Creep Stage Research Articles

Study on creep behaviors and nonlinear creep constitutive model for sandy marine hydrate-bearing sediments

Marine natural gas hydrate (NGH) production is critically affected by reservoir damage, which is usually presented as creep deformation. Clarifying the creep behaviors of hydrate-bearing sediments (HBS) is essential for predicting potential geoengineering risks during long-term NGH mining. In this study, a series of multi-step loading creep tests on HBS samples are conducted and a modified creep model specialized for sandy HBS is proposed. The creep strain, creep rate, and long-term strength are experimentally evaluated under various hydrate saturation (Sh) and/or effective confining pressure (Pc). Three typical creep stages of deceleration creep, stable creep, and accelerated creep are observed in all experiments. The results show that the creep deformation of HBS is enhanced with the decrease in Sh under the same axial load. The long-term strength decays linearly with decreasing Sh and Pc. The creep model is established by modification of both the Kelvin element and the ideal viscoplastic element in the conventional Nishihara model. A nonlinear viscous coefficient and a time-damaged elastomer considering are introduced to describe the nonlinear creep and damage characteristics of HBS. The model is able to describe the whole failure process, especially the accelerated creep stage. The results might have some significance on the prediction of nonlinear failure behaviors of the reservoir during long-term NGH mining.

Effect of temperature on the creep properties of polycrystalline Cu-Ni alloy: insight from molecular dynamics simulation

Creep is a phenomenon where a particular material tends to deform due to highly subjected parameters, such as temperature and pressure. This deformation is promoted by the diffusion of the material across the grain boundary, as critically assessed by Coble in 1963. This phenomenon is primarily crucial since the most critical application of materials is subjected to high temperature and pressure. This study intends to assess the effect of temperature of polycrystalline Cu-Ni alloy by utilizing molecular dynamics simulation. The simulation is run with different temperatures, thus allowing studying the critical differences between the applied parameters. The results show that the temperature affects the creep rate at every creep stage, primary and secondary, by a significant value. This is due to the deformation promoted by the diffusion of atoms across the grain boundary, decreasing the crystallinity of polycrystalline Cu-Ni alloy. Although the effect of temperature on the creep mechanism of polycrystalline Cu-Ni alloy seems straightforward, it is necessary to assess whether it increases the creep rate at a low temperature in further detail.

Measurement of Creep Stress Exponent of TC17 Titanium Alloy by Nanoindentation Method at Room Temperature.

The creep stress exponent is commonly employed to characterize the deformation mechanism during the steady-state creep stage, serving as an indicator of creep behavior. The creep phenomenon of high melting point metallic materials is not obvious at room temperature. However, the nanoindentation method proves suitable for investigating the creep properties of metallic materials under such conditions. Consequently, this paper places emphasis on measuring the creep stress exponent of TC17 titanium alloy at room temperature using the load preservation stage of the nanoindentation method with a constant loading rate. In order to investigate the effects of loading rate and maximum load on the experimental results, different loading rates were applied to the diamond Berkovich indenter to reach different maximum loads. The indenter was held under the maximum load for a duration of 360 s, and the relationship between the indentation strain rate and indentation stress during the holding process was used to obtain the creep stress exponent of the material at room temperature. The findings indicate that within the loading rate range of 1.25 to 15 mN/s and maximum load range of 50 to 300 mN, the influence on the experimental results is insignificant. Ultimately, the distribution range of the creep stress exponent for TC17 titanium alloy at room temperature was measured to be 8.524-8.687.

A novel nonlinear fractional viscoelastic–viscoplastic damage creep model for rock-like geomaterials

In this study, a novel nonlinear fractional viscoelastic–viscoplastic damage creep model is developed for rock-like geomaterials in an attempt to describe the 3-stage creep behaviour. The proposed model consists of viscoelastic and viscoplastic parts. The former considers the viscoelastic response at different time scales, and incorporates the improved Kelvin and Maxwell components modified by the Abel dashpot. The two Abel dashpots represent the effects of the time dependence on the decaying and steady creep stages. The latter part is described by using a plastic slider parallel to a damaged Abel dashpot, and characterises the viscoplastic response adjusted by the overstress and non-orthogonal viscoplastic flow theory in the accelerated creep stage. The proposed model was written in finite difference form and transcribed into object-oriented C++ for implementation in FLAC3D. By calibrating the available experimental data, the numerical simulation with the proposed model shows a successful description of the full 3-stage behaviour. In addition, the proposed model adequately predicts the delayed deformation caused by the accelerated creep in the tunnel simulation, which provides a valid reference for the subsequent support.

