis indicates that the springback reaches the minimum value when age forming is performed at 210 °C for 20 h using a single-curvature die with a radius of 400 mm, and the tensile strength reaches the maximum value when age forming is performed at 180 °C for 15 h using a single-curvature die with a radius of 1000 mm. The orders of the importance for the three factors of pre-deformation radius, aging temperature and aging time on the springback and tensile strength were determined. By analyzing the predicted results of the multiple quadratic regression and RBFANN methods, the prediction accuracy of the RBFANN model is higher than that of the regression model.

Influence of yield-to-tensile strength ratio(Y/T) on failure assessment of defect-free and corroded X70 steel pipeline

The effect of yield-to-tensile strength ratio(Y/T) on failure pressure of X70 pipeline without and with corrosion defects was investigated.The stress-strain response of materials was characterized by a power-law hardening curve.Two formulas to estimate the strain hardening exponent n for a special Y/T were obtained by least squared regression method and the influence of Y/T on n was analyzed.As an application of n-Y/T expression,the analytical solutions of burst pressure for X70 pipeline without and with corrosion defects were also obtained.The results indicate that the burst pressure of defect-free X70 pipe without corrosion defects is a function of the Y/T,pipe geometry t0/D0 and engineering tensile strength,and increases as Y/T or t0/D0 increases; whilst the burst pressure of corroded X70 pipe decreases with the increase of defect depths,d/t.Comparisons indicate that the present analytical solutions closely match available experimental and numerical data.

TENSILE STRENGTH OF RANDOM ORIENTED SHORT FIBER COMPOSITE

This paper shows a calculation model and a method for predicting the tensile strength of the random distributed short fiber composite.On the basis of Renjie Mao's model,the longitudinal tensile strength of the aligned short fiber composite is formulated.Considering the transverse tensile strength and in plane shear strength of the unidirectional fiber composite,and the stress transformation relations of two couples of axes,the stress of the unidirectional fiber composite when it is loaded at an arbitrary angle is obtained.With the aid of an equivalence relation,the calculation formulation of the tensile strength of the random short fiber reinforced composite is deduced.

TENSILE STRENGTH AND CREEP RESISTANCE OF Mg-9Al-1Zn BASED ALLOYS WITH CALCIUM ADDITION

Small amount of calcium addition to the Mg-9Al-0.8Zn-0.2Mn (AZ91) alloy resulted in obvious influence on mechanical properties. The yield strength of the alloys increased with the increase of Ca addition and the maximum strength was obtained from the alloy containing 0.15% of Ca. The creep resistance at the temperatures between 150-220°C was also significantly increased with Ca addition. The creep rate (at 200°C, 50 MPa) of the alloy with 0.15% Ca addition was one order of magnitude lower than that of the base alloy (AZ91). Microstructural observations revealed that the addition of calcium refined the microstructure and enhanced the thermal stability of the β precipitates, which accounted for the improvement of creep resistance at high temperatures.

Effects of laser energy density on forming accuracy and tensile strength of selective laser sintering resin coated sands

Baozhu sand particles with size between 75 μm and 150 μm were coated by resin with the ratio of 1.5 wt.% of sands. Laser sintering experiments were carried out to investigate the effects of laser energy density(E = P/v), with different laser power(P) and scanning velocity(v), on the dimensional accuracy and tensile strength of sintered parts. The experimental results indicate that with the constant scanning velocity, the tensile strength of sintered samples increases with an increase in laser energy density; while the dimensional accuracy apparently decreases when the laser energy density is larger than 0.032 J·mm-2. When the laser energy density is 0.024 J·mm-2, the tensile strength shows no obvious change; but when the laser energy density is larger than 0.024 J·mm-2, the sample strength is featured by the initial increase and subsequent decrease with simultaneous increase of both laser power and scanning velocity. In this study, the optimal energy density range for laser sintering is 0.024-0.032 J·mm-2. Moreover, samples with the best tensile strength and dimensional accuracy can be obtained when P = 30-40 W and v = 1.5-2.0 m·s-1. Using the optimized laser energy density, laser power and scanning speed, a complex coated sand mould with clear contour and excellent forming accuracy has been successfully fabricated.

