Creep Constitutive Model Research Articles

Strength and creep characteristics of methane hydrate-bearing clayey silts of the South China Sea

Natural gas hydrates are abundantly detected in the clayey-silty deposits of the South China Sea (SCS). The long-term hydrate extraction process may trigger creep deformation and failure of the clayey-silty reservoir. Hence, it is essential to evaluate the creep properties of the clayey-silty hydrate reservoir for safe production. Current research mainly focused on rapid failure, while neglecting time-dependent creep deformation of the clayey-silty hydrate reservoir. In this study, a number of triaxial shear and creep experiments were carried out on methane hydrate-bearing clayey silts (HBCSs) in the SCS in order to investigate their strength and creep deformation characteristics. The results indicated that: (1) the increase of effective stress enhances the shear strength and deformation, and the presence of hydrates enhances the shear strength while reducing the deformation; (2) the creep strain and strain rate increase as the creep stress ratio and effective stress rise; (3) the accelerated creep stage only occurs at higher effective stress in HBCSs and not in hydrate-free clayey silts (HFCSs), and the creep strain and strain rate of the HBCSs are lower than those of the HFCSs. The experimental data will contribute to the construction and verification of creep constitutive models for HBCSs in the SCS.

Derivation of Creep Parameters for Surrounding Rock through Creep Tests and Deformation Monitoring Data: Assessing Tunnel Lining Safety

Tunnel instability and lining integrity are intimately tied to the creep properties of the surrounding rock. The acquisition of rock mass creep parameters is critical in ascertaining the appropriate timing for lining construction. Nevertheless, creep tests on rock specimens conducted in a controlled setting cannot be straightforwardly extrapolated to rock mass creep analysis. This study performs laboratory-based creep tests on mudstone samples and establishes the corresponding creep constitutive model. The integration of a Mohr–Coulomb element with the Burgers model in series serves to characterize the yield creep behavior of the rock mass. Additionally, the research outlines a series of 100 orthogonal experiments utilizing randomized creep parameters and formulates a GA-BP neural network inversion model. Employing long-term deformation measurements from the crown and sidewalls of the project site, this study deduces the creep parameters of the mudstone in the investigated tunnel section and examines the prolonged deformation traits of the surrounding rock. Drawing on the deformation traits of the surrounding rock and the forces impacting the primary support and lining structures, this paper evaluates the earliest and latest viable lining casting periods and pinpoints an optimal timing interval for lining implementation. The methodologies employed herein can serve as a benchmark for analogous endeavors internationally.

Stress relief simulation for post-weld heat treatment process of pressure equipment: Creep constitutive equation considering temperature and stress variations

Due to the limited testing methods and high costs, researches on the evolution law of residual stress in the post-weld heat treatment (PWHT) process of pressure equipment are mainly by numerical simulation, in which the selection of a reasonable and reliable creep constitutive model is crucial to ensure the accuracy of numerical predictions. It is worth noting that the temperature changes and residual stress variation during the heat treatment process result in the following creep characteristics: the creep occurs under different temperatures during the heat treatment processes of heating, holding, and cooling; the creep occurs under different residual stress level where the residual stress varies during the heat treatment stages. Thus, to accurately simulate the stress release behavior during the PWHT process, the proper creep constitutive model must involve the influences of the temperature and the stress state. Meanwhile, current heat treatment simulation usually adopts simplified qualitative approaches, and the creep constitutive models often ignore the physical mechanisms and characteristics of actual creep processes, such as the Norton, the Norton-Bailey, and the Omega models. As a result, the accuracy of heat treatment simulation is limited. In this paper, a new creep constitutive relation under varying temperature and stress is proposed. The hyperbolic-sinusoidal function is used to represent the complete three stages of creep, which compensate the inaccuracy prediction at the first and the third creep stages. Moreover, the Arrhenius function is introduced to characterize the creep response under varying temperature conditions, which enables the prediction of residual stress evolution throughout the entire heating-holding-cooling process of heat treatment. Then, a typical pressure vessel cylindrical circumferential weld is simulated. The stress release during the heat treatment is calculated, and the efficacy of the proposed model is validated through surface residual stress testing. It is found that the creep behavior is a crucial factor in numerical simulation of heat treatment, and the creep constitutive relation can significantly affect the accuracy of heat treatment simulation. The simulation utilizing the hyperbolic-sinusoidal temperature-dependent creep model is much more accurate compared to the classical simulation. The simulation results are much more consistent to the experimental results. Specifically, the traditional model often underestimates the stress state, the residual stress drops abruptly during the heating stage. The residual stress evolution mechanism is simulated using the new model: The majority of residual stress are released during the heating process which primarily relies on the creep strain transformation (contributes up to 85%). The stress state does not change during the holding stage and slight higher at the cooling stage.

