Creep Evolution Research Articles

A wellbore creep model based on the fractional viscoelastic constitutive equation

Abstract To simulate the evolution of wellbore creep accurately, predict and prevent severe accidents such as borehole wall sloughing, casing collapse and sticking of the drill, based on previous studies, the springpot element was introduced into the classical element model and the creep compliances of the fractional constitutive models were deduced. The good fitting effect of fractional constitutive model was verified. The study shows the fractional constitutive model can simulate creep with high accuracy and less input parameters, and the physical significance of the input parameters are clearer. According to the correspondence principle of viscoelastic theory, a wellbore creep model including drilling and killing processes was built up. By adjusting the value of fractional orders, the model can transform between the models of ideal elastic material and standard solid, which implies the classical wellbore shrinkage model based on standard solid model and ideal elastic model are just special cases of this model. If the fractional order is adjusted, the creep curve will change asymmetrically, which can be can be regulated by the speeding up of the transient creep and lowering the rate of steady creep, which can not be accomplished by adjusting one parameter in the classical models. The fractional constitutive model can fit complicated non-linear creep experiment data better than other models.

10.34: Creep properties of grade S275JR steel at high temperature

ABSTRACTThe paper describes an ongoing research project which aims to determine the creep properties of European steel Grade 275JR. The purpose of the research is to develop a reliable temperature‐, stress‐ and time‐dependent creep model for this alloy, since there is very little information available in the scientific community regarding its creep properties. The research within the project is focused on a series of stationary creep tests, which will be used to obtain time‐dependent creep strains in the temperature range 400–600°C. The stress range for which the creep evolution is studied in this project is between 25% and 90% of the value of the stress at 0.2% strain at any particular temperature level. Comparisons between the creep output for the alloy analysed and existing creep data are presented in the paper.

Basic creep of concrete-coupling between high stresses and elevated temperatures

The prestressed concrete confinement vessel is the third and last barrier in French Nuclear Power Plants (NPP). In case of a severe accident (loss of cooling agent of the reactor for instance), pressure and temperature will increase in the nuclear vessel (+0,5 MPa and 180 °C during 2 weeks). Due to elevated temperatures, the evolution of basic creep will be accelerated. High compressive stresses would appear and induce higher delayed strains and damage. The modelling of basic creep and its couplings with temperature is then very important for the safety of the structure (tightness of the concrete vessel). Here, we present a model considering the following elements: a coupling between creep and damage is introduced, kinetics of basic creep is affected by temperature by the means of an Arrhenius thermo-activation, damage due to the increase in temperature (under stress or not) is taken into account. The model is compared with the available experimental results. This work is a part of the MACENA project.

Evolution of superdislocation structures during tertiary creep of a nickel-based single-crystal superalloy at high temperature and low stress

A second-generation nickel-based single crystal superalloys DD6 were creep tested in the [001] direction (within 15°) at 1100 °C/140 MPa. The specimen tested until rupture was investigated using scanning and transmission electron microscopy to determine the evolution of the dislocation behaviors during tertiary creep. It was found that the tertiary creep deformation was highly localized and inhomogeneous along the gauge length, and the types of superdislocations in γ′ rafts varied with the distances from the rupture surface, including individual screw dislocations, antiphase boundary-coupled dislocation pairs, and superlattice intrinsic stacking faults. It can be concluded that γ′ rafts shearing events occur in the following sequence with the evolution of tertiary creep: individual screw dislocations, antiphase boundary-coupled dislocation pairs, and superlattice intrinsic stacking faults. The origin of these transformations of superdislocation types and its influence on tertiary creep rate are discussed. It is proposed that at the microscopic level, a more reasonable explanation for the strain softening mechanism during the tertiary creep of nickel-based superalloys at high temperatures and low stresses is the emergence of new superdislocation types with higher mobility rather than the density rise of a single type of superdislocation produced during the later secondary creep stage.

