Creep Strain Rate Research Articles

Using Nanoindentation to Characterize the Mechanical and Creep Properties of Shale: Load and Loading Strain Rate Effects.

The mechanical and creep properties of shale strongly influence artificial hydraulic fracturing, wellbore stability, and the evaluation of reservoir performance in shale gas exploration. This study characterized these mechanical and creep properties at the microscale through nanoindentation tests and evaluated their dependence on the indentation test parameters, specifically, the indentation load and the loading strain rate. The mechanical parameters (the Young’s modulus and hardness) of shale were strongly influenced by the magnitude of an indentation load (2–400 mN). Both parameters decreased sharply as the load increased from 2 to 200 mN; they then remained relatively stable at loads of 200–400 mN, suggesting that large indentation loads (200–400 mN) can be used to detect the mechanical responses of bulk shale. In contrast, both parameters increased slightly as the loading strain rate increased from 0.005 to 0.1 s–1. The indentation creep (CIT), related to creep behavior, and the creep strain rate sensitivity (m), related to the creep mechanism of shale, both increased with increasing the indentation load, whereas they decreased with increasing the loading strain rate. This demonstrates that increasing the load or decreasing the loading strain rate can increase creep deformation in shale during nanoindentation creep testing. The values of m varied from 0.040 to 0.124 under different loading conditions, suggesting that dislocation power-law creep may be the main mechanism controlling creep in shale. This study standardizes the testing parameters for the characterization of the mechanical properties of shale by nanoindentation testing and also advances our understanding of the deformation mechanisms of shale at the microscale.

Recent progress on the modelling of the minimum creep strain rate and the creep cavitation damage and fracture

ABSTRACT Modelling of the long-term creep damage and lifetime is very challenging due to their strong stress level dependence. Aiming at developing a set of creep damage constitutive equations suitable for long-term service, research was carried out in modelling of the minimum creep strain rate, creep cavitation damage and rupture, and the coupling between creep cavitation damage and creep deformation. Firstly, based on the stress driven concept, the cavity nucleation model and cavity growth model were calibrated together using cavity histogram. Then, a simple analytical equation was derived to model creep cavitation damage. Furthermore, the creep cavitation damage model offered the theoretical background and supports for the stress-based extrapolation method and time-based extrapolation method. Two case studies were carried to explore the opportunities. This paper summarizes some of the progresses. This paper contributes to the generic methodology as well as the specific knowledge to the topic area.

Experimental study on high-temperature relaxation behavior of carbon fiber reinforced polymer cable

In order to fully investigate the relaxation behavior of carbon fiber reinforced polymer (CFRP) cable exposed to high temperature, both steady state-constant displacement and temperature (ST-CDT), and transient state-constant displacement and temperature (TR-CDT) tests were conducted on specimens. The failure modes, stress loss laws and rupture times of high-temperature relaxation specimens were determined under ST-CDT and TR-CDT conditions. After high-temperature relaxation tests, high-temperature tensile tests were conducted on samples without rupture to obtain its residual mechanical properties. Final stress losses and stress loss rates of CFRP cable specimens determined by ST-CDT tests were compared with these of TR-CDT tests to clarify the effect of temperature-load path. A high-temperature relaxation model was developed to characterize the variation law of stress losses for CFRP cables under ST-CDT and TR-CDT conditions. A correlational model between stress loss and creep strain rates in steady stages of CFRP cables under high temperature was calibrated. The obtained results demonstrated that high-temperature stress losses of CFRP cables were closely correlated with target temperature, initial stress level and relaxation duration. The application of initial pre-tension load before heating accelerated the stress loss rate in transition relaxation stage and final stress loss of CFRP cable under high temperature.

An extended gradient-enhanced damage-plasticity model for concrete considering nonlinear creep and failure due to creep

For high stress levels, the dependence of the creep strain rate of concrete on the acting stress is nonlinear. Furthermore, very high stress levels may lead to a critical growth of microcracks resulting in material failure. For the lifetime assessment of creep sensitive concrete structures by means of numerical simulations, the realistic description of nonlinear creep is crucial. However, many concrete models are formulated for either nonlinear time-independent material behavior, or time-dependent material behavior, restricted to linear creep. This is the motivation for extending a damage-plasticity model, aiming at a unified and computationally efficient approach for representing the highly nonlinear time-dependent material behavior of concrete. Well established approaches for modeling the evolution of material properties, inelastic deformation, damage, creep and shrinkage serve as basis for considering nonlinear creep and material failure due to high sustained acting stress. The extended material model for concrete is validated by comprehensive experimental results from the literature.

