Transient Creep Stage Research Articles

A Coupled Model of Multiscaled Creep Deformation and Gas Flow for Predicting Gas Depletion Characteristics of Shale Reservoir at the Field Scale

The viscoelastic behavior of shale reservoirs indeed impacts permeability evolution and further gas flow characteristics, which have been experimentally and numerically investigated. However, its impact on the gas depletion profile at the field scale has seldom been addressed. To compensate for this deficiency, we propose a multiscaled viscoelasticity constitutive model, and furthermore, a full reservoir deformation–fluid flow coupled model is formed under the frame of the classical triple-porosity approach. In the proposed approach, a novel friction-based creep model comprising two distinct series of parameters is developed to generate the strain–time profiles for hydraulic fracture and natural fracture systems. Specifically, an equation considering the long-term deformation of hydraulic fracture, represented by the softness of Young’s modulus, is proposed to describe the conductivity evolution of hydraulic fractures. In addition, an effective strain permeability model is employed to replicate the permeability evolution of a natural fracture system considering viscoelasticity. The coupled model was implemented and solved within the framework of COMSOL Multiphysics (Version 5.4). The proposed model was first verified using a series of gas production data collected from the Barnett shale, resulting in good fitting results. Subsequently, a numerical analysis was conducted to investigate the impacts of the newly proposed parameters on the production process. The transient creep stage significantly affects the initial permeability, and its contribution to the permeability evolution remains invariable. Conversely, the second stage controls the long-term permeability evolution, with its dominant role increasing over time. Creep deformation lowers the gas flow rate, and hydraulic fracturing plays a predominant role in the early term, as the viscoelastic behavior of the natural fracture system substantially impacts the long-term gas flow rate. A higher in situ stress and greater formation depth result in significant creep deformation and, therefore, a lower gas flow rate. This work provides a new tool for estimating long-term gas flow rates at the field scale.

Shear creep characteristics and creep constitutive model of bolted rock joints

The shear creep behavior of bolted rock joints is closely related to the long-term stability of bolt-reinforced high slopes and underground caverns. To investigate the controlling effect of bolts on rock joint shear creep, limestone samples from the Wudongde dam site area in southwest China were collected and processed, and multistep shear creep tests were conducted on both bolted an unbolted rock joints. The results show that the shear creep of bolted rock joints includes the instantaneous strain stage, transient creep stage and steady-state creep stage, yet the accelerating creep typically occurs instantaneously and is unobservable. By comparing the shear creep process of bolted and unbolted rock joints, it is observed that the presence of bolts decelerates the deterioration of joint surfaces, resulting in a shorter duration of transient creep and lower creep rate. Furthermore, the bolt alters the creep failure mode of the rock joint from brittle failure to plastic failure. Based on experimental results, the reinforcement effect of the bolt through joint creep is analyzed, and the stress evolution during creep is divided into three stages, i.e., the stress-compatibility stage, the stress-compensation stage, and the stress-limitation stage. We summarize how the bolt compensates for stress loss caused by joint surface deterioration through increased shear and axial forces, thereby reducing the creep rate and creep deformation of the rock joint. Based on the stress compensation mechanism of the bolt, a B-Q-N (Burgers-shear force Qo-axial force No) creep constitutive model for bolted rock joints is proposed. When the creep behavior of the unbolted rock joint and the anchorage parameters are known, the B-Q-N model can describe the shear creep behavior of bolted rock joints without experimental data for parameter identification, as well verified by our tests.

On the effect of tempering temperature on the long-term creep behavior of a 10% Cr steel with low nitrogen and high boron contents

The effect of a decrease in the tempering temperature from 770 to 750 °C on the long-term creep behavior of a 10% Cr martensitic steel with 0.008 wt % B and 0.003 wt % N was studied. The evolution of microstructure and precipitation distribution during creep was examined using the interrupted tests under an applied stress of 120 MPa at 650 °C. It was found that a higher dislocation density, a finer lath structure and finer carbides after tempering at 750 °C did not provide higher long-term creep strength than after tempering at 770 °C. The creep rupture time was about 30% shorter. Effect of changes in the dislocation density, lath width, sizes of M23C6 carbides and Laves phase particles, and precipitation of V-rich MX phase on the strengthening contribution at the onset of creep and at the transient, apparent steady-state and tertiary stages was analyzed. The higher dislocation density formed by the tempering at a lower temperature provided a higher climb velocity at the transient creep stage. The higher driving force for recovery was not fully compensated by the higher strength exerted by smaller M23C6 carbides. This led to faster annihilation of the lath boundaries and a decrease in internal stress and, consequently, to an order of magnitude higher minimum creep rate of the steel after tempering at 750 °C as compared to tempering at 770 °C.

