Isochronous Stress-strain Curves Research Articles

Long-term mechanical properties of sludge-cured lightweight soil under the superimposed effects of drying-wetting and freezing-thawing

ABSTRACT Sludge-cured lightweight soils have unique advantages in roadbed treatment due to their properties such as low density and high strength. Its long-term mechanical law based on the superposition of drying-wetting and freezing-thawing (D-W-F-T) is studied through creep experiment. The test results show that: with the increase of the number of D-W-F-T, the deformation of the soil gradually increases, and the deformation tends to be stable when it reaches a certain number of times; the stress-strain isochronous curves are obviously nonlinear in general; The long-term strength increases with the increase of density and confining pressure, and decreases with the increase of the number of D-W-F-T; by comparing the isochronous stress-strain curve cluster method and the steady state creep rate vs. The comparative analysis suggests that the steady state creep rate versus stress level curve method be used to determine the long term strength.

Study on creep characteristics and the isochronous stress–strain curve of Ni-Cr-Mo superalloy

ABSTRACT C276 superalloy is considered as a potential structural material for advanced nuclear reactor with good mechanical properties and corrosion resistance. High-temperature creep behaviour of C276 alloy was investigated in the temperature range of 650°C–700°C and at stresses of 140–430 MPa. A linear relationship was fitted between stress and minimum creep rate in the logarithmic coordinate system. The rupture time is analysed for life prediction in terms of isotherm extrapolation method, Monkman–Grant relation, and Larson–Miller parameter method, respectively. The isochronous stress–strain curves as a means of representing stress–strain–time relations under creep conditions were established by the parameter method. The fracture surface morphology of ruptured specimens was characterised by a scanning electron microscope to elucidate the failure mechanism.

Study on Creep Characteristics and Long-Term Strength of Mud-Calcareous Conglomerates in the Three Gorges Reservoir Area

The study of the time-dependent properties of engineering rock masses is a frontier topic in rock mechanics. In this study, creep tests and stress relaxation tests were conducted on mud-calcareous conglomerates from the Three Gorges Reservoir Area, and the long-term strength values of the conglomerate specimens were determined via different methods based on the test curves. By comparing these mainstream long-term strength determination methods, it was found that each of these methods have their own drawbacks. For example, the transition creep method requires a high accuracy of the test curve and only obtains an approximate strength interval rather than an accurate value. The long-term strength values determined by the isochronous stress–strain curve method are strongly influenced by subjective factors, among other things. Therefore, this paper proposes a new method for determining long-term strength, called the steady-state creep rate method, based on stress intervals. By comparison, the long-term strength values determined via this method are in good agreement with the transition creep method, the volume expansion method, and the stress relaxation method.

Creep behavior and long-term strength characteristics of pre-peak damaged sandstone under conventional triaxial compression

A series of creep tests were carried out on sandstone specimens with different pre-peak instantaneous damage characteristics under different confining pressures. The results revealed that the creep stress was the key factor affecting the occurrence of the three stages of creep, and the steady-state creep rate increased exponentially with increasing creep stress. Under the same confining pressure, the larger the instantaneous damage of the rock specimen was, the more quickly creep failure occurred and the lower the creep failure stress was. For the pre-peak damaged rock specimens, the strain threshold for accelerating creep was the same for a given confining pressure. The strain threshold increased with increasing confining pressure. In addition, the long-term strength was determined using the isochronous stress–strain curve and the variation in the creep contribution factor. The results revealed that the long-term strength decreased gradually with increasing pre-peak instantaneous damage under lower confining pressures. However, the instantaneous damage had little effect on the long-term strength under higher confining pressures. Finally, the macro–micro-failure modes of the sandstone were analyzed according to the fracture morphology observed via scanning electron microscopy. It was found that the macroscale creep failure patterns of the sandstone specimens could be divided into a shear-dominated failure mode under high confining pressures and a mixed shear-tensile failure mode under low confining pressures. At the microscale, as the confining pressure increased, the micro-fracture mode of the sandstone changed gradually from a single brittle fracture to a mixed brittle and ductile fracture mode.

