Effective Tensile Stress Research Articles

The effect of stress gradient on the formation of topologically close packed phases in a Ni-based single crystal superalloy at 1050 °C

The formation of topologically close packed (TCP) phases is detrimental to the mechanical properties of Ni-based single crystal (SX) superalloys, which are used in harsh environments with high temperature and gradient stress caused by centrifugal force during service. In order to study the precipitation behavior of TCP phases in coupling with temperature and stress gradient, a third generation Ni-based SX superalloy is selected to conduct force holding experiments at 1050 °C for 8 hours. Stress gradient can be realized under constant load by designing tensile samples with cross-sectional area continuously changed. The results indicate that the area fraction of TCP phases varies at different positions of the sample, where the effective tensile stress is different. The area fraction of TCP phases decreases at the thinner region of the sample, which means that the amount of TCP phases decreases as applied stress increases. At the thinnest position, where the stress is estimated to be 400 MPa, almost no TCP was observed. The inhibition of stress on the formation of TCP phase may be due to the reduction of Re concentration in the γ matrix, because of the segregation of Re at γ/γ′ phase interfacial dislocation cores and the dissolving of γ′ phase.

Elastic constant ratio for fatigue evaluation on rubber isolators

AbstractIn this study, a new concept of the elastic constant ratio was introduced to derive an S‐N base function, which has removed the requirement of the shear modulus to be measured in previous work, allowing much wider applications in fatigue prediction with significant reduction in the costs involved in conducting experiments and acceleration of the design process in industries. In this approach, the damage parameter was the effective tensile stress verified for both positive and negative R ratios (the ratio between the minimum stress and the maximum stress). Existing work only provided a general description of the criterion without detailed explicit equations, which does not provide sufficient clarity to the reader and could lead to variable fatigue life predictions. Here, detailed equations are introduced on the calculation procedure to allow accurate results to be obtained for fatigue assessment. The applicability of the approach was validated using two industrial components, that is, the Metacone spring and the bush spring. The maximum values of the damage parameter corresponded to the same failure locations observed in the experiments. The suggested S‐N base function, correlated with different materials and failure cycles, could be applied in a fatigue design stage and failure analysis for rubber isolators.Highlights For the first time, an elastic constant ratio is introduced on different rubbers. There is no additional test required for the material constants to save cost. The approach is experimentally validated on two industrial isolators. Monitoring stiffness in tests cannot determine the crack initiation accurately.

Gravity‐Driven Jointing in Layered Rocks: Mechanical Analysis and Numerical Modeling

AbstractThe origin of open‐mode fractures or joints, common in sedimentary basins (reservoirs), remains incompletely understood. These fractures require effective tensile stress for their formation, yet they usually develop at depths where effective compressive stresses dominate. Through 2‐D finite‐difference elastoplastic modeling, we demonstrate that effective tensile stresses and fracturing can be internally generated in stiff competent layers separated by compliant incompetent layers. Two primary factors drive this phenomenon: the layered structure of sedimentary units with varying mechanical properties of the layers and the lithostatic compression of the unit, leading to its gravity‐driven horizontal widening or stretching. This stretching occurs when the average horizontal stress over the unit’s thickness is compressive. Various mechanisms can accommodate the stretching, including preexisting faults or weak zones, free borders like canyons, and horizontal extension of tectonic or gravitational origin. Tensile horizontal effective stresses σxx occur within the competent layers, while the incompetent layers generally remain under effective compression. The magnitude of σxx increases with the lithostatic stress or burial depth, as does the tensile strength σt of incompletely lithified sediments. Jointing occurs within depth intervals where |σxx| > σt. In our modeling approach, effective tensile stresses σxx are generated due to lithostatic compression σv. In the previous numerical modeling studies, these stresses resulted from extension directly applied to the lateral boundaries of the layers and did not depend on σv. We provide an analysis of the distinctions between these two approaches.