A Study of Tensile Strength Tests of Arborous Species Root System in Forest Engineering Technique of Shallow Landslide

One experiment was conducted, through tensile tests of Albazzia and Eucalypt roots culled from the fields. The other experiment was conducted, by testing anti-drawing strength of these root systems in the Albazzia and Eucalypt lands. These two experiments had an aim to give insights into the maximum tensile strength and anti-drawing strength of the root systems. Results indicated that the maximum tensile strength of root system is in an exponential relation with the diameter of root system while the maximum tensile strength is positively correlative with the diameter of root system. Anti-drawing force of root system together with root diameter, length, and soil bulk density are folded into a regression equation in an attempt to figure out the static friction coefficient between root system and its ambient soil.

Establishing empirical relationships to predict grain size and tensile strength of friction stir welded AA 6061-T6 aluminium alloy joints

AA 6061-T6 aluminium alloy(Al-Mg-Si alloy) has gathered wide acceptance in the fabrication of light weight structures requiring a high specific strength and good corrosion resistance.Compared with the fusion welding processes that are routinely used for joining structural aluminium alloys,friction stir welding(FSW) process is an emerging solid state joining process in which the material welded does not melt and recast.Joint strength is influenced by the grain size and tensile strength of the weld nugget region.Hence,an attempt was made to develop empirical relationships to predict grain size and tensile strength of friction stir welded AA 6061-T6 aluminium alloy joints.The empirical relationships are developed by response surface methodology(RSM) incorporating FSW tool and process parameters.A linear regression relationship was also established between grain size and tensile strength of the weld nugget of FSW joints.

Dynamic rock tensile strengths of Laurentian granite: Experimental observation and micromechanical model

Tensile strength is an important material property for rocks. In applications where rocks are subjected to dynamic loads, the dynamic tensile strength is the controlling parameter. Similar to the study of static tensile strength, there are various methods proposed to measure the dynamic tensile strength of rocks.Here we examine dynamic tensile strength values of Laurentian granite(LG) measured from three methods: dynamic direct tension, dynamic Brazilian disc(BD) test, and dynamic semi-circular bending(SCB). We found that the dynamic tensile strength from direct tension has the lowest value, and the dynamic SCB gives the highest strength at a given loading rate. Because the dynamic direct tension measures the intrinsic rock tensile strength, it is thus necessary to reconcile the differences in strength values between the direct tension and the other two methods. We attribute the difference between the dynamic BD results and the direct tension results to the overload and internal friction in BD tests. The difference between the dynamic SCB results and the direct tension results can be understood by invoking the non-local failure theory. It is shown that, after appropriate corrections, the dynamic tensile strengths from the two other tests can be reduced to those from direct tension.

Compressive and tensile strength of polymer-based fiber composite sand

Traditional soil additives like Portland cement and lime are prone to cause the brittle fracture behavior of soil,and possibly,environmental impacts.This study explores the potential use of polyurethane organic polymer and sisal fiber in improving the mechanical performance of sand.The effects of polymer content,fiber content,and dry density on the unconfined compressive strength(UCS)and direct tensile strength(DTS)of the polymer-fiber-sand composite were evaluated.The results showed significant increase in UCS and DTS of the reinforced sand with the increase of polymer content,fiber content,and dry density.At high dry density condition,a single peaked stress−strain curve is often observed.Higher polymer content is beneficial to increasing the peak stress,while higher fiber content contributes more to the post-peak stress.The combined use of polymers and fibers in soil reinforcement effectively prevents the propagation and development of cracks under the stress.Scanning electron microscopy(SEM)test was also performed to investigate the micro-structural changes and inter-particle relations.It was found through SEM images that the surface coating,bonding,and filling effects conferred by polymer matrix greatly enhance the interfacial interactions,and hence provide a cohesive environment where the strength of fibers could be readily mobilized.

