Exponential Creep Research Articles

CREEP BEHAVIOR OF STEEL FIBER REINFORCED LIGHTWEIGHT CONCRETE BEAMS UNDER FLEXURAL LOADING

Lightweight concrete reduces the dead load and the thermal conductivity of structural concrete members. The application of steel fibers improves its properties to more ductile behavior. In recent years, many researchers focused on the flexural and tensile creep behavior of FRC. However, most of the studies investigated the creep of normal-weight concrete. This paper presents a flexural creep study on lightweight aggregate concrete (LWAC) reinforced with steel fibers under four-point flexural loading. The study considered two different lightweight concretes with oven-dry densities below 1,200 kg/m3 and below 1,600 kg/m3 as well as three different steel fiber contents (0.5, 0.75, and 1.0 vol.-%). The twelve prismatic beams were tested in a cracked state under defined stress levels in a period of 490 days. The results show that there was no exponential creep rate and no failure during the test. Additionally, this study's experimental flexural creep coefficients were compared with the calculated compression creep coefficients of Eurocode 2 and with other studies using a similar test setup.

CREEP BEHAVIOR OF STEEL FIBER REINFORCED LIGHTWEIGHT CONCRETE BEAMS UNDER FLEXURAL LOADING

Lightweight concrete reduces the dead load and the thermal conductivity of structural concrete members. The application of steel fibers improves its properties to more ductile behavior. In recent years, many researchers focused on the flexural and tensile creep behavior of FRC. However, most of the studies investigated the creep of normal-weight concrete. This paper presents a flexural creep study on lightweight aggregate concrete (LWAC) reinforced with steel fibers under four-point flexural loading. The study considered two different lightweight concretes with oven-dry densities below 1,200 kg/m3 and below 1,600 kg/m3 as well as three different steel fiber contents (0.5, 0.75, and 1.0 vol.-%). The twelve prismatic beams were tested in a cracked state under defined stress levels in a period of 490 days. The results show that there was no exponential creep rate and no failure during the test. Additionally, this study's experimental flexural creep coefficients were compared with the calculated compression creep coefficients of Eurocode 2 and with other studies using a similar test setup.

CREEP OF A THICKWALLED QUASILINEAR VISCOELASTIC TUBE UNDER A CONSTANT EXTERNAL AND INTERNAL PRESSURE

We consider the creep problem for a quasilinear viscoelastic model of a thickwalled tube, loaded with constant internal and external pressure; the material is supposed to be incompressible. An exact solution to this problem was received by one of the authors in previous papers, assuming the state of a tube to be plain deformation; hereby we study properties of this solution for arbitrary material functions of quasilinear viscoelasticity constitutive relation. A criterion of stress stationarity is derived; the stress field of a thickwalled tube under a constant pressure evolves in time in the case of unbounded creep function and arbitrary nonlinearity function, except some particular types. The monotonicity of stress field components is studied: the radial stress monotonicity depends only on internal and external pressure values (for internal pressure, greater than an external one, it is negative and increases in radii). For other stress components, there are derived sufficient conditions of monotonicity. For an exponential nonlinearity function and unbounded creep function, a creep curve is determined to be concave up at the initial moment, and concave down during prolonged observation; the creep curve of a bipower nonlinearity function model may change its convexity. The stressstrain state of a model with a bounded creep function is proved to be bounded.

Spark plasma sintering for high-speed diffusion bonding of the ultrafine-grained near-α Ti–5Al–2V alloy with high strength and corrosion resistance for nuclear engineering

The paper demonstrates the prospects of spark plasma sintering (SPS) for the high-speed diffusion bonding of the high-strength ultrafine-grained (UFG) near-α Ti–5Al–2V alloy. The effect of increased diffusion bonding intensity in the UFG Ti alloys is discussed also. The bonding areas of the UFG near-α Ti–5Al–2V alloy obtained by SPS are featured by high density, strength, and corrosion resistance. The rate of bonding in the UFG alloys has been shown to depend on the heating rate non-monotonously (with a pronounced maximum). At the stage of continuous heating and isothermic holding, the bonding kinetics was found to be determined by the exponential creep rate, the intensity of which in the coarse-grained alloys is limited by the diffusion rate in the crystal lattice α-Ti. In the UFG alloy, the exponential creep processes associated with gliding and climb of dislocations, the activation energy of which corresponds to the diffusion activation energy in the lattice dislocation nuclei, may take place simultaneously with the grain boundary sliding and Coble creep, the activation energy of which corresponds to the grain boundary diffusion activation energy.