Study on creep characteristics and component model of saline soil in hexi corridor

Accurate mastery of the creep characteristics of unsaturated saline soil is extremely important for the long-term stability and safe operation of all types of buildings. In this paper, the research object focused on the saline soil of the Zhangye area, Hexi corridor. The indoor triaxial CU creep test was carried out by means of graded loading to study the creep characteristics of saline soil under different salt content and loading stress. The Merchant and Burgers models were used to predict the creep behavior of the saline soils, and the predicted results were compared with the experimental values. The results showed that the triaxial creep curve of saline soil developed in stage III. Namely, transient creep stage, deceleration creep stage and steady-state creep stage. The creep deformation increases with the increase of salt content and loading stress. The stress–strain isochronous curve has non-linear growth, and the cluster of curves develops from dense to sparse after increasing to long-term strength (100∼150 kPa). The parameters of the Merchant and Burgers model vary with salt content and loading stress, and the creep curve predicted by the Burgers model is closer to the test value.

Exact analytical solutions for bending creep behavior of viscoelastic laminated arches with interlayers

In this work, an exact analytical solution is proposed in order to investigate the bending creep behavior of viscoelastic laminated arches with interlayers under a distributed load. In the analytical model, both the lamina layers and bonding interlayers are considered as viscoelastic materials, which are described by Burgers model for transient and steady-state creep stages. The stress and displacement fields in each viscoelastic lamina layer are obtained on the basis of the exact elasticity theory as well as Boltzman superposition principle. The general solution of stresses and displacements with unknown coefficients is derived by utilizing the Fourier series expansion approach. The interlayer slip effect in the laminated arches is considered in the continuity conditions. By employing analytical Laplace transformation, the coefficients are further determined according to the continuity and load conditions. The present solution is compared to the finite element solution and they show a good agreement. The influences of various parameters are investigated in detail on the bending creep behavior of the arch.

Micro-mechanism of brittle creep in saturated sandstone and its mechanical behavior after creep damage

Understanding the micro-mechanism of brittle creep in saturated rocks and studying their mechanical behaviors after creep damage are of great significance to the design of rock engineering and the prediction of the long-term evolution of the Earth's crust. In this study, we first performed a series of uniaxial creep tests with different creep stage cut-offs on saturated intact sandstones. The brittle creep mechanism of the specimens was explored microscopically by analyzing P-wave velocity, acoustic emission (AE), and nuclear magnetic resonance (NMR) measurements. Then, specimens with different degrees of creep damage were subjected to a secondary short-term loading test or creep test, and their short- and long-term mechanical behaviors, together with AE monitoring, were systematically investigated. The experimental results show that (1) the anisotropy of the specimens increases significantly during creep, with the axial and lateral P-wave velocities exhibiting a difference of 30% at the onset of tertiary creep. (2) The tensile cracks dominate the transient creep stage and the early part of the steady creep stage, while the shear cracks dominate thereafter. (3) The porosities of the specimens increase with the loading stages, and the porosity increments corresponding to small pores are greater than those corresponding to large pores, for all creep stages. (4) Specimens with different degrees of creep damage show greater deformability, and their short-term and creep mechanical parameters, except for uniaxial strength, change dramatically. (5) The AE characteristics of creep-damaged specimens differ significantly from those of intact specimens, and the Kaiser stress memory effect was observed during reloading, with the memory stress being the previous creep stress.

