Nonlinear Creep Research Articles

On the simulation of the small punch creep test—applied to 316L(N) austentic steels

ABSTRACT This paper describes a numerical analysis to predict the deformation and time to rupture of the small punch creep test for 316 L(N) austenitic steel. The constitutive model incorporates elasto-plastic nonlinear kinematic hardening and creep with primary, secondary and tertiary creep calibrated to the RCC-MRx code data. The computations are assessed by comparing with experimental data for a 500 µm thick sample clamped with a diameter of 5 mm loaded with a force 300,400 and 500N at 700°C. The model predicts the experimental observations quite well with respect to minimum deflection rate and time to rupture and its location using a local critical strain criterion. A very important feature is that the deformation and total effective strain distribution at rupture are almost identical for all loads as function of the time divided by the time to rupture.

A novel refined Caputo kernel and constitutive concepts for semi-exact nonlinear dynamic and creep analyses of suddenly pressurized hollow fractional-order visco-hyperelastic cylinders

Some reports have confirmed that discretizing the mass, damping, and stiffness characteristics of a continuum can result in remarkable deviations from the experimental results; as all these properties are intertwined and coupled within a single material. The viscoelastic constitutive laws with fractional-order time derivatives can model this integrity much more accurately, due to their capability of using a set of an infinite number of orders. Here, an innovative constitutive model with a nonlinear hyperelastic memory element that treats simultaneously the fractional-order viscoelasticity and Mooney-Rivlin hyperelasticity of the continuum is proposed to track the suppression of the short-term dynamic stresses and displacements and the redistribution of the long-term creep stress and deformations of the suddenly pressurized thick cylinders. While the spatial variations of the quantities of the incompressible cylinder are treated by an exact analytical approach, the resulting time-dependent system of equations is converted by a novel numerical solution scheme to an integrodifferential system that contains integer-order partial derivatives and a time-growing number of integral terms. An enhancement to Caputo's singular-kernel integral definition of the fractional-order derivatives is proposed here to replace these derivatives with equivalent integrals whose integer derivatives are computed based on second-order Taylor's expansion. The integer-order and fractional-order time derivatives are then computed numerically using the second-order Runge-Kutta and accumulation-based trapezoidal techniques, respectively. Finally, comparisons are made among the dissipative pattern and time variations of the dynamic/vibration stresses and large-deformations of the hyperelastic and fractional-order visco-hyperelastic cylinders in addition to the assessment of the effects of the constitutive parameters of the fractional-order model. Results show that while the larger magnitudes of both the nonlinear viscosity coefficients and fractional-order time derivatives diminish the resulting deformations and stresses, they respectively lead to smaller and larger frequencies of oscillation.

Fractional-Order Modeling of Piezoelectric Actuators with Coupled Hysteresis and Creep Effects

A novel fractional-order model, incorporating coupled hysteresis and creep effects, is proposed for typical piezoelectric actuators in this study. Throughout the actuation process, various nonlinear behaviors such as piezoelectric hysteresis, non-local memory, peak transition, and creep nonlinearity are accurately characterized by the model. Offering a simpler structure and superior tracking performance compared to conventional models, the proposed fractional-order model parameters are identified using a method that integrates actuator dynamics and employs the particle swarm optimization algorithm. Experimental validation on a piezoelectric actuation platform confirms the model’s superior accuracy and simplified structure, contributing to a deeper understanding of piezoelectric actuation mechanisms and providing an efficient modeling tool for enhanced system performance.

A nonlinear creep model for transversely isotropic rock based on fractional calculus theory

A nonlinear creep model based on fractional calculus theory is proposed to better describe the creep characteristics of transversely isotropic rock. The model includes a Hooke elastomer, a fractional Abel dashpot, a Kelvin body, and a nonlinear viscoplastic body, which effectively capture the three stages of creep (including the primary, steady-state, and accelerating creep stages) while also reflect the influence of different bedding angles on creep behavior. The parameters of the model are identified by the Levenberg–Marquardt algorithm. Compared to previous models assuming constant Poisson’s ratio for transversely isotropic rock, our nonlinear creep model demonstrates improved accuracy and rationality.