The Brittle‐Ductile Transition Predicted by a Physics‐Based Friction Law

AbstractA theory of the brittle‐ductile transition (BDT) is shown to be a direct consequence of a recently developed physics‐based constitutive law for rock friction (Aharonov & Scholz, 2018, https://doi.org/10.1002/2016JB013829), which assumes exponential creep on contacts. The theory was previously tested against experimental data for sliding at low ambient temperature and stress. Here, theoretical interpretation of experimental data at high temperature and stress shows that at some point the real area of contact reaches a maximum value beyond which it becomes fixed. The constitutive law shows that this marks the onset of the BDT, beyond which sliding changes from frictional to an exponential flow law for low‐temperature plasticity. Application to the Earth's crust shows that beyond this point, strength fall linearly with depth until it intersects the power law for bulk flow of the country rock, which marks the lower boundary of the BDT. Modeling, constrained by experimental data for granite, predicts that the BDT starts at a temperature of about 300°C, at a depth of 11–13 km in the continental crust, depending on fault slip rate and temperature gradient. The completion of the BDT is similarly calculated to occur around 475°, at 16–18 km, in agreement with laboratory and field observations. The BDT is thus found to be a region spanning about 175°C with a width of several kilometers. Within the exponential flow region, the structural outcome would be a relatively narrow mylonitized fault zone, which widens into a broader region of shear at the base of the BDT.

Effect of Nonlinear Functions on Prediction of the Creep Behavior in Fibrous Composites Theoretically

This paper presents the analysis of the creep behavior for safe designing the fibrous composite devices. Special theoretical method is presented for analyzing the second stage creep of the short fiber composites subjected to axial load using nonlinear displacement functions. Behavior of creeping matrix is described by an exponential creep law, whilst the fibers behave elastically in general. The major plan of the present research work is prediction of the creep behavior in the fibrous composites for preventing unwanted events, over and above, controlling the creep deformation rate theoretically and numerically. Finally, good compatibilities are seen between finite element method and present theoretical method results. As an important result and finding, in general, the mentioned behaviors are ascending along with soft gradients, and so they are controllable and desired.DOI: http://dx.doi.org/10.5755/j01.mech.24.2.19535

Contact problem for a solid indenter and a viscoelastic half-space described by the spectrum of relaxation and retardation times

The mechanical properties of a material which is modeled by an exponential creep kernel characterized by a spectrum of relaxation and retardation times are studied. The research is carried out considering a contact problem for a solid indenter sliding over a viscoelastic half-space. The contact pressure, indentation depth of the indenter, and the deformation component of the friction coefficient are analyzed with respect to the case of half-space material modeled by single relaxation and retardation times.

Contact Problem for a Viscoelastic Half-Space and a Rough Rigid Cylinder under the Conditions of Hydrodynamic Lubrication

A model has been proposed for use in studying the combined effect of the roughness of a rigid punch and the viscous properties of a base separated by a thin lubricant layer exerted on the characteristics of contact interactions and the sliding friction force. The problem of the motion of a thin a lubricant layer between a fixed rigid cylinder with a regular relief, as well as the surface of a moving viscoelastic half-space, the rheological properties of which are described by an integral operator with an exponential creep kernel, has been considered. The pressure and thickness of the lubricating layer, as well as the deformation component of the frictional force depending on the sliding velocity, have been analyzed. A comparison of the results of solutions of contact problems for viscoelastic and elastic rough bodies in the presence of a lubricant has been presented.