Interface Strengthening of α-Mg/C14–Mg2Ca Eutectic Alloy

This study investigates the effect of the α/C14 interface on the creep strength of α-Mg/C14–Mg2Ca eutectic alloy at 473 K under a stress of 40 MPa. The α/C14 interface is composed of terraces and steps, with terraces parallel to the (1101)α pyramidal plane of the α-Mg lamellae and to the (1120)C14 columnar plane of the C14–Mg2Ca lamellae. The creep curves of the alloy exhibit three stages: a normal transient creep stage, a minimum creep rate stage, and an accelerating stage. The minimum creep rate is proportional to the lamellar spacing, indicating that the α/C14 lamellar interface plays a creep-strengthening role. In the high-resolution transmission electron microscopy image captured of the specimen after the creep test, <a> dislocations can be mainly seen within the soft α-Mg lamellae, and they are randomly distributed at the α/C14 interface. In contrast, dislocations are rarely introduced in the hard C14–Mg2Ca lamellae. It is deduced that the α/C14 interface presents a barrier to dislocation gliding within the α-Mg lamellae and does not help rearrange the dislocations.

Root Cause of Degradation in the Creep Strength of Martensitic Steel

Creep curves of Grade 91 and 92 steels were analyzed by applying an exponential law to the temperature, stress, and time parameters to investigate the formation process of the Z-phase, which lowers the long-term rupture strength of high-Cr martensitic steel. The activation energy (Q), activation volume (V), and Larson–Miller constant (C) were obtained as functions of creep strain. At the beginning of creep, sub-grain boundary strengthening occurs because of dislocations that are swept out of the sub-grains, and this is followed by strengthening owing to the rearrangement of M23C6 and the precipitation of the Laves phase. Heterogeneous recovery and subsequent heterogeneous deformation start at an early stage of transient creep near several of the weakest boundaries because of the coarsening of the precipitates; this results in the simultaneous decreases in Q, V, and C even in transient creep. Further, this activity triggers an unexpected degradation in strength because of the accelerated formation of the Z-phase even in transient creep. The stabilization of M23C6 and the Laves phase is important to mitigate the degradation of the long-term rupture strength of high-strength martensitic steel. The stabilization of the Laves phase is especially important for Cr-Mo systems because Fe2Mo is easily coarsened at approximately 600 °C compared to Fe2W in Grade 92 steel.

Analysis of the Degradation in the Creep Strength of High-Cr Martensitic Steels

To investigate the formation process of the Z-phase, which lowers the long-term rupture strength of high-Cr martensitic steel, the creep curves of Grades T91, T92, and P92 were analyzed along with the experimental steels of 9Cr-1W and 9Cr-4W by applying an exponential law to the temperature, stress, and time parameters. The activation energy (Q ), activation volume (V ), and Larson-Miller constant (C ) were obtained as functions of creep strain. At the beginning of creep, sub-grain boundary strengthening occurs due to dislocations that are swept out of the sub-grains, which is followed by strengthening due to the rearrangement of M23C6 and the precipitation of the Laves phase. After Q  reaches a peak, heterogeneous recovery and subsequent heterogeneous deformation begin at an early stage of transient creep in the vicinity of several of the weakest boundaries due to coarsening of the precipitates. This activity triggers an unexpected degradation in strength due to the accelerated formation of the Z-phase. Stabilization of M23C6 and the Laves phase is important for mitigating the degradation of the long-term rupture strength of high-strength martensitic steel. The stabilization of the Laves phase is especially important for the Cr-Mo systems because Fe2Mo is easily coarsened at ~600 °C as compared to Fe2W. Lowering the hardness and Si content also prevents excess hardening due to the Laves phase, which also mitigates the degradation. The online monitoring of creep curves and the QVC  analysis render it possible to detect signs of long-term degradation under targeted conditions within a relatively short period.