Практическая реализация инженерной методики определения напряженного состояния в горизонтальных сечениях железобетонных подпорных стен

Retaining walls made of reinforced concrete are widely used in hydraulic engineering and transport construction. Since their rear faces are covered with ground filling, it seems difficult to control the stressed state of the rear working fittings, which in some cases led to deviations in the work of structures from the project. In this article, corner type retaining walls are considered. The purpose of the work was to develop and test an engineering technique for determining the stress state in horizontal sections of retaining walls made of reinforced concrete. In the framework of this work, studies were conducted on the structures of reinforced concrete retaining walls that interact with the soils of the base and backfill. At the same time, using the provisions of structural mechanics and the theory of reinforced concrete, an engineering technique was developed that allows calculating the stress state of reinforced concrete retaining walls along horizontal sections. To test the proposed calculation methodology, the in-situ data of instrumental surveys of the operated lower retaining walls of the PSPP water intake (pumped storage power plant) were used on the basis of the “reinforcement unloading” method in relation to the facing structural reinforcement of the walls. The developed method was practically implemented to assess the effective tensile stresses in the rear working reinforcement, as well as the compressive stresses in the concrete of retaining walls.

Damage of porous building stone by sodium carbonate crystallization and the effect of crystallization modifiers

Salt crystallization is an aggressive weathering mechanism affecting porous building materials. The extensive use of Portland cement, a source of alkalis, in modern buildings and restoration interventions makes sodium carbonate salts important weathering agents. Herein, we study salt damage to a porous stone commonly used in the Andalusian built heritage (Santa Pudia limestone) due to stress generation associated with the precipitation of natron (Na2CO3·10 H2O). We performed cyclic crystallization tests combined with thermodynamic and poromechanical calculations to determine salt crystallization pressure and effective tensile stress suffered by the material. The outcome reveals that in-pore natron crystallization during cooling/evaporation generates stresses exceeding the tensile strength of the wet substrate, leading to extensive damage by fracturing and material loss. Damage is reduced using aminotris(methylenephosphonic) acid (ATMP), a common phosphonate-based crystallization modifier that induces non-damaging efflorescence growth as opposed to damaging subflorescence growth, which takes place in its absence.

Adjustment of a novel β′-type precipitate in a creep-aged Mg−15 wt%Gd alloy

A Mg−15 wt%Gd binary alloy was prepared by hot-extrusion and then creep-aged at 200 °C under a constant stress of 200 MPa in this work. Compared with the traditional aging, creep aging clearly accelerated the age-hardening response, as the aging time for the peak yield strength was shorten from 72h to ∼16h. In the peak-creep-aged sample, a novel precipitation structure, named as β′H herein, was observed as the dominant precipitate. Interestingly, these dense β′H precipitates preferred to distributing along a certain direction which generally deviated from the extrusion direction (ED) by 54–67°. Aberration-corrected high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) characterization revealed that this novel β′H precipitate is composed of distorted Gd-rich hexagonal units, with the chemical formula of Mg7Gd2 and having a monoclinic structure, a = 0.671 nm, b = 1.727 nm, c = 0.521 nm and β = 100.7°. Density functional theory (DFT) calculations suggest that the applied stress during creep aging could provide an effective tensile stress for the motion of the surrounding Mg atoms when forming the β′H structure.

Prediction and demonstration of periodic tensile cracking in rate-dependent porous cement

Periodic tensile cracks are shown to occur when cylinder-shaped saturated cement specimens are subjected to rapid decompression, with the spacing between the cracks scaling as a power law of the decompression time. This behavior is predicted by theory, which is specified to this scenario based on prior work that was more general and applied to compaction bands. Specifically, the formation of the tensile cracks is shown to coincide with periodicity that naturally arises in the effective stress when the material follows a Terzaghi-type consolidation law, although in reverse for dilation and with material deformation described by a rate-dependent viscoplastic law. When strain rate is proportional to effective stress to a power that is greater than one, periodic regions of tensile effective stress arise through the poromechanical fluid–solid coupling. The theoretically-predicted exponent of the resulting power-law relationship between tensile cracks spacing and unloading time successfully brackets the experimental results, for which it is observed that the exponent is slightly stronger than a square-root relationship (0.28 to 0.67) at testing temperatures of 20 ℃ and 90 ℃. These results demonstrate that rapid-depressurization leads to periodic fracturing that could, on the one hand, be detrimental to the isolation provided by cement used to seal wellbores in the petroleum industry. On the other hand, the periodic tensile cracks could also be favorable to production if generated in low-permeability reservoir rocks such as shales that are targeted for petroleum production or granites that are targeted for geothermal energy.