A microstructural based creep model applied to alloy 718

In this work a creep model based on the microstructural evolution of precipitation strengthening metals is presented. The model describes the influence of precipitates on the threshold stress as well as the power-law and the exponential creep rates depending on the aging condition. To show the predictive capabilities of this model, it was applied to the nickel based superalloy Alloy 718. This alloy is precipitation strengthened by the γ′ and γ’’ phases. Thermo-kinetic simulations based on a calibrated MatCalc routine were performed to determine the evolution of the volume fraction and mean radius of the precipitates. In addition, sequential creep and tensile tests were performed to characterize the mechanical material behavior. The simulated microstructural evolution and the corresponding measured mechanical properties were used to parametrize the creep model. Finally, the fully parametrized model was applied to simulate deformation mechanism diagrams for different aging conditions. From these diagrams the purely elastic, the power-law and the exponential deformation regimes can be estimated depending on the precipitate volume fraction and mean precipitate radius.

Direct shear of olivine single crystals

Knowledge of the strengths of the individual dislocation slip systems in olivine is fundamental to understanding the flow behavior and the development of lattice-preferred orientation in olivine-rich rocks. The most direct measurements of the strengths of individual slip systems are from triaxial compression experiments on olivine single crystals. However, such experiments only allow for determination of flow laws for two of the four dominant slip systems in olivine. In order to measure the strengths of the (001)[100] and (100)[001] slip systems independently, we performed deformation experiments on single crystals of San Carlos olivine in a direct shear geometry. Experiments were carried out at temperatures of 1000 ° to 1300 °C, a confining pressure of 300 MPa, shear stresses of 60 to 334 MPa, and resultant shear strain rates of 7.4 × 10−6 to 2.1 × 10−3 s−1. At high-temperature (≥1200 °C) and low-stress (≤200 MPa) conditions, the strain rate of crystals oriented for direct shear on either the (001)[100] or the (100)[001] slip system follows a power law relationship with stress, whereas at lower temperatures and higher stresses, strain rate depends exponentially on stress. The flow laws derived from the mechanical data in this study are consistent with a transition from the operation of a climb-controlled dislocation mechanism during power-law creep to the operation of a glide-controlled dislocation mechanism during exponential creep. In the climb-controlled regime, crystals oriented for shear on the (001)[100] slip system are weaker than crystals orientated for shear on the (100)[001] slip system. In contrast, in the glide-controlled regime the opposite is observed. Extrapolation of flow laws determined for crystals sheared in orientations favorable for slip on these two slip systems to upper mantle conditions reveals that the (001)[100] slip system is weaker at temperatures and stresses that are typical of the asthenospheric mantle, whereas the (100)[001] slip system is weaker at conditions typical of the lithospheric mantle. These observations demonstrate that the relative strength of the dislocation slip systems in olivine and, thus, the development of lattice-preferred orientation and anisotropic viscosity in olivine-rich rocks are strongly dependent upon temperature and stress.

Study of the upper die clamping conditions in the small punch test

A parametric study of small punch tests on miniaturized discs under constant deflection rate and constant force has been performed to study the influence of various upper die conditions on the test results. A comparison between the experimental results and the simulations by means of the finite element method is presented, under different clamping conditions. Heat resistant steel P22 has been selected for this investigation. The elasto-plastic behaviour of the disc was described by multilinear isotropic hardening. Norton power-law and exponential creep constitutive relationships have been applied in the ANSYS FE model of the SPT arrangement under creep conditions. The investigation confirms relatively small influence of the upper die conditions for both types of small punch tests for the steel under investigation.

The Algorithm of Identification of Fractional Exponential Creep Cores on Experimental Data

The Algorithm of Identification of Fractional Exponential Creep Cores on Experimental Data

Thermo-Dynamics and Stress Characteristics on High Strength Hydraulic Concrete Material

High strength hydraulic concrete was introduced based on its thermo-dynamic and strain-stress characteristics. The compound exponential thermo-dynamic creep model was established. The temperature rise models were interpreted. The bisection constitutional model was deduced as the approach to express the strain-stress non-linearity of high strength hydraulic concrete. The key parameters on thermo-dynamic characteristics and strain-stress ones of high strength hydraulic concrete were offered. The models and parameters in this paper are useful for engineering application and theoretical research.