Analysis on Degradation in Creep Strength of 9Cr-W Martensitic Steel

In order to clarify the creep mechanism of high Cr martensitic steel, creep curves of 9Cr-1W and 9Cr-4W steels were analyzed applying an exponential law to the temperature, stress, and time parameters. The activation energy, Q, the activation volume, V, and the Larson-Miller constant, C, are obtained as functions of creep strain. At the beginning of creep, sub-grain boundary strengthening by swept dislocations out of sub-grains occurs followed by strengthening due to the rearrangement of M23C6 and the precipitation of Laves phase. After Q reaches a peak, heterogeneous recovery and subsequent heterogeneous deformation begin at an early stage of transient creep in the vicinity of some weakest boundaries due to coarsening of the precipitates, which triggers the unexpected degradation in strength due to the accelerating coarsening of precipitates. Stabilizing not only M23C6 but also Laves phase is important to mitigate the degradation of rupture strength of martensitic steel. The above creep mechanism for martensitic steel can be applicable to the explanation for the degradation in long term rupture strength of high Cr martensitic steel, Grades 91 and 92.

Effect of Lamellar Spacing on Creep Strength of <i>α</i>-Mg/C14-Mg<sub>2</sub>Ca Eutectic Alloy

In tensile tests, α-Mg/C14-Mg2Ca eutectic alloy with a lamellar structure is plastically deformed above 473 K but ruptures before yielding at temperatures below 423 K. This study investigates the effect of the α/C14 interface on the creep strength of α-Mg/C14-Mg2Ca eutectic alloy at 473 K under 40 MPa stress. The creep curves of the alloy exhibited three stages: a normal transient creep stage, minimum creep-rate stage, and accelerating stage. The minimum creep rate was proportional to the lamellar spacing, indicating that the α/C14 lamellar interface plays a creep-strengthening role. In high-resolution transmission electron microscope observations of the specimens after the creep test, a dislocations appeared within the α-Mg lamellae and were randomly distributed on the α/C14 interface. It was deduced that the α/C14 interface presents a barrier to dislocation glide and does not annihilate and/or rearrange its dislocation caused by the creep test.

Compressive creep behavior of extruded Mg-4Sm-2Yb-0.6Zn-0.4Zr alloy

Abstract A high-strength Mg-4Sm-2Yb-0.6Zn-0.4Zr extruded alloy with bimodal microstructure was creep tested in compression at temperatures of 200 °C and 225 °C under applied stress in the range of 120–200 MPa. The creep curves of the alloy are dominated by a steady-state creep stage and a transient primary creep stage. An abnormal decrease of creep rate is observed in the later period of the steady-state creep stage, particularly the creep at high stress levels more significant, and the underlying reasons are proposed. Moreover, the alloy exhibits high stress exponents (n = 8.7 at 200 °C and n = 7.4 at 225 °C) and activation energies ranging from 225 kJ/mol to 310 kJ/mol. It is shown that the high stress exponents can be well rationalized by the commonly adopted threshold stress method in this work, which results in the modified stress exponents near 5, suggesting five power law, with some indicator of dislocation creep. Transmission electron microscopic observations revealed that cross-slip of dislocations is the dominant creep mechanism in recrystallized grains, while cross-slip of dislocations is operative in hot-worked grains. Besides, a fraction of γ phase in hot-worked regions was transformed to γ′ phase during creep while not in recrystallized regions, thus coexistence of γ and γ’ in hot-worked regions. Also, these γ-typed phases play an important role in creep of the studied alloy. Finally, the studied alloy owns better creep resistance than those of benchmark Mg alloys such as AE and AX series alloys.

Study on Nonlinear Damage Creep Model for Rocks under Cyclic Loading and Unloading

To determine the nonlinear creep characteristics of rocks under cyclic loading and unloading conditions, a nonlinear Kelvin model and damage viscoplastic model are proposed. The models are connected in series with a linear elastic body to establish a nonlinear damage creep model. The differential damage constitutive equations of the proposed creep model under one‐dimensional and three‐dimensional stress states are derived based on the creep mechanics and elasticity theory. The damage and unloading creep equations are then obtained based on the superposition principle, and a simple and feasible method for determining the model parameters is determined. Finally, the step cyclic loading and unloading creep test data for lherzolite and limestone are used to verify the rationality and feasibility of the nonlinear damage creep model. The results show that the theoretical creep curves of the nonlinear damage creep model are consistent with the experimental curves which indicates that the proposed model can not only determine the creep properties of lherzolite and limestone under cyclic loading and unloading but also determine the nonlinear characteristics of rocks in the transient and steady‐state creep stages and particularly within the accelerating creep stage.