Effect of Re/Ru on constituents distribution and creep performance of nickel-based single crystal alloys

ABSTRACT The effects of Re/Re on the element distribution and creep performance of nickel-based single crystal alloy by using atom probe tomography (APT) and creeping property testing has been studied. Results show that the elements Re, Ru, W, Mo, Cr, and Co are the former of γ phase; the elements are distributed in γ and γ‘ phases of two alloys according to various ratios. Some of the Ru atoms in Re-containing alloy make more Al, Ta atoms are dissolved in γ matrix and make more Mo, W, and Re atoms dissolving in γ‘ phase, which increases the alloying degree of γ“, γ phases to enhance the strength and creep resistance of alloy. Particularly, the Re and W atoms dissolved in γ” phase are excluded, during creep, for the enrichmrnt in γ phase near the interface to form their peak content; the lattice distortion coming from the enriched Re and W atoms restrains dislocations gliding to delay the γ’ phase from being sheared. The deformed mechanisms of alloy in the later stage of creep are the dislocations gliding in γ phase and shearing γ’ phase. Wherein, the dislocations of shearing γ’ phase are both glided on {111} planes and cross-glided from {111} to {001} planes to form the KW locks, the ones that restrain the gliding and cross-gliding of dislocations for improving the creep resistance of alloy. While the interaction of the Ru with Re and W atoms make some Reand W atoms reserved in the γ′ phase to delay the diffusion of other elements, which prevents the KW locks from being released, to keep the good resistance of alloy.

Modelling the creep behaviour and induced failure of clay rock from microscale viscosity to large-scale time-dependant gallery convergences using a multiscale numerical approach

The large-scale creep behaviour of Callovo-Oxfordian (COx) clay rock is modelled from small-scale viscous mechanisms of the rock using a multiscale numerical approach in the context of radioactive waste repositories. At the mesoscale, the saturated non-homogeneous rock is represented in digital 2D Representative Elementary Areas (REAs) as a cracked composite material consisting of rigid elastic mineral inclusions (quartz, calcite, and pyrite) embedded in a clay matrix. The modelling of these materials is considered within double-scale finite element framework, in which the homogenised responses of the REA to the enforced global kinematics serve as a numerical constitutive relation at the macroscale. To reproduce the rock creeping, two viscous mechanisms have been introduced to consider the creep of the clay matrix: either the viscoplasticity of the clay aggregates or the viscoelasticity of their contacts, or both. Firstly, laboratory biaxial creep tests of clay rock samples are simulated. A three-stage creep stage is reproduced and the creep failure process is discussed. Then, large-scale underground engineering structures are modelled to reproduce its time-dependent behaviour. It is found that the developed multiscale model is able to provide some valuable insights into the large-scale creep behaviour of clay rocks through the morphological and material small-scale characterization of REA.

Design of a constitutive model based on the evolution of creep cavities damage for 9Cr-1Mo steel

Considering the impact creep cavity evolution damage of 9Cr-1Mo steel, a new creep constitutive model was established based on the damage-coupled Norton equation and the strain hardening term in the theta projection method model, and the parameters were solved by optimization technique. The creep behavior was compared with that of the Kachanov-Robotnov model. According to the simulation results, the proposed constitutive model can represent the strengthening phenomenon during the first creep stage of 9Cr-1Mo steel. It provides a more accurate description of the behavior during the three creep periods.