(De)compaction of porous viscoelastoplastic media: Model formulation

AbstractA nonlinear viscoelastoplastic theory is developed for porous rate‐dependent materials filled with a fluid in the presence of gravity. The theory is based on a rigorous thermodynamic formalism suitable for path‐dependent and irreversible processes. Incremental evolution equations for porosity, Darcy's flux, and volumetric deformation of the matrix represent the simplest generalization of Biot's equations. Expressions for pore compressibility and effective bulk viscosity are given for idealized cylindrical and spherical pore geometries in an elastic‐viscoplastic material with low pore concentration. We show that plastic yielding around pores leads to decompaction weakening and an exponential creep law. Viscous and plastic end‐members of our model are consistent with experimentally verified models. In the poroelastic limit, our constitutive equations reproduce the exact Gassmann's relations, Biot's theory, and Terzaghi's effective stress law. The nature of the discrepancy between Biot's model and the True Porous Media theory is clarified. Our model provides a unified and consistent formulation for the elastic, viscous, and plastic cases that have previously been described by separate “end‐member” models.

Creep in an electrodeposited nickel

This paper reports the experimental results on the creep behavior of electrodeposited ultrafine-grained nickel and its particle-reinforced nanocomposite. The objective of this research was to further improve the knowledge of the creep behavior of monolithic nickel and to explore the role of nano-sized SiO2 particles in the potential creep strengthening of electrodeposited Ni nanocomposite. The creep behavior and microstructure of the pure ultrafine-grained nickel and its nanocomposite reinforced by 2 vol% nano-sized SiO2 particles were studied at temperatures in the range from 293 to 573 K and at the applied tensile stresses between 100 and 800 MPa. The results indicate that the creep resistance of the nanocomposite may be noticeably improved compared to the monolithic nickel due to the interaction of the particles with dislocation motion. It was found that the applied stress interval can be divided into lower and higher stress intervals corresponding to dislocation (power-law) and exponential creep regions, respectively. Analysis of the creep data leads to the suggestion that the creep behavior of both electrodeposited nickel and its nanocomposite in power-law region may be grain boundary controlled. However, the mechanism responsible for the observed creep behavior at lower temperatures and the highest stresses is still not well established.

Comparison of Creep Properties of Four Copper Alloys and Creep Based Stress Analysis of a Rocket Engine Combustion Chamber

Abstract Regeneratively cooled liquid rocket engine combustion chambers are of double walled construction in which the hot inner wall will be usually fabricated out of a high thermal conductive material like copper alloy. Such a material will be subjected to the creep phenomenon accompanied by high stresses exceeding the elastic limit. Creep constitutive modeling and creep based stress analysis of such chambers assumes significance in this context to evaluate the maximum duration, temperature and thrust levels to which the engine can safely be operated. Comparison of high temperature creep properties of four copper alloys viz. NARloy-Z, Cu-8Cr-4Nb Cu-4Cr-2Nb and Cu-Cr-Zr-Ti commonly used for thrust chamber fabrication is done based on results of creep tests at different stress and temperature levels. Published data of creep properties of the first three alloys is made use of whereas tests are conducted for the fourth alloy for generation of creep data. The Norton and Exponential creep models are employed for representing the creep properties of the above materials and the best material identified. The Least Square Fit method is employed for evaluating the constants in the above models. Finally finite element modeling and creep based stress analysis of a cryogenic engine thrust chamber with inner wall of the chosen material is conducted using ANSYS code.drawn. Results are presented in graphical and tabular forms and conclusions

Correlation between creep and hot tensile behaviour for 2.25Cr-1Mo steel from 500ºC to 700ºC Part 1: an Assessment According to usual Relations Involving stress, temperature, strain rate and Rupture Time

Hot tensile and creep tests were carried out on 2.25Cr-1Mo steel at 9 temperature levels between 500ºC and 700ºC , using 5 different crosshead speeds, namely: 0.01 - 0.25 - 1.0 - 5.0 and 20 mm/min, and 17 levels of stress for creep from 34 to 414 MPa. The experimental work involved the analysis of data from 30 hot tensile tests and 50 constant load creep tests, with rupture times varying from 2 to about 1300 hours. Each of these set of data were analyzed separately according to their own methodologies, but an attempt was made to find a correlation between them. A new criteria is proposed for converting hot tensile data to creep data, which makes possible the analysis of the two kinds of results according to the Norton, Zener-Hollomon, Arrhenius and Monkman-Grant relations. The results shows remarkable compatibility, indicating consistent transition from the region of power-law to exponential creep behaviour.

