Creep Law Research Articles

Numerical prediction of the creep behaviour of an embankment built on soft soils subjected to preloading

This work analyses the ability of the Singh-Mitchell and Taylor creep laws associated with a Modified Cam Clay model to predict the creep behaviour of a soft soil subjected to preloading. Firstly, the creep laws and constitutive model are validated by the results of CIU triaxial tests, creep oedometer tests and multi-stage triaxial tests, carried out in order to reproduce the effect of the preloading. After that, the creep laws/model are used to predict the long-term behaviour of an embankment built on soft soils subjected to preloading. The numerical predictions incorporating the creep phenomenon show a constant rate of increase in the settlement and the horizontal displacements, with a constant relationship between the settlement and the horizontal displacements.

CREEP RESISTANCE OF FERRITIC-MARTENSITIC STEEL 16Cr12MoWSiVNbB (EP-823)

Base characteristics of ferritic-martensitic heat resisting steels with 12 % of chrome are parameters of their strength and creep resistance at temperatures of 600 – 750 °С. Steel 16Cr12MoWSiVNbB (EP-823) is considered as the basic material for manufacturing environments fuel rods (TVEL) of a developed reactor with natural safety of BRESTtype. In the literature, there are data about its mechanical characteristics for tensile tests in a range of temperatures of 20 – 750 °С and the limited characteristics of rupture strength. Data on its creep velocity is absent. Laws of creep of steel EP-823 were investigated on metal of three heats with weight of 3 kg. The compression tests at air were applied for cylindrical samples of 5 ÷ 6 mmat temperatures of 600 – 760 °С and stresses of 70 – 310 MPa. The base of compression tests did not exceed 11 hours. The structure after quenching and tempering consisted of tempered martensite and 6 – 12 vol. % of delta-ferrite, the grain size was less 20 μm. It is shown, that the description of creep tests results in double logarithmic (log (σ) – log (έ)) coordinates provides the best concurrence of results of approximation and experiment, than in half-logarithmic (σ – log (έ)). The analysis of parametrical dependences on Hollomon’s PS = (T/1000)[CS – log (έ) and to Larsen-Miller’s PE = (T/1000)[СE – log (σ)] has allowed to find the equations for creep velocity for the set pressure level of 100 – 220 MPa in the form of log (έ) = –19,355 + 9,17 (T/1000) log (σ) and ultimate strength of creep under the set admissions for creep velocity of 0,01 – 1 %/hour in the form of log (σ) = 4,304 – – 0,109 (T/1000) [20 – log (έ)]. Calculations of ultimate strength of creep and creep velocity on pair models and models of Hollomon (Larsen-Miller) give close results, but the preference should be given the second ones as these models consider all three varied factors. Data of control tests under the scheme of a tensile in the same conditions are cited. It is shown, that between results of tests on compression and on tensile at definition of durability characteristics, there is the linear dependence expressed by the equation σ0.2 at compression = 1.3σ0.2 at tensile. At the analysis of creep it has been established, that creep velocity for steel of one grade (09Cr12W3NbB) and for one heat at different type of loading (tensile or compression) have similar values while creep velocities for steel of one grade (EP-823), but of different heats even at one type of loading – compression, can differ substantially.

Approaches of concrete creep using mesomechanics: numerical simulation and predictive model

Simulation and prediction of fully-aggregated concrete creep is a fairly crucial but complex task in civil engineering and material science due to the heterogeneity of concrete with mixture compositions. To investigate the contribution of each composition to the concrete creep and the relationship between the basic creep laws of concrete and mortar, a numerical concrete (NC) model on meso-scale is established with a 3D finite element algorithm taking into account aggregates, mortar matrix and the interfacial transition zone (ITZ). This NC model can emulate the complex mesostructure of concrete and calculate its creep by recurrence formulas without recording the history of stress in terms of the elastic aging creep theory. After being validated by existing laboratory experimental data, the proposed model is further employed to study the influential factors such as the content and elastic modulus of aggregate as well as the action of aggregates and mortar matrix via ITZ. Based on the numerical simulations and theoretical analysis, a new predictive model of concrete creep is finally proposed which is able to well interpret the dilution and restraint effects of aggregate and the interaction among compositions.

Effect of Structural and Phase State on the Creep of an Ultrafine-Grained Ti–Al–V–Mo Titanium Alloy

The effect of the phase composition on the regularities of creep of the ultrafine-grained Ti–Al–V–Mo titanium alloy at the temperature of 723 K and in the range of strain rates from 10–7 to 10–5 s–1 has been studied in this work. It has been found that the formation of the nonequilibrium phase composition in the ultrafine-grained alloy leads to a violation of the power law of creep. It has been shown that this violation is associated with the development of the β → α phase transformation during creep and with the redistribution of alloying elements. The physical causes of a decrease in the effective energy of activation of the creep of the alloy with ultrafine-grained structure and nonequilibrium phase composition have been discussed.