Intermediate temperature creep damage mechanisms of a directionally solidified Ni-based superalloy

ABSTRACT Microstructure evolution and damage mechanisms during the creep deformation of a directionally solidified Ni-based superalloy were evaluated. The creep deformation behaviour was studied along the longitudinal direction (i.e. along the solidification direction), at a moderate temperature of 870 °C, and applied stresses ranging from 310 to 450 MPa concerning the service conditions in industrial gas turbine blades. It was shown that at the lower stress levels of about 310 MPa, the average creep strain rate decreased by two orders of magnitude, while tertiary creep appeared as the dominant stage. Progressive coarsening of γ’ precipitates was also observed, meantime γ’ precipitate shearing was confirmed to occur over the evaluated range of stresses.

Effect of temperature and humidity on the creep and aging behavior of adhesive joints under static loads

ABSTRACT To study the creep and aging behavior under the combined effect of temperature, humidity and static load, polyurethane adhesive was selected to make butt joints. The creep properties of the joint were analyzed experimentally under different static loads in hygrothermal environment. At the same time, an aging test under the combined effect of temperature, humidity and static load was carried out, and the variation law of the residual strength of the joint with the load and loading time was obtained. The complex fracture behavior of polyurethane adhesive joints was studied from macro to microscale. The results show that the hygrothermal environment had a significant effect on the creep properties of polyurethane adhesive joints. The creep strain rate of the joint was significantly higher, and the failure fracture time was shorter in the high temperature and humidity environment. When the temperature, humidity and static load were coupled, the joint failure strength decreased with time. With increasing load, the decline rate of the failure strength increased significantly. The interface failure of the joints and the hydrolysis reaction of the polyurethane adhesive were the main reasons for reducing the failure strength.

Influences of Post-Heat Treatment on the Microstructure Evolution and Creep Properties of Ni-Based Superalloy IN718 Fabricated by Electron Beam Melting

In this study, the Ni-based superalloy IN718, fabricated using an electron beam melting process, was investigated in as-built and various heat-treated conditions. The relationships between the microstructure characteristics and creep properties were elucidated. Under testing conditions of 650 °C and 650 MPa, the direct-aged specimen exhibited the lowest steady-state creep rate, at 0.15 × 10−8 s−1. The superior creep resistance can be attributed to the higher volume fraction of γ’/γ”-strengthening precipitates within the grain and fine δ precipitates along the grain boundaries. Being coherent to the γ matrix, the nano-sized γ’/γ” precipitates effectively hindered the dislocation motion in the grain interior. In addition, controlled grain boundary δ precipitates inhibited grain boundary sliding and decelerated the steady-state creep strain rate during creep deformation.

Creep Behavior ofγ-TiAl-Based Alloys with Fully Lamellar Microstore

AbstractRecent investigations have demonstrated that the interface spacing in fully lamellar microstructures has a major influence on the creep behavior of γ-TiAl-based alloys. In this paper, the dependence of the creep properties on interface spacing in fully lamellar Ti-46.5 at.% Al-4 at.% (Cr, Nb,Ta, B) sheet material was studied. Creep tests were conducted over a temperature range of 700 to 800 °C and at stresses between 100 and 260 MPa. The results indicate that the primary creep strain as well as the minimum creep rate decrease with decreasing interface spacing. A model which considers the limitation of the free dislocation path by stored dislocations as well as by geometrical obstacles was applied to explain the role of the interface spacing on both the primary creep strain and secondary creep rate. The applicability of the model has been verified by comparing calculated creep curves with experimentally obtained ones.

Change in the elastic and rheological properties of structurally heterogeneous geomaterials under multiple weak impacts

The paper discusses the lab-scale studies of the effect exerted by multiple weak impacts on creep in a sample of an equivalent geomaterial additionally subjected to static compression. It is found that under weak impacts for a long time, the creep strain rate first grows and then lowers down to a stationary value. Weak impacts initiate P-waves in the sample. The P-wave velocity increases non-monotonously with growing number of impacts. The change in the elastic and rheological properties of the material is connected with the change in its internal structure under the influence of external loading.

