Creep Constitutive Model Research Articles

Viscoelastic plastic creep constitutive model based on energy conservation law and strain energy theory

Viscoelastic plastic creep constitutive model based on energy conservation law and strain energy theory

Comparison of inelasticity creep failure evaluation codes for elevated-temperature non-nuclear pressure equipment

PurposeTo ensure the reliable and safe operation of elevated-temperature pipes and equipment in the long term, it is essential to thoroughly assess the creep rupture life. Nevertheless, there is currently no design code that specifies a creep rupture life evaluation method for non-nuclear elevated-temperature equipment. The paper aims to discuss this issue.Design/methodology/approachAn analysis was conducted to compare the differences and conservativeness in calculating creep strain using three major codes (ASME-CC-2843, API-579 and BS-7910) based on the results of the 316H creep constitutive model and creep strain prediction. In addition, the creep resistances of 316H, 304H and 347H were compared. Subsequently, the ANSYS Usercreep subroutine was developed to compare the discrepancies between different codes under multiaxial stress conditions using numerical simulations.FindingsBS-7910 employs the Norton creep model with calculation parameters for the average creep strain rate, which is not applicable for the engineering design stage. ASME-CC2843 code primarily focuses on the primary and secondary creep stages, making it more suitable for non-nuclear pipeline and equipment design. For 316H, the creep strain curves predicted by ASME-CC2843 and API-579 typically intersect at a specific point. By combining the creep strain predicted by ASME-CC2843 and API-579, 347H exhibits superior predicted creep resistance compared to 316H, whereas 316H exhibited better predicted creep resistance than 304H.Originality/valueThis study provides a guide for future evaluation methods and material choices for non-nuclear equipment and pipelines operating at elevated temperatures.

Fractional Derivative-based Burger Creep Model for Soft Rocks and its Verification Using Tunnel Monitoring Results and Experimental Data

AbstractConsidering the creep behavior of soft and weak rocks is critical for analyzing the long-term stability of underground constructions. This paper introduces a novel creep constitutive model to characterize the creep behavior of rocks under uniaxial and triaxial stress states. The fractional derivative Abel dashpot was used to improve the Burger model, and a viscoplastic component was added in series with the modified Burgers model to replicate the tertiary phase of rock creep. The effectiveness of the model was verified using creep test data from various soft rocks and monitoring measurements from a tunnel excavated in heavily jointed weak rock masses. Furthermore, a sensitivity analysis was carried out to assess the impact of the model parameters on creep deformation, and a comparative study was performed to evaluate the efficacy of the suggested model in modeling the accelerated stage of rock creep compared with some existing models. The strong agreement observed between the calculated results and both the creep test data and tunnel monitoring measurements underscores the accuracy and validity of the proposed model. The comparative analysis further revealed that the proposed model offers the highest fitting efficiency for describing the tertiary stage of rock creep. These findings suggest that the model effectively captures the creep behavior of rocks and precisely represents the entire creep process.

Microscopic and Macroscopic Creep Damage Behavior and Constitutive Model of Sandstone Subjected to Static and Dynamic Coupled Loading

Microscopic and Macroscopic Creep Damage Behavior and Constitutive Model of Sandstone Subjected to Static and Dynamic Coupled Loading

Constitutive modeling of creep behavior considering microstructure evolution for directionally solidified nickel-based superalloys

During creep at elevated temperatures, the performance of directionally solidified nickel-based superalloys experiences progressive degradation, accompanied by significant microstructure evolution. In this study, creep tests of varying durations were conducted on smooth specimens, revealing typical microstructure evolution, including dissolution, coarsening, and rafting of the γ′ phase. The process of microstructure evolution during creep was precisely quantified utilizing an advanced image processing technique. Subsequently, a phenomenological model was formulated to predict the evolution of the γ/γ′ microstructure. Furthermore, with the introduction of the microstructure evolution model, a multiscale creep constitutive model was established within the framework of crystal plasticity. This model encompasses various dislocation strengthening mechanisms, including dislocation bypassing, dislocation pairs shearing, and dislocation hardening. The constitutive model can accurately describe both the microstructure evolution and creep deformation of the DZ406 superalloy at various temperatures, with maximum errors of 18.13% and 24.31%, respectively. Finally, the model under multiaxial stress conditions was validated through creep tests on specimens with a film-cooling hole. The maximum prediction errors for microstructure evolution and creep life were 30.46% and 28.00%, respectively.