Non-Conservatism of ASME BPVC Section III Division 5 Isochronous Stress–Strain Curves for 316H Stainless Steel at Low Stresses

Abstract Future Gen IV high-temperature reactors are expected to operate above 450 °C where creep effects are significant in safety-related structures, e.g., reactor vessels. The ASME Boiler and Pressure Vessel Code (BPVC) Section III Division 5 provides the rules and methodologies for design of such high-temperature components. Of high relevance to the designer are the isochronous stress–strain curves (ISSCs) part of the rules for deformation limits in the code. The ISSCs are an important method to estimate accumulated inelastic strains at a given stress and duration at elevated temperatures. In this study, the ISSCs for 316H stainless steel in the current edition of the ASME BPVC Section III Division 5 have been reevaluated between 593 °C and 750 °C by adopting a physics-informed minimum creep rate model to reconstruct them. It is demonstrated that the current ASME Section III Division 5 minimum creep rate model underpredicts creep rates compared to experimental data at low stresses (e.g., 650 °C, <40 MPa). By employing a physics-informed minimum creep rate model which captures both diffusive- and dislocation glide/climb-controlled creep regimes, this deficiency is addressed. The ASME ISSCs for 316H stainless steel are then reconstructed by adopting this modified minimum creep rate model. It was found that the ASME ISSCs could underestimate total accumulated strains at ∼σ/σy <0.65 for durations t >1000 h by >10 times which could give rise to non-conservatism in inelastic strain. Experimental data at various temperatures confirm the findings. Potential approaches to address this non-conservatism in inelastic strain and the implications to design are discussed.

Creep Properties of Expansive Soils under Triaxial Drained Conditions and its Nonlinear Constitutive Model

The creep behaviors of expansive soils play an important role in landslide prediction and long-term stability analysis. In this paper, triaxial drained compression creep tests of expansive soils were conducted on the improved stress-controlled triaxial apparatus. The test results show that only transient deformation and attenuation creep occur with low deviator stress, and the increment of axial strain increases exponentially with deviator stress increasing; while deviator stress reaches a certain value, attenuation creep, steady creep and accelerated creep all occur in a creep curve. Meanwhile, the volumetric strain presents the shear shrinkage characteristic at the initial stage of loading, and the shear shrinkage is small. With the extension of loading time, the volumetric strain gradually varies from shear contraction to dilatancy. When entering the accelerated creep stage, the development rate of volumetric strain increases sharply. Besides, isochronous stress-strain curves of expansive soils indicate that their creep process possesses nonlinear characteristics, and the nonlinear degree is related to creep time and stress level. Imitating the empirical formula of cyclic cumulative deformation of clay, a new nonlinear creep model is presented, which may well describe the creep property of expansive soils. Furthermore, critical failure stress could be obtained based on the proposed creep model. The ratio of the critical failure stress to conventional shear failure stress ranges from 70% to 80%, with average of 75.56%, therefore, critical failure stress may be estimated by conventional triaxial tests with the margin of error 5.5% within.

An Experimental Study on the Creep Characteristics of Sandstone in the Interval of Different Critical Stresses

Creep tests on brittle sandstone specimens were performed to investigate the time-dependent characteristics in the interval of different critical stresses. The results showed that failure will not occur when the loaded stress σ1 is less than the critical stress of dilation σcd, while all specimens were destroyed when σ1 is larger than σcd. In addition, the value of σcd was very close to the long-term strength obtained by the method of the isochronous stress-strain curve. Therefore, σcd can be regarded as the long-term strength of the sandstone specimens. When σ1 is larger than σcd, the time required for the failure of specimen tf decreases with the increase of σ1; the creep rate dε/dt increases with time t, and the specimen will be destroyed when it reaches a maximum value (dε/dt)max. Both relationships tf and σ1 and (dε/dt)max and σ1 can be described by the exponential function. Then, a nonlinear damage creep model considering the deformation damage and strength damage in the interval of different critical stresses was established, which can describe the whole creep process and predict the failure time of sandstone specimens.

A Minimum Creep Rate for 2-1/4Cr-1Mo Steel Consistent With the ASME Section III, Division 5 Rules

Abstract This technical note describes a minimum creep rate model for 2-1/4Cr-1Mo steel that is consistent with the current creep strain equation embedded in the ASME Boiler & Pressure Vessel Code Section III, Division 5, Subsection HB, Subpart B isochronous stress–strain curves. Minimum creep rate models for all the Section III, Division 5 Class A materials are required for the development of improved high temperature design methods. Of all the Class A materials, only 2-1/4Cr-1Mo does not have a readily identifying minimum creep rate term in the current isochronous stress–strain curve model.

