Anisotropic time-dependent behaviors of shale under direct shearing and associated empirical creep models

Understanding the anisotropic creep behaviors of shale under direct shearing is a challenging issue.In this context,we conducted shear-creep and steady-creep tests on shale with five bedding orientations (i.e.0°,30°,45°,60°,and 90°),under multiple levels of direct shearing for the first time.The results show that the anisotropic creep of shale exhibits a significant stress-dependent behavior.Under a low shear stress,the creep compliance of shale increases linearly with the logarithm of time at all bedding orientations,and the increase depends on the bedding orientation and creep time.Under high shear stress conditions,the creep compliance of shale is minimal when the bedding orientation is 0°,and the steady-creep rate of shale increases significantly with increasing bedding orientations of 30°,45°,60°,and 90°.The stress-strain values corresponding to the inception of the accelerated creep stage show an increasing and then decreasing trend with the bedding orientation.A semilogarithmic model that could reflect the stress dependence of the steady-creep rate while considering the hardening and damage process is proposed.The model minimizes the deviation of the calculated steady-state creep rate from the observed value and reveals the behavior of the bedding orientation's influence on the steady-creep rate.The applicability of the five classical empirical creep models is quantitatively evaluated.It shows that the logarithmic model can well explain the experimental creep strain and creep rate,and it can accurately predict long-term shear creep deformation.Based on an improved logarithmic model,the variations in creep parameters with shear stress and bedding orientations are discussed.With abovementioned findings,a mathematical method for constructing an anisotropic shear creep model of shale is proposed,which can characterize the nonlinear dependence of the anisotropic shear creep behavior of shale on the bedding orientation.

Effect of Interface Form on Creep Failure and Life of Dissimilar Metal Welds Involving Nickel-Based Weld Metal and Ferritic Base Metal

For dissimilar metal welds(DMWs)involving nickel-based weld metal(WM)and ferritic heat resistant steel base metal(BM)in power plants,there must be an interface between WM and BM,and this interface suffers mechanical and microstructure mismatches and is often the rupture location of premature failure.In this study,a new form of WM/BM interface form,namely double Y-type interface was designed for the DMWs.Creep behaviors and life of DMWs containing double Y-type interface and conventional I-type interface were compared by finite element analysis and creep tests,and creep failure mechanisms were investigated by stress-strain analysis and microstructure characterization.By applying double Y-type interface instead of conventional I-type interface,failure location of DMW could be shifted from the WM/ferritic heat-affected zone(HAZ)interface into the ferritic HAZ or even the ferritic BM,and the failure mode change improved the creep life of DMW.The interface premature failure of I-type interface DMW was related to the coupling effect of microstructure degradation,stress and strain concentrations,and oxide notch on the WM/HAZ interface.The creep failure of double Y-type interface DMW was the result of Type IV fracture due to the creep voids and micro-cracks on fine-grain boundaries in HAZ,which was a result of the matrix softening of HAZ and lack of precipitate pinning at fine-grain boundaries.The double Y-type interface form separated the stress and strain concentrations in DMW from the WM/HAZ interface,preventing the trigger effect of oxide notch on interface failure and inhibiting the interfacial microstructure cracking.It is a novel scheme to prolong creep life and enhance reliability of DMW,by means of optimizing the interface form,decoupling the damage factors from WM/HAZ interface,and then changing the failure mechanism and shifting the failure location.

A creep model for ultra-deep salt rock considering thermal-mechanical damage under triaxial stress conditions

To investigate the specific creep behavior of ultra-deep buried salt during oil and gas exploitation,a set of triaxial creep experiments was conducted at elevated temperatures with constant axial pressure and unloading confining pressure conditions.Experimental results show that the salt sample deforms more significantly with the increase of applied temperature and deviatoric loading.The accelerated creep phase is not occurring until the applied temperature reaches 130℃,and higher temperature is beneficial to the occurrence of accelerated creep.To describe the specific creep behavior,a novel three-dimensional(3D)creep constitutive model is developed that incorporates the thermal and mechanical variables into mechanical elements.Subsequently,the standard particle swarm optimization(SPSO)method is adopted to fit the experimental data,and the sensibility of key model parameters is analyzed to further illustrate the model function.As a result,the model can accurately predict the creep behavior of salt under the coupled thermo-mechanical effect in deep-buried condition.Based on the research results,the creep mechanical behavior of wellbore shrinkage is predicted in deep drilling projects crossing salt layer,which has practical implications for deep rock mechanics problems.