A physics knowledge-based surrogate model framework for time-dependent slope deformation: Considering water effect and sliding states

The surrogate model serves as an efficient simulation tool during the slope parameter inversion process. However, the creep constitutive model integrated with dynamic damage evolution poses challenges in development of the required surrogate model. In this study, a novel physics knowledge-based surrogate model framework is proposed. In this framework, a Transformer module is employed to capture strain-driven softening-hardening physical mechanisms. Positional encoding and self-attention are utilized to transform the constitutive parameters associated with shear strain, which are not directly time-related, into intermediate latent features for physical loss calculation. Next, a multi-layer stacked GRU (gated recurrent unit) network is built to provide input interfaces for time-dependent intermediate latent features, hydraulic boundary conditions, and water-rock interaction degradation equations, with static parameters introduced via external fully-connected layers. Finally, a combined loss function is constructed to facilitate the collaborative training of physical and data loss, introducing time-dependent weight adjustments to focus the surrogate model on accurate deformation predictions during critical phases. Based on the deformation of a reservoir bank landslide triggered by impoundment and subsequent restabilization, an elasto-viscoplastic constitutive model that considers water effect and sliding state dependencies is developed to validate the proposed surrogate model framework. The results indicate that the framework exhibits good performance in capturing physical mechanisms and predicting creep behavior, reducing errors by about 30 times compared to baseline models such as GRU and LSTM (long short-term memory), meeting the precision requirements for parameter inversion. Ablation experiments also confirmed the effectiveness of the framework. This framework can also serve as a reference for constructing other creep surrogate models that involve non-time-related across dimensions.

Study on the creep constitutive model of layered rockconsidering anisotropic and damage factors after hightemperature exposure

The failure of layered rock after high temperature exposure is a major concern in deep underground engineering projects. This paper proposes an improved Nishihara creep constitutive model that considers damage factors and the bedding angle, which overcomes the shortcomings of the deviation in the description of the conventional Nishihara model in the acceleration stage. The constitutive model is verified by the conventional triaxial creepiest. The theoretical curve has a high degree of fitting with the experimental curve. The experimental results show that a temperature of [Formula: see text] has an obvious influence on the steady creep rate and the creep strain of layered sandstone, and [Formula: see text] can be regarded as the temperature threshold for the long-term strength and change from anisotropic to isotropic of layered sandstone. The irreversible melting mixing phenomenon at the boundary of mineral particles with increasing temperature is the mechanism by which different treatment temperatures affect the anisotropy degree of layered rock.

Features and Constitutive Model of Hydrate-Bearing Sandy Sediment’s Triaxial Creep Failure

In the longstanding development of hydrate-bearing sediment (HBS) reservoirs, slow and permanent deformation of the formation will occur under the influence of stress, which endangers the safety of hydrate development projects. This paper takes hydrate-bearing sandy sediment (HBSS) as the research object and conducts triaxial compression creep tests at different saturation degrees (20%, 30%, and 40%). The results show that the hydrate-containing sandy sediments have strong creep characteristics, and accelerated creep phenomenon will occur under the long-term action of high stress. The longstanding destructive power of the specimen progressively raises with the increase in hydrate saturation, but the difference in the triaxial strength of the specimen progressively increases. This indicates that the damage to the hydrate structure during long-term loading is the main factor causing the strength decrease. Further, a new nonlinear creep constitutive model was developed by using the nonlinear Burgers model in series with the fractional-order viscoplastic body model, which can well describe the creep properties of HBSS at different saturation levels.

