Effect of lateral stress on frictional properties of a fracture in sandstone

The injection of large volumes of natural gas into geological formations,as is required for underground gas storage,leads to alterations in the effective stress exerted on adjacent faults.This increases the potential for their reactivation and subsequent earthquake triggering.Most measurements of the frictional properties of rock fractures have been conducted under normal and shear stresses.However,faults in gas storage facilities exist within a true three-dimensional(3D)stress state.A double-direct shear experiment on rock fractures under both lateral and normal stresses was conducted using a true triaxial loading system.It was observed that the friction coefficient increases with increasing lateral stress,but decreases with increasing normal stress.The impact of lateral and normal stresses on the response is primarily mediated through their influence on the initial friction coefficient.This allows for an empirical modification of the rate-state friction model that considers the influence of lateral and normal stresses.The impact of lateral and normal stresses on observed friction coefficients is related to the propensity for the production of wear products on the fracture surfaces.Lateral stresses enhance the shear strength of rock(e.g.Mogi criterion).This reduces asperity breakage and the generation of wear products,and consequently augments the friction coefficient of the surface.Conversely,increased normal stresses inhibit dilatancy on the fracture surface,increasing the breakage of asperities and the concomitant production of wear products that promote rolling deformation.This ultimately reduces the friction coefficient.

Evaluation of frictional pressure drop correlations for air-water and air-oil two-phase flow in pipeline-riser system

Accurate prediction of the frictional pressure drop is important for the design and operation of subsea oil and gas transporting system considering the length of the pipeline. The applicability of the correlations to pipeline-riser flow needs evaluation since the flow condition in pipeline-riser is quite different from the original data where they were derived from. In the present study, a comprehensive evaluation of 24prevailing correlation in predicting frictional pressure drop is carried out based on experimentally measured data of air-water and air-oil two-phase flows in pipeline-riser. Experiments are performed in a system having different configuration of pipeline-riser with the inclination of the downcomer varied from-2°to-5°to investigated the effect of the elbow on the frictional pressure drop in the riser. The inlet gas velocity ranges from 0.03 to 6.2 m/s, and liquid velocity varies from 0.02 to 1.3 m/s. A total of885 experimental data points including 782 on air-water flows and 103 on air-oil flows are obtained and used to access the prediction ability of the correlations. Comparison of the predicted results with the measured data indicate that a majority of the investigated correlations under-predict the pressure drop on severe slugging. The result of this study highlights the requirement of new method considering the effect of pipe layout on the frictional pressure drop.

A smoothed assumed enhanced strain method for frictional contact with constant strain elements

This paper presents a finite element framework for imposing frictional contact conditions on embedded fracture faces,implemented by the constant-strain assumed enhanced strain(AES)method,where penalty method is used to impose both non-penetration constraint and Coulomb’s law of friction.The proposed constant-strain AES method for modeling embedded frictional contact can be cast into an integration algorithm similar to those used in the classical plasticity theory,where displacement jump is calculated from the local traction equilibrium at Gauss point,so the method does not introduce any additional global degrees of freedom.Moreover,constant-strain elements are often desirable in practice because they can be easily created automatically for large-scale engineering applications with complicated geometries.As encountered in other enriched finite element methods for frictional contact,the problem of normal contact pressure oscillations is also observed in the constant-strain AES method.Therefore,we developed a strain-smoothing procedure to effectively mitigate the oscillations.We investigated and verified the proposed AES framework through several numerical examples,and illustrated the capability of this method in solving challenging nonlinear frictional contact problems.

Existence and numerical approximation of a solution to frictional contact problem for electro-elastic materials

In this paper,a frictional contact problem between an electro-elastic body and an electrically conductive foundation is studied.The contact is modeled by normal compliance with finite penetration and a version of Coulomb’s law of dry friction in which the coefficient of friction depends on the slip.In addition,the effects of the electrical conductivity of the foundation are taken into account.This model leads to a coupled system of the quasi-variational inequality of the elliptic type for the displacement and the nonlinear variational equation for the electric potential.The existence of a weak solution is proved by using an abstract result for elliptic variational inequalities and a fixed point argument.Then,a finite element approximation of the problem is presented.Under some regularity conditions,an optimal order error estimate of the approximate solution is derived.Finally,a successive iteration technique is used to solve the problem numerically and a convergence result is established.