Experimental study on brittle-to-ductile transition mechanism of lower Silurian organic-rich shale in south China

Brittle-ductile transition conditions and mechanisms are key scientific issues embedded in the reservoir deformation-related difficulties faced during shale gas exploration and exploitation. In this study, shale deformation experiments under different temperatures, confining pressure and differential stress were conducted using a NaCl solid confining pressure medium, taking the Lower Silurian marine shale from South China as an example. We aimed to clarify the characteristic textures and structures of brittle and ductile deformation in organic-rich shale and then, to reveal the conditions and mechanisms of the brittle-to-ductile transition under the deep in-situ environment of high-temperature, high-confining pressure and high-stiffness surrounding strata. Deformation characteristics of experimentally deformed shale showed significant differences between brittle and ductile deformed shale in terms of fracture development, failure combining form, deformation distribution homogeneity, shear angle and the structures and textures within intensely deformed zones. The micro-deformation structures of brittle deformed shale are characterized by the development of fractures and the simple mechanical crushing of shale blocks and mineral particles. The strong deformation zones of ductile deformed shale mainly show micro-deformation features, such as solid-state rheological deformation and accompanying fragmentation, rounding and directional arrangement of mineral particles. Comparison of control group experiments supported the conclusion that increasing confining pressure significantly improves the elastic modulus and compressive strength of shale and leads to a transition from large-area uniform deformation to narrow-band concentrated deformation. A confining pressure of 75–100 MPa is required for the brittle-to-ductile deformation transition of the target shale at 200 °C. An elevated temperature enhances shale deformation in the yield and creep stages. Finally, we revealed the progressive process and mechanism of brittle-to-ductile transition with the increase of confining pressure; that is, increasing confining pressure leads to a gradual transition of the shale micro-deformation mechanism, from brittle failures to ductile rheological deformation, by suppressing tension fracturing and enhancing friction.

Creep Characteristics of a Strongly Weathered Argillaceous Sandstone Sliding Zone and the Disaster Evolution Mechanism of the Huaipa Landslide, China

The creep characteristics of sliding zones strongly influence slope deformation and long-term stability, as well as the occurrence of landslide catastrophes. In this paper, large-scale triaxial creep tests were performed on the strongly weathered argillaceous sandstone sliding zone of the Huaipa landslide in the Henan Province, China, to study its creep characteristics and long-term strength in natural and saturated states. Three-dimensional numerical simulations were conducted to analyze the deformation creep law and catastrophic evolution mechanism of the slope after excavation and rainfall. The results show that the sliding zone underwent appreciable creep deformation prior to failure, and that the progression of specimen damage with an increasing stress level followed decay creep → steady creep → accelerated creep. The stress level played a decisive role in the creep deformation, with higher stress levels resulting in higher instantaneous displacement, creep displacement, and longer times required to reach steady creep. The stress level also determined the specimen’s creep stage. When the stress level was low, the adjustment of the specimen’s internal structure was dominated by air space compression and particle movement, whereas particle fragmentation mostly occurred at high stress levels. The long-term rock strength was approximately 62–66% of the instantaneous strength, the internal friction angle decreased by approximately 8° relative to the instantaneous strength, and the cohesion decreased by approximately 30%. The slope foot unloaded and deformed owing to the excavation of a bauxite mine at its front edge, after which the slope deformed via creep. The landslide disaster occurred when the deformation was significantly accelerated and the slope started to slide as a whole once the sliding zone became water saturated owing to continuous rainfall. The simulation results indicate that the landslide can be divided into a front edge bulging zone, central sliding zone, and trailing edge tension zone, which provides valuable insight on the creep deformation evolution process and the disaster mechanism of the landslide under the action of front edge excavation and rainfall.

Microstructure Evolution and Dislocation Mechanism of a Third-Generation Single-Crystal Ni-Based Superalloy during Creep at 1170 °C.

The present study investigates the creep behavior and deformation mechanism of a third-generation single-crystal Ni-based superalloy at 1170 °C under a range of stress levels. Scanning electron microscopes (SEM) and transmission electron microscopes (TEM) were employed to observe the formation of a rafted γ' phase, which exhibits a topologically close-packed (TCP) structure. The orientation relationship and elemental composition of the TCP phase and matrix were analyzed to discern their impact on the creep properties of the alloy. The primary deformation mechanism of the examined alloy was identified as dislocation slipping within the γ matrix, accompanied by the climbing of dislocations over the rafted γ' phase during the initial stage of creep. In the later stages of creep, super-dislocations with Burgers vectors of a<010> and a/2<110> were observed to shear into the γ' phase, originating from interfacial dislocation networks. Up to the fracture, the sequential activation of dislocation shearing in the primary and secondary slipping systems of the γ' phase occurs. As a consequence of this alternating dislocation shearing, a twist deformation of the rafted γ' phase ensued, ultimately contributing to the fracture mechanism observed in the alloy during creep.