Understanding the creep behaviors and mechanisms of Mg-Gd-Zn alloys via machine learning

Mg-Gd-Zn based alloys have better creep resistance than other Mg alloys and attract more attention at elevated temperatures.However,the multiple alloying elements and various heat treatment conditions,combined with complex microstructural evolution during creep tests,bring great challenges in understanding and predicting creep behaviors.In this study,we proposed to predict the creep properties and reveal the creep mechanisms of Mg-Gd-Zn based alloys by machine learning.On the one hand,the minimum creep rates were effectively predicted by using a support vector regression model.The complex and nonmonotonic effects of test temperature,test stress,alloying elements,and heat treatment conditions on the creep properties were revealed.On the other hand,the creep stress exponents and creep activation energies were calculated by machine learning to analyze the variation of creep mechanisms,based on which the constitutive equations of Mg-Gd-Zn based alloys were obtained.This study introduces an efficient method to comprehend creep behaviors through machine learning,offering valuable insights for the future design and selection of Mg alloys.

Creep property research of new martensite heat-resistant steel G115

G115 steel was jointly developed by China Iron & Steel Research Institute Group Co.,Ltd.and Baosteel for usage in 600-650 ℃ ultrasupercritical boiler tubes.Using a hot extruded G115 tube,creep tests were conducted under a constant stress of 130 MPa and temperatures of 625,650 and 675 ℃.Comparing creep curves under different temperatures,it is observed that the creep performance of a G115 tube is more sensitive to temperature than stress.Steady-state creep rates of creep specimens are significantly increased by enhancing the temperature.A micro-structural analysis of ruptured creep specimens under a stress of 130 MPa and temperatures of 650 ℃ and 675 ℃ was performed;the fracture mechanism of creep specimens under these two temperatures mainly included the appearance of creep holes on the grain boundary and a decrease in the martensite lath density.

Creep constitutive model considering nonlinear creep degradation of fractured rock

Stability analysis of underground constructions requires a model study of rock masses’ long-term performance. Creep tests under different stress conditions was conducted on intact granite and granite samples fractured at 30° and 45° angles. The experimental results indicate that the steady creep strain rates of intact and fractured rock present an exponential increase trend with the increase of stress level. A nonlinear creep model is developed based on the experimental results, in which the initial damage caused by fracture together with the damage caused by constant load have been taken into consideration. The fitting analysis results indicated that the model proposed is more accurate at identifying the full creep regions in fractured granite, especially the accelerated stage of creep deformation. The least-square fit error of the proposed creep model is significantly lower than that of Nishihara model by almost an order of magnitude. An analysis of the effects of elastic modulus, viscosity coefficient, and damage factors on fractured rock strain rate and creep strain is conducted. If no consideration is given to the effects of the damage, the proposed nonlinear creep model can degenerate into to the classical Nishihara model.

Improving creep strength of the fine-grained heat-affected zone of novel 9Cr martensitic heat-resistant steel via modified thermo-mechanical treatment

The infamous type Ⅳ failure within the fine-grained heat-affected zone (FGHAZ) in G115 steel weldments seriously threatens the safe operation of ultra-supercritical (USC) power plants.In this work,the traditional thermo-mechanical treatment was modified via the replacement of hot-rolling with cold rolling,i.e.,normalizing,cold rolling,and tempering (NCT),which was developed to improve the creep strength of the FGHAZ in G115 steel weldments.The NCT treatment effectively promoted the dissolution of preformed M_(23)C_(6)particles and relieved the boundary segregation of C and Cr during welding thermal cycling,which accelerated the dispersed reprecipitation of M_(23)C_(6) particles within the fresh reaustenitized grains during post-weld heat treatment.In addition,the precipitation of Cu-rich phases and MX particles was promoted evidently due to the deformation-induced dislocations.As a result,the interacting actions between precipitates,dislocations,and boundaries during creep were reinforced considerably.Following this strategy,the creep rupture life of the FGHAZ in G115 steel weldments can be prolonged by 18.6%,which can further push the application of G115 steel in USC power plants.