Modelling Basic Creep of Concrete at Elevated Temperatures and Stresses

The prestressed concrete confinement vessel is the third and last barrier in Nuclear Power Plants (NPP). In case of a severe accident (loss of cooling agent of the reactor for instance), pressure and temperature will increase in the nuclear vessel (0,5 MPa and 180°C during 2 weeks). Due to elevated temperatures, the evolution of basic creep will be accelerated. In this case, due to internal pressure, some tensile stresses could appear in specific parts of the structure and induce cracking. The modelling of basic creep and its couplings with temperature is very important for the safety of the structure (tightness of the concrete vessel). Here we present a model considering the following elements: a coupling between creep and damage is introduced, kinetics of basic creep is affected by temperature by the means of an Arrhenius thermo-activation, damage due to the increase of temperature is taken into account. The model is compared with the available experimental results. This work is a part of the MACENA project.

An aseismic slip transient on the North Anatolian Fault

AbstractConstellations of Synthetic Aperture Radar (SAR) satellites with short repeat time acquisitions allow exploration of active faults behavior with unprecedented temporal resolution. Along the North Anatolian Fault (NAF) in Turkey, an 80 km long section has been creeping at least since the 1944, Mw 7.3 earthquake near Ismetpasa, with a current Interferometric Synthetic Aperture Radar (InSAR)‐derived average creep rate of 8 ± 3 mm/yr (i.e., a third of the NAF long‐term slip rate). We use a dense set of SAR images acquired by the COSMO‐SkyMed constellation to quantify the spatial distribution and temporal evolution of creep over 1 year. We identify a major burst of aseismic slip spanning 31 days with a maximum slip of 2 cm, between the surface and 4 km depth. This result shows that fault creep along this section of the NAF does not occur at a steady rate as previously thought, highlighting a need to revise our understanding of the underlying fault mechanics.

Geodetic observations of postseismic creep in the decade after the 1999 Izmit earthquake, Turkey: Implications for a shallow slip deficit

AbstractThe relationship between aseismic slip and tectonic loading is important for understanding both the pattern of strain accumulation along a fault and its ability to generate large earthquakes. We investigate the spatial distribution and temporal evolution of aseismic creep on the western North Anatolian Fault (NAF) using time series analysis of Envisat interferometric synthetic aperture radar (InSAR) data, covering the full extent of the 1999 Izmit and Düzce earthquake ruptures and spanning 2002–2010. Discontinuities in the line‐of‐sight velocity across the fault imply that fault creep reaches the Earth's surface at an average fault‐parallel rate of ∼5 mm/yr along an ∼80 km section of the NAF. By combining InSAR and published GPS velocities, we are able to extract the vertical and east‐west components of motion and show that the Adapazari basin is subsiding at a rate of ∼6 mm/yr. Vertical motions have biased previous estimates of creep in this region. The displacement time series close to the fault is consistent with an afterslip model based on rate‐and‐state friction, which predicts a rapid deceleration in fault creep rate after the Izmit earthquake to a near‐steady state ∼5 mm/yr after 5 years. Projecting our model 200 years into the future we find that the cumulative displacement of 1–1.3 m is insufficient to account for the shallow coseismic slip deficit observed in previous studies. Distributed off‐fault deformation in the shallow crust or transient episodes of faster slip are likely required to release some of the long‐term strain during the earthquake cycle.

Creep of Eight Years Old Cement Paste

The paper presents research of shrinkage of the cement paste. The tested specimens wereprepared eight years ago from Portland cement CEM II and water. The observation was focused onthe evolution of creep in long time and for very old material. The material properties like a compressionstrength and Modulus of elasticity were observed according with the creep.

Analysis of creep and modulus loss of the wood cell wall

This paper proposes a nonlinear constitutive model for the wood cell wall based on the nonequilibrium thermodynamics. The wood cell wall is modeled as a long fiber-reinforced composite with cellulose microfibril enclosed by hemicellulose and lignin. An internal variable is introduced into the Helmholtz free energy of the cell wall system, to describe the modulus loss of hemicellulose due to moisture absorption. The viscoelastic behavior of the wood cell wall changes with its moisture content, which leads to different creep evolutions even under the same loading level. To account for this phenomenon, another internal variable is introduced to depict the creep behavior of the wood cell wall, which is correlated with the irreversible energy dissipation processes such as stick–slip mechanism in the wood cell wall. Based on five elastic coefficients of transverse isotropy predicted by the present model, the creep behaviors of the wood cell wall with different microfibril angles are theoretically analyzed and show good agreements with experiment results.