A Finite Strain Elastic-Viscoplastic Consolidation Model for Layered Soft Soils Considering Self-Weight and Nonlinear Creep

A Finite Strain Elastic-Viscoplastic Consolidation Model for Layered Soft Soils Considering Self-Weight and Nonlinear Creep

A theta projection model for compressive creep behaviour of refractories at high temperature: application to alumina-spinel

Thermomechanical loads are normally applied to refractory materials throughout their service life whichever is their practical use (e.g. steel ladle, rotary kiln furnaces). Among all the phenomena that the refractories are exposed to, the influence of creep behaviour is essential in determining their performance. Creep of refractories is usually represented by simple creep laws such as Norton-Bailey, which lack the capacity for generalization. The theta projection creep method, on the other hand, was proposed in the twentieth century to predict the creep of metals and alloys across different temperatures and stresses. The model is represented by one exponential equation capable of representing the complete creep curve, and coefficients that are temperature and stress-dependent, thus enabling the representation of complex nonlinear creep behaviour. Since refractories have similar creep responses to metals, the theta projection creep model is validated to characterize the compressive creep behaviour of alumina-spinel refractories at temperatures between 1200 and 1500 °C. Creep data from steady-state and transient temperature creep tests are used to calibrate the model. A regression by the least square method is applied to calculate the model’s parameters. The model shows good flexibility in fitting the test data of the alumina-spinel refractory over the three creep stages. A temperature and stress dependence model is derived for the theta coefficients, reducing the number of material parameters necessary to describe the material's behaviour. The experimental creep curves are presented, as well as the curves resulting from the identified parameters. The implications of the chosen creep data set on the definition of the model and its adequacy for this novel application are discussed.

An elastic-viscoplastic creep model for describing creep behavior of layered rock

To describe the full-stage creep behavior of layered rock accurately, a new elastic-viscoplastic creep model is proposed based on fractional order theory in this manuscript, which consists of a Hooke elastomer, a fractional Abel dashpot, a Kelvin body, and a new non-linear visco-plastic component. The non-linear creep model can not only describe the changes in three creep stages (primary creep, steady-state creep and accelerating creep) but also reflect the influence of different bedding angles of rock. The constitutive equations of the non-linear creep model are deduced by the empirical model method and plastic theory method, respectively. The parameters of the non-linear creep model are identified using the Levenberg-Marquardt algorithm from Origin. It shows that the creep model in this paper are highly consistent with the experimental data under different load levels, creep stages and bedding angles, and the accuracy and rationality of the model are verified. Moreover, the creep constitutive equations for layered rock derived by the two methods have the same fitting effect on the same set of experimental data.

The creep characteristics and related evolution of particle morphology for calcareous sand

In the study, the creep characteristics and meso-mechanism of calcareous sand under different stresses are explored through triaxial creep tests. The influence of particle size on calcareous sand creep is also considered. Furthermore, the particularity of calcareous sand creep is revealed by comparing with the creep behavior of silica sand. The results show that during creep, the calcareous sand is more stable than silica sand due to the interlocking of irregular particles. When creep deviatoric stress is small, the creep of calcareous sand is manifested as nonlinear attenuation creep (primary creep), and the creep deformation is smooth without creep failure. With the increase of creep deviatoric stress, the creep deformation is concentrated, resulting in a strain concentration zone similar to the shear band, and the associated creep rate first decreases and then suddenly increases, finally, creep failure occurs. With increasing particle size of calcareous sand, the particle crushing increases, which induces a higher creep deformation, however, the overall creep failure is not generated. During the graded creep of calcareous sand, an obvious creep structural effect is observed, which is temporary and results in a significantly reduction of creep rate. Only after the previous creep structure effect is destroyed by the continuously creep process, the creep response can restore to its original behavior. The meso-behavior is represented by particle morphology, i.e., the fractal dimension and aspect ratio. It is found that both confining pressure and particle size can influence the evolution of particle morphology during creep. With the increase of confining pressure, the fractal dimension of calcareous sand decreases which means that particle grinding is always existent, while the aspect ratio of small-sized calcareous sand after creep decreases first and then stabilizes (slightly increases), suggesting that the overall particle breakage is the main cause of deformation. However, the aspect ratio of large-sized calcareous sand continually decreases, indicating that the main contribution for its deformation is angular cracking. The mesoscopic behavior of silica sand is basically unaffected by creep, and its creep deformation is mainly caused by particle rearrangement.

