Creep Model Research Articles

Determination of creep behavior of vessel steel Q345R at elevated temperatures

Vessel steel Q345R is widely used in pressure applications in China due to its martensitic structure, often operating in high-temperature, high-stress environments. This study investigates its susceptibility to creep strain, which can lead to significant deformation and structural damage, compromising safety. Thermal creep tests for Q345R steel were conducted within the temperature range of 400 °C–600 °C under various stress ratios. Results indicate that, below 500 °C, stages I and II predominate creep curves, with stage II evolving slowly. However, as temperature rises, stage II becomes predominant, with stage III emerging earlier, especially under high stress, leading to accelerated creep and potential fracture. Temperature significantly influences creep rates, with even minor stress increments at elevated temperatures inducing substantial creep effects. Through fitting by creep strain curves, parameters for three different time hardening creep models were determined. Subsequently, material CREEP subroutines based on these models were developed and integrated into ABAQUS to simulate the entire creep test process. The simulation results validate the ability of calibrated creep models to accurately characterize Q345R steel's creep properties, facilitating the evaluation of safety in high-temperature service structures.

Energy evolution and damage model of sandstone under seepage-creep-disturbance loading

The geological environment of deep coal seam is complex, and the failure mechanism of coal seam under the action of seepage pressure and disturbance stress is unclear, which restricts the development of deep ground engineering. In this study, triaxial compression test of sandstone under seepage-creep-disturbance loading (SCD) was carried out to analyze the characteristics of disturbance deformation, creep rate and permeability. The focus was on the energy evolution law of sandstone under SCD, and the damage creep model was constructed based on the energy proportion. The results show that the creep increment of sandstone under disturbed load was significantly higher than that under undisturbed load, and the stress level can promote the expansion and development of microcracks, in which the creep increment under high stress level showed a jump increase. The total energy and elastic energy of sandstone showed a step change with time. The damage factor under disturbance load was defined in the form of energy dissipation ratio, and the corresponding coupling damage factor was determined by considering the seepage factor and creep factor, which can reflect the coupled damage deformation of sandstone under SCD. Based on fractional order theory, a nonlinear damage creep model describing sandstone deformation under SCD was established by connecting the acceleration element in series with the Nishihara model and introducing the coupling damage factor. This study can provide research ideas for water inrush of coal seam rock mass.

Effects of Damage and Fractional Derivative Operator on Creep Model of Fractured Rock

Effects of Damage and Fractional Derivative Operator on Creep Model of Fractured Rock

Creep Phenomena, Mechanisms, and Modeling of Complex Engineering Alloys

Metal creep has been a subject of extensive study for more than 110 years because it affects the useful life of engineering components operating at high temperatures. This is even more true with ever-increasing operating temperatures of propulsion/power-generation systems and the environmental regulations to reduce greenhouse emissions. This review summarizes the recent development in creep modeling with regards to creep strain evolution, creep rate, creep ductility, creep life, and fracture mode, attempting to provide a comprehensive mechanism-based framework to address all the important creep phenomena and the long-standing issue of long-term creep life prediction with microstructural evolution and environmental effects.

Forward and inverse problems for creep models in viscoelasticity.

This study examines a class of time-dependent constitutive equations used to describe viscoelastic materials under creep in solid mechanics. In nonlinear elasticity, the strain response to the applied stress is expressed via an implicit graph allowing multi-valued functions. For coercive and maximal monotone graphs, the existence of a solution to the quasi-static viscoelastic problem is proven by applying the Browder-Minty fixed point theorem. Moreover, for quasi-linear viscoelastic problems, the solution is constructed as a semi-analytic formula. The inverse viscoelastic problem is represented by identification of a design variable from non-smooth measurements. A non-empty set of optimal variables is obtained based on the compactness argument by applying Tikhonov regularization in the space of bounded measures and deformations. Furthermore, an illustrative example is given for the inverse problem of isotropic kernel identification. This article is part of the theme issue 'Non-smooth variational problems with applications in mechanics'.