Modeling creep in polymeric composites: Developing a general integrated procedure

General integrated procedure for evaluating creep in polymeric composites is developed which is applicable to any arbitrary composite structures. Non-linear long-term creep phenomenon of composites is simulated on the basis of viscoelastic behavior of polymer. Limited short-term experimental measurements on pure resin are required to simulate creep evolution in composite laminates. The modeling procedure starts at lamina level and results are extended to the laminate level relying on incremental procedure. In each sub-step, the stress/strain distributions are updated in accordance with modified mechanical properties. Adaptive time step selection is developed to reduce required runtime for modeling procedure. The results of the theoretical creep evaluation are in a good agreement with available long-term experimental data for composite plates. A case study on cylindrical structure is also performed and obtained results are compared with published data. It is revealed that for the case of cylindrical structure taking into account variations of fiber orientations and cylinder radius arisen from creep evolution is of great importance.

A friction to flow constitutive law and its application to a 2‐D modeling of earthquakes

AbstractEstablishment of a constitutive law from friction to high‐temperature plastic flow has long been a challenging task for solving problems such as modeling earthquakes and plate interactions. Here we propose an empirical constitutive law that describes this transitional behavior using only friction and flow parameters, with good agreements with experimental data on halite shear zones. The law predicts steady state and transient behaviors, including the dependence of the shear resistance of fault on slip rate, effective normal stress, and temperature. It also predicts a change in velocity weakening to velocity strengthening with increasing temperature, similar to the changes recognized for quartz and granite gouge under hydrothermal conditions. A slight deviation from the steady state friction law due to the involvement of plastic deformation can cause a large change in the velocity dependence. We solved seismic cycles of a fault across the lithosphere with the law using a 2‐D spectral boundary integral equation method, revealing dynamic rupture extending into the aseismic zone and rich evolution of interseismic creep including slow slip prior to earthquakes. Seismic slip followed by creep is consistent with natural pseudotachylytes overprinted with mylonitic deformation. Overall fault behaviors during earthquake cycles are insensitive to transient flow parameters. The friction‐to‐flow law merges “Christmas tree” strength profiles of the lithosphere and rate dependency fault models used for earthquake modeling on a unified basis. Strength profiles were drawn assuming a strain rate for the flow regime, but we emphasize that stress distribution evolves reflecting the fault behavior. A fault zone model was updated based on the earthquake modeling.

Prediction of Creep Properties of Fiber-Reinforced Closed-Cell Metallic Foams

The anti-creep capability of metallic foams is important to structural applications at elevated temperatures. Currently, available creep models for opened-cell foam materials are usually derived by rather simplified meso-structural models. Here, we try to predict the creep properties of new fiber-reinforced closed-cell foams with more realistic 3D meso-structures. In the study, three-dimensional Voronoi structures are constructed to describe the inner structure of closed-cell foams, and reinforcing fibers are modeled by line segments penetrating through cell walls. Based on the recommended model, not only the steady creep strain rates of both the unreinforced and the reinforced foam materials are well predicted with considering the effects of temperature, stress, and relative density, but also the creep evolution features of metal foam are revealed from the meso-deformation behaviors. It is found that, at moderate temperature and stress, the creep rate of the fiber-reinforced metallic foam can also be well described by a power law with respect to the foam relative density. The influence of addition of fibers on the creep properties is parametrically studied and it is shown that addition of fibers has a positive effect on restricting the creep rate. It is observed that during creep, the stresses of cell walls are redistributed and become more homogeneous with time. When the creep rate of metallic foam reaches steady state depends on when the stresses of cell walls become homogeneous.

Multiscale fatigue damage characterization in short glass fiber reinforced polyamide-66

This paper aims at studying fatigue damage behavior of injection molded 30wt% short glass fiber reinforced polyamide-66 composite (PA66/GF30). The evolution of dynamic modulus, hysteresis area, cyclic creep and temperature during fatigue tests were analyzed and discussed. Damage analyses by X-ray micro-computed tomography (μCT) technique on interrupted fatigue tests at several percentages of total fatigue life were performed to further understand the damage mechanisms and evolution during fatigue loading. It can be observed that experimental results related to the evolution of dynamic modulus, strain, temperature and energy dissipation are important and consistently complement each other for damage evaluation of PA66/GF30. During fatigue loading, diffuse damage occurs over the entire specimen though the damage does not necessarily exhibit the same level between different locations inside the specimen. The μCT analysis of voids characteristics demonstrates that the damage continuously increases during fatigue loading. The damage is developed notably along fiber interface in the form of fiber/matrix interfacial debonding.