Analysis of the Tunneling Blast Safety Criterion Based on Longitudinal Shocks

In modern tunneling construction, the blasting seismic effect seriously threatens the safety and stability of the existing engineering construction. Meanwhile, due to the complexity of blasting loading, there is a very large difference from real blasting by using the sample triangle dynamic loading model or trapezoid dynamic loading model to analyze the blasting vibration problem. In this paper, based on the analysis of the pressure change, volume expansion, fracture development, and blasting gas motion, an accurate blasting loading model was proposed. Then, adopting plane longitudinal shock theory, the coupled loading of multiple holes can be obtained. Subsequently, the 3D simulation analysis of the tunnel blasting shows an error of 2% compared with on-site monitoring data, meeting engineering requirements. Finally, based on the simulation results, regression prediction function of the velocity curve and effective tensile stress curve under different safety criteria are established, achieving accurate prediction of the damage degree of the host rock and liner line under different engineering requirements.

Mechanical Properties and Brittleness Characterization Method of Low-Rank Coal and Its Char Particles under a Uniaxial Compression Test

The mechanical properties of low-rank coal and its char particles are of great significance in many energy and chemical process applications. The 2.8–4.0 mm narrow size range irregularly shaped particles of Shenhua sub-bituminous coal and Huolinhe lignite and their 800 °C chars were studied by using a uniaxial compression test. The results showed that their mechanical properties such as effective elastic modulus, crushing force, crushing energy, and tensile stress fitted well with Weibull and logistic distributions. Statistically, the strength of both kinds of coal chars was higher than that of raw coal. The distribution of mechanical parameters of lignite and its char particles was more dispersed and had a wider range of variation. The brittleness index composed of compressive stiffness and breakage energy could well describe the particle failure mode, and the brittleness of sub-bituminous coal was greater than that of lignite. Image-based particle size distribution analysis revealed that samples with higher brittleness and strength would produce less volume of fragments conforming to fractal distribution during the crushing process. This indicates that the crushing process of coal particles with brittleness and high strength is relatively fast and their cracks are not fully developed.

Nonlinear stretching mechanics of planar Archimedean-spiral interconnects for flexible electronics

Stretchable island-bridge structures are widely used in flexible inorganic electronics. The recently proposed Archimedean-spiral interconnects are good candidates for achieving a high level of stretchability. The optimal design of the Archimedean spiral depends on systematic exploration of the geometric variables, which is still lacking in theoretical fundamentals. In this work, a theoretical model for the mechanical responses of Archimedean-spiral interconnects under the in-plane stretching is developed based on the finite deformation plane-strain beam theory. The key parameters of the mechanical responses including the effective tensile stress, maximum strain and deformed configurations are analytically derived and validated by finite element analysis for a wide range of geometric variables. The theoretical and numerical results demonstrate that the stress–strain responses and elastic stretchability can be well tailored by three nondimensionless variables. Quantitative comparison shows that the Archimedean-spiral interconnects may have certain advantage over the widely-adopted serpentine interconnects. The results obtained in this work are beneficial for facilitating ultra-stretchable spiral interconnects for future stretchable electronics.

Predicting shear strength of steel fiber reinforced concrete beam-column joints by modified compression field theory

A theoretical model based on modified compression field theory (MCFT) to predict the shear strength of steel fiber reinforced concrete (SFRC) beam-column joints is proposed in this paper. The model considers the contribution of steel fibers to the shear bearing capacity while equating the effect of randomly distributed steel fibers at cracks to the effective tensile stress of steel fibers. Moreover, it regards cracked SFRC as a new material with their own stress–strain relationship and establishes the equilibrium equation, coordination equation, and constitutive equation according to the average stress and average strain. The proposed model is validated by comparing it with the experimental data of 68 existing shear failure tests performed on SFRC and reinforced concrete beam-column joints and comparing with the predicted shear strength results of Gao's model, Tang's model, and ACI Code 318-14′s model. In general, the proposed model given in the paper is accurate for predicting the shear strength of SFRC beam-column joints.