Investigation of three-stage compressive creep of a spinel forming refractory castable containing 8% MgO

A spinel forming castable with an initial MgO content of 8%, commonly applied in refractory linings in the steel industry, was characterised with regard to the creep behaviour. Three creep stages were observed for 1300, 1400, and 1500 °C for application relevant loads between 3 and 8 MPa for sintered samples. The parameters of the Norton–Bailey creep model were determined for all three creep stages. The added microsilica increased the creep strain rate in the temperature range above 1300 °C. The fitting of the results for only one temperature carries the risk of over-fitting. This was observed for the first creep stage at 1400 and 1500 °C. Nevertheless, for the investigated material, it was not possible to achieve a common fit for a larger temperature range. The evaluation of the creep parameters by different combinations of measurements allowed to obtain statistical information about the creep parameters.

Strain rate effect on the mechanical properties of ZrB2-SiC ceramics characterized by nanoindentation

ZrB2-SiC ceramics are one of the most promising materials for high temperature applications, and their mechanical properties are key indicators that determine whether they can long-time serve safely. In this work, the mechanical properties of ZrB2-SiC ceramics are determined by nanoindentation under six different strain rates. The relative density of ZrB2-SiC ceramics prepared by spark plasma sintering reaches 99.1%. The effects of strain rate on the elastic modulus, hardness, creep and pop-in behaviors are discussed in detail. Results show that the effect of strain rate on the elastic modulus can be ignored. The hardness increases with the increase of strain rate, and the increase gradually slows down. The relationship between the natural logarithms of hardness and strain rate can be accurately described as a linear function. The creep strain rate under indentation declines rapidly in the initial holding stage, and then gradually transitions into a constant in the steady-state creep stage under different strain rates. The pop-in load and displacement also showed obvious strain rate-dependence, based on which the shear strength of ZrB2 gains was estimated and compared with the theoretical value.

New insights into hydration-induced creep behavior of shale: A comparison study of brittle black shale and clayey oil shale at micro-scale

During hydraulic fracturing for shale gas development, water softening and creep deformation of shale rock are two common engineering problems that severely impair production performance. In order to understand the mineralogical and microstructural control on this mechanism from microscale, a brittle black shale from Lower Silurian Longmaxi Formation (named as LMX shale) and a clayey oil shale from Paleogene Youganwo Formation (YGW shale), which represent two members of shale family with different mineral constitutes and microstructures, were selected for hydration process under various durations (0.5 h–96 h) and temperatures (25 °C and 50 °C). The accompanied changes of microstructural and mechanical properties during hydration at microscale were investigated via nuclear magnetic resonance (NMR) and nanoindentation, respectively. Based on NMR T2 spectra, peak T2 time and water-infiltrated pore increment for both LMX and YGW shales rise sharply within the first 12 h, whereas remain invariable hereafter. And the values increase at higher temperature. For YGW shale, the maximum peak T2 time is lower but the incremental porosity is higher than LMX shale, respectively. Such difference indicates an occurrence of gradually enlarged and connected pores inside LMX shale after hydration, while a greater number of disconnected pores have been developed in YGW shale, comparatively. For both shales, great strength deterioration and creep enhancement are monitored within the first 12 h of hydration. The modulus reduction could be as high as 26.27% and 80.16% after 96 h soaking at 50 °C for LMX and YGW shales, respectively. Creep strain rate sensitivity increases from 0.026 to 0.234 for LMX shale, and 0.011 to 0.099 for YGW shale with intensified softening degree. The softening mechanism for LMX brittle shale is dominated by secondary pores and cavities generated as a result of dissolution of carbonate cementation and grain detachment after water infiltration, while microstructural integrity of YGW oil shale is degraded by clay swelling. Due to different mineral constitutes and microstructures, creep deformation for clayey YGW shale is mainly mediated by dislocation movement of fine clay grains, whereas diffusion creep plays the key role in coarse-grained LMX shale. This comparative study with two distinct shale samples provides the mineralogy- and microstructure-based framework for interpreting water softening process and creep mechanism of shale, which benefits hydraulic fracture design in different shale formations so as to enhance shale oil/gas production.