Time-dependent creep analysis of rotating ferritic steel disk using Taylor series and Prandtl–Reuss relation

Abstract In this article, initial thermo-elastic and time-dependent creep evolution response of rotating ferritic steel disk (1/2 Cr, 1/2 Mo, 1/4 V) is carried out using a long-term creep constitutive equation. The material creep properties are defined by the Θ projection concept based on experimental results previously conducted on ferritic steel. Loading is an inertia body force due to rotation and a constant temperature field throughout the disk. The equilibrium equation, stress–strain and strain–displacement relations are employed to obtain a constitutive differential equation containing variable and time-dependent coefficients. To achieve history of stresses, displacement and creep strains, a numerical procedure using Taylor series and Prandtl–Reuss relation is utilized offering radial, circumferential and effective stresses and strains histories. The effect of angular velocity on creep stresses and displacements after 20 years are also reported. It is observed that a considerable redistribution occurs for stresses and strains. It is also found that an increasing rate happens for stresses and strains which must be considered for the safe design of ferritic steel disks. Moreover, increasing angular velocity raises the effective, radial, and circumferential stresses. To validate the solution approach, a composite disk was considered and its thermo-elastic and time-dependent creep behaviors were achieved. An exceptionally good agreement was found between the results obtained in this current study and the results available in the literature.

The analysis of time-dependent creep in FGPM thick walled sphere under electro-magneto-thermo-mechanical loadings

Time-dependent creep response of a smart sphere made of functionally graded piezoelectric material (FGPM) is investigated. The vessel is subjected to an internal pressure, a uniform temperature field, an electric potential and a uniform magnetic field. Under such a loading condition initial elastic stresses are locked in the vessel at zero time. Due to high temperature, creep evolution causes stress redistribution in the sphere which is followed by electric potential redistribution across the thickness of the sphere. History of radial stresses is always reflected by history of electric potential which can be used for condition monitoring of the smart sphere. From the initial elastic stresses it has been found that imposing an electric potential decreases effective stresses. It has also been concluded from history of electric potential that electric potential redistribution is decreasing due to creep evolution and therefore this is followed by increasing effective stresses.

Spatiotemporal evolution of surface creep in the Parkfield region of the San Andreas Fault (1993–2004) from synthetic aperture radar

The Parkfield section of the San Andreas Fault (SAF) is defined as a transitional portion of the fault between slip-release behavior types in the creeping section of the SAF to the northwest and the apparently locked section to the southeast. The Parkfield section is characterized by complex frictional fault behavior because it represents a transition zone from aseismic creep to stick-slip regime. At least six historic earthquakes of M w ~ 6 have occurred in this area in 1881, 1901, 1922, 1934, 1966, and 2004. It was observed in the 2004 M w 6.0 Parkfield earthquake that ~ 70% of the total (coseismic and postseismic) moment release occurred aseismically. To understand the SAF behavior in this area, it is of particular interest to measure and analyze, not only the spatial evolution of the surface displacement in this area, but also its evolution over time. Using radar data acquired by the European Space Agency's European Remote Sensing (ERS1-2) satellites, we constructed descending interferograms and retrieved time series of surface displacements along the central SAF for the decade preceding the 2004 Parkfield earthquake. We focus on characterizing the space and time evolution of surface creep in the Parkfield and Cholame sections. The spatial pattern of the interseismic displacement rate indicates that tectonic strain was not uniformly distributed along the strike of the fault between 1993 and 2004. Our data indicate not only a decrease in the creep rate from the Parkfield section to south of Highway-46 from 1.4 ± 0.3 cm/yr to 0.6 ± 0.3 cm/yr, but also a small but significant creep-rate increase in the Cholame section to 0.2 ± 0.1 cm/yr. The evidence for episodic creep in the Cholame section of the SAF south-east of Parkfield is in contrast with previously published interpretations of GPS and trilateration data. The Cholame section of the SAF merits close monitoring because it was likely the nucleation site of the 1857 Fort Tejón earthquake and because it has shown recent evidence of deep slow slip as revealed by deep tremors.