Creep failure characteristics and characterization of constitutive behaviors of jointed sandstone under multi-level loading of seepage pressure

To study creep failure behaviors of jointed rock mass with seepage pressure as the main damage driving force, creep tests under multi-level loading of seepage pressure were conducted on sandstone with different joint dip angles. In addition, a memory-dependent nonlinear seepage–creep model was established for jointed sandstone. The results show that jointed sandstone experiences three creep stages (initial, steady-state, and accelerated creep stages) in creep tests under multi-level loading paths of seepage pressure. Jointed sandstone with joint dip angles of 30° and 60° undergoes shear failure, while that with the joint dip angle of 45° is subject to tensile–shear failure. Under the same seepage pressure, the sandstone with the joint dip angle of 45° has a greater creep rate in the steady-state creep stage than that with joint dip angles of 30° and 60°. In the volumetric compression stage, the permeability increases at the instant of applying each level of seepage pressure, followed by gradual reduction and stabilization of permeability. In the volumetric dilation stage, the permeability gradually rises. The theory of memory-dependent derivative reflecting the time memory effect was introduced to establish the memory-dependent nonlinear viscoelastic–plastic seepage–creep model for jointed sandstone. The results obtained using the theoretical model conform to the test data. Moreover, the creep failure criterion of the rock was proposed. The creep acceleration starts to increase from 0 and the critical steady state transitions to a non-steady state, suggesting that the rock will soon be damaged. The calculation formula for critical time corresponding to the critical steady state of creep was also deduced. The critical time to onset of creep can serve as an early warning of the creep failure of rocks.

Investigation of three-step heat treatments on the microstructure and steady-state creep behaviors of (TiB + TiC + Y2O3)/α-Ti composite

The microstructure and steady-state creep behaviors of as-cast and heat-treated (TiB + TiC + Y2O3)/α-Ti composites were systematically investigated in this study. The relevant properties of the matrix alloy are also provided for comparative analysis. The matrix alloy exhibits the coarse Widmannstatten structure. After heat treatment, the microstructure of the composite transforms from the basket-weave structure to a trimodal structure with spheroidized TiC and Y2O3 particles and some merged TiB whiskers. Compared to the matrix alloy, the steady-state creep rates of the as-cast and heat-treated composites are decreased by 29% and 40%, respectively. After creep, serious β-Ti dissolution in the matrix alloy and the as-cast composite contributes to the instability of α/β interfaces and precipitated silicides. The morphology of β-Ti phases in the heat-treated composite remains stable during creep and many dislocations are observed inside the secondary α-Ti phases, which is the main reason for the improvement of the creep performance. Extensive dynamic recrystallization occurred during the steady-state creep stage, and the dislocation structure undergoes significant evolution, along with a large number of sub-grains and dislocation walls. The coarse reinforcements play a role in the particle stimulated nucleation, while the small TiC and Y2O3 spherical particles provide little contribution to dynamic recrystallization. Dislocation climbing is the main creep control mechanism, and the creep rate keeps the constant through dislocation rearrangement and dislocation annihilation.

Laboratory study and constitutive modeling of time-dependent properties of a naturally filled discontinuity

Time-dependent properties of naturally filled discontinuities play a critical role in ensuring the long-term stability of tunnels. This study developed a novel sampling method to prepare samples of naturally filled discontinuities, which were then subjected to shear creep tests under varying normal stresses. The time-dependent properties, including creep deformation, instantaneous deformation, steady-state creep rate, and long-term strength, were carefully analyzed. The results showed an exponential increase in cumulative creep deformation and steady-state creep rate with the augmentation of shear stress. Notably, under lower normal stress (0.2 MPa), the local compaction and rotation of stone particles within the fillers of the discontinuity samples lead to a reduction in creep deformation. Drawing on the experimental results, a new rheological element based on the Kachanov–Rabotnov creep damage theory was proposed. By incorporating this nonlinear element in series with the classical Burgers model, a constitutive creep model was established to describe the three creep stages of naturally filled discontinuities. The presented experimental data, and the developed creep model, can serve as valuable references for ensuring the long-term stability and safety of tunnels traversing through discontinuities.