In search of an ice history that is consistent with composite rheology in Glacial Isostatic Adjustment modelling

Global reconstructions of the Earth's Quaternary ice sheet history such as ICE-6G assume that mantle rheology is linear and Earth properties are laterally homogeneous. However, these assumptions are unrealistic because high temperature/pressure creep experiments show that both linear and non-linear creep laws operate simultaneously in the mantle. Also surface geology and seismic tomography show that mantle properties vary laterally. This study uses the Coupled Laplace-Finite Element Method to find an ice model that is consistent with an Earth model with composite rheology where both linear and non-linear creep laws operate simultaneously in the mantle, and the effective viscosity is laterally heterogeneous.We use the ICE-6G ice model as initial load on a composite rheology Earth model and iteratively improve both the ice and Earth model parameters until they fit observations of Glacial Isostatic Adjustment or GIA (relative sea level and land uplift rate) well simultaneously. We thereby focus on North America and northern Europe. Our best combination model, called ICE-C(M_C), also fits gravity rate-of-change data in both areas. This finding removes the obstacle in using composite rheology in GIA studies since previous work found it impossible for composite rheology to fit both relative sea level and land uplift rate data simultaneously. It shows that composite rheology is clearly an alternative to linear rheology in future GIA studies.The ICE-C model is at the last glacial maximum (LGM) position from 26 ka BP (thousand years before present) to 19 kaBP, which implies that composite rheology also supports the timing of LGM proposed by Clark et al. (2009). The model is found to be significantly thicker in the center of rebound in Fennoscandia than ICE-6G from the LGM to about 8 kaBP, but significantly thinner around the Fennoscandian coastline from LGM to about 12 kaBP. These changes in the lower boundary conditions in northern Europe may affect the reconstruction of past climate there. Regional differences in ice thickness between ICE-C and ICE-6G are also found in Laurentia. During LGM there are negligible differences in total ice volume between ICE-C and ICE-6G, thus it remains questionable if a composite rheology may help in solving the missing ice problem. ICE-C is also consistent with meltwater pulses 1A and 1B. Mantle viscosities and creep parameters of Earth model M_C are consistent with previous findings from GIA modeling and microphysics experiments.

Creep damage characterization of UNS N10003 alloy based on a numerical simulation using the Norton creep law and Kachanov–Rabotnov creep damage model

The calculation of inelastic creep damage is important for the structural integrity evaluation of the elevated temperature structure in a thorium molten salt reactor (TMSR). However, a creep damage theory model and numerical simulation method have not been proposed for the key materials (UNS N10003 alloy) in the TMSR. In this study, creep damage characterization of UNS N10003 alloy is investigated using the Norton creep law and Kachanov–Rabotnov (K–R) creep damage model. First, the creep experimental data of the UNS N10003 alloy at 650 °C were adopted to fit the material constants of the two models. Then, the creep damage behavior of the UNS N10003 alloy was analyzed and discussed under uniaxial and multi-axial stress states. The results indicated that the K–R creep damage model is more suitable for the UNS N10003 alloy than the Norton model. Finally, the numerical simulation method was developed by a user-defined UMAT subroutine and subsequently verified through a finite element analysis (FEA). The FEA results were in agreement with the theoretical solutions. This study provides an effective method for the inelastic creep damage analysis of the elevated temperature structure in the TMSR.

Very Slow Creep Tests on Salt Samples

The objective of this paper is to assess the creep law of natural salt in a small deviatoric stress range. In this range, creep is suspected to be much faster than what is predicted by most constitutive laws used in the cavern and mining industries. Five 2-year, multistage creep tests were performed with creep-testing devices set in a gallery of the Altaussee mine in Austria to take advantage of the very stable temperature and humidity conditions in this salt mine. Each stage was 8-month long. Dead loads were applied, and vertical displacements were measured through gages that had a resolution of 12.5 nm. Loading steps were 0.2, 0.4, and 0.6 MPa, which are much smaller than the loads that are usually applied during creep tests (5–20 MPa). Five salt samples were used: two samples were cored from the Avery Island salt mine in Louisiana, United States; two samples were cored from the Gorleben salt mine in Germany; and one sample was cored from a deep borehole at Hauterives in Drome, France. During these tests, transient creep is relatively long (6–10 months). Measured steady-state strain rates ( $$\dot {\varepsilon }$$ = 10−13–10−12 s−1) are much faster (by 7–8 orders of magnitude) than those extrapolated from relatively high-stress tests (σ = 5–20 MPa). When compared to n = 5 within the high-stress domain for Gorleben and Avery Island salts, a power-law stress exponent within the low-stress domain appears to be close to n = 1. These results suggest that the pressure solution may be the dominant deformation mechanism in the steady-state regime reached by the tested samples and will have important consequences for the computation of caverns or mines behavior. This project was funded by the Solution-Mining Research Institute.