Frictional sliding of infilled planar granite fracture under oscillating normal stress

This paper investigates the frictional behavior of the infilled rock fracture under dynamic normal stress.A series of direct shear tests were conducted on saw-cut granite fractures infilled with quartz using a selfdeveloped dynamic shear apparatus,and the effects of normal load oscillation amplitude,normal load oscillation period and sliding velocity were studied.The test results reveal that the shear response can be divided into three stages over a whole loading-unloading process,characterized by different time spans and stress variations.Generally,a smaller oscillation amplitude,a longer oscillation period and a fast shear velocity promote the stability of the friction system,which is also confirmed by the Coulomb failure criterion calculated based on the observed periodic apparent friction coefficient.The dynamic strengthening/weakening phenomenon is dependent on the oscillation amplitude and product of sliding velocity and oscillation period(vT).Also,the rate and state friction law incorporating the parameter a that characterizes the normal stress variation is employed to describe the dynamic friction coefficient but exhibits an incompetent performance when handling intensive variation in normal stress.Finally,the potential seismicity induced by oscillating normal stress based on the observed stress drop is analyzed.This work helps us understand the sliding process and stability evolution of natural faults,and its benefits for relative hazard mitigation.

Frictional behavior of quartz gouge during slide-hold-slide considering normal stress oscillation

Slide-hold-slide(SHS)test is an essential experimental approach for studying the frictional stability of faults.The origin SHS framework was established based on a consistent constant normal stress,which cannot truly reflect the stress disturbance around fault zones.In this paper,we conducted a series of'dynamic SHS tests',which includes normal stress oscillations in the relaxation stage with different oscillation amplitudes and frequencies on synthetic quartz gouge using a double direct shear assembly.The experimental results reveal that the amplitude of the normal load oscillation has a remarkable effect on the frictional relaxation and healing patterns.However,the frequency of the normal load oscillation has a minor effect.Additionally,the shear loading rate is proportional to the normal loading rate during the relaxation stage,and the normal stiffness of the quartz layer remains nearly constant under various loading conditions.The creep rate during the hold phase is not obviously affected by the normal load oscillation,while the precursory slip is also sensitive to the oscillation amplitude.This study provides insights into the evolution of frictional stability in discontinuities and is beneficial for controlling relative disasters in fault zones.

Anomalous{1012}tensile twinning and subsequent detwinning in a friction stir processed carbon fiber-reinforced Mg composite

1.Main text Owing to their low density and high specific strength,magnesium alloys and magnesium-based composites have great potential as structure metal materials in applications where lightweight matters[1–4].Deformation twins[5],especially the{1012}tension twins(also called tensile or extension twins)with a low critical resolved shear stress(CRSS)[6],are commonly observed in Mg alloys.They can provide the much-needed deformation along the c-axis in their hcp structure resulting from the very few easily activated slip systems in this crystal structure[7].The tensile twinning activation usually follows the macroscopic Schmid factor law[2],i.e.,the twin variant with the highest Schmid factor occurs,and it only appears when its Schmid factor is positive.