Effect of Polypropylene Fibers on the Long-term Tensile Strength of Concrete

The influence of low volume fraction of polypropylene（PP） fibers on the tensile properties of normal and high strength concretes was studied. The experimental results indicate that the addition of PP fibers in concrete leads to a reduction in tensile strength during the age of 28 d. Whereas, after 28 days, there is a notable effect in tensile strength due to PP fibers restraining the formation and growth of microcracks in concrete, which improves the continuity and integrality of concrete structure, Thus, a low volume fraction of PP fibers is beneficial to enhancing the long-term tensile strength of concrete materials and improving the durability of concrete structures.

Distribution and tensile strength of Hornbeam （Carpinus betulus） roots growing on slopes of Caspian Forests, Iran

Biomechanical characteristics of the root system of hornbeam （Carpinus betulus） were assessed by measuring Root Area Ratio （RAR） values and tensile strength of root specimens of eight hornbeam trees growing on hilly terrain of Northern Iran. RAR values of the roots were obtained using profile trenching method at soil depth of the top 0.1 m. In total 123 root specimens were analyzed for tensile strength. Results indicate that in general, RAR decreases with depth, following a power function. The RAR values in up and down slopes have no significant statistical differences. In most cases, the maximum RAR values were located in soil depth of the top 0.1 m, with maximum rooting depth at about 0.75 m. The minimum and maximum RAR values along the profiles were 0.004% and 6.431% for down slope and 0.004% and 3.995% for up slope, respectively. The number of roots in the up and down slope trenches was not significantly different. In the same manner as for RAR, number of roots distributing with depth was satisfactorily approximated a power function. The penetration depths of above 90 percent of the roots were at soil depths of 50 cm and 60 cm for up and down slopes, respectively. Results of Spearman＇s bivariate correlation showed no significant correlation between the RAR value with tree diameter and gradient of slope and number of roots. The mean value of root tensile strength was 31.51 ± 1.05 MPa and root tensile strength decreased with the increase in root diameter, following a power law equation. Using ANCOVA, we found intraspecies variation of tensile strength.

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.

Study of the theoretical tensile strength of Fe by a first-principles computational tensile test

This paper employs a first-principles total-energy method to investigate the theoretical tensile strengths of bcc and fcc Fe systemically. It indicates that the theoretical tensile strengths are shown to be 12.4, 32.7, 27.5 GPa for bcc Fe, and 48.1, 34.6, 51.2 GPa for fcc Fe in the [001], [110] and [111] directions, respectively. For bcc Fe, the [001] direction is shown to be the weakest direction due to the occurrence of a phase transition from ferromagnetic bcc Fe to high spin ferromagnetic fcc Fe. For fcc Fe, the [110] direction is the weakest direction due to the formation of an instable saddle-point ＇bct structure＇ in the tensile process. Furthermore, it demonstrates that a magnetic instability will occur under a tensile strain of 14%, characterized by the transition of ferromagnetic bcc Fe to paramagnetic fcc Fe. The results provide a good reference to understand the intrinsic mechanical properties of Fe as a potential structural material in the nuclear fusion Tokamak.

Dynamic tensile strength and failure mechanisms of thermally treated sandstone under dry and water-saturated conditions

To study the tensile strength and failure mechanisms of rock with hydro-thermal coupling damage under different loading rates,a series of static and dynamic splitting tests were conducted on thermally treated sandstone under dry and water-saturated conditions.Experimental results showed that high temperatures effectively weakened the tensile strength of sandstone specimens,and the P-wave velocity declined with increasing temperature.Overall,thermal damage of rock increased gradually with increasing temperature,but obvious negative damage appeared at the temperature of 100℃.The water-saturated sandstone specimens had lower indirect tensile strength than the dry ones,which indicated that water-rock interaction led to secondary damage in heat-treated rock.Under both dry and water-saturated conditions,the dynamic tensile strength of sandstone increased with the increase of strain rate.The water-saturated rock specimens showed stronger rate dependence than the dry ones,but the loading rate sensitivity of thermally treated rock decreased with increasing treatment temperature.With the help of scanning electron microscopy technology,the thermal fractures of rock,caused by extreme temperature,were analyzed.Hydro-physical mechanisms of sandstone under different loading rate conditions after heat treatment were further discussed.