The reduced order model for creep using dynamic mode decomposition

Given the computational challenges associated with finite element methods in analyzing creep behavior in high-temperature components, this work presents an advanced method for modeling thermal creep in complex structures through a reduced order model (ROM) developed via dynamic mode decomposition (DMD). The results indicate that the ROM using DMD can predict long-term structural responses related to creep based on short-term data with high accuracy, enhancing significantly computational efficiency. The application of ROM allows for the rapid estimation of creep effects in complex structures, like monoliths in the MegaPower reactor, thereby improving the design efficiency. The eigenvalues of the creep related ROM all fall in the unit circle on the complex plane, indicating that creep is a stable development process. The DMD with improved time mode coefficient can reconstruct strain-rate related plastic deformation and cyclic visco-plastic deformation process. Additionally, we derive the necessary stress updating algorithm and consistent tangent operator matrix for the 316H unified visco-plastic constitutive equation in 2023 edition ASME code, ensuring accurate modeling of material creep behavior under high temperatures in this paper. This work provides a valuable tool for the safe design and operation of critical components in nuclear engineering and other high-temperature applications.

Study on a concise and unified unstable creep model for rocks

Study on a concise and unified unstable creep model for rocks

Comparison study of creep constitutive laws in compaction of porous stainless steel 316 L

Modeling Powder Metallurgy Hot Isostatic Pressing (PM-HIP) is of paramount importance due to its critical role in modern manufacturing. Accurate modeling of PM-HIP and understanding the associated deformation behavior are essential for optimizing the process and advancing the design and production of high-performance materials in critical applications. To accurately simulate the deformation behavior during PM-HIP, this paper presents a comprehensive investigation of modeling PM-HIP processes using various creep models incorporating rate-dependent plasticity embedded into Finite Element Analysis (FEA). This study experimentally and computationally compares four distinct creep models: Kuhn McMeeking, power law creep, unified creep law, the rate-dependent creep that was modified by Abouaf et al. and with modification of Van Nguyen et al. for density dependency. The results showed the modified Abouaf's Model, uniquely designed to account for both primary and secondary creep, consistently exhibits the closest alignment with experimental outcomes compared to the other three creep models tested.

A Creep Model of Steel Slag–Asphalt Mixture Based on Neural Networks

To characterize the complex creep behavior of steel slag–asphalt mixture influenced by both stress and temperature, predictive models employing Back Propagation (BP) and Long Short-Term Memory (LSTM) neural networks are described and compared in this paper. Multiple stress repeated creep recovery tests on AC-13 grade steel slag–asphalt mix samples were conducted at different temperatures. The experimental results were processed into a group of independent creep recovery test results, then divided into training and testing datasets. The K-fold cross-validation was applied to the training datasets to fine-tune the hyperparameters of the neural networks effectively. Compared with the experimental curves, both the effects of BP and LSTM models were investigated, and the broad applicability of the models was proven. The performance of the trained LSTM model was observed by a 95% confidence interval around the fit errors, thereby the creep strain intervals for the testing dataset were obtained. The results suggest that the LSTM model had enhanced prediction compared the BP model for creep deformation trends of steel slag–asphalt mixture at various temperatures. Due to the potent generalization strength of artificial intelligence technology, the LSTM model can be further expanded for forecasting road rutting deformations.

A unified creep and fatigue life prediction approach for 316 austenitic stainless steel using machine and deep learning

Abstract316 Austenitic stainless steel (AusSS) is extensively utilized in high‐temperature industrial applications such as boiler tubes and nuclear reactor pressure vessels. These components commonly experience failure under high‐temperature and high‐pressure conditions, attributed to either creep or fatigue. Existing classical models for creep and fatigue life prediction focus on a singular failure mode (either creep or fatigue) and consider physical features only. This study aims to develop a unified life prediction model for both creep and fatigue phenomena. It synthesizes information from 12 additional unexplored chemical and microstructural features from the National Institute of Materials Science (NIMS), Japan database, and previously published literature. Machine learning (such as decision tree, random forest, and XGBoost) and deep learning (like deep neural network) algorithms are employed in the modeling process. The trained models have been cross‐validated against unseen creep and fatigue life data, demonstrating superior prediction accuracy of 96.1% for deep neural network compared with classical models.