Linear and nonlinear tensile creep of steam-cured UHPC

In bridges, UHPC can bear significant sustained tensile stress without cracking under service loading. Its significant impact on the long-term behavior of large-span bridges due to tensile creep characteristics becomes evident. In this paper, both linear and nonlinear tensile creep behavior of steam-cured UHPC was experimentally investigated by using dog-bone-shaped specimens under sustained direct tension for a duration of 360 days. The tensile creep test was conducted under varied tensile stress levels ranging from 0.3ft to 0.9ft. Tensile creep coefficients were calculated by using the experimental results. Nonlinear tensile creep occurs in the steam-cured UHPC when the sustained tensile stress is larger than 0.3ft. The threshold of nonlinear tensile creep is lower than that of normal-strength concrete under compression. When the sustained tensile stress is larger than 0.8ft, tensile creep failure occurs a short time after loading. The nonlinear creep impact under tension is less pronounced than that under compression due to the distinct function of steel fibers within UHPC when subjected to compression and tension force. The findings in the scanning electron microscopy (SEM) test reveal that the mechanism driving the nonlinear tensile creep of UHPC is the damage growth at the fibers-matrix interface under the high sustained tensile stress. A design-oriented model for the creep coefficient of UHPC is developed, which incorporates both linear and nonlinear creep effects. The model’s credibility is verified using the experimental results.

Calculation of reinforced concrete structures: considerations on developing new theory (continued)

Introduction. The authors develop the results of their previously published study in order to build up a nonlinear dissipative theory of concrete compressive strength. The present paper explores possibilities to improve the theory of calculation of concrete and reinforced concrete structures in the light of the accumulated knowledge.Aim. To introduce an approach to developing a nonlinear dissipative theory of concrete compressive strength in the absence of regulatory documents for loading modes, using instead the standard classification of loads.Results. The authors refer to the non-linear hereditary creep theory as the most accurate but time-consuming, and keeping its positive properties, reduce its equation of state to the equation of ageless concrete with its simplicity in application. In addition, the equation of state of concrete is solved in elementary functions and closed form in practically important cases.The overwhelming majority of published scientific data on the behavior of creep curves in the area of reliable performance of reinforced concrete structures indicates smoothness and continuity of the curves. Considering that, the data obtained in short-term tests can be extended to the whole time interval, thus providing possibility for express analyses of the strain properties of concrete.The study estimated the reversibility of creep strain and found out dissipativity of elastic strain. The authors established a nonlinear relation between strain and constant stress and introduced an approach to developing a nonlinear dissipative theory of concrete compressive strength in the absence of regulatory documents for loading modes, using instead the standard classification of loads.Conclusions. The considered experimental data were recognized to provide qualitative information due to their apparent deficit. In order to obtain quantitative evaluation, the experiments should be reproduced a sufficient number of times.