On the Development of Creep Laws for Rubber in the Parallel Rheological Framework

ABSTRACT It is widely known that filler-reinforced rubber material in tires shows a very complicated material behavior when subjected to cyclic loadings. One of the most interesting effects for rolling tires is the nonlinear rate-dependent behavior, which is implicitly linked to the amplitude dependency of dynamic stiffness (Payne effect) at a given frequency and temperature. This effect, however, cannot be described by a conventional linear viscoelastic constitutive law, e.g., the Prony series model. Several nonlinear viscoelastic material models have been proposed in the last decades. Among others, Lapczyk et al. (Lapczyk, I., Hurtado, J. A., and Govindarajan, S. M., “A Parallel Rheological Framework for Modeling Elastomers and Polymers,” 182nd Technical Meeting of the Rubber Division of the American Chemical Society, Cincinnati, Ohio, October 2012) recently proposed a quite general framework for the class of nonlinear viscoelasticity, called parallel rheological framework (PRF), which is followed by Abaqus. The model has an open option for different types of viscoelastic creep laws. In spite of the very attractive nonlinear rate-dependency, the identification of material parameters becomes a very challenging task, especially when a wide frequency and amplitude range is of interest. This contribution points out that the creep law is numerically sound if it can be degenerated to the linear viscoelastic model at a very small strain amplitude, which also significantly simplifies model calibration. More precisely, the ratio between viscoelastic stress and strain rate has to converge to a certain value, i.e., the viscosity in a linear viscoelastic case. The creep laws implemented in Abaqus are discussed in detail here, with a focus on their fitting capability. The conclusion of the investigation consequently gives us a guideline to develop a new creep law in PRF. Here, one creep law from Abaqus that meets the requirements of our guideline has been selected. A fairly good fit of the model is shown by the comparison of the simulated complex modulus in a wide frequency and amplitude range with experimental results.

Effect of Material Property Difference on the Creep Behavior of Bending Specimen

The application of small specimen testing techniques in the evaluation of creep properties of materials in-service arise. In order to acquire the creep data accurately and conveniently, the bending test with small beam specimens has been proposed and validated for the metal materials. Initially, the fact that material behaves different creep rates under tension and compression is ignored for simplification. Thus, the effect of material property difference on the creep behavior of bending specimen is analyzed in the present paper. On the basis of Norton creep law, the deformation behavior of three type’s specimens under tension and compression is theoretically described. Assumed different creep exponents and constants, finite element models of these beam bending specimens are established. The creep response is simulated. Meanwhile, the effect of material property under different stress state is further investigated. The results show that the stress exponent has a significant effect on the creep curves. Usually, the stress exponent can be evaluated based on the displacement rate or strain rate. However, if large discrepancy of creep properties under tension and compression exits, it will yield disparate results for the steady-state stress exponent. It is suggested that the stress exponent determined solely by bending test should be accepted with a certain degree of reliability, especially for the non-metal materials.

Integration schemes with substepping algorithms for creep analysis in geomaterials

SummaryThis paper describes a robust and efficient methodology for predicting displacements, deformations, and stresses in geomaterials that are susceptible to creep. The methodology is based on two integration schemes, which consider substepping algorithms. The first scheme is used for integrating space‐time relations in a global sense, whereas the second scheme is used for integrating stress‐stain relations in a local sense. Different from previous studies, both integration schemes are easy to implement and general in the sense that they can be applied to any type of creep law. Through an in‐house finite element simulator, several numerical tests are performed. They include triaxial and wellbore closure analyses considering soft soils and salt rocks. The results show that the combination of both schemes leads to stable and accurate solutions with reduced computational time.

Olivine intergranular plasticity at mantle pressures and temperatures

The ductile behavior of olivine-rich rocks is critical to constrain thermal convection in the Earth's upper mantle. Classical olivine flow laws for dislocation or diffusion creep fail to explain the fast post-seismic surface displacements observed by GPS, which requires a much weaker lithosphere than predicted by classical laws. Here we compare the plasticity of olivine aggregates deformed experimentally at mantle pressures and temperatures to that of single crystals and demonstrate that, depending on conditions of stress and temperature, strain accommodated through grain-to-grain interactions – here called intergranular strain – can be orders of magnitude larger than intracrystalline strain, which significantly weakens olivine strength. This result, extrapolated along mantle geotherms, suggests that intergranular plasticity could be dominant in most of the upper mantle. Consequently, the strength of olivine-rich aggregates in the upper mantle may be significantly lower than predicted by flow laws based on intracrystalline plasticity models.