Analysis of Mechanical Properties for the Heat Resistant Co-Modified 12 and 9% Cr Steels

An analysis of mechanical properties has been performed for 12% Cr and 9% Cr steels by means of tension tests at 20 and 650°C and yield tests at 650°C and applied stresses of 200–100 MPa with a step of 20 MPa. The yield strength and ultimate tensile strength of the 12% Cr steel are, correspondingly, 614 and 710 MPa at 20°С and 365 and 390 MPa at 650°C. At both temperatures, the strength properties of the 12% Cr steel under tension are better than for the 9% Cr steel due to higher values of contributions from solid-solution hardening (+30 MPa) and substructural hardening (+23 MPa) to the room-temperature yield strength. The analysis of creep properties shows that the time to fracture at high stresses for the 12% Cr steel is much longer than for the 9% Cr steel due to a more prolonged transient creep stage and, at low applied stresses, there is almost no difference in the creep behavior of the 12% Cr and 9% Cr steels. The 1% creep limit estimated from the empirical dependence between the stress and the time required to attain the strain with a degree of 1% for the 12% Cr steel is 82 MPa, being comparable with the 1% creep limit of the 9% Cr steel.

Time-dependent behaviour of clay-concrete interfaces with different contact surface roughnesses under shear loading

Mechanical properties of the interface between a pile and soil greatly affect the bearing capacity of a pile. The creep of soil causes a long-term strength of the pile–soil interface to be smaller than its instantaneous shear strength. It is helpful to understand the settlement deformation and strength characteristics of friction piles from the micromechanism by studying the shear creep mechanical properties of the clay–concrete interface. In this work, we carry out shear creep tests on the interfaces between clay and concrete slabs with different roughnesses under different normal stresses. We analyze the influence of the joint roughness coefficient (JRC) on the long-term cohesion and long-term friction angle of the interface. We propose an instantaneous damage factor of the shear modulus and improve the Nishihara creep model with the instantaneous damage effect of the shear modulus. The experimental results show: (1) the whole process test curve of the shear creep shows that the specimen is rapidly destroyed after the transient creep stage and the steady-state creep stage, but the tertiary creep stage is not obvious. (2) The long-term shear strength of the clay-concrete interface is greatly affected by the change in the normal stress under the same JRC conditions, and the long-term shear strength of the interface increases linearly with increasing normal stress. (3) The relationship between the long-term shear strength and normal stress of the interface can be described by the Mohr–Coulomb failure criterion, and the long-term cohesion and long-term friction angle under different JRC conditions can be calculated accordingly. There exists a critical value JRCcr for the long-term cohesion, and the long-term cohesion of the interface first increases and then decreases as the JRC increases. When the long-term cohesion of the interface decreases to a certain extent, it fluctuates around the long-term cohesion value of clay. Moreover, the long-term friction angle of the interface fluctuates slightly with varying JRC, and there is no obvious change rule. (4) Considering the instantaneous damage of the shear modulus, we establish a relationship between the instantaneous shear modulus and the damage factor and introduce the damage factor into the Nishihara creep model. The shear creep mechanical parameters of the clay–concrete specimens under multistage loading are inversed.

Creep strength breakdown and microstructure in a 9%Cr steel with high B and low N contents

A 9%Cr–3%Co steel with high B and low N contents exhibits creep strength breakdown at a temperature of 923 K after 3000 h. Specific feature of this steel is a distinct difference between short-term and long-term creep regimes for transient, steady state and tertiary creep stages. This behavior is unusual for high Cr steels and attributed to low density of M23C6 carbides precipitated on lath boundaries during tempering. Precipitation of Laves phase along these boundaries during transient creep followed by its coarsening affects significantly the creep mechanisms and results in the well-defined difference in mechanical behavior between the short- and long-term creep regimes. In contrast, the strain-induced formation of a small amount of Z-phase particles scarcely changes the creep behavior.