A novel time-dependent damage constitutive model for hard rock materials

The mechanical behavior of deep hard rocks plays a crucial role in the long-term safety and stability of engineering structures. This work focuses on studying the instantaneous and time-dependent fracture propagation of hard rock materials from a theoretical perspective. A new unified constitutive model, based on a modified Mohr–Coulomb (M-C) criterion, is proposed to accurately represent the short and long-term mechanical properties of hard rocks. To capture the strain hardening and strain softening behaviors, damage is utilized as an internal mechanism-driven variable, controlling the expansion and contraction of the plastic yield surface. Additionally, a combination of time-dependent damage law and viscoplastic theory is employed to account for nonlinear creep deformation characteristics. By considering the time-dependent effects, the model can be applied to both instantaneous loading and creep conditions. The general algorithm format is derived in detail, and an explicit integration algorithm is utilized to update the time-dependent damage evolution. Finally, the proposed model is validated by comparing its predictions with the short and long-term mechanical responses of Beishan granite and Rumei dacite. This comprehensive constitutive model improves our understanding of continuum damage mechanics and provides a scientific basis for analyzing and evaluating the long-term safety and stability of deep hard rock engineering projects.

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.

Cooling Methods under High-Temperature Effects on Creep Properties and Nonlinear Creep Damage Model of Quartz Sandstone

Cooling Methods under High-Temperature Effects on Creep Properties and Nonlinear Creep Damage Model of Quartz Sandstone

Thermal–viscoelastic analysis of polymethyl methacrylate using a fractional differential viscoelastic model

Vacuum forming is used to manufacture large molded parts. As forming conditions have a significant effect on the dimensional accuracy, these should be determined accordingly. In this study, a geometric nonlinear creep analysis of polymethyl methacrylate (PMMA), which is a common thermoplastic resin, was carried out at the target temperature of 393.15[Formula: see text]K and target strain of approximately 50% for vacuum forming. The proposed fractional differential viscoelastic model was extended to a three-element model, consisting of a single hyperelastic spring and two fractional differential (FD) models. It was further extended by time–temperature superposition (TTS) for thermo-viscoelastic analysis. The model determined all material constants by measuring the temperature/frequency sweeps at small strain amplitudes of 0.01% using dynamic mechanical analysis (DMA). Numerical analysis confirmed the validity of the proposed method through creep and stress-relaxation tests by DMA at the target temperature/strain. The results demonstrated that the finite element analysis constructed using the proposed method could predict the mechanical properties during vacuum-forming-oriented creep tests. These results are expected to provide important insights into the complex mechanical behavior of PMMA, which varies with the temperature and strain rate.

Creep Instability Mechanism and Control Technology of Soft Coal Roadways Based on Fracture Evolution Law

To address the challenging issues of large deformation, control difficulties, and susceptibility to failure in the support structure of soft coal roadways, this study utilizes the CVISC block creep model in UDEC software. The model incorporates Coulomb slip without cohesive contact to simulate the characteristics of soft coal, such as its loose, fragile, and small-block nature. Additionally, a soft coal nonlinear discrete element creep model is developed to investigate the creep characteristics of soft coal under triaxial compression, with the aim of revealing the underlying creep destabilization mechanism in soft coal tunnels. Based on the research findings, a primary, strong active support technology is proposed. This approach involves the use of high-preload, high-strength anchor rods and anchor cables, as well as the implementation of steel mesh and plastic woven mesh to enhance surface protection. The study highlights that: (1) The shear cracks inside the coal body of the soft coal specimen transform into tensile cracks under external force, leading to an increase in the number of tensile cracks. This is an important symbol of accelerated creep in soft coal. Improvement in peripheral pressure helps inhibit the generation of tensile cracks inside the specimen. (2) The rapid development of creep and inter-particle tensile fissures within the coal body particles themselves, along with the change in stress state after the excavation of the roadway, are the main reasons for the overall creep damage of the roadway. (3) The support force in the early stage of shed cable support is small, which cannot inhibit the accelerated development of tensile fissures. This leads to continuous deformation of the roadway, resulting in the failure of the support structure in the later stage and aggravated roadway damage. (4) The new support technology helps control surface deformation by enhancing the strength of the roadway protection surface. This suppresses the development speed and number of tensile fissures during roadway deformation, improves the starting strength of the roadway for accelerated creep, and enables effective control of the overall deformation of the soft coal roadway. Thus, the effectiveness of roadway support is remarkable.

Creep of Concrete in Shell Structures: Nonlinear Theory.