Effect of rock loading rate based on crack extension and propagation

When subjected to constant static load, after a period of damage accumulation and crack development, the rock will fail under a load lower than its compressive strength. The transform of loading rate may have a certain influence on the mechanical properties of rock. In order to investigate the effect of loading rate on mechanical properties of red sandstone, the propagation form of internal cracks in the subcritical propagation stage in rock under static loading is defined as tensile. Based on Maxwell model, the expression of effective tensile stress for crack extension in rock is deduced, which explains the phenomenon of rock tensile failure. Based on the uniaxial compression test of red sandstone under different loading rates, and the surface deformation field of specimens is analysed with the method of digital image correlation, and the corresponding relationship between the loading rate effect and the change of mechanical properties as well as the energy accumulation and release characteristics is analysed, the phenomenon of rock tensile failure is further verified. This research can be effectively applied to geotechnical engineering disaster warning.

Inducing Tensile Failure of Claystone Through Thermal Pressurization in a Novel Triaxial Device

Complex coupled thermo-hydromechanical (THM) loading paths are expected to occur in clay rocks which serve as host formations for geological radioactive waste repositories. Exothermic waste packages heat the rock, causing thermal strains and temperature induced pore pressure build-up. The drifts are designed in such a way as to limit these effects. One has to anticipate failure and fracturing of the material, should pore pressures exceed the tensile resistance of the rock. To characterise the behaviour of the Callovo-Oxfordian claystone (COx) under effective tension and to quantify the tensile failure criterion, a laboratory program is carried out in this work. THM loading paths which correspond to the expected in situ conditions are recreated in the laboratory. To this end, a special triaxial system was developed, which allows the independent control of radial and axial stresses, as well as of pore pressure and temperature of rock specimens. More importantly, the device allows one to maintain axial effective tension on a specimen. Saturated cylindrical claystone specimens were tested in undrained conditions under constrained lateral deformation and under nearly constant axial stress. The specimens were heated until the induced pore pressures created effective tensile stresses and ultimately fractured the material. The failure happened at average axial effective tensile stresses around 3.0 MPa. Fracturing under different lateral total stresses allows one to describe the failure with a Hoek–Brown or Fairhurst’s generalized Griffith criterion. Measured axial extension strains are analysed based on a transversely isotropic thermo-poroelastic constitutive model, which is able to satisfactorily reproduce the observed behaviour.

Experimental and Numerical Investigation on Basic Law of Dense Linear Multihole Directional Hydraulic Fracturing

Using the dense linear multihole to control the directional hydraulic fracturing is a significant technical method to realize roof control in mining engineering. By combining the large-scale true triaxial directional hydraulic fracturing experiment with the discrete element numerical simulation experiment, the basic law of dense linear holes controlling directional hydraulic fracturing was studied. The results show the following: (1) Using the dense linear holes to control directional hydraulic fracturing can effectively form directional hydraulic fractures extending along the borehole line. (2) The hydraulic fracturing simulation program is very suitable for studying the basic law of directional hydraulic fracturing. (3) The reason why the hydraulic fracture can be controlled and oriented is that firstly, due to the mutual compression between the dense holes, the maximum effective tangential tensile stress appears on the connecting line of the drilling hole, where the hydraulic fracture is easy to be initiated. Secondly, due to the effect of pore water pressure, the disturbed stress zone appears at the tip of the hydraulic fracture, and the stress concentration zone overlaps with each other to form the stress guiding strip, which controls the propagation and formation of directional hydraulic fractures. (4) The angle between the drilling line and the direction of the maximum principal stress, the in situ stress, and the hole spacing has significant effects on the directional hydraulic fracturing effect. The smaller the angle, the difference of the in situ stress, and the hole spacing, the better the directional hydraulic fracturing effect. (5) The directional effect of synchronous hydraulic fracturing is better than that of sequential hydraulic fracturing. (6) According to the multihole linear codirectional hydraulic fracturing experiments, five typical directional hydraulic fracture propagation modes are summarized.