Nanoindentation Creep Behavior of Single‐Crystal Bi2Se3 Topological Insulator

A single‐crystal Bi2Se3 topological insulator is fabricated using the Bridgman–Stockbarger method. The crystal structure and atomic lattice parameters are identified by X‐ray diffraction analysis. The nanoindentation size effect on creep displacement, activation volume, and strain rate sensitivity (SRS) with different maximum holding loads between 1000 and 5000 μN is investigated using depth‐sensing nanoindentation. Furthermore, the effect of the loading rate on the steady‐state creep displacement and SRS is analyzed and discussed. Results show Bi2Se3's low resistance to plastic deformation and a significant increase of creep displacement with increasing holding load and holding rate. Additionally, creep strain rate, activation volume, and SRS are also calculated from the secondary stage creep, and results are compared with those of other flexible electronic materials.

Creep characteristics and constitutive model of bio-based concrete in aqueous environment

Bio-based materials generally have high porosity, which are prone to biodegradation during the long-term application, especially in a humid environment. To better understand the impact of the aqueous environment on creep performance of bio-based concrete, the effects of the loading method (single-stage and multi-stage), axial force (50 kN, 100 kN, 150 kN), and water pressure (1 MPa, 2 MPa, 3 MPa) on the long-term creep characteristics of bio-based apricot shell concrete are investigated in this study, with a creep duration of up to 1051 h. The results show that water pressure has a significant effect on the creep properties of apricot shell concrete. The creep strain and creep rate of apricot shell concrete gradually decrease with the increase of water pressure, which attributes to the water confining pressure that restrains the propagation of micro-cracks and consequently reduces the creep strain. Moreover, the creep strain and creep rate of apricot shell concrete increase with the increase of axial force. The creep behavior of bio-based apricot shell concrete in low load level is well described by a proposed Burgers piecewise creep model, which is recommended to express the long-term creep behavior of bio-based apricot shell concrete in the aqueous environment.

Investigation of creep properties and the cytoskeletal structures of non‐tumorigenic breast cells and triple‐negative breast cancer cells

This article presents the correlation of creep and viscoelastic properties to the cytoskeletal structure of both tumorigenic and non-tumorigenic cells. Unique shear assay and strain mapping techniques were used to study the creep and viscoelastic properties of single non-tumorigenic and tumorigenic cells. At least 20 individual cells, three locations per cell, were studied. From the results, lower densities in the volume of actin, and keratin 18 structures were observed with the progression of cancer and were correlated to the increased creep rates and reduced mechanical properties (Young's moduli and viscosities) of tumorigenic (MDA-MB-231) cells. The study reveals significant differences between the creep and viscoelastic properties of non-tumorigenic breast cells versus tumorigenic cells. The variations in the creep strain rates are shown to be well characterized by lognormal distributions, while the statistical variations in the viscoelastic properties are well-described by normal distributions. The implications of the results are discussed for the study of discrete cell behaviors, strain and viscoelastic responses of the cell, and the role of cell cytoskeleton in the onset and progression of cancers.

Ligament size effect in creep of nanoporous gold

Spherical nanoindentation creep tests are conducted on four nanoporous gold samples with ligament sizes of 30, 103, 417, and 986 nm. We find the ligament-size dependent creep, increase of total creep strain and creep strain rate with increasing ligament size, in the range of ligament sizes from 103 nm to 986 nm while the most pronounced creep is shown for ligament size of 30 nm. By coating a 2-nm-thick alumina layer on the ligaments, creep increased for ligament sizes ranging from 103 nm to 986 nm, while it decreased for ligament size of 30 nm. The ligament-size dependent creep and effect of surface coating are discussed with dominant dislocation mechanism in the ligaments under the dislocation-mediated creep for each ligament size.