Modeling of Rheological Deformation of Inhomogeneous Rock and Associated Time-Dependent Response of Tunnels

An exponential creep model on the basis of material properties degradation law was applied in the paper to simulate the rheological behavior of inhomogeneous rock and time-dependent response of rock tunnels. The primary, secondary, and tertiary creep regimes associated with damage were observed in the simulations, indicating that the macroscopic creep failure is linked to clusters of microstructure damage evolution at a mesoscale. Simulations on the time-dependent response of tunnels in the long-term under different coefficients of lateral pressure show that creep deformation and damage occurs in rock mass at tunnel sidewalls around rock mass under the coefficient of lateral pressure less than unity, whereas creep deformation and damage occurs at the roof and floor of the tunnel under the coefficient of lateral pressure larger than unity. Under the hydrostatic pressure of the coefficient of lateral pressure equal to unity, creep deformation and damage randomly occurs and damage localization forms and failure occurs at weak zone of the tunnel. Furthermore, tunnel closure displacements of the tunnel wall along the horizontal direction under three coefficients of lateral pressure are directly proportional to the coefficients of lateral pressure. Tunnel closure will be a maximum in the maximum principal stress direction and a minimum perpendicular to it for the coefficients of lateral pressure differing from unity.

Shear deformation of polycrystalline wadsleyite up to 2100 K at 14–17 GPa using a rotational Drickamer apparatus (RDA)

Shear deformation experiments on polycrystalline wadsleyite (water content, ∼200–2200 H/106 Si) have been conducted at 14.4–17.0 GPa, 1690–2100 K, and strain rates of 2.6–16 × 10−5 s−1 using a rotational Drickamer apparatus (RDA) at a synchrotron facility. The stress was measured from the orientation dependence of lattice spacing for the (013), (211), (141), (240) and (244) planes. On the basis of the mechanical and microstructural observations, we infer that deformation occurs by exponential creep through the Peierls mechanism at relatively low temperatures of 1690–2030 K. However, a sample deformed at the temperature of 2100 K showed significant grain‐size reduction, and most of small grains are dislocation‐free, although sub‐boundaries were observed in some grains in the sample. We interpret these observations as evidence for dynamic recrystallization and that diffusion creep (and grain boundary sliding) plays an important role after dynamic recrystallization caused by power law creep. Consequently, the strength observed in the high‐temperature conditions determined by the present study provides an important constraint on strength of diffusion creep and a lower limit for that of the power law dislocation creep. We conclude that the strength of wadsleyite in the power law dislocation creep is higher than or comparable to that of olivine and the strength of wadsleyite in the Peierls regime is similar to that of olivine.

Sudden and gradual compaction of shallow brittle porous rocks

Porous brittle rocks fail in shear and compaction. Rate and state friction describes such failure on a planar surface, while end‐cap failure describes the failure of a continuum. Both formalisms include Coulomb failure in shear at low normal tractions. Rate and state friction includes slow compaction of gouge by normal traction when shearing is not occurring. Rate and state friction also represents slow compaction of porous sandstone. End‐cap failure includes both grain crushing and shear. Micromechanically, all these mechanisms involve exponential creep at stresses of a few gigapascals. Rate and state friction is modeled by tabular real contacts where shear and extrusion occur. The observed compaction rate depends on the normal traction to a modest power of ∼27 for gouge and ∼10 for sandstone. End‐cap failure involves grain cracking in the neighborhood of the grain‐grain contact. Its rate should depend on the normal traction raised to a power of ∼100. This strong rate dependence is not measurable in practice as a failure cascade commences once some grains crack. Materials with pointy contacts including unwelded tuff and “regolith” in the uppermost tens of meters that has repeatedly been damaged by strong seismic waves compact in this manner at dynamic stresses modestly above their ambient lithostatic stress. This failure produces significant nonlinear attenuation of compressional P waves with sustained dynamic accelerations that are a modest fraction of the ambient acceleration of gravity.