Viscoelastic-plastic damage creep model for salt rock based on fractional derivative theory

Salt rock is widely used as an excellent material for energy storage owing to its low permeability, high safety, and stable mechanical properties. In this study, salt rock was subjected to a gradual loading creep test through the conventional uniaxial compression test. The loading time of each stage was approximately 14 days, and the total creep time exceeded five months. The steady-state creep rate of salt rock under different stresses and the corresponding creep strain law were positively correlated with the increase in stress and time. In addition, the long-term strength of the salt rock, determined via the isochronous stress–strain curve inflection point method, was 12 MPa. Furthermore, the viscoelastic–plastic damage-creep model of salt rock was established based on the theory of fractional derivatives. This proposed model was compared with the Nishihara model, and a sensitivity analysis of the parameters was performed based on the results of the nonlinear fitting of the fractional derivative. The rationality of the model was verified based on the results, especially for the accelerated creep phase. Moreover, the constitutive relationship of the model was straightforward and easy to apply. The proposed model provides a theoretical basis for future creep laws based on experimental data. The results reflected the creep law of salt rock to a certain extent and are expected to serve as a reference to studies on the long-term stability of deep salt rock.

Discussion on Determination Method of Long-Term Strength of Rock Salt

Due to the extremely low permeability and the excellent creep behavior, rock salt is the optimal surrounding rock of underground energy storage. The long-term safe operation of the rock salt energy storage is closely related to the creep behavior and long-term strength of rock salt, but few researches focus on the long-term strength of rock salt. In order to more accurately predict the long-term strength of rock salt, the isochronous stress–strain curve method and the volume expansion method for determining the long-term strength were analyzed and discussed based on axial compression tests and axial creep tests. The results show that the isochronous stress–strain curve method is intuitive but will greatly increase the test cost and test time to obtain a satisfactory result. The volume expansion method is simple, but the long-term strength obtained according to the inflection point of volumetric strain is much greater than the actual long-term strength of rock salt. Therefore, a new method applicable to rock salt was proposed based on the evolution of damage in rock salt in this paper, which takes the corresponding stress value at the damage initiation point as the long-term strength. The long-term strength determined by this method is consistent with that by the isochronous stress–strain curve method. The method is more economical and convenient and aims to provide a reference for the long-term stability study of underground salt caverns.

Moisture content effect on the creep behavior of loess for the catastrophic Baqiao landslide

Understanding the creeping behavior of loess is of great importance as large-scale loess landslides are closely related with creep behavior. At present, it is still challenging to predict and estimate the long-term stability of such landslides. This is in a large degree due to the poor understanding of moisture control on creep behavior of loess. The purpose of this study is to decipher the loess creep behavior under various moisture contents (MCs) using loess specimens obtained from Baqiao landslide, Xi’an of China, using multi-loading triaxial creep tests under different MCs of 9%, 12%, 15%, 18% and 21%. Based on the laboratory test results, a series of relationships between the creep rate at the steady-state creep stage and the initial strain and initial shear modulus are revealed. Meanwhile, a method for obtaining the long-term strength of loess specimens, namely, the Steady-state Creep Rate Slope Method (SCRSM), is proposed. SCRSM resolves the issue in several conventional methods such as the Isochronous Stress-Strain Curve Method, the Tangent Method of Steady Creep Rate when MCs are of concern. Such an improvement is primarily due to a better way of finding the inflection point of the steady-state rate. It is found that SCRSM is robust and accurate to determine the long-term strength of loess specimens. Furthermore, we propose a modified Burgers model with a newly introduced nonlinear parameter n to overcome deficiencies of conventional creep models. This modified Burgers model is flexible to fit the creep test curves of loess, and can describe the curves at the accelerated creep stage more accurately. Lastly, the main factors triggering the Baqiao landslide is analyzed considering stratum lithology, rainfall and excavation. In general, this study provides a basis for understanding the evolutional process of loess landslides as well as guidelines for prevention, controlling and prediction of loess landslides.