Creep behavior of epoxy adhesives subjected to different hygrothermal aging conditions—nanoindentation creep tests and theoretical study

Epoxy adhesives have been extensively used in the aerospace, marine, and automotive industries to join different components. A major concern with the use of epoxy adhesives is their viscoelastic behavior in aggressive service conditions such as hygrothermal ageing. Surveying the creep behavior of adhesives is of paramount importance to increase long-term durability. In this work, nanoindentation creep tests were performed on an epoxy adhesive exposed to distilled water and seawater at 55 °C for various ageing durations (0, 14, 38, 160, 251, 383, 582, and 800 h). The hardness, modulus, creep displacement, and creep rate sensitivity were quantitatively investigated to elucidate the effect of hygrothermal ageing. All the mechanical properties were found to decrease with the ageing time. The adhesive subjected to distilled water showed lower creep resistance due to higher absorption of moisture. In addition, linear relationships were observed between different mechanical properties and moisture contents irrespective of ageing conditions. Subsequently, the generalized Kelvin model was applied to investigate the creep compliance and the dependence of different deformation types (elastic, viscoelastic, and viscous deformation) on the ageing time and ageing conditions. The motion of molecular structures was also discussed. Finally, a modified creep model was proposed based on the generalized Kelvin model and continuum damage theories, which established the relationship between the dry and aged adhesive via the moisture-dependent degradation factors. The predicted creep displacements coincided well with the experimental results for the case, demonstrating the reliability of the creep model.

Densification mechanism and microstructural evolution of Si3N4 composites with CeO2 as additives during spark plasma sintering

The densification mechanism of CeO2 doped Si3N4 ceramics during spark plasma sintering (SPS) was investigated. The sintering process was observed to undergo significant densification at the intermediate stage of sintering (1435 °C–1816 °C), and the density and grain size of CeO2 doped Si3N4 ceramic were found to be greater than those of pure Si3N4 ceramic under the same sintering conditions. To determine the densification mechanism, a creep model was utilized to determine the densification mechanism which could be interpreted based on the values of the stress exponent (n) and the apparent activation energy (Q d). The results revealed that the Q d of pure Si3N4 (381.15 kJ mol−1) is higher than that of Si3N4-CeO2 powder (265.61 kJ mol−1). Moreover, the stress exponent n of Si3N4-CeO2 powder (1.12–1.33) was higher than that of pure Si3N4 powder (1.00–1.18). This can be attributed to the fact that the addition of CeO2 resulted in the formation of a liquid phase at the grain boundary which leading to a shift in the controlling mechanism from grain boundary diffusion to grain boundary sliding.

Laboratory Testing and Numerical Modeling of Creep Behavior of HDPE Geomembranes under Multistage Loading

Abstract Geomembranes are essential impermeable materials commonly employed in the fields of hydraulic engineering and geoenvironmental engineering. However, their long-term operation may result in significant creep deformation, particularly under high loads. This paper mainly presents the effect of loading mode on the creep characteristics of high-density polyethylene (HDPE) geomembranes. A series of creep tests of geomembranes under multistage loading were conducted and compared with single loading creep tests. Under multistage loading, creep strain increased in a step-like manner. When the cumulative load level is lower than 50 %, the creep of geomembranes can attain a stable state. When the cumulative load level attains 60 %, the creep may enter a constant-rate creep stage. Compared with single loading creep, the creep under multistage loading attained a stable state earlier for a relatively low load level, and the deformations were smaller. The creep strain rate was significantly reduced at a constant-rate creep stage for a relatively high load level. The multistage loading was beneficial to the creep deformation control of geomembranes. Furthermore, an enhanced creep model was proposed to describe the creep behavior under multistage loading, including the stable state and constant-rate creep stage. The predictions were in good agreement with the experimental data.