Experimental Study on the Short-Term Uniaxial Creep Characteristics of Sandstone-Coal Composite Samples

In this investigation, the uniaxial short-term creep tests with multi-step loading were conducted on the sandstone-coal composite samples, and the characteristics of creep strength, creep deformation, acoustic emission (AE), and creep failure of composite samples were studied, respectively. The creep strength of the composite sample decreased with the stress-level duration, which was mainly determined by the coal and influenced by the interactions with the sandstone. The creep deformation and damage of sandstone weakened the deformation and damage accumulation within the coal, resulting in the larger strength for the composite sample compared with the pure coal sample. The axial creep strain of composite sample generally increased with the stress-level or the stress-level duration under same conditions. The AE characteristics of composite sample were related to the creep strain rate, the stress level, the stress level duration, and the local failure or fracture during creep loading. The micro or macro failure and fracture within the composite sample caused the rise in the axial creep strains and the frequency and intensity of AE signals, especially the macro failure and fracture. The creep failures of composite samples mainly occurred within the coal with the splitting ejection failure accompanied by the local shear failure, and no obvious failures were found within the sandstone. The coal in the composite sample became more broken with the stress-level duration.

Experimental analysis and constitutive modeling of anisotropic creep damage in a wrought age-hardenable Al alloy

Many components of aerospace and automotive engineering manufactured from forged age-hardening aluminum alloys operate at high temperature in the range 0.3Tm–0.5Tm, where Tm is the melting temperature. Experimental data for uni-axial creep on specimens sampled from a forged AA2014 alloy component show that inelastic strain rates depend significantly on the orientation of loading with respect to the material flow direction during the manufacturing stage. Based on the recently developed constitutive model of anisotropic creep, hardening/recovery, softening and overageing processes, this paper addresses experimental analysis and modeling tertiary creep regime up to the final stage of creep rupture. The emphasis is placed on the damage evolution equation in order to account for different damage mechanisms depending on the loading mode and loading direction relative to grain axis: cavitation on elongated grain boundaries as well as decohesions and microcracks around and inside coarse grain particles. Experimental data of creep strain rates for longitudinal and transverse loading directions at 130, 150 and 170 °C have been used to calibrate the model. The validation of the model was carried out by comparing experimental and modeled creep curves in the case of a 30°angle between the loading and the material flow direction during forging. The results show that the assumed damage mechanisms and the developed damage evolution equation are able to reflect both the anisotropic accelerated creep and the time to creep rupture for different stress levels and loading directions.

Uncovering the creep deformation mechanism of rock-forming minerals using nanoindentation

The creep phenomenon of rocks is quite complex and the creep mechanisms are far from being well understood. Although laboratory creep tests have been carried out to determine the creep deformation of various rocks, these tests are expensive and time-consuming. Nanoindentation creep tests, as an alternative method, can be performed to investigate the mechanical and viscoelastic properties of granite samples. In this study, the reduced Young’s modulus, hardness, fracture toughness, creep strain rate, stress exponent, activation volume and maximum creep displacement of common rock-forming minerals of granite were calculated from nanoindentation results. It was found that the hardness decreases with the increase of holding time and the initial decrease in hardness was swift, and then it decreased slowly. The stress exponent values obtained were in the range from 4.5 to 22.9, which indicates that dislocation climb is the creep deformation mechanism. In addition, fracture toughness of granite’s rock-forming minerals was calculated using energy-based method and homogenization method was adopted to upscale the micro-scale mechanical properties to macro-scale mechanical properties. Last but not least, both three-element Voigt model and Burgers model fit the nanoindentation creep curves well. This study is beneficial to the understanding of the long-term mechanical properties of rock samples from a micro-scale perspective, which is of great significance to the understanding of localized deformation processes of rocks.

Dislocation-climbing bypass over dispersoids with different lattice misfit in creep deformation of FeCrAl oxide dispersion-strengthened alloys

The creep strain rate of FeCrAl oxide dispersion-strengthened alloys, as a promising accident-tolerant fuel (ATF) cladding of the light-water reactors, is accelerated in YAlO3 dispersoids by two to three orders of magnitude compared with Y4Zr3O12 dispersoid at 1273 K and even occurs at an applied stress less than threshold stress for dislocation detachment. Two approaches were carried out to interprete new findings and to clarify their mechanism. By optimizing the relaxation of the dislocation line energy at the dispersoid interface, numerical analyses proved the accerelated dislocation-climbing in the YAlO3 dispersoids. The other is a more atomistic approach. The force on the dislocation induced by the stress field around the dispersoid was analyzed in terms of the Peach–Koehler relationship. The accelerated creep strain rate in YAlO3 dispersoids is attributed to a larger force induced by larger lattice misfit with less coherency in YAlO3 dispersoid.