Three-dimensional nonlinear model of rock creep under freeze-thaw cycles.

In areas with large differences between day and night temperature, the freeze-thaw cycle and frost heaving force in rock mass generate cracks within the rock, which seriously threatens the stability and safety of geotechnical engineering structures and surrounding buildings. This problem can be solved by developing a reasonable model that accurately represents the rock creep behavior. In this study, we developed a nonlinear viscoelastic-plastic creep damage model by introducing material parameters and a damage factor while connecting an elastomer, a viscosity elastomer, a Kelvin element, and a viscoelastic-plastic element in series. One- and three-dimensional creep equations were derived, and triaxial creep data were used to determine the model parameters and to validate the model. The results showed that the nonlinear viscoelastic-plastic creep damage model can accurately describe rock deformation in three creep stages under freeze-thaw cycles. In addition, the model can describe the time-dependent strain in the third stage. Parameters G1, G2, and η20' decrease exponentially with the increase in the number of freeze-thaw cycles while parameter λ increases exponentially. These results provide a theoretical basis for studying the deformation behavior and long-term stability of geotechnical engineering structures in areas with large diurnal temperature differences.

Effects of shear stress path and roughness on shear creep behavior of marine clay-concrete interface

Floating piles have been widely employed as foundations in coastal regions abounding with marine clay. A growing concern for these floating piles is their long-term performance of bearing capacity. To better understand the time-dependent mechanisms behind the bearing capacity, in this paper a series of shear creep tests was conducted to study the effects of load paths/steps and roughness on shear strain of the marine clay-concrete interface. Four main empirical features were observed from the experimental results. First, the creep process of the marine clay-concrete interface can be largely decomposed into the instantaneous creep stage, the attenuation creep stage and the uniform creep stage. Second, the creep stability time and the shear creep displacement generally increase as the shear stress level increases. Third, the shear displacement rises as the number of loading steps drops under the same shear stress. The fourth feature is that under the shear stress condition, the rougher the interface is, the smaller the shear displacement is. Besides, the load-unloading shear creep tests suggest that: (a) shear creep displacement typically contains both viscoelastic and viscoplastic deformation; and (b) the proportion of unrecoverable plastic deformation increases with increasing shear stress. These tests confirm that the Nishihara model can provide a well-defined description of the shear creep behavior of marine clay-concrete interfaces.

Triaxial Creep Damage Model for Salt Rock Based on Fractional Derivative

The long-term stability of underground energy reserves is closely linked to salt rock creep. To study the creep behavior of salt rock, creep tests were conducted on salt rock specimens under various confining pressures and axial stresses. The test results reveal that the creep of salt rock is influenced by the combined effect of confining pressure and deviatoric stress, which represents the difference between axial and confining pressure. Subsequently, a long-term strength and time-controlled viscoplastic damage body is proposed by considering the plastic deformation in the steady-state creep stage. The viscoplastic damage body is connected in series with the fractional-order Maxwell model to form a new six-element nonlinear creep model generalized to three-dimensional form. The applicability of the new model was verified using triaxial creep test data of salt rock, and it was found to describe the creep curve more accurately compared to the Nishihara model. A sensitivity analysis of the model parameters indicates that different parameters affect various creep stages, and creep curves under different loads can be adjusted by changing these parameters.

A nonlinear rheological shear constitutive model of bolted joints considering initial damage and damage evolution

Understanding the shear mechanics mechanism of bolted joints is of great significance for predicting and preventing geological disasters. Most current studies seldom consider the rheological effects of bolted joints. In this paper, a comprehensive rheological constitutive model is proposed, accounting for initial damage and damage evolution across different rheological stages and bolt characteristics. The model incorporates an elastoplastic Hooke body for instantaneous deformation, parametric nonlinear Kelvin and viscous models for attenuation and steady creep stages, and a visco-plastic model based on time-dependent shear strength for accelerated creep stage. Additionally, a bolt-rock cooperative deformation model is introduced, considering the evolution of the bolt's elastic modulus. The resulting elasto-viscoplastic constitutive model effectively describes the shear rheological behavior of bolted joints, with its validity and superiority demonstrated through comparisons with shear creep tests and the Maxwell model. This research aims to provide valuable theoretical guidance for the construction and reinforcement of rock mass engineering projects.