Anti-creep pretension determination of a mesh reflector antenna for long term surface accuracy retention

During the in-orbit service, mesh reflector antennas inevitably withstand the long-term creep behavior, resulting in changes in material properties and loss of cable tensions, thus decreasing the structural stiffness and surface accuracy. Pretension design plays an important role for mesh reflector antennas in achieving high surface accuracy, and different levels of pretension also affect the antenna’s creep behavior in the time dimension, which can be actively utilized to improve stability of the antenna surface accuracy. In this paper, we present an anti-creep pretension determination method for mesh reflector antennas to improve the surface accuracy stability. The creep model in the discretized time domain is adopted to describe the cable creep behavior. The time-related nonlinear equilibrium equation of the mesh reflector antenna is established with the force density method. The time-related tangent stiffness matrix is derived and adopted to solve the nonlinear equilibrium equation by the Newton-Raphson method, providing an effective way to analyze the antenna creep phenomenon in the discretized time domain. Aiming to minimize the long-term peak value of the time-variant surface error, the pretension schemes are generated and optimized. Finally, this approach is effectively applied to a thirty-unit mesh reflector antenna and its feasibility and effectiveness are verified.

Changing of the excess conductivity near the irreversibility temperature of the top seeded YBa2Cu3O7−x

A top seeded YBa2Cu3O7-x (YBCO) superconductor was grown using a bulk Nd123 seed crystal. Orientation peaks directed in the c-axis were observed from the X-ray diffraction measurement for the Y123 sample, indicating single crystal behavior. Magneto-resistivity measurements were carried out as a function of temperature under applied magnetic fields up to 4 T. The superconducting transition temperature (Tc) of the sample was obtained to be approximately 93 K and the excess conductivity curve was obtained experimentally from the resistivity measurement at zero magnetic field. The critical exponents were found to be λsfw = 2.26 ± 0.25, λ3D = 0.47 ± 0.03 and λ2D = 0.82 ± 0.07 for the short wave fluctuation (SWF) region and the mean field region characterized by 3D and 2D fluctuations, respectively. The crossover temperature determined from the crossover from 2D to 3D regime was found to be 96.37 K. The irreversible temperatures determined from the magneto-resistivity measurements and the irreversibility field line of the sample was obtained using the giant flux creep (gfc) model. The sample exhibits a behavior consistent with the gfc and the vortex glass model according to the n parameter calculated from the resistivity temperature measurements. The width enlarges with the applied magnetic field and was found to be approximately 4 K at 4 T for the Y123 sample. The sample was in the 3D regime below 96.37 K, while the sample was in the 2D regime between 96.37 K and 101.35 K. On the other hand, the reversible region was confined between 93.95 K and 93.33 K at 0 T. It was observed that 3D fluctuations are dominant in the reversible region, whereas 2D fluctuations are dominant in the irreversible region.

Deformation behaviour of concrete with different moisture contents subjected to compressive creep and cyclic loading

The expected long-term deformations of concrete structures are calculated using creep models, derived from experiments performed with constant mechanical loads. However, in the majority of real structures, such as bridges, constant creep loads are superimposed with cyclic loads of substantial magnitude. Additionally, such structures are subject to changes in environmental conditions (temperature and humidity). Deformation measurements of existing bridges have shown significant underestimations by established creep models, which might be traced back to the superimposition of cyclic loads and different moisture contents. Therefore, the developments of strains, viscoplastic strains and modulus of elasticity under creep and cyclic loading of a normal strength concrete have been comparatively investigated for two different pore moisture contents (approx. 100 and 75%). The results show that viscous strains due to cyclic loading are significantly higher than those due to creep loading at the mean stress level of cyclic loading. Furthermore, the strains are higher for the higher moisture content. The differences in the development of the modulus of elasticity and viscoplastic strains of both load types give clear indication for load type dependent microstructural deformation mechanisms. The results obtained concerning the influence of the load type and the moisture content need to be considered for the improvement of existing models.