Durability prediction of brittle rocks based on type-I crack extension theory

When subjected to long-term static loading, with the accumulation of damage and fracture, brittle rock would fails when the static loading is lower than the compressive strength of the rock, and the increasing of the static loading can generally shorten the time required for the brittle rock failure. To explore the relationship between the durability of the brittle rock and the applied static loading, in this paper, the propagation modes of the microcracks in brittle rock under the static loading in the subcritical crack growth stage are uniformly attributed to the tensile mode, and the total time required for microcrack propagation in the subcritical crack growth stage is chosen as the criterion for judging the durability index of brittle rock. Based on the Maxwell model, the local effective tensile stress that drives crack propagation is derived. The phenomenon of brittle rock exhibiting tensile failure under the compressive stress is preliminarily explained, and the corresponding requirements for this phenomenon to occur are also presented. A new expression of rock durability prediction with a clear physical meaning is established. The key parameter, i.e., the durability index “n” in the newly derived expression is obtained through fitting, and the relationship between the durability index and the rock type is preliminarily analysed. This study may provide an approach for preliminarily estimating the durability of brittle rock.

Characterizing crack morphology toward improving ductile mode cutting of calcium fluoride

Delaying the onset of brittle mode cutting does not only involve the augmentation of slip deformation but could also be tackled from the perspective of suppressing the leading causes for crack formation. This work studies the micro-cutting of calcium fluoride single crystals with diamond turning and orthogonal plunge-cutting. An applied coating shows promise to enhance ductile mode cutting during diamond turning and also alters the crack morphology during cutting in the brittle regime. Conventionally, calcium fluoride exhibits anisotropic pyramidal cracks that were associated with the activation of the {111} cleavage plane while the adoption of the coating prior to micro-cutting alters the cracks to become laminar in nature associated with the (1‾11‾) cleavage plane. The resistance to deformation of the coating is proposed to create reaction stress along the shear plane of the workpiece to reduce the effective tensile stresses acting on cleavage planes. Crystal plasticity finite element method modelling demonstrates the relationship between the coating stress distribution and the intensified concentration of shear stresses in the workpiece, which confirms the notion of the reaction stress acting along the shear plane. Moreover, the simulations with the coating present the affected tensile stresses acting on a majority of the {111} cleavage planes with the exception of the (1‾11‾) cleavage plane, which supports the crack orientations in brittle mode cutting.

Prediction of Bench Blasting Vibration on Slope and Safety Threshold of Blasting Vibration Velocity to Undercrossing Tunnel

The reconstruction and expansion project of oil reserve base often faces the excavation and blasting of the slope and undercrossing tunnel at the same time. Due to the flammable and explosive liquid storage nearby, the tight construction period, and the high requirements of collaborative construction, once the blasting accident occurs, the consequences are unimaginable. To facilitate safe and timely cooperative blasting construction of the slope and undercrossing tunnel, a vibration monitoring test of the slope and tunnel surrounding rock is conducted. The vibration response characteristics of the rock surrounding the slope and tunnel are analyzed, and a mathematical prediction model for the peak particle velocity (PPV) with consideration of the influence of the relative slope gradient (H/D) is established based on dimension analysis theory, which improves the prediction accuracy of PPV at the slope surface. ANSYS/LS‐DYNA is used to establish a 3D finite element model for the slope and tunnel, and the dynamic response of the tunnel surrounding rock under blasting load is verified through field monitoring data. A linear statistical relationship between PPV and effective tensile stress (ETS) of the tunnel surrounding rock is established. The PPV safety criterion of the tunnel surrounding rock under blasting load is proposed to be 10 cm/s according to the first strength theory, and hence, the minimum safety distance from the tunnel working face to the slope surface is calculated to be 36 m. Finally, the excavation timing arrangement of the slope and tunnel is proposed, which has been successfully applied to the expansion project, and the construction period has been effectively shortened by 45 days while ensuring construction safety. The research results have great guiding significance to similar cooperative blasting excavation engineering for high slope and adjacent tunnel with safety and efficiency.