The disparate data problem: The calibration of creep laws across test type and stress, temperature, and time scales

Creep data exists in a diaspora. It is not always available in the regime (short, intermediate-, and long-term) or form (minimum-creep-strain-rate, creep deformation, stress-rupture, etc.) of interest. This is particularly true for new alloys where the time-to-qualification can take between 10 and 20 years. For new alloys, extrapolation is performed using short-term creep data. When incorporating the uncertainty of the creep data, the probability distribution in extrapolations expands with time; eventually leading to unrealistic predictions. Standards recommend that extrapolation should not exceed three times the duration of the longest experiment. For example, a creep deformation model calibrated using short-term creep deformation data (e.g. 103 h) is highly unlikely to generate realistic creep deformation predictions near 105 h. This study proposes integrating disparate creep data in the calibration process of continuum damage mechanics based constitutive laws that are capable of simultaneously predicting minimum-creep-strain-rate, stress-rupture, deformation, and damage. It is hypothesized that cross-calibrating CDM constitutive models to any and every form of available creep data (across test type, stress range, and temperature range) will lead to more reliable extrapolations. This is demonstrated by integrating minimum-creep-strain-rate, stress-rupture, and short-/intermediate-term creep deformation data into the calibration process of two CDM constitutive models. Successful extrapolations are performed for minimum-creep-strain-rate, stress-rupture, and creep deformation. In addition, the approach facilitates the development of creep design maps that can be used for material selection and design and to compare the interpolation and extrapolation ability of the existing creep models.

Quartz Flow Law Revisited: The Significance of Pressure Dependence of the Activation Enthalpy

AbstractAn accurate flow law for dislocation creep of quartz aggregates is critical for the understanding of continental rheology, numerical modeling of lithospheric processes, and the interpretation of microstructures of natural quartz‐bearing mylonites. Despite many decades of research, considerable discrepancies still exist among quartz flow laws determined from different experiments. We demonstrate that the key to reconcile these discrepancies is to consider the pressure dependence of the activation enthalpy. From existing high‐quality creep experiments on quartz aggregates, we critically identified test runs having microstructures and stress‐strain curves indicating steady state regimes 2 and 3 dislocation creep and used the data to obtain a set of flow law parameters most consistent among existing experiments. Because estimates of strain rate and stress from natural mylonites are bound with large uncertainties, they cannot be used to construct a flow law better than one determined from well‐controlled creep experiments. A large number of geological studies and modern GPS observations suggest that crustal scale ductile shear zones likely flow at a strain rate range between 10−13 and 10−11 s−1. In this strain rate range, our flow law predicts flow stresses broadly consistent with stress estimates from many natural mylonites based on well‐calibrated piezometers for dynamically recrystallized quartz grains.

Analysis of Steady State Creep Behaviour in Spherical Vessels Made of Composite Material

Abstract This study deals with estimation of steady state creep stresses and strain rates in composite spherical vessels subjected to internal and external pressures. The creep behaviour of the material was described by threshold stress based creep law used for composite materials. The well established von-Mises yield criterion has been also used in this analysis. The effect of reinforcement size and reinforcement volume content on the stresses and creep rates in the spherical vessels was studied. The creep stresses in the spherical pressure vessels do not have significant variation except of effective stress. On the other hand, the tangential, radial as well as effective strain rates in the spherical vessel reduced to significant extent by using lesser diameter particles and increasing the quantity of silicon carbide particles.

Experimental Investigation on the Effects of Ambient Freeze–Thaw Cycling on Creep Mechanical Properties of Sandstone Under Step Loading

In order to study the creep mechanical properties of sandstone subjected to graded loading under the condition of freeze-thaw cycles, 15 freeze-thaw cycles were conducted with four groups of rock samples. The porosity variation of sandstone before and after the freeze-thaw cycles were obtained by using the nuclear magnetic resonance (NMR) technique. The results show that under the action of freeze-thaw cycles, the cohesion between particles inside the rock decreases, the pore structure deteriorates continuously, and the porosity of the rocks increases. During the graded loading creep test, the rock underwent macroscopic failure under low-level loading. Moreover, the fracture morphology showed tensile-shear failure characteristics, which caused obvious decreases in the long-term strength of the rock. The comprehensive analysis of the experimental data to establish the creep model and constitutive equation under the condition of the freeze-thaw cycle, and discuss the relationship between creep model parameters and freeze-thaw factors. The nonlinear creep mode can effectively reflect the graded loading creep law of frozen and thawed sandstone.