Mechanical properties and biocompatibility characterization of 3D printed collagen type II/silk fibroin/hyaluronic acid scaffold

Damage to articular cartilage is irreversible and its ability to heal is minimal. The development of articular cartilage in tissue engineering requires suitable biomaterials as scaffolds that provide a 3D natural microenvironment for the development and growth of articular cartilage. This study aims to investigate the applicability of a 3D printed CSH (collagen type II/silk fibroin/hyaluronic acid) scaffold for constructing cartilage tissue engineering. The results showed that the composite scaffold had a three-dimensional porous network structure with uniform pore sizes and good connectivity. The hydrophilicity of the composite scaffold was 1071.7 ± 131.6%, the porosity was 85.12 ± 1.6%, and the compressive elastic modulus was 36.54 ± 2.28 kPa. The creep and stress relaxation constitutive models were also established, which could well describe the visco-elastic mechanical behavior of the scaffold. The biocompatibility experiments showed that the CSH scaffold was very suitable for the adhesion and proliferation of chondrocytes. Under dynamic compressive loading conditions, it was able to promote cell adhesion and proliferation on the scaffold surface. The 3D printed CSH scaffold is expected to be ideal for promoting articular cartilage regeneration.

Calibrating high-dimensional rock creep constitutive models for geological disaster prevention: An application of data assimilation methods

The study of rock creep phenomena is of paramount importance due to its potential to trigger geological disasters, such as landslides. To predict and prevent such disasters, creep constitutive models are widely employed to comprehend the time-dependent deformation of rocks. These models encompass various mechanical parameters that describe the intricate stress-strain behaviors. Nevertheless, significant challenges persist in achieving accurate and consistent parameter estimation and state prediction. In this study, we introduce three advanced data assimilation (DA) methods, including one Markov chain Monte Carlo method, DREAM(KZS), and two ensemble smoother methods, ESMDA and ILUES. This marks the first application of such methods for calibrating rock creep models in the scenario of geological disaster prevention. We conducted numerical simulations under both low- and high-dimensional conditions to assess the performance of these DA methods. For the single partition model, all three DA methods demonstrated promising results. In the high-dimensional case, DREAM(KZS) displayed inefficiency, while both ESMDA and ILUES proved to be still effective. ESMDA offered improved data matching but tended to underestimate parameter uncertainties, whereas ILUES excelled in addressing the issue of equifinality. In a real-world case focusing on characterizing creep deformation at the Mogu tilting deformation body near the Lianghekou Dam, China, we employed all three DA methods, and they collectively demonstrated satisfactory performance. Particularly noteworthy is the enhanced performance of the DREAM(KZS) method during the accelerated creep phase, even in the presence of limited data. The findings of this research bear significant importance in reducing uncertainties associated with model parameters in the realm of rock mechanics, thereby advancing our capabilities in predicting and preventing disasters.

Unified viscoplastic constitutive model for creep–fatigue behavior of austenitic stainless steel 304 under axial–torsional loading

Unified viscoplastic constitutive model for creep–fatigue behavior of austenitic stainless steel 304 under axial–torsional loading

Room-Temperature Creep Deformation of a Pressure-Resistant Cylindrical Structure Made of Dissimilar Titanium Alloys

The long-term safety of pressure-resistant structures used in deep-sea equipment may be threatened by creep deformation. The creep deformation behavior of a pressure-resistant structure made of different titanium alloys, Ti-6Al-4V and Ti-4Al-2V, at room temperature is investigated in this research. The kinetics and mechanisms underlying creep deformation in these materials is explained by proposing an improved constitutive model considering the effects of stress level, loading rate and environmental temperature field, offering crucial information for optimizing design parameters and guaranteeing the lifespan of the structure. Model parameters are determined for the two types of titanium alloys based on tensile creep testing results and validated through a simulation of the experimental process. In this study, a material creep model was used to predict the long-term deformation of large pressure-resistant titanium structures to ensure safe long-term operation. The safety factor used in the model is 1.5. Finite element analyses are conducted for the creep behavior of the pressure-resistant structure under real operating circumstances based on the creep constitutive model. The simulation predicts stress distribution, strain evolution, and deformation size over long periods of time by integrating complicated geometries, boundary conditions, and material characteristics. The present research can provide basic information for the local impacts of creep deformation on the inside of facilities, which helps refine design strategies to reduce possible damage risks.