Experimental investigation on frictional properties of stressed basalt fractures

The frictional strength and sliding stability of faults are crucial in interpreting earthquake mechanisms and cycles.Herein,we report friction experiments on basalt fractures,using a self-designed triaxial apparatus that allows direct shear of samples under coupled hydro-mechanical conditions.Velocitystepping(VS)and slide-hold-slide(SHS)experiments are performed on both bare and gouge-bearing surfaces of Xiashan basalt subjected to cyclic shear velocities at 1e30 mm/s,effective normal stresses of 1e5 MPa,and pore pressures of 70e300 kPa.The measured basalt friction coefficients are in the range of 0.67e0.74,which is sensitive to gouge thickness,normal stress,and water.Specifically,a reduction in friction coefficient is observed with an increment in gouge thickness,normal stress,and pore pressure.Based on the microscopic observation of the pre-and post-shearing sliding surfaces,this weakening effect in friction coefficient can be attributed to powder lubrication.Furthermore,the VS test results reveal predominantly velocity-strengthening behavior at investigated slip velocities,and this velocity strengthening behavior does not appear to be influenced by variations in normal stress,gouge thickness,and water.However,changes in sliding velocity and normal stress can lead to a shift between stable and unstable sliding.Specifically,stable sliding is favored by high sliding velocities and low normal stress applied in this study.Finally,we analyze the experimental data by calculating the rate-and-state parameters using the rate-and state-dependent friction(RSF)theory.Importantly,the calculated friction rate parameter(a-b)supports the velocity-strengthening behavior.Both frictional relaxation(Dmc)during hold periods and frictional healing(Dm)upon re-shearing are linearly proportional to the logarithmic hold time,which may be attributed to the growth in true contact area with hold time.This study sheds light on the roles of sliding velocity,and gouge thickness in controlling frictional strength and stability of basalt fractures.

A review of linear friction welding of Ni -based superalloys

Ni-based superalloys are one of the most important materials employed in high-temperature applications within the aerospace and nuclear energy industries and in gas turbines due to their excellent corrosion,radiation,fatigue resistance,and high-temperature strength.Linear friction welding(LFW)is a new joining technology with near-net-forming characteristics that can be used for the manu-facture and repair of a wide range of aerospace components.This paper reviews published works on LFW of Ni-based superalloys with the aim of understanding the characteristics of frictional heat generation and extrusion deformation,microstructures,mechanical proper-ties,flash morphology,residual stresses,creep,and fatigue of Ni-based superalloy weldments produced with LFW to enable future optim-um utilization of the LFW process.

Effects of friction stir processing and nano-hydroxyapatite on the microstructure,hardness,degradation rate and in-vitro bioactivity of WE43 alloy for biomedical applications

Nowadays,magnesium alloys are emerging in biomedical implants for their similar properties to natural bones.However,the rapid degradation of magnesium alloys in biological media hinders successful implantation.Refinement of microstructure,as well as reinforcement particles can significantly improve the degradation rate.In this work,multi-pass friction stir processing(FSP)was proposed to synthesize WE43/nano-hydroxyapatite(n HA)surface composite,the microstructure,reinforced particle distribution,micro-hardness,corrosion behavior and in-vitro bioactivity were studied.The subsequent FSP passes of WE43 alloy and WE43/n HA composite refined the grain size which was reduced by 94.29%and 95.92%(2.63 and 1.88μm,respectively)compared to base metal after three passes.This resulted in increasing the microhardness by 120%(90.86 HV0.1)and 135%(105.59 HV0.1)for the WE43 and WE43-n HA,respectively.It is found that increasing FSP passes improved the uniform distribution of n HA particles within the composite matrix which led to improved corrosion resistance and less degradation rate.The corrosion rate of the FSPed WE43/n HA composite after three passes was reduced by 38.2%(4.13 mm/year)and the degradation rate was reduced by 69.7%(2.87 mm/y).This is attributed to secondary phase(Mg24Y5and Mg41Nd5)particle fragmentation and redistribution,as well as a homogeneous distribution of n HA.Additionally,the growing Ca-P and Mg(OH)2layer formed on the surface represented a protective layer that reduced the degradation rate.The wettability test revealed a relatively hydrophilic surface with water contact angle of 49.1±2.2°compared to 71.2±2.1°for base metal.Also,biomineralization test showed that apatite layer grew after immersion 7d in simulated body fluid with atomic ratio of Ca/P 1.60 approaching the stoichiometric ratio(1.67)indicating superior bioactivity of FSPed WE43/n HA composite after three passes.These results raise that the grain refinement by FSP and introduction of n HA particles significantly improved the degradation rate and in-vitro bioactivity of WE43 alloy for biomedical applications.