Enhanced creep resistance in Mg-Y-Nd alloy via regulating prior thermo-mechanical treatment

In this study,the tensile creep behavior of a hot-rolled Mg-4Y-3.5Nd alloy subjected to different prior thermo-mechanical treatments was investigated at 220℃.Five groups of samples were prepared using different combinations of the solid solution(S),aging treatment at 220℃ for 30 h(A),and hot compression at 490℃ to a true strain of 0.25(C).The abbreviations for the samples are S,SA,SC,SAC,and SCA.Upon examining the yield strength and creep resistance,it was found that creep resistance could not be directly predicted by the yield strength.The stability of the deformation bands(DBs)induced by prior thermo-mechanical treatment plays an important role in determining the creep resistance.The dislocation of the DBs and demonstrated the best creep resistance in the SAC sample,which were prepared using a solid solution,aging treatment,and subsequent hot compression.However,despite the highest yield strength,frequent dislocation motions destroyed the stability of the DBs and deteriorated the creep resistance of the SCA sample,which were prepared using a solid solution,hot compression,and subsequent aging treatment.Among the thermo-mechanical treatments used in this study,the application of aging treatment was important to obtain the resultant creep resistance.When the aging treatment was performed prior to hot compression,the creep resistance could be further enhanced based only on hot compression.Accordingly,the sequence from the strongest to the weakest creep resistance was SAC>SC>S>SCA>SA.

Experiment and constitutive modelling of creep deformation in the frozen silt-concrete interface

To ensure the long-term safety and stability of bridge pile foundations in permafrost regions,it is necessary to investigate the rheological effects on the pile tip and pile side bearing capacities.The creep characteristics of the pile-frozen soil interface are critical for determining the long-term stability of permafrost pile foundations.This study utilized a self-developed large stress-controlled shear apparatus to investigate the shear creep characteristics of the frozen silt-concrete interface,and examined the influence of freezing temperatures(−1,−2,and−5°C),contact surface roughness(0,0.60,0.75,and 1.15 mm),normal stress(50,100,and 150 kPa),and shear stress on the creep characteristics of the contact surface.By incorporating the contact surface’s creep behavior and development trends,we established a creep constitutive model for the frozen silt-concrete interface based on the Nishihara model,introducing nonlinear elements and a damage factor.The results revealed significant creep effects on the frozen silt-concrete interface under constant load,with creep displacement at approximately 2-15 times the instantaneous displacement and a failure creep displacement ranging from 6 to 8 mm.Under different experimental conditions,the creep characteristics of the frozen silt-concrete interface varied.A larger roughness,lower freezing temperatures,and higher normal stresses resulted in a longer sample attenuation creep time,a lower steady-state creep rate,higher long-term creep strength,and stronger creep stability.Building upon the Nishihara model,we considered the influence of shear stress and time on the viscoelastic viscosity coefficient and introduced a damage factor to the viscoplasticity.The improved model effectively described the entire creep process of the frozen silt-concrete interface.The results provide theoretical support for the interaction between pile and soil in permafrost regions.

High density dislocations enhance creep ageing response and mechanical properties in 2195 alloy sheet

The creep strain of conventionally treated 2195 alloy is very low,increasing the difficulty of manufacturing Al-Cu-Li alloy sheet parts by creep age forming.Therefore,finding a solution to improve the creep formability of Al-Cu-Li alloy is vital.A thorough comparison of the effects of cryo-deformation and ambient temperature large pre-deformation(LPD)on the creep ageing response in the 2195 alloy sheet at 160℃with different stresses has been made.The evolution of dislocations and precipitates during creep ageing of LPD alloys are revealed by X-ray diffraction and transmission electron microscopy.High-quality 2195 alloy sheet largely pre-deformed by 80%without edge-cracking is obtained by cryo-rolling at liquid nitrogen temperature,while severe edge-cracking occurs during room temperature rolling.The creep formability and strength of the 2195 alloy are both enhanced by introducing pre-existing dislocations with a density over 1.4×10^(15)m^(−2).At 160℃and 150 MPa,creep strain and creep-aged strength generally increases by 4−6 times and 30−50 MPa in the LPD sample,respectively,compared to conventional T3 alloy counterpart.The elongation of creep-aged LPD sample is low but remains relevant for application.The high-density dislocations,though existing in the form of dislocation tangles,promote the formation of refined T1 precipitates with a uniform dispersion.