Creep characteristics and constitutive model of coal under triaxial stress and gas pressure

AbstractCreep behavior is one of the most important mechanical behaviors of coal. In the present study, we systematically carried out a series of creep experiments of briquette samples under triaxial compression and gas pressure. The experimental results showed that the creep deformation characteristics of coal were related to deviatoric stress and gas pressure. The accelerating creep stage initiated when the deviatoric stress reached or exceeded the yield stress until failure took place. In contrast, when the deviatoric stress was less than the yield strength, only transient and steady creep stage occurred. Besides, gas pressure played a positive role in the creep process of coal. The axial strain of coal slightly increased with gas pressure (range from 0.13 to 0.40 MPa) when the effective triaxial stress remained constant. For example, in the steady creep stage (σ1 = 9 MPa, p = 0.13 MPa), the axial strain of sample S1 is 2.710% and that of sample S2 is 3.361%, that is, coal samples with high gas pressure have higher axial strain. Moreover, gas pressure has two main effects on the mechanical behavior of coal. One is that the coal adsorbs gas molecules resulting in swelling strain and swelling stress, and the other is that the gas pressure may compress the coal particles. Considering the swelling stress and gas pressure, we intensively studied the effective stress formula of coal containing gas. Then, the effective stress was taken into consideration in the nonlinear Nishihara creep model. Furthermore, the tertiary creep factor n was introduced in the nonlinear model to control the creep deformation evolution with time so that the nonlinear model could accurately describe the full creep stage of coal. In contrast, due to the lack of such a controlling parameter, the Nishihara model failed to reproduce the accelerating creep stage.

Effects of grain dissolution–diffusion sliding and hydro-mechanical interaction on the creep deformation of soft rocks

The creep deformation behaviour of soft rocks is one of the most important research fields in geotechnical engineering. In this study, a theoretical model was developed to investigate the coupled effects of the grain dissolution–diffusion sliding and the hydro-mechanical interaction on the creep behaviour of soft rocks. Experimental results validated the model. The results demonstrate that the creep of soft rocks is primarily dependent on the shear stress on the sliding surface, the average thickness of the hydrated film and the amplitude of the cosinusoidal sliding surface. These three parameters can be used to describe the meso-mechanism of soft rock creep stages, i.e. the transient creep stage, steady-state creep stage, and accelerated creep stage. In addition, this study’s findings show that the chemical potential field promotes the mineral dissolution and diffusion on the grain sliding surface and changes its morphology, thereby resulting in the redistribution of stress.

Study on the Transient Creep Stage by Small Beam Specimen with Fixed Constraints

Three-point bending specimen with fixed constraint (TPBSF) has potential advantages in engineering application because of its simple stress state and easily achievement of rupture data. It is critical to accurately evaluate the creep curve of TPBSF for the application in engineering. In this study, TPBSF behavior of aluminium alloy A7N01 at 653K has been investigated at various loads in the range 12-20N. The creep curve clearly exhibited transient, steady-state and tertiary stages. The creep displacement data has been analysed according to the Garofalo’s equation. The rate of exhaustion of transient creep exhibited similarly dependence on load as steady-state displacement rate. It indicates that the transient and steady-state creep displacement of TPBSF obey the same kinetics law. The time to attain the steady-state stage and the rupture time are approximately inversely proportional to the rate of exhaustion of transient creep. The transient stage of TPBSF creep accounts for about 34% of the overall creep time. It is useful for predicting TPBSF creep deformation and residual life of the material.

Atomic scale investigations of carbon-based cathode materials deformation mechanism during aluminum electrolysis

The creep strain of full graphitic cathode blocks has been measured with a laboratory cell. The creep tests were performed three times under extern load 2–6 MPa and at temperature of 950 °C for 15 min, 50 min and 100 min respectively after starting the electrolysis. The deformation mechanisms in the carbon cathodes for aluminum electrolysis have been comprehensively studied at the atomic scale by high resolution transmission electron microscopy (HRTEM) and selected area electron diffraction (SAED). The microstructural observation confirms that the governing deformation mechanism for the carbon cathode is basal plane dislocation pile-ups and dislocation tangles at the stage of transient creep. Microstructure rearrangement of the carbon cathode including deformation bands, rotating, delamination and propagation of microcracks deteriorates its creep resistance at the stage of steady-state creep. The deformation of carbon cathodes is closely correlated with the accumulation and amorphization of the graphite during aluminum electrolysis.