A new insight into LPSO phase transformation and mechanical properties uniformity of large-scale Mg-Gd-Y-Zn-Zr alloy prepared by multi-pass friction stir processing

A large-scale fine-grained Mg-Gd-Y-Zn-Zr alloy plate with high strength and ductility was successfully prepared by multi-pass friction stir processing(MFSP)technology in this work.The structure of grains and long period stacking ordered(LPSO)phase were characterized,and the mechanical properties uniformity was investigated.Moreover,a quantitative relationship between the microstructure and tensile yield strength was established.The results showed that the grains in the processed zone(PZ)and interfacial zone(IZ)were refined from 50μm to 3μm and 4μm,respectively,and numerous original LPSO phases were broken.In IZ,some block-shaped 18R LPSO phases were transformed into needle-like 14H LPSO phases due to stacking faults and the short-range diffusion of solute atoms.The severe shear deformation in the form of kinetic energy caused profuse stacking fault to be generated and move rapidly,greatly increasing the transformation rate of LPSO phase.After MFSP,the ultimate tensile strength,yield strength and elongation to failure of the large-scale plate were 367 MPa,305 MPa and 18.0% respectively.Grain refinement and LPSO phase strengthening were the major strengthening mechanisms for the MFSP sample.In particularly,the strength of IZ was comparable to that of PZ because the strength contribution of the 14H LPSO phase offsets the lack of grain refinement strengthening in IZ.This result opposes the widely accepted notion that IZ is a weak region in MFSP-prepared large-scale fine-grained plate.

Comprehensive modeling of frictional pressure drop during carbon dioxide two-phase flow inside channels using intelligent and conventional methods

Environmentally friendly nature of CO_(2),associated with its safety and high efficiency,has made it a widely used working fluid in heat exchangers.Since CO_(2)has strange thermophysical features,specific models are required to estimate its two-phase characteristics,particularly frictional pressure drop(FPD).Herein,a widespread dataset,comprising 1195 experimental samples for two-phase FPD of CO_(2)was adopted from 10 sources to fulfill this requirement.The literature correlations failed to provide satisfactory precisions and exhibited the average absolute relative errors(AAREs)between 29.29% and 67.69% from the analyzed data.By inspiring the theoretical method of Lockhart and Martinelli,three intelligent FPD models were presented,among which the Gaussian process regression approach surpassed the others with AARE and R^(2)values of 5.48% and 98.80%,respectively in the test stage.A novel simple correlation was also derived based on the least square fitting method,which yielded opportune predictions with AARE of 19.76% for all data.The truthfulness of the newly proposed models was assessed through a variety of statistical and visual analyses,and the results affirmed their high reliability over a broad range of conditions,channel sizes and flow patterns.Furthermore,the novel models performed favorably in describing the physical attitudes corresponding to two-phase FPD of CO_(2).Eventually,the importance of operating factors in controlling the FPD was discussed through a sensitivity analysis.

Prediction of corrosion rate for friction stir processed WE43 alloy by combining PSO-based virtual sample generation and machine learning

The corrosion rate is a crucial factor that impacts the longevity of materials in different applications.After undergoing friction stir processing(FSP),the refined grain structure leads to a notable decrease in corrosion rate.However,a better understanding of the correlation between the FSP process parameters and the corrosion rate is still lacking.The current study used machine learning to establish the relationship between the corrosion rate and FSP process parameters(rotational speed,traverse speed,and shoulder diameter)for WE43 alloy.The Taguchi L27 design of experiments was used for the experimental analysis.In addition,synthetic data was generated using particle swarm optimization for virtual sample generation(VSG).The application of VSG has led to an increase in the prediction accuracy of machine learning models.A sensitivity analysis was performed using Shapley Additive Explanations to determine the key factors affecting the corrosion rate.The shoulder diameter had a significant impact in comparison to the traverse speed.A graphical user interface(GUI)has been created to predict the corrosion rate using the identified factors.This study focuses on the WE43 alloy,but its findings can also be used to predict the corrosion rate of other magnesium alloys.