An improved creep model for unsaturated reticulated red clay

Establishment of a creep model is an important method to analyze the relationship between soil creep deformation and time,and the element model is widely used for studying soil creep.However,the element creep model is employed for fitting saturated soil,and the mechanical element model is generally linear,which cannot well fit the nonlinear deformation of the soil with time in practice.The creep process of the soil is not only time-dependent,but also related to the deviatoric stress level.Therefore,the fractional calculus theory and a parameter n reflecting the effect of deviatoric stress level on the creep properties of the soil were introduced into the element model,and the fractional qBurgers creep model was established by using the fractional Koeller dashpot and Caputo fractional calculus.The proposed model was used to fit the triaxial test data of reticulated red clay under different net confining pressures and matric suctions by unsaturated triaxial apparatus.The proposed model can well describe the nonlinearity of unsaturated reticulated red clay,has memory and global correlation to the creep development process of unsaturated reticulated red clay,and has clear physical meaning.The functional relationships of the model parameters with the matric suction,net confining pressure and deviatoric stress level were deduced,so that the creep curves of unsaturated reticulated red clay can be obtained for any conditions,which is of great value for the study of unsaturated soils.

Pore-pressure and stress-coupled creep behavior in deep coal:Insights from real-time NMR analysis

Understanding the variations in microscopic pore-fracture structures(MPFS) during coal creep under pore pressure and stress coupling is crucial for coal mining and effective gas treatment. In this manuscript, a triaxial creep test on deep coal at various pore pressures using a test system that combines in-situ mechanical loading with real-time nuclear magnetic resonance(NMR) detection was conducted.Full-scale quantitative characterization, online real-time detection, and visualization of MPFS during coal creep influenced by pore pressure and stress coupling were performed using NMR and NMR imaging(NMRI) techniques. The results revealed that seepage pores and microfractures(SPM) undergo the most significant changes during coal creep, with creep failure gradually expanding from dense primary pore fractures. Pore pressure presence promotes MPFS development primarily by inhibiting SPM compression and encouraging adsorption pores(AP) to evolve into SPM. Coal enters the accelerated creep stage earlier at lower stress levels, resulting in more pronounced creep deformation. The connection between the micro and macro values was established, demonstrating that increased porosity at different pore pressures leads to a negative exponential decay of the viscosity coefficient. The Newton dashpot in the ideal viscoplastic body and the Burgers model was improved using NMR experimental results, and a creep model that considers pore pressure and stress coupling using variable-order fractional operators was developed. The model’s reasonableness was confirmed using creep experimental data. The damagestate adjustment factors ω and β were identified through a parameter sensitivity analysis to characterize the effect of pore pressure and stress coupling on the creep damage characteristics(size and degree of difficulty) of coal.

Calculation of Mass Concrete Temperature and Creep Stress under the Influence of Local Air Heat Transfer

Temperature-induced cracking during the construction of mass concrete is a significant concern.Numerical simulations of concrete temperature have primarily assumed that the concrete is placed in an open environment.The problem of heat transfer between the air and concrete has been simplified to the concrete’s heat dissipation boundary.However,in the case of tubular concrete structures,where air inlet and outlet are relatively limited,the internal air temperature does not dissipate promptly to the external environment as it rises.To accurately simulate the temperature and creep stress in tubular concrete structures with enclosed air spaces during construction,we establish an air–concrete coupled heat transfer model according to the principles of conjugate heat transfer,and the accuracy of the model is verified through experiments.Furthermore,we conduct a case study to analyze the impact of airflow within the ship lock corridor on concrete temperature and creep stress.The results demonstrate that enhancing airflow within the corridor can significantly reduce the maximum concrete temperature.Compared with cases in which airflow within the corridor is neglected,the maximum concrete temperature and maximum tensile stress can be reduced by 12.5℃ and 0.7 MPa,respectively,under a wind speed of 4 m/s.The results of the traditional calculation method are relatively close to those obtained at a wind speed of 1 m/s.However,the temperature reduction process in the traditional method is faster,and the method yields greater tensile stress values for the corridor location.