Microscopic deformation mechanism and characteristics of carbonaceous slate during the creep process

Carbonaceous slate exhibits a significant creep deformation that seriously affects the construction and operation of underground projects. To investigate the microstructural changes characteristics and reveal the microscopic deformation mechanism of the carbonaceous slate during the creep process, multiple methods were performed, including the triaxial creep test, SEM and MIP. The following conclusions were drawn: The rock samples underwent three stages during the creep test: microporosity closure at a low-stress level, material densification at an intermediate stress level, and microcracks emerging and expanding to failure at the high stress. The creep deformation was particularly significant in the first and third processes. The lamellar particles are compressed or bent under stress in parallel and vertical directions, showing the anisotropic properties of deformation. The deformation of the rock sample is related to the angle between the bedding and the orientation of major principal stress, and the effect of the anisotropy decreases with the increased stress level. The sprouting and expansion of microfractures occur at high-stress levels, showing pressure dissolution of mineral particles, migration of very fine particles, and cement damage between lamellar particles. Finally, the horizontal samples formed a combined rupture surface composed of the laminar surface and the fracture surface intersecting it, showing brittle damage, while the vertical samples formed a fracture surface parallel to the laminar surface, showing a ductile damage pattern. Those results could provide the basis for a further understanding of the mechanical properties of carbonaceous slate and the improvement of its creep model and parameters. It was significant for the stability analysis and deformation prediction of engineering structures using numerical simulation.

Long-term creep behavior of glulam member under compression and bending moment

ABSTRACT In this study, 12 glulam members were designed and tested, considering the effects of stress ratio and relative eccentricity. After the 180-day test period, the results showed that increasing the stress ratio and relative eccentricity led to large initial elastic deformation and creep deformation, and the creep coefficients at 180 days for the glulam members under higher stress ratio and relative eccentricity were lower than those for the glulam members under lower stress ratio and relative eccentricity. Typical empirical and mechanical models and a modified model were chosen to fit the creep coefficient curves. The fitting analysis indicated that the values of the R 2 for all creep models were larger than 0.90, reflecting the goodness of fit. Employing the modified model, the prediction of the creep coefficient for the compressive-bending glulam member over 50 years was conducted. The results found that the glulam members under high relative eccentricity and stress ratio exhibited low creep coefficients, of which values approached to 0.7. Compared to creep coefficients specified in current standards and literature, the creep coefficient of 1.5 at a 50-year period for the compressive-bending glulam members was recommended, aiming to provide a reference to the long-term design of the compressive-bending glulam member in practice.

Uniaxial compressive creep tests by spark plasma sintering of 70% theoretical density α-uranium and U-10Zr

Metallic fuels hold numerous advantages over conventional uranium dioxide fuels and are a key component of several liquid metal-cooled advanced reactor concepts including sodium fast reactors. These fuels undergo rapid swelling during early burnup; consequently, they spend most of their reactor lifetime in a porous state. The presence of this porosity alters many of the mechanical properties of the fuel including creep impacting fuel deformation during axial swelling. This work investigates the creep behavior of the porous fuel using a spark plasma sintering technique. Creep tests were performed for the first time on porous α-phase uranium and uranium with 10 wt. % zirconium (U-10Zr) samples. The samples of α-phase uranium and U-10Zr were fabricated from depleted uranium by spark plasma sintering and subjected to uniaxial compressive creep testing. Calculated stress exponents were found to be 2.6±1.6 and 5.7±1.4 for α-U and U-10Zr, respectively, and calculated activation energies were found to be 61.6±1.1kJ/mol for α-U. The creep data were also used to evaluate existing porosity inclusive in creep models.

In situ observation of the multistep process of cold sintering

AbstractA compact cold sintering stage was constructed to densify ceramic samples in capillary tubes for the purpose of conducting in situ experiments designed to elucidate fundamental cold sintering mechanisms. The stage was used to successfully densify samples composed of ZnO/CH₃COOH mixtures under a range of pressures (25–175 MPa) over a modest temperature range (room to 150°C) in capillary tubes (0.75 mm inner diameter). The progression of the cold sintering process of ZnO was monitored by both piston displacement and a camera. These measurements allowed the strain rate and fluid extraction during densification to be recorded. The results of these measurements are compared to existing models of cold sintering and pressure solution creep, and direct correlations are observed between abrupt changes to the densification rate during constant heating rate experiments and the observation of solvent extraction from the powder compact.