A new interpretation for formation of orthogonal joints in quartz sandstone

Abstract Two vertical and orthogonal systematic joint sets are generally arrayed in a grid pattern on the bedding surface, which are the significant features of flat-lying sandstone terrains. Although extensive researches are reported on this topic, many fundamental problems have still not been solved. Such mutually perpendicular opening-mode fractures are an obvious manifestation of effective tensile stresses in two orthogonal directions in the horizontal bedding plane. A good understanding of these orthogonal joint systems is a key to structural analysis, landscape interpretation, and guidance of resolving a number of very practical problems in engineering, mining and hydrologic projects. Based on an anatomic investigation on the orthogonal joints in the Potsdam sandstone of Cambrian age at Ausable Chasm (New York State, USA) and Beauharnois (Quebec, Canada), we proposed that the orthogonal joints may result from the auxetic effects of quartz-rich sandstone rather than local or regional rotation of the maximum tensile stress (σ3) direction by about 90°. The sandstone beds with negative Poisson's ratios are so fascinating that, when placed under vertical burial compression and layer-parallel extension in one direction (σ3), it becomes stretched in the transverse direction (σ2), producing two orthogonal sets of mutual abutting and intersecting joints (J1 and J2 normal to σ3 and σ2, respectively), and both are normal to the bedding surface. Joint set J1 is more closely-spaced than J2 by a factor of ∼3.3, which is correlated with an average Poisson's ratio of −0.3 for the Potsdam sandstone at the time of joint formation.

A hybrid simulation approach to evaluate stimulation micro-seismic events and production potential of fractured geothermal reservoirs

This study presents an integrated approach to simulate fluid flow and to predict the micro seismic events during stimulation and circulation of cold water over a longer term in geothermal reservoirs. The integrated approach based on new three dimensional fully coupled thermo-poroelastic numerical model for evaluation of energy recoverable. In the presented approach, the fracture aperture due to fracture slippage is calculated by shear and dilation. The shear slippage is controlled by the concept of shear failure using linear Mohr-Coulomb criterion. The numerical model is validated against an analytical Oda’s model for permeability tensor calculation and against an analytical solution for thermo-poroelastic model. The heat transfer between the rock and fluid is modelled by using the conductive heat transfer within the reservoir rock and convective heat transfer in discrete fractures. The thermal stress changes are included in the model to be studied by using roughness induced shear displacement principle in a poro-thermo-elastic environment. The fracture aperture changes are estimated by using an analytical model based on the distributed dislocation technique. The roughness of fracture surfaces is used in the calculation of residual fracture aperture. The presented approach is used to study the potential of permeability enhancement for Habanero geothermal reservoir at a depth of 3600 m. The result show that the increasing in tensile effective stress tend to increase the fracture aperture within the zone of cooling. This increasing in fracture aperture led to significant changes in pressure distribution (decrease in impedance) and hence, increase in the flow rate.

Bolt Strength in Sectional Body Construction of Valves

Abstract ASME B16.34-2017 Section 6.4.2 provides requirements for valves with bolted body joints and threaded body joints. The section states that valves with bodies of sectional construction such that bolted or threaded body joints are subject to piping mechanical loads in addition to the pressure rating for which the valve is designed, shall satisfy the following requirements. For bolted joints, the requirement is a simple formula where the product of pressure rating class designation and ratio of area bounded by the effective outside periphery of a gasket or O-ring or other seal-effective periphery and total effective bolt tensile stress area are less than a certain constant. For bolts of strength less than 137.9 MPa, the value of constant reduces as a multiple of 50.76 times the bolt tensile strength in MPa required or provided in a sectional construction. Section 6.4.3 cautions that the minimum requirements of ASME B16.34 may fall short in scenarios due to valve design, special gaskets, high temperature service, creep characteristics, etc. This paper reviews and studies this ASME B16.34 requirement, which was triggered by failure of a valve with section body construction in the field. Traditionally, valves have been considered as rigid bodies when analyzing a piping system for stresses, support loads, terminal point loads, and deflections. The rigid modeling assumes that the strength of the valve is much higher than an equivalent straight length of pipe. Some computer programs have a provision that permits modeling the valve as a multiple like three- or four-times pipe section modulus. This paper compares the strength of piping and valves based on inherent valve body thickness, body sectional bolting provided, and strength of the equivalent piping flanges. The paper provides conclusions for the user to be aware of so that pre-emptive actions can be taken when using valves with sectional body construction.