Decadal Forecasts of Large Earthquakes along the Northern San Andreas Fault System, California: Increased Activity on Regional Creeping Faults Prior to Major and Great Events

The three largest earthquakes in northern California since 1849 were preceded by increased decadal activity for moderate-size shocks along surrounding nearby faults. Increased seismicity, double-difference precise locations of earthquakes since 1968, geodetic data and fault offsets for the 1906 great shock are used to re-examine the timing and locations of possible future large earthquakes. The physical mechanisms of regional faults like the Calaveras, Hayward and Sargent, which exhibit creep, differ from those of the northern San Andreas, which is currently locked and is not creeping. Much decadal forerunning activity occurred on creeping faults. Moderate-size earthquakes along those faults became more frequent as stresses in the region increased in the latter part of the cycle of stress restoration for major and great earthquakes along the San Andreas. They may be useful for decadal forecasts. Yearly to decadal forecasts, however, are based on only a few major to great events. Activity along closer faults like that in the two years prior to the 1989 Loma Prieta shock needs to be examined for possible yearly forerunning changes to large plate boundary earthquakes. Geodetic observations are needed to focus on identifying creeping faults close to the San Andreas. The distribution of moderate-size earthquakes increased significantly since 1990 along the Hayward fault but not adjacent to the San Andreas fault to the south of San Francisco compared to what took place in the decades prior to the three major historic earthquakes in the region. It is now clear from a re-examination of the 1989 mainshock that the increased level of moderate-size shocks in the one to two preceding decades occurred on nearby East Bay faults. Double-difference locations of small earthquakes provide structural information about faults in the region, especially their depths. The northern San Andreas fault is divided into several strongly coupled segments based on differences in seismicity.

Static Bending Creep Properties of Glass Fiber Surface Composite Wood

To study the static bending creep properties of glass fiber reinforced wood,glass fiber reinforced poplar(GFRP)specimens were obtained by pasting glass fiber on the upper and lower surfaces of Poplar(Populus euramevicana,P),the performance of Normal Creep(NC)and Mechanical Sorptive Creep(MSC)of GFRP and their influencing factors were tested and analyzed.The test results and analysis show that:(1)The MOE and MOR of Poplar were increased by 17.06%and 10.00%respectively by the glass fiber surface reinforced composite.(2)The surface reinforced P with glass fiber cloth only exhibits the NC pattern of wood and loses the MSC characteristics of wood,regardless of the constant or alternating changes in relative humidity.(3)The instantaneous elastic deformation,viscoelastic deformation,viscous deformation and total creep deflection of GFRP are positively correlated with the stress level of the external load applied to the specimen.Still,the specimen’s creep recovery rate is negatively correlated with the stress level of the external load applied to the specimen.The static creep deflection and viscous deformation of GFRP increase with the increase of the relative humidity of the environment.(4)The MSC maximum creep deflection of GFRP increased by only 7.41%over the NC maximum creep deflection,but the MSC maximum creep deflection of P increased by 199.25%over the NC maximum creep deflection.(5)The Burgers 4-factor model and the Weibull distribution equation can fit the NC and NC recovery processes of GFRP well.

Experimental investigation of creep behavior of clastic rock in Xiangjiaba Hydropower Project

There are many fracture zones crossing the dam foundation of the Xiangjiaba Hydropower Project in southwestern China. Clastic rock is the main media of the fracture zone and has poor physical and mechanical properties. In order to investigate the creep behavior of clastic rock, triaxial creep tests were conducted using a rock servo-controlling rheological testing machine. The results show that the creep behavior of clastic rock is significant at a high level of deviatoric stress, and less time-dependent deformation occurs at high confining pressure. Based on the creep test results, the relationship between axial strain and time under different confining pressures was investigated, and the relationship between axial strain rate and deviatoric stress was also discussed. The strain rate increases rapidly, and the rock sample fails eventually under high deviatoric stress. Moreover, the creep failure mechanism under different confining pressures was analyzed. The main failure mechanism of clastic rock is plastic shear, accompanied by a significant compression and ductile dilatancy. On the other band, with the determined parameters, the Burgers creep model was used to fit the creep curves. The results indicate that the Burgers model can exactly describe the creep behavior of clastic rock in the Xiangjiaba Hydropower Project.