Research on a creep constitutive model of compacted graphite cast iron and its parameter identification method

AbstractIn order to accurately predict the minimum creep rate under the actual working conditions of compacted graphite cast iron cylinder head, this paper conducted creep experiments in the temperature range of 723.15–823.15 K and the stress range of 100–300 MPa. The creep damage evolution and damage mechanisms under test conditions were also analyzed. Then the data fitting performances were analyzed and compared from three aspects: the optimization‐seeking algorithm, the form of the objective function and the construction of the creep constitutive model. Finally, the chosen optimization algorithm combined with the proposed objective function and creep constitutive model resulted in 100% of the predicted values within the 3 times error band and 26.67% of the predicted values within the 1.5 times error band. This improves the prediction accuracy while reducing the effect of data overfitting.

Creep constitutive model of rock based on strength time-dependent characteristics

The long-term stability and safety of supporting rock mass engineering has become the focus of rock mechanics research due to the continuous mining of deep resources. The single-specimen method was used to determine the mechanical parameters of undamaged specimens subjected to creep for 10, 60, and 100 h under different stress levels. The time-dependent model of mechanical parameters is established by analyzing the change law of mechanical parameters under the influence of stress and time. Results show that the decrease in the internal friction angle of rock is substantially less than that of cohesion under the influence of overstress difference and time, and the decrease in internal friction angle has minimal effect on the long-term stability of the rock. Therefore, cohesion should be considered in the long-term stability design when the roadway surrounding rock is devised in practice. The established strength parameter model can describe the variation of rock strength parameters under different stress states and time effects. The strength model also reflects the essential characteristics of varying rock strength parameters with stress and time. Meanwhile, the experimental curves are in good agreement with the theoretical ones. Therefore, the creep model based on the degradation of strength parameters established in this paper can reflect the creep characteristics of the rock at different stages. This model can also describe the accelerated creep characteristics of sandstone under high-stress state. Therefore, the rock creep model developed in this paper is reasonable and feasible for describing the creep properties under different stress states.

Damaged creep constitutive models of rock-like materials containing multiple flaws and their relationships to those of the intact materials

A number of pre-flawed specimens made of sandstone-like material with four different numbers and five different angles were prepared and tested in three various loading paths to investigate the time-dependent mechanical behaviors. It was determined that the deformations and strengths increase and decrease with increasing flaw number and decreasing flaw angle, respectively. The ratio of the long-term strength to the uniaxial compressive strength of specimens with the same pre-existing flaws varies within a small range (0.637–0.729). The specimens in the creep tests exhibited more shear failures than those in the uniaxial compression tests. A modified Burgers model was then developed. By using different parameter values, it can well describe the entire creep phases of all the pre-flawed and intact specimens, which is in accordance with the principles of damage mechanics. In view of this, pre-existing flaws were regarded as a type of damage to the intact material, and a damage creep model was developed that can derive the creep curves of fractured materials from those of the intact material. This idea provides a reference for the study of the damage creep model of fractured rock masses.

Investigation on damage creep constitutive model of rock under the coupled effect of freeze–thaw cycles and loading

AbstractThe investigation on damage creep properties of rock under freeze–thaw conditions are essential for assessing the long‐term stability of rock mass engineering in cold regions. This research analyzed the damage characteristics of rock under the coupled effect of freeze–thaw cycles and loading; the damage variable under the coupled effect of freeze–thaw cycles and loading was proposed. A damage creep constitutive model was developed, and the determination method for the model parameters was proposed. The rationality of the model was calibrated using test data, and the calculation results of the proposed model were compared with classical Nishihara model. Additionally, the research analyzed the variation of model parameters with the number of freeze–thaw cycles and discussed the damage creep mechanisms of rock under the coupled effect of freeze–thaw cycles and loading.