Creep properties and damage constitutive model of salt rock under uniaxial compression

To study the creep property of salt rock, uniaxial compression creep tests on salt rock specimens were carried out. The test results indicate that there is no steady creep of the salt rock used in this test in a strict sense. Even in the steady creep stage, the creep rate of salt rock changes continuously over time, but with a relatively smaller change range. When the axial stress does not exceed 9.5 MPa, the isochronous stress–strain curve of salt rock is approximately straight. While the axial stress exceeds 9.5 MPa, the isochronous stress–strain curve deflects to the strain axis, and the larger the axial stress, the more obvious the deflection. Thus, the long-term strength of the salt rock used in this test can be determined as 9.5 MPa. A mathematical expression for predicting the creep failure time of rock is proposed on the basis of assuming the change rule of rock strength over time conforms to the Usher function. Then starting from the variation in deformation modulus with respect to time in the creep process of salt rock, the elastic modulus of the damaged rock material is characterized by the deformation modulus, and the creep damage evolution equation of rock is established. Combined with the continuous damage mechanics theory, a new creep damage constitutive model for rock is proposed. The rationality of the model is verified using the uniaxial compression creep test results of salt rock. The results show that the new model can not only describe the attenuation and the steady creep of salt rock under low stress level, but also reflect the whole creep failure process under high stress level. The predicted curves under different axial stresses are all in good agreement with the test data.

Evaluation of Simplified Creep Design Methods Based on the Case Analysis of Tee Joint at Elevated Temperature

Based on a tee joint, the simplified creep design methods of ASME code, elastic-perfectly plastic (EPP) analysis of Code Case N-861 (CC N-861) and the inelastic analysis by isochronous stress strain (ISS) curve, were evaluated and compared to nonlinear finite element creep analysis (FECA). Results indicate that both EPP and FECA lead to a greater inelastic strain than ISS curve-based results. By contrast, the ISS-based analysis induces a smaller usage fraction (damage) than FECA due to the underestimated inelastic strain. In addition, the smallest usage fraction (damage) is obtained by using EPP analysis of CC N-861 in which case the remarkable bending strain is involved.

Micromechanical investigation of creep-recovery behavior of carbon nanotube-reinforced polymer nanocomposites

Creep-recovery behavior of polymer nanocomposites reinforced by carbon nanotubes (CNTs) is investigated using a 3-dimensional unit cell-based micromechanical model. The representative volume element (RVE) of the model consists of three phases including aligned CNTs, polymer matrix and CNT/polymer interphase formed due to non-bonded van der Waals interaction. The CNTs and polymer are assumed to be as transversely isotropic elastic and isotropic nonlinear viscoelastic materials, respectively. The effects of volume fraction and diameter of the CNTs, loading level and interphase including the materials behavior and size on the creep-recovery strain of the nanocomposite are examined. The predicted elastic and creep-recovery responses for pure polymer and CNT-reinforced polymer nanocomposite are found to be in good agreement with available experiment. Also, the isochronous stress–strain curves during the creep cycle for the nanocomposite under transverse and axial loadings are presented. The results clearly demonstrate that the overall transverse creep strain is dependent on the polymer nonlinear viscoelastic behavior and interphase material, as the applied loading increases. The results also reveal that the overall behavior of the nanocomposite is similar to the elastic response in the axial direction. Moreover, the isochronous stress–strain curves are extracted for biaxial and triaxial loading.

Experimental study on creep deformation and long-term strength of unloading-fractured marble

In order to take account of the unloading fractures in rocks due to the excavation, unloading-fractured marble specimens were obtained by the triaxial unloading tests. Then, creep tests on the unloading-fractured marble specimens under different stress levels and confining pressures were performed. Based on the creep tests, the creep deformation characteristics were studied and the results show that the creep curves exhibit the three stages of the idealised creep curve. Special attentions were paid on that the creep deformation and creep rate in lateral direction are far greater than that in axial direction and the lateral creep reaches the accelerated stage earlier than the axial creep. There are stress thresholds correspond to the inflection point of stress–strain relationship in lateral and axial directions, respectively, and the lateral threshold is less than the axial one. The creep failure is mainly caused by the strong expansion in lateral direction. Moreover, both the creep rate and deformation have positive relationships with the axial stress but decrease as confining pressure increases. The failure strain increases with increasing confining pressure. Then, the long-term strengths determined by the axial and lateral isochronous stress–strain curves, respectively, are discussed. Through the comparative analysis, the lateral creep reflects the creep characteristics of unloading-fractured marble more clearly and the long-term strength determined by the lateral isochronous stress–strain curves is safer for engineering applications.