Study on the fractional creep model of roadway filling paste under the coupling effect of pore water pressure and stress

Filling paste in deep roadways is significantly affected by groundwater, especially high pore water pressure, which increases the complexity and variability of the filling paste's mechanical properties. To explore the creep characteristics and long-term stability of filling paste under varying pore water pressure, the MTS815.03 test system is used to conduct creep tests under different pore water pressures and stress. Then the creep deformation of the filling paste under the complex pressure field of static pore water pressures is analyzed. Finally, through the one-to-one correspondence between the numerical simulation of the creep model and the characteristic points of the creep curve, a method for determining the creep parameters under the complex pressure field of static pore water pressures is proposed. Results show that the creep test curves of filling paste under different pore water pressures and stress are in good agreement with the model curves. This shows that the creep constitutive model in this research can better reflect the whole process of creep deformation of filling paste. The result also verifies the rationality of the proposed method to determine creep model parameters. The newly proposed creep model can effectively compensate for the traditional Nishihara model, which is inability to reflect the acceleration of creep and can more accurately describe the creep characteristics of the primary and steady-state creep stages.

Research on the bearing creep characteristics and constitutive model of gangue filling body

The creep characteristics and potential deformation patterns of gangue backfill material are crucial in backfill mining operations. This study utilizes crushed gangue from the Gangue Yard in Fuxin City as the research material. An in-house designed, large-scale, triaxial gangue compaction test system was used. Triaxial compaction creep tests were conducted on gangue materials with varying particle size distributions. Analysis was performed based on different particle sizes, stresses, and confinement pressures. The study investigates the creep characteristics of the gangue under different conditions and explores the underlying causes. It reveals the relationship between the creep deformation of gangue materials and the passage of time. Mathematical methods are applied to develop a triaxial compaction creep power law model for gangue backfill materials. Finally, the creep results are fitted using an empirical formula approach.

Quantitative evaluation of PI-RDL interfacial delamination in fan-out wafer-level packaging during unbiased highly accelerated stress test

Fan-Out Wafer-Level Packaging (FOWLP) is increasingly utilized for its superior performance, facilitated by flexible heterogeneous integration. Despite its advantages, the interface between Polyimide (PI) and Redistribution Layers (RDL) is susceptible to significant vulnerabilities, notably delamination. This study introduces a quantitative method to assess PI-RDL interface delamination in FOWLP under unbiased Highly Accelerated Stress Tests (uHAST), a standard approach in accelerated reliability testing characterized by high humidity and temperature. Central to our methodology is the development of a time–temperature-moisture equivalence-based creep constitutive model, which significantly enhances our understanding of the impact of temperature and moisture on creep behavior. Furthermore, we have developed an innovative “open moisture absorption” method for preparing samples for four-point bending tests, enabling precise quantification of the time-induced degradation of PI-RDL interfacial fracture toughness under saturated conditions. Our comprehensive finite element model integrates moisture diffusion, the newly developed creep constitutive model, and solid mechanics to accurately simulate the accumulation of strain energy release rate during uHAST, facilitating precise predictions of delamination initiation times in FOWLP. Experimental validation under two uHAST conditions—130 °C/85 %RH for 96 h and 110 °C/85 %RH for 264 h—demonstrates the effectiveness of our approach, predicting the delamination initiation time at the PI-RDL interface with over 80 % accuracy. This predictive methodology is pivotal in enhancing the structural optimization and extending the service life of FOWLP in varied environmental conditions.