Nonlinear creep characteristics of extruded Poly (vinylidene fluoride-co-hexafluoropropylene) with high ß-phase content under extreme conditions: Design, characterization, and modeling

This study is concerned with the nonlinear creep characteristics of extruded Poly (vinylidene fluoride-co-hexafluoropropylene) (PVDF-HFP) dominated by β-phase polymorphs over the temperature range 40 °C − 80 °C and tensile stress levels between 5 MPa and 12.5 MPa. The measured data using the developed experimental setup as well as the dynamic mechanical analyzer invariably suggested a nonlinearity taking place at temperatures near to 60 °C, where αc-relaxation began corresponding to 100 °C above the measured glass transition temperature of PVDF-HFP. The results from accelerated testing conditions indicated the transition to tertiary creep stage at 24% to 28% strain, irrespective of test condition, referred to as critical strain range. Following the identification of Findley power law model constant at different test conditions, a generalized temperature- and stress-dependent model was developed with only 7 constants. The comparisons between the measured and modeled data conveyed the model effectiveness in describing the nonlinear creep characteristics of the polymer over the measured temperature and stress levels. Time-temperature-compliance master curves were consequently constructed using the developed generalized model, which in combination with the critical strain failure criterion, provided the essential design data including the maximum allowable ranges of stress and temperature for achievement of 20 years creep life.

Analysis of an improved Nishihara creep model considering plastic strain accumulation

Rock-engineering structures, particularly subway excavation rock-engineering structures, are subjected to the long-term effects of external loading that may gradually damage and cause creep and severe plastic deformations or even progressive failure. The traditional Nishihara creep model cannot accurately describe the accelerated creep stage of rock with particularly obvious nonlinear characteristics. Based on this model, a damage variable that can consider the plastic strain accumulation is introduced in this study to replace the viscoplastic body in the traditional model with a damaged viscoplastic body and establish an improved Nishihara creep model. Using the superposition principle, the creep equations of the improved model in the one- and three-dimensional stress states are derived. The accuracy and rationality of the improved model are verified using uniaxial and conventional triaxial creep tests of mudstone and sandstone under different confining pressures. The improved model can not only accurately reflect the nonlinear characteristics of the creep curve in the decay and constant velocity stages but also describe the accelerated creep characteristics of mudstone and sandstone in a high-stress state. Its applicability and accuracy are superior to those of the traditional model. This study can provide a theoretical reference for subway tunnel excavation and stability analysis of deep roadway surrounding rocks.

Experimental Investigation on Deformation and Permeability of Clayey–Silty Sediment during Hydrate Dissociation by Depressurization

The sediments in the South China sea are mainly composed of clayey silt, characterized by weak cementation, low strength, and poor permeability. These characteristics lead to slow gas and water transport and low gas production efficiency in the production process, which is not conducive to reservoir stability. Therefore, this paper studied the influence of different factors on the displacement and permeability of hydrate-bearing sediments by using remolded cores from the South China Sea. It was found that, when the depressurization method was used for hydrate decomposition, the displacement change in sediments could be divided into three stages: depressurization stage, decomposition stage, and creep stage. During the decompression stage, sediment deformation was rapid and displacement was small. During the decomposition process of hydrates, sediment deformation was slow and displacement was maximum. The creep stage had the slowest deformation and the smallest displacement. The displacement increased with the increase in initial porosity, hydrate saturation, effective pressure, and depressurization amplitude. The permeability of the sediments was lower than that of the original sediments after hydrate decomposition. This permeability damage increased with the increase in the sediment porosity, hydrate saturation, depressurization range and effective pressure. Furthermore, the displacement of sediments was positively correlated with the permeability damage.