Ultimate creep load and safety assessment of P91 steel pipe with local wall thinning at high temperature

Safety assessment of pipe with local wall thinning (LWT) at high temperature is highly important in power and nuclear engineering. Based on strain criterion and isochronous stress–strain curves at high temperature, this paper studied the ultimate creep load of pipe with LWT under creep condition by orthogonal experimental design and finite element numerical simulation. Firstly, the influence of LWT geometries was analyzed, which indicated that relative defect depth was the most significant factor to ultimate creep load. Secondly, the ultimate creep load formulas were regressed based on the ultimate creep loads of pipe with LWT at different creep times. And safety assessment curves for the pipe with LWT at high temperature by different strain criteria were proposed. Finally, the engineering method of allowable load of pipe with LWT by different strain criteria was constructed. The research results try to improve the safety assessment and structure integrity analysis of pipe with LWT at high temperature.

Experimental Researches on Long-Term Strength of Granite Gneiss

It is important to confirm the long-term strength of rock materials for the purpose of evaluating the long-term stability of rock engineering. In this study, a series of triaxial creep tests were conducted on granite gneiss under different pore pressures. Based on the test data, we proposed two new quantitative methods, tangent method and intersection method, to confirm the long-term strength of rock. Meanwhile, the isochronous stress-strain curve method was adopted to make sure of the accuracy and operability of the two new methods. It is concluded that the new methods are suitable for the study of the long-term strength of rock. The effect of pore pressure on the long-term strength of rock in triaxial creep tests is also discussed.

A generalized hysteresis energy method for fatigue and creep-fatigue life prediction of 316L(N)

Abstract Creep-fatigue interaction is extremely important for the life prediction of structural components subjected to high temperature conditions. The widely used life prediction methods such as time fraction rule and ductility exhaustion method are found to be insufficient in long time regimes and cannot give a clear physical explanation for the material failure. In this paper, a generalized life prediction model is proposed on the basis of the hysteresis energy and law of energy conservation. The influence of hold time on the cyclic stress–strain behavior is described based on isochronous stress–strain curves and stress relaxation during hold time is evaluated with the time hardening rule. An analytical approach is set up to calculate the hysteresis energy for the creep-fatigue tests. The generalized hysteresis energy is used as a model parameter to predict the fatigue and creep-fatigue life of 316L(N) and it is found to have a power law relationship with the number of cycles to failure. The fatigue and creep-fatigue life predicted with the new energy-based method shows a good correlation with the experimental results from different researchers.

Creep properties of cement and asphalt mortar

In order to study the long-term deformation properties of cement and asphalt mortar (CA mortar), the creep properties of CA mortar on different load levels were studied by independently designed creep testing apparatus. The experimental results show that the creep deformation of CA mortar can be divided into the attenuation creep stage in which the deformation rate decreases gradually and the steady creep stage in which the creep rate is relatively stable. The greater the load is, the bigger the deformation rate and the creep deformation in every stage are. The specific creep of type I CA mortar is bigger than that of type II CA mortar. The long-term strength of two kinds of CA mortar is 0.4σp which is calculated by the method of isochronous stress–strain curves. A creep model of CA mortar based on the thermodynamic theory is established, and the correlation coefficients between fitting results of model and experimental results are all greater than 0.98. The study results can improve the structural design theory of ballastless slab track.

Improved methodology for determining tensile elastic and plastic strain components of alloy 617

This paper presents an improved methodology for calculating tensile elastic and plastic strain components in total creep strain, which are needed in the generation of the isochronous stress-strain curves (ISSC). The procedures for the RCC-MR code and Blackburn’s methods to determine the total strain are analyzed in detail, and a new method is proposed to determine the tensile elastic and plastic strain components. To practically obtain the tensile elastic and plastic strain components for Alloy 617, high-temperature tensile tests were conducted at 800, 850, 900, and 950°C. Using the tested data, three methods of the RCC-MR code, Blackburn, and the newly proposed method were applied and compared. In the elastic regime, the three methods were identical in the tensile curves, but in the plastic regime, Blackburn’s method was higher in the stress-strain curves than the RCC-MR code. The difference gap for the two methods was larger with an increase in the plastic strain. In addition, the proposed new method revealed almost midway values for the two methods. It was suggested that the proposed method is useful to determine tensile and plastic strain components.