The creep of concrete is one of the main problems threatening concrete structural development and the stability and safety of structures. However, the nonlinear theory is the key to solving the problem of taking into account the physical and mechanical properties of concrete creep in shell structures. To create such a theory, the original shell is replaced by a continuous equivalent elastic shell. To determine the stress-strain state of the structure, the equations of nonlinear creep and crack growth are derived, and a deformation model of the section is created. The behavior of the structure at all stages of the life cycle is investigated by solving the solving systems of differential equations of equilibrium, motion, and perturbation of the equivalent shell. The values of the ratios of dependence of long-term and short-term critical loads on deformations, forces, cracks, etc., are given. The accuracy of the solution of the developed nonlinear theory is compared with the linear theory of concrete creep as well as experimental data. The results show that, according to the linear theory, for the values for the short term and long term, up to 56% and up to 39% of critical loads are overestimated, respectively. The creep process in practical engineering can be effectively controlled by the results of the proposed theory.

Linear and nonlinear creep of UHPC under compression: Experiments, modeling, and verification

Linear and nonlinear creep of UHPC under compression: Experiments, modeling, and verification

A numerical and experimental meso-mechanical approach for the prediction of creep of concrete

A two-step meso-scale approach is proposed to predict the creep of concrete. The approach requires the creep of cement paste as input, combined with meso-scale analysis of digital images of mortar and concrete that are obtained from X-ray microCT scanning. For the generation of input data and validation of the model, a comprehensive series of creep tests are carried out on cement paste, mortar and concrete cylinders for a period of 6 months. The model uses a robust and automatic quadtree decomposition algorithm to convert digital images into meshes, which are then solved using the scaled boundary finite element method based on a continuum approach. The proposed model is separately validated on the mortar and the concrete scale respectively. In the first step, knowing the creep response of cement paste from the tests, the creep of mortar is simulated by considering it as a two-phase composite comprising of viscoelastic cement paste and elastic fine aggregates. Validation of the predicted response is obtained through comparison with the measured creep response of mortar. A similar procedure is then applied for concrete which is treated as a two-phase composite of viscoelastic mortar and elastic coarse aggregates. Finally, by accounting for damage of the mortar phase, it is demonstrated that the nonlinear creep of concrete observed at high stress levels can be attributed to material damage developed at the meso-scale.

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.

STABILITY OF RODS WITH INITIAL IMPERFECTIONS IN THE FORM OF ECCENTRICITY OF LOAD APPLICATION UNDER LINEAR AND NON-LINEAR CREEP CONDITIONS

Stability of a compressed rod having initial imperfections in the form of eccentricity of applied load under conditions of linear and nonlinear creep is considered. It is noted that all real elements have some initial imperfections in the form of technological deflections, eccentricities of applied loads, etc., so they begin to bulge from the very beginning of loading. Another important factor in stability theory is the consideration of material creep. In this regard, the loading process is divided into two phases: the instantaneous loading process and the creep phase under constant external load. Moreover, creep can be time-limited or unrestricted. In the paper formulas for determination of critical forces of stability loss of the rod having initial imperfections, under short-term and long-term action of load are obtained. The equation allowing to determine time of the first crack appearance is derived. Derived are equations the roots of which are loads at action of which the first cracks appear at initial moment of time and at arbitrarily long period of load action. Analysis of acting force determining the character of rod deformation is executed. From the constructed stability equation it is possible to determine the critical force corresponding to the critical length of the section with cracks. For similar problems in nonlinear formulation formulas for determining critical force and critical displacement corresponding to maximum load are obtained. For the case of long duration load the equation which establishes relationship between load and displacement is obtained. Equation for determination of critical force under prolonged action of load has been derived. It has been established that critical displacement is the same under short- and continuous action of load. It is shown that at any intermediate moment critical displacement can be achieved under load lying in certain interval. Keywords: stability, rod, initial imperfection, eccentricity, linear creep, non-linear creep, critical force, crack, critical displacement.