Microstructure based model for creep of single crystal superalloys in the high temperature and low stress creep regime

A new constitutive creep model for Ni-base superalloys has been developed that links the instantaneous creep response to incremental microstructure changes occurring during creep. The structure starts with cuboidal γ′- particles embedded in the γ-phase, and transitions to a rafted structure. In the present Kocks-Mecking type of model, the dislocation density ρ is considered as a state variable that evolves during creep. The increase of ρ depends on the γ-channel width in the γ/γ′-microstructure. Recovery, i.e., the reduction of ρ, is modelled from thermally activated, mechanically assisted climb. The strain rate is also modelled from the very same recovery process. The model successfully describes creep curves in a range of temperatures and load stresses with a maximum of five physical parameters. Once the model has been calibrated, it can be used to predict creep curves for other temperatures, stresses, and microstructures if the channel width evolution is known. The model is even capable of making reasonable predictions when fitted only to a single experiment. Extrapolations to different alloys with moderately varying compositions are possible.

Review of the creep constitutive models for rocks and the application of creep analysis in geomechanics

AbstractThe creep behavior of rocks has been broadly researched because of its extensive application in geomechanics. Since the time-dependent stability of underground constructions is a critical aspect of geotechnical engineering, a comprehensive understanding of the creep behavior of rocks plays a pivotal role in ensuring the safety of such structures. Various factors, including stress level, temperature, rock damage, water content, rock anisotropy, etc., can influence rocks’ creep characteristics. One of the main topics in the creep analysis of rocks is the constitutive models, which can be categorized into empirical, component, and mechanism-based models. In this research, the previously proposed creep models were reviewed, and their main characteristics were discussed. The effectiveness of the models in simulating the accelerated phase of rock creep was evaluated by comparing their performance with the creep test results of different types of rocks. The application of rock’s creep analysis in different engineering projects and adopting appropriate creep properties for rock mass were also examined. The primary limitation associated with empirical and classical component models lies in their challenges when it comes to modeling the tertiary phase of rock creep. The mechanism-based models have demonstrated success in effectively simulating the complete creep phases; nevertheless, additional validation is crucial to establish their broader applicability. However, further investigation is still required to develop creep models specific to rock mass. In this paper, we attempted to review and discuss the most recent studies in creep analysis of rocks that can be used by researchers conducting creep analysis in geomechanics.

Compaction localization in geomaterials: A mechanically consistent failure criterion

Compaction bands play a key role in the deformation processes of porous rocks and explain different aspects of physical processes in geological formations. The state-of-the-art description of the localized strains that lead to compaction banding has limitations from the mechanical point of view. Thus, we describe the phenomenon using a consistent axiomatic formulation. We build a viscoplastic model using minimal assumptions; we base our model on six principles to study compaction band strain localization triggered by viscous effects. We analyze different stress states to determine the conditions that trigger compaction bands. Laboratory experiments show that a material undergoes different strain localizations depending on the confinement pressure; thus, we perform a series of numerical experiments that reproduce these phenomena under varying triaxial compression conditions. These simulations use a simple viscoplastic constitutive model for creep based on Perzyna’s viscoplasticity and show how confinement changes the strain localization type for different triaxial tests.

A thermodynamically consistent creep constitutive model considering damage mechanisms

This paper derives a physically-based creep-damage and life prediction model through the basic laws of thermodynamics. The model divides creep damage into two parts: one corresponding to high temperature and low stress, related to cavity nucleation and cavity growth, and the other corresponding to high stress, related to dislocation movement. The creep strain rate consists of two components: diffusion creep, which is assumed to occur in all stress ranges, and dislocation-related creep, which activates when the external stress exceeds a certain threshold. The proposed model characterizes damage by the degradation of creep free energy. It accurately describes creep behavior over a wide stress range, including the transition phenomena observed in creep strain rate curves and creep life curves. This provides a constitutive reference for simulating long-term creep damage and life based on short-term creep data.

New approach for predicting time-dependent deformation of shale rock: a modified fractional-order creep constitutive model

New approach for predicting time-dependent deformation of shale rock: a modified fractional-order creep constitutive model