Triaxial creep tests of weak sandstone from fracture zone of high dam foundation

The lithology of fracture zone which was developed at the dam foundation of a hydropower station is weak sandstone with poor integrity and pore cementation contact.Its creep properties have a significant impact on the deformation and stability of the dam.Based on the characteristics of loose organizational structure,high moisture content and poor mechanical properties,the triaxial compression tests and creep tests were carried out,respectively.The results show significant non-linear,low strength and no obvious strength peaks.Both axial and lateral strains are achieved more than 3%when the tests are failed.The weak sandstone has a significant creep property,but only transient and steady state appear under low stress.Increased stress causes creep intensified and lateral strain gradually exceeds axial strain.In the failure stage,it has characteristics of large axial plastic deformation,obvious volumetric ductility dilation and large steady creep rate.The accelerated creep appears shortly after transient loading under confining of pressures 1.0 MPa and 1.5 MPa.Therefore,an improved Burgers creep model considering the non-linear characteristics of weak sandstone is built based on hyperbolic equation and the creep parameters are identified.This model can well describe the creep properties of weak sandstone.

Triaxial mechanical creep behavior of sandstone

Based on laboratory results of time-dependent mechanical behavior tests,we investigated short-term and mechanical creep behavior of sandstone,observed in conventional triaxial compression experiments at room temperature,using a servo-controlled rheology testing machine.Given our short-term experimental test results,we confirmed deviatoric creep stress levels of sandstone.Multiple deviatoric stress levels were applied in steps to each sample.Each deviatoric stress level before the final failed deviatoric stress was maintained for 48 h or longer.Time-dependent variations of axial strains of sandstone samples are discussed and evaluated.During the creep tests,complete tertiary creep curves of sandstone were observed under failed deviatoric stress levels with different confining pressures.Slices of coal in sandstone samples can lead to distinct tertiary creep deformation failure.

DETERMINATION OF CREEP PARAMETERS FROM INDENTATION CREEP EXPERIMENTS

The possibilities of determining creep parameters for a simple Norton law material are explored from indentation creep testing. Using creep finite element analysis the creep indentation test technique is analyzed in terms of indentation rates at constant loads. Emphasis is placed on the relationships between the steady creep behavior of indentation systems and the creep property of the indented materials. The role of indenter geometry, size effects and macroscopic constraints is explicitly considered on indentation creep experiments. The influence of macroscopic constraints from the material systems becomes important when the size of the indenter is of the same order of magnitude as the size of the testing material. Two methods have been presented to assess the creep property of the indented material from the indentation experimental results on the single-phase-material and two-phase-material systems. The results contribute to a better mechanical understanding and extending the application of indentation creep testing.

Primary-transient creep and anelastic backflow of pure copper deformed at low temperatures and ultra-low strain rates

Creep and anelastic backflow behaviors of pure copper （4N Cu） with grain size dg=40 μm were investigated at low temperatures of T〈0.3Tm （Tm is melting point） and ultra-low creep rates of ε≤1×10^-10 s^-1 by a high strain-resolution measurement （the helicoid spring specimen technique）. Analysis of creep data was based on the scaling factors of creep curves instead of the conventional extrapolated steady-state creep rate. Power-law creep equation is suggested to be the best for describing the primary transient creep behavior, because the pre-parameter does not apparently change with elapsed time. The observed anelastic strains are 1/6 of the calculated elastic strains, and linear viscous behavior was identified from the logarithm plot of the anelastic strain rate versus anelastic strain （slope equals 1）. Therefore, the creep anelasticity is suggested to be due to the unbowing of there-dimensional network of dislocations.