Experimental studies and constitutive modelling of the hardening of aluminium alloy 7055 under creep age forming conditions

A test programme has been designed to characterise the creep-ageing behaviour of Aluminium Alloy 7055, commonly termed AA7055, under creep age forming (CAF) conditions. Creep ageing tests have been carried out for a range of stress levels at 120 °C for 20 h, which is the typical period for a CAF process. Interrupted creep tests have also been carried out to rationalise the effect of stress levels on age hardening. Based on experimental observations, a set of mechanism-based unified creep ageing constitutive equations has been formulated, which models creep induced evolution of precipitates, dislocation hardening, solid solution hardening and age-precipitation hardening. A multiple-step reverse process has been introduced to determine, from creep ageing test data, the values of constants arising in the constitutive equations. Close agreement between experimental data and computed results are obtained for creep and age hardening data for the stress range tested. The determined equation set has been integrated with the commercial FE code MSC.MARC via the user defined subroutine, CRPLAW, for CAF process modelling. In addition to springback, the evolution of precipitate size and creep induced precipitation hardening can be predicted.

Arrest and recovery of frictional creep on the southern Hayward fault triggered by the 1989 Loma Prieta, California, earthquake and implications for future earthquakes

[1] Theodolite measurements across the right-lateral Hayward fault, San Francisco Bay, California, show a dramatic reduction in surface creep rate from 5 to 10 mm/yr before the 1989 Loma Prieta earthquake to nearly zero creep rate after the earthquake. A ∼6 year period of nearly zero surface creep was followed by sudden fault creep that accumulated about 20–25 mm of right-lateral displacement followed by an eventual return to a steady creep by year ∼2000. This creep behavior can be explained as a result of a sudden shear stress reduction on the fault and is consistent with model predictions for a fault imbedded in an elastic medium with slip governed by laboratory-derived friction laws. We infer friction parameters on the fault using a spring-slider model and a boundary element model with the rate- and state-dependent friction laws. The state (healing) term in the friction law is critical for reproducing the observed evolution of surface creep; a popular simplified rate-dependent friction law is insufficient. Results suggest that the creep event extended to a depth of ∼4–7.5 km. The inferred critical slip distance, dc, is 1–2 orders of magnitude larger than lab values, and inferred aσ values imply low effective fault-normal stresses of 5–30 MPa. This range of effective normal stress and inversion results for (a − b)σ imply very small values for a − b of 10−5 to 10−3, suggesting the fault has nearly velocity-neutral frictional properties. Earthquake simulations with such small a − b values show that creeping areas on the Hayward fault may be capable of rupturing during earthquakes.

Reflection on the ductility of irradiated zircaloy-4 fuel rod cladding

Abstract An approach is presented that allows the computational determination of the ductility of irradiated zircaloy-4 cladding by transferring experimental results yielded under conditions atypical for normal power operation to typical loadings encountered in an usual pressurized water reactor. The transfer bases on a damage function that describes the gradual development of material separations during the cladding creep in the reactor. The numerical values of the needed equation parameters are derived from experimental results. Creep and damage evolutions are coupled leading to a simultaneous computation of both processes. The calculations indicate that the minimum strains that irradiated cladding material can accommodate are greater than 5% under pure pressure loading up to hoop stresses of 100 MPa and greater 7% when fuel swelling corresponding to a linear rod power of maximum 400 W/cm dictates the creep.

Sensing Creep Evolution in 410 Stainless Steel by Magnetic Measurements

The creep evolution was followed by conducting magnetic measurements on ferromagnetic steel samples exposed to different creep strains at a constant temperature. 410 stainless steel (410 SS) rods were submitted to creep at 625°C applying a constant stress of 124 MPa for different creep times. A magnetic hysteresis curve was generated for every sample. It was found that the shape of the hysteresis curves varied with creep time. The extent of creep was assessed by measuring magnetic saturation, coercivity, and remanence. The changes in microstructure due to creep are related to variations in magnetic properties, which are explained in terms of possible magnetic domain pinning. It was observed that the microstructural changes due to creep are better correlated with the coercivity of the material. In summary, it is feasible to use a magnetoelastic sensor to detect the partial level of creep in a ferromagnetic material by nondestructive examination.