General-Variable Order Fractional Creep Constitutive Model for Cemented Backfill Materials: Considerations of Particle Size, Dosage, and Confining Pressure

General-Variable Order Fractional Creep Constitutive Model for Cemented Backfill Materials: Considerations of Particle Size, Dosage, and Confining Pressure

Influence of post-weld heat treatment on welding residual stress in U-rib-to-deck joint

Welding residual stress (WRS) significantly influences the fatigue life and safety of welded steel structures. Post-weld heat treatment (PWHT) is a common method employed to mitigate WRS. In present study, the WRS evolution law and relaxation mechanism of U-rib-to-deck joints was investigated during PWHT. High-temperature heat treatment tests with varying holding times were conducted on U-rib-to-deck joints to reduce WRS. The WRS distributions were measured using the hole-drilling method before and after PWHT. ABAQUS software, incorporating the Norton-Bailey creep constitutive model, was employed to simulate the WRS evaluation during both welding and PWHT processes. The simulated values were validated against the measured data, and the effects of different holding times, holding temperatures, and heating and cooling rates during PWHT on WRS relaxation were discussed. The results demonstrate that PWHT effectively reduces WRS and leads to a more uniform distribution. Extending the PWHT holding time from 0.5 h to 1 h and 2 h results in a gradual decrease in WRS relaxation at 600 °C, primarily occurring in the high-value stress region of the weld zone with a small amplitude. Elevating the PWHT temperature from 500 °C to 550 °C and subsequently to 600 °C amplifies the significance of WRS relaxation. Variations in heating and cooling rates (200 °C/h and 80 °C/h, 100 °C/h and 40 °C/h, 50 °C/h and 20 °C/h) lead to a gradual decrease in WRS relaxation across the entire model. Furthermore, considering the creep effect, the stress relaxation rate in the weld is approximately 70 %–80 %, which found to be about 2–3 times higher than that without considering the creep effect. By understanding the evolution law and relaxation mechanism, this study provides valuable insights for designing PWHT processes and assessing their impact on structural safety and fatigue life.

Multi-stepped creep constitutive model based on asymptotic damage evolution behavior of sandstone

Multi-stepped creep constitutive model based on asymptotic damage evolution behavior of sandstone

Influence of crystal orientations on the creep fracture of a nickel-based single crystal superalloy

Due to the anisotropy of the modulus of face-centered cubic cells, the nickel-based single crystal alloys exhibits substantial anisotropy at high temperatures. Their creep properties, especially the creep rupture lives, are related to the actuation of the slip system and the magnitude of the shear stress on the slip plane. The creep orientation sensitivity has been analyzed through creep experiments, as well as the microstructure and morphology of the fracture. On the macroscale, the necking sections of [001], [011] and [111] orientations are circular, elliptical and circular, respectively. Meanwhile, on the microscopic scale, the damage evolution caused by the expansion of the internal micropores in the single crystal alloy under the three orientations shows fourfold symmetry, double symmetry and triple symmetry, respectively. Based on the crystal plasticity theory, an anisotropic creep constitutive model and damage model are established to reflect the difference in creep deformation and damage evolution caused by orientation. The numerical simulations of the whole creep process of a second generation nickel-based single crystal superalloy show that the creep constitutive model and damage model can simulate the deformation and damage of the specimen under different orientations, and the creep life can be obtained.

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.

Numerical analysis of the breakwater failure at the Sergipe Terminal Port

The breakwater failure at the Sergipe Harbor is a well-known event among the Brazilian geotechnical community, which provided great knowledge about the behavior of embankments on soft soils, although some questions still remain, since the back analysis diverged from the field outcome. In this context, this work aims to carry out a numerical analysis of the construction of the breakwater using the finite element method to understand the mechanisms of failure. A fully coupled flow-deformation analysis was performed in Plaxis 2D software, using the Soft Soil Creep and Mohr-Coulomb constitutive soil models. The Volume Method was also applied to estimate the stability of the slopes, from the calculated numerical displacements. The interpretation of the results allowed to verify that the analysis simulated behaviors that had been raised as responsible for the failure. High excess pore pressure levels were generated in the phase at which failure occurred, in addition to a strain softening behavior, which, alongside the progressive failure, could justify why the back analysis considering unrealistic gains in undrained strength, calculated by the increase of the vertical effective stresses, had provided missed factors of safety. Although shear deformations and horizontal displacements were verified for both sides of the breakwater, the “shared failure” assumption could not be verified, since the shear stress was mobilized in the rockfill.