Erratum to:Oil-soluble polymer brushes-functionalized nanoMOFs for highly efficient friction and wear reduction

Erratum to Liu,J.,Qian,Y.,Li,D.et al.Oil-soluble polymer brushes-functionalized nanoMOFs for highly efficient friction and wear reduction.Friction 12(7):1499-1511(2024).https://doi.org/10.1007/s40544-023-0823-x The authors regret that there was a misspelling of the author Dongsheng Li’s name on the webpage of this article,and the author information on the webpage of this article should be corrected as.

Using Optical Tweezers to Study the Friction of the Red Blood Cells

In the last two decades the study of red blood cell elasticity using optical tweezers has known a rise appearing in the scientific research with regard to the various works carried out. Despite the various work done, no study has been done so far to study the influence of friction on the red blood cell indentation response using optical tweezers. In this study, we have developed a new approach to determine the coefficient of friction as well as the frictional forces of the red blood cell. This approach therefore allowed us to simultaneously carry out the indentation and traction test, which allowed us to extract the interfacial properties of the microbead red blood cell couple, among other things, the friction coefficient. This property would be extremely important to investigate the survival and mechanical features of cells, which will be of great physiological and pathological significance. But taking into account the hypothesis of friction as defined by the isotropic Coulomb law. The experiment performed for this purpose is the Brinell Hardness Test (DB).

Study on Chaotic Characteristics of the Friction Process between High Hardness Alloy Steel and Cemented Carbide under C60 Nanoparticle Fluid Lubrication

Friction and wear phenomenon is a complex nonlinear system,and it is also a significant problem in the process of metal cutting.In order to systematically analyze the friction and wear process of tool material-workpiece material friction pair in the cutting process of high hardness alloy steel under different lubrication conditions,the chaotic characteristics of friction process between high hardness alloy steel and cemented carbide under the lubrication C60 nano-particles fluid are studied based on the chaos theory.Firstly,the friction and wear experiments of the friction pair between high hardness alloy steel and cemented carbide tool are carried out based on the ring-block friction and wear tester,and the results of friction force signal in time domain and wear width are obtained.Then,the friction signals in time domain are processed and transformed based on phase space reconstruction and recurrence plot theory,and the recurrence plots of different experimental groups under different lubrication conditions are generated.The evolution law of recurrence plot is further observed and studied,and the recursive quantitative index is analyzed.Finally,the cutting experiments of tool wear are carried out.The results show that the proposed method can intuitively and accurately reveal the wear evolution process and the wear feature identification law of the tool material-high hardness alloy steel pair under different lubrication conditions.Meanwhile,it is found that when the concentration of C60 nanoparticles is 200∼300 ppm,the stability of the friction pair system is best.The proposed method can provide a strategy for wear prediction in cutting process,and provide a theoretical basis and technical support for antifriction lubrication methods in practical cutting applications.

Effect of thermo-mechanical conditions during constrained friction processing on the particle refinement of AM50 Mg-alloy phases

Constrained Friction Processing(CFP)is a novel solid-state processing technique suitable for lightweight materials,such Mg-and Al-alloys.The technique enables grain size refinement to fine or even ultrafine scale.In this study,the effect of CFP on the microstructural refinement of AM50 rods is investigated in terms of particle size and morphology of the eutectic and secondary phases originally present in the base material,in particular the eutecticβ-Mg_(17)Al_(12)and Al-Mn phases.For that purpose,as-cast and solution heat-treated base material and processed samples were analyzed.The Al_(8)Mn_(5) intermetallic phase was identified as the main secondary phase present in all samples before and after the processing.A notorious refinement of these particles was observed,starting from particles with an average equivalent length of a few micrometers to around 560 nm after the processing.The refinement of the secondary phase refinement is attributed to a mechanism analogous to the attrition comminution,where the combination of temperature increase and shearing of the material enables the continuous breaking of the brittle intermetallic particles into smaller pieces.As for the eutectic phase,the results indicate the presence of the partially divorcedβ-Mg_(17)Al_(12)particles exclusively in the as-cast base material,indicating that no further phase transformations regarding the eutectic phase,such as dynamic precipitation,occurred after the CFP.In the case of the processed as-cast material analyzed after the CFP,the thermal energy generated during the processing led to temperature values above the solvus limit of the eutectic phase,which associated with the mechanical breakage of the particles,enabled the complete dissolution of this phase.Therefore,CFP was successfully demonstrated to promote an extensive microstructure refinement in multiple aspects,in terms of grain sizes of theα-Mg phase and presence and morphology of the Al-Mn and eutecticβ-Mg_(17)Al_(12).