Hygrothermomechanical creep and stress redistribution analysis of thick-walled FGM spheres with temperature and moisture dependent material properties and inelastic radius changes

In the present research, effects of the hygrothermal degradation of the material properties on rates of the creep strains and stresses and stress redistributions of thick-walled FGM spheres subjected to internal and external pressures, temperature rises, and diffusions are investigated. In this regard, the non-linear time-dependent governing equations of the sphere are derived based on the theory of elasticity, Prandtl-Reuss flow rule, and Norton's creep law and solved using a special iterative solution scheme. The main novelties of the present research are: (i) analyzing the FGM sphere as it is; without dividing it into isotropic homogeneous sub-spheres, (ii) considering the temperature and moisture dependencies of the elastic modulus of the FGM material, (iii) proposing a more general numerical procedure instead of the traditional successive elastic or Taylor's expansion procedures, and (iv) successively updating of the inner and outer radii of the vessel to consider the resulting inelastic creep deformations. Results reveal that the moisture absorption generally increases the maximum values of both the elastic and creep portions of the stresses, strains, and stress and strain rates. The creep process reduces the circumferential stresses in the interior regions and increases them in the outer regions, but even in presence of moisture absorption, the area beneath the radial distribution curve of the circumferential stress remains unchanged.

On the Densification Kinetics of Metallic Powders Under Hot Uniaxial Pressing

A new model undertaking the densification kinetics of uniaxially pressed metallic powders at constant temperature is proposed. This model is developed according to the power law of creep, and the expression of the ‘net pressure’ derived by the authors in a previous work. This net pressure describes the ‘geometrical hardening’ experienced by the powder mass, during compression. In order to validated the model three different powders were uniaxially pressed, aluminium, tin and lead, being obtained data from hot compaction experiments. The similarity between the model predicted curves and the experimental data is quite acceptable. In addition, the goodness of the model is contrasted with two other theoretical models addressing the same problem. The approach developed can be useful to model hot uniaxial pressing and electrical consolidation processes, which start with loose powders, i.e., not previously cold compacted powders.

Dislocation dynamics modelling of the power-law breakdown in olivine single crystals: Toward a unified creep law for the upper mantle

In the present work, we use a numerical modelling approach based on 2.5-dimensional dislocation dynamics simulations to investigate the transition between the power and the exponential laws in olivine for temperatures ranging between 800 K and 1700 K and stresses between 100 and 500 MPa. We model the deformation of an olivine crystal by the interplay of glide and climb of dislocations. Plastic strain is produced by glide, the amount of gliding dislocations being controlled by climb acting as a recovery mechanism. Within this framework, and without the need of introducing any other mechanism, our model reproduces a power law breakdown above 200 MPa. Consequently, we conclude that the use of two rheological laws to describe the creep of olivine can be motivated by convenience, but is not imposed by theoretical needs. Alternatively a unified creep law can be proposed to describe the rheology of olivine in a wide range of temperature relevant for the upper mantle. This flow law may have an exponential form and describe the entire range of experimental data, from room temperature to 1800 K at both low and high stresses, using a single adjusting parameter, the so-called mechanical resistance σ˜. We also propose an alternative mathematical expression based on a sigmoid function, which is more suitable for implementation in geodynamical models.

Torsion Of Solid Rods with Account for the Different Resistance of the Material to Tension and Compression Under Creep

Experiments on tension and compression of solid samples cut out from a 60-mm thick plate of an Ti–Al–Sn–V alloy at a temperature of 700◦C are used to determine that this alloy possesses small anisotropy and a different resistance to tension and compression under creep. The approximations of the power law of creep are obtained for each series of these experiments and each direction in the plate. Two models based on the transformed space of stresses are used to simulate the torsion of solid samples. The models account for the different resistance to tension and compression under creep. A series of experiments are carried out on the torsion of solid round rods cut out in the normal direction of the plate. It is shown that the computational and experimental results satisfactorily agree.

Calculation of Three-Layer Panels with Polyurethane Foam Filler Taking into Account the Rheological Properties of the Middle Layer

The article deals with the processing of shear creep curves for foamed polymers, as well as a technique for calculating three-layer beams, taking into account the nonlinear creep of the aggregate. The Maxwell-Gurevich equation is used as the creep law. An example of calculation of a three-layer panel with a middle layer of polyurethane foam is given.