Crystal plasticity study of the effect of asymmetric structure of diffusive film cooling hole on heterogeneous creep and fracture behavior of NBSC superalloy

The heterogeneous creep and fracture behavior of nickel-based single crystal (NBSC) superalloys with inclined and diffusive holes are investigated. The analyses are made by creep experiments and crystal plasticity (CP) simulation with a modified creep constitutive model that accounts for both plastic and creep shear slip near the cooling hole. The study indicates that the cooling hole has a creep-strengthening effect on the NBSC superalloy, resulting in an extended creep duration for specimens with cooling holes than those without holes. Meanwhile, the asymmetric structure of diffusive and machined-tapered inclined cooling holes causes localized stress concentration around outlet side of the holes, which leads to asymmetric deformation and decreased rupture strain. Moreover, the interaction between neighboring holes causes shear slip and creep deformation more dominantly at side holes than at the center hole. Thus, preferential initiation of microcrack occurs around the side holes. The specimen without a hole displays typical ductile fracture, whereas the specimen with cooling holes displays a combined cleavage-like and ductile fracture due to the localized stress concentration induced by plastic shear slip around the hole. In addition, as loading stress increased, the creep lifetime and rupture strain decreased, while the characteristics of cleavage-like rupture increased.

A true triaxial creep constitutive model of rock considering the coupled thermo-mechanical damage

The main emphasis in contemporary mineral resource extraction has shifted towards deep Earth resources to address economic development requirements. The influence of temperature has emerged as an undeniable factor as engineering projects delve deeper into the Earth. The definition of a damage variable, which considers the coupled thermo-mechanical damage, has been proposed within the framework of damage mechanics. This definition aims to accurately describe the different stages of rock creep behavior in high-temperature environments. Furthermore, a constitutive model has been developed to describe the creep behavior of rocks under the combined influence of temperature and true triaxial stress. This model considers the series connection of the elastic body, nonlinear Kelvin body, Heard body, and visco-elastic-plastic body. The model has been parameterized and validated using available creep test data, and the equation for the yield surface of rocks under true triaxial stress has been derived through data fitting. The findings suggest that the developed constitutive model is capable of accurately describing the properties of rock creep behavior at different stages in high-temperature conditions, thus confirming its rationality and precision.

Investigation on creep mechanism of CF/PEEK composite material using molecular dynamics

Carbon fiber/Poly ether ether ketone (CF/PEEK) subjects to external loads during service life, high bonding quality of the interface is the key to structural integrity. In order to control the creep slippage of CF/PEEK, explaining the interfacial creep mechanism details are essential. This paper constructs an intercalation model for the CF/PEEK molecular interface and uses molecular dynamics (MD) simulation to demonstrate the evolution mechanism of the interface under different load levels. To verify the effectiveness of the model, the structural morphology, glass-transition temperature, and density of the molecular model were compared with experimental measurements. In terms of interface shear creep, stage Ш creep transitioned from constant to accelerated, the creep curves and corresponding interface microstructure under different stress states were simulated by MD. At the same time, the sliding and debonding processes were explained from an energy perspective. Furthermore, a creep constitutive model was proposed to fit the molecular scale. This study comprehensively interprets the shear creep behavior of the CF/PEEK interface from simulation to constitution.

New insight into the fitness of 13Cr stainless steel in H2S-containing environment at high temperature

In the oil and gas industry, the selection of tubing and casing materials is required to follow international standard ISO 15156. However, it does not provide guidance on selecting stainless steel materials for H2S-containing wells above 232 °C, which raises uncertainty about the suitability of 13Cr steel. This work focuses on investigating the mechanical degradation and failure mechanisms of 13Cr stainless steel exposed to high-temperature conditions and proposed a creep constitutive model. Then, the corrosion and cracking mechanisms of 13Cr stainless steel at temperatures ranging from 150 °C to 350 °C were elucidated. Results show that 13Cr stainless steel meets the current material selection criteria (GB/T34907-2017) for mechanical properties and creep resistance. In the range of 150–250 °C, the localized corrosion is dominant, and stress-oriented hydrogen-induced cracking occurs at 150 °C. As the temperature increases from 250 °C to 350 °C, although the maximum value of uniform corrosion rate is as high as 0.2960 mm/a, the cracking does not happen. Therefore, with the implementation of suitable protective measures, 13Cr stainless steel can be utilized in wells that the temperatures ranging from 250 °C to 350 °C and H2S partial pressures up to 0.17 MPa. This aligns with the global carbon-neutral agenda.