Interfacial friction effects on sealing performances of elastomer packer

Elastomer sealing performance is of critical importance for downhole tools application including the use of fracturing(Frac)plugs during multi-stage hydraulic fracking.In practice sealing performances of such plugs are normally evaluated through pressure tests,and in numerical simulation studies,maximum contact stress,average contact stress and contact length data are used to determine sealing quality between a packer and casing.In previous studies,the impact of friction forces on sealing performance is often overlooked.This work aims to fill this knowledge gap in determining the influence of friction forces on elastomer packer sealing performances.We first determined the most appropriate constitutive hyperelastic model for the elastomers used in frac plug.Then we compared analytical calculation results with Finite Element Analysis simulation using a simplified tubular geometry and showed the significant influences on interfacial friction on elastomer packer stress distribution,deformation,and contact stress after setting.With the demonstration of validity of FEA method,we conducted systematic numerical simulation studies to show how the interfacial friction coefficients can affect the maximum contact stress,average contact stress,contact stress distribution,and maximum mises stress for an actual packer used in plug products.In addition,we also demonstrated how the groove in a packer can affect packer deformation and evolvement during setting with the consideration of interfacial stress.This study underscores the critical role that friction forces play in Frac plug performance and provides a new dimension for optimizing packer design by controlling interfacial interactions at the packer contact surfaces.

On the role of sliding friction effect in nonlinear tri-hybrid vibration-based energy harvesting

This work aims to develop an experimental investigation into the effectiveness of the sliding-mode approach for hybrid vibration-based energy harvesting.A proposed sliding-mode triboelectric-electromagnetic-piezoelectric energy harvesting model involves a cantilever beam with a tip mass exposed to magnetic and frictional forces.The experimental findings indicate that the system can achieve its peak inter-well oscillation output within a low-frequency range of 4 Hz–6 Hz.Friction has a lesser impact on the open-circuit voltage output at an excitation acceleration of 1.5g compared with 1g.The distribution of tri-stability changes with the presence of friction.This model provides a deeper understanding of the influence of the dry friction coefficient(0.2–0.5) on the interactive behaviors of different generator units.

Improvement of Microstructure and Mechanical Properties of Rapid Cooling Friction Stir-welded A1050 Pure Aluminum

Two-mm thick A1050 pure aluminum plates were successfully joined by conventional and rapid cooling friction stir welding(FSW), respectively. The microstructure and mechanical properties of the welded joints were investigated by electron backscatter diffraction characterization, Vickers hardness measurements, and tensile testing. The results showed that liquid CO_(2) coolant significantly reduced the peak temperature and increased the cooling rate, so the rapidly cooled FSW joint exhibited fine grains with a large number of dislocations. The grain refinement mechanism of the FSW A1050 pure aluminum joint was primarily attributed to the combined effects of continuous dynamic recrystallization, grain subdivision, and geometric dynamic recrystallization. Compared with conventional FSW, the yield strength, ultimate tensile strength, and fracture elongation of rapidly cooled FSW joint were significantly enhanced, and the welding efficiency was increased from 80% to 93%. The enhanced mechanical properties and improved synergy of strength and ductility were obtained due to the increased dislocation density and remarkable grain refinement. The wear of the tool can produce several WC particles retained in the joint, and the contribution of second phase strengthening to the enhanced strength should not be ignored.