Time-dependent performance assessment of mountain tunnels considering the hazards associated with squeezing soft rock and nonuniform steel corrosion in RC lining structure

Mountain tunnels buried in squeezing soft rock inevitably undergo a rapid degradation with time due to creep behaviors of surrounding rock. The performance of tunnel would become more exacerbated when steel corrosion occurs in lining structures. High failure risk of tunnel lining within a short time after construction would significantly shorten its service life. Since the properties of rock mass in space and the corrosion of reinforcements in space–time exhibit a high uncertainty in practices, it is necessary to perform a reliable performance assessment of tunnels by incorporating the concept of random field-based reliability analysis. In this study, a novel approach for reliability assessment of mountain tunnels under the hazards associated with creep behavior and non-uniform steel corrosion is presented. A creep constitutive model of rock is introduced firstly; Random field-based modeling for the spatial-variant properties of rock mass is proposed; and a spatio-temporal approach for describing the spatial variability and stochastic process of steel corrosion is established. Numerical simulation for the deteriorated mountain tunnel is implemented by integrating the FLAC3D with MATLAB. In an illustrative example, both deterministic and probabilistic analysis on structural performance were conducted. The time-dependent deformation, axial forces and bending moments of lining structure are investigated.

Evaluating the Time-Dependent Behavior of Deeply Buried Tunnels in Soft Rock Environments and Relevant Measures Guaranteeing Their Long-Term Stability

The time-dependent behavior and long-term stability of deep-buried tunnels in soft rocks have received lots of considerations in tunnel engineering and allied sciences. To better explore and deepen the engineering application of rock creep, extensive research studies are still needed, although fruitful outcomes have already been obtained in many related investigations. In this article, the Weilai Tunnel in China’s Guangxi province is studied, taking its host rocks as the main research object. In fact, aiming at forecasting the time-varying deformation of this tunnel, a novel elasto-visco-plastic creep constitutive model with two variants is proposed, by exploiting the typical complex load–unload process of rock excavation. The model is well validated, and good agreements are found with the relevant experimental data. Moreover, the time-dependent deformation rules are properly established for the surrounding rocks, by designing two new closed-form solutions based on the proposed creep model and the Hoek–Brown criterion. To investigate the effects of the major creep parameters and the geological strength index (GSI) of the surrounding rocks on the time-dependent trend of the tunnel, an in-depth parametric study is carried out. It is shown that the convergence deformation of the surrounding rocks is remarkably influenced by the GSI and creep parameters. The convergence deformations calculated from the closed-form solutions conform well to the on-site monitoring data. In only 27 days after excavation, the creep deformation of the Weilai tunnel overtakes 400 mm, which is enormous. To guarantee the long-term stability of this tunnel, a robust support scheme and its long-term monitoring with appropriate remote sensors are strongly suggested.

A Fractional Creep Constitutive Model Considering the Viscoelastic-Viscoplastic Coexistence Mechanism.

In order to improve the accuracy and universality of the nonlinear viscoelastic-plastic mechanical behavior characterization method of asphalt mixture, a new criterion for the division of the creep process of materials was established based on the strain yield characteristics, and the coexistence mechanism of Viscoelastic-Viscoplastic strain was proposed in the subsequent yield phase; then, a viscoelastic element was constructed in the form of a parallel connection of two fractional viscoelastic elements based on fractional calculus theory, and its mathematical equations were derived; with novel viscoelastic elements, a constitutive model characterizing the whole creep process of asphalt mixtures was developed and its analytical expression was derived. The laboratory short-term creep test of Cement and Asphalt Mortar (CA mortar) and the simulation test data of asphalt mixtures from the references were used to verify the constitutive model. The results show that the creep constitutive model of asphalt mixture established in this paper has excellent fitting accuracy for different phases of the creep process of asphalt mixture under different stress levels, where the minimum fitting correlation values R2 for CA mortar, asphalt mixture (applied to pavement engineering), and asphalt sand are 0.9976, 0.981, and 0.979, respectively. Therefore, this model can be used to provide a theoretical reference for the study of the characterization of the mechanical behavior of asphalt materials.