Macroscopic Creep Research Articles

Shear deformations in calcium silicate hydrates

The calcium silicate hydrate (C–S–H) gel is the phase that provides cohesive strength to cement. The mechanics of the C–S–H gel at the molecular level is key to the durability of infrastructures made of concrete, controlling for example their macroscopic creep and shrinkage. The existing experimental techniques cannot access the nanostructure and properties of this very heterogeneous phase, and therefore atomistic simulations constitute a valuable alternative. Here we consider two established model systems for the solid part of the C–S–H gel that are representative of perfectly ordered and very disordered molecular structures: crystal tobermorite and glassy C–S–H. Using reactive force field simulations, we calculate elastic properties that match with experimental values from the literature. The analysis of the large deformations under shear indicates that the shear strain localizes preferentially at nanoscale sites that are rich in highly confined water. Implications of our findings for a colloidal description of the C–S–H gel mechanics and for the macroscopic properties of cement are finally discussed.

Study of creep cavitation behavior in tempered martensitic steel using synchrotron micro-tomography and serial sectioning techniques

Two three-dimensional (3-D) techniques, namely X-ray microtomography and serial sectioning, have been applied for characterization of creep cavitation behavior in tempered martensitic steel. For this purpose samples have been extracted from a series of specimens that were subjected to creep tests over the stress range of 120–180MPa at 600°C. The presence of creep voids in the series of samples was un-ambiguously detected in a non-destructive manner using synchrotron X-ray microtomography with a resolution of 1μm. The 3-D visualization of the datasets provided an assessment of the spatial distribution and morphology of the creep voids as a function of creep stress and high temperature exposure time. The quantitative analyses of the image datasets enabled the development of functional relationships between the macroscopic creep parameters (such as rupture ductility, applied stress, creep life) and cavitation characteristics (such as volume fraction, and number density). The quantitative analyses also provided an evaluation of manifestations of growth and coalescence processes in the respective datasets. A transition of cavitation behavior of the steel has been found to occur in the stress range of 120–150MPa at 600°C. The evolution in the pattern of cavitation and its relation to the prior-austenite boundary was explored by combining micro-tomography and serial sectioning techniques, which revealed a new possibility in the progress of cavitation in the long term creep exposed specimens of 9–12% Cr heat resistant steels.

Geometrical influence for creep damage evaluation of IN738LC using electron backscatter diffraction

The Ni-based superalloy IN738LC is an outstanding heat-resistant material, but it does have the disadvantage of being brittle. Therefore creep degradation such as deformation of components or initiation of microscopic creep voids only appear at the end of its available creep life. To date, electron backscatter diffraction (EBSD) in conjunction with scanning electron microscopy has been used for damage evaluation. Some results showed that the misorientation was correlated with the magnitude of macroscopic plastic or creep strains. In this study, by using the EBSD method, the characteristics of the change and distribution tendencies of crystallographic misorientation on creep life have been investigated. In addition, the geometrical influence of stress concentrated areas for misorientation analysis has been investigated, which is important to evaluate damage in practical components like blades. As a result, the grain reference orientation deviation parameter which corresponds to the spread of creep strain has been found to be useful to estimate creep life among the misorientation parameters. Also, misorientation analysis allows the evaluation of creep damage before the appearance of obvious defects without being subjected to the geometrical influence of the stress concentrated areas.

Anelasticity in austenitic stainless steel

Time-dependent anelastic deformation mechanisms arise in austenitic stainless steel when load is removed during a high-temperature creep test. This phenomenon is investigated by conducting creep tests, with intermittent load removal, on AISI Type 316H austenitic stainless steel at 550 and 650°C, supported by in situ measurement of creep-induced intergranular residual strains by neutron diffraction. All the cyclic tests exhibit anelastic behaviour on unloading and develop substantially lower load-on creep strain rates, reduced ductility and longer rupture times than baseline steady-load creep tests at similar conditions. The mechanisms underlying the observed anelastic behaviour and changes in macroscopic creep properties are discussed with reference to the development of intergranular strains and dislocation behaviour.

Micromechanics of brittle creep in rocks

In the upper crust, the chemical influence of pore water promotes time dependent brittle deformation through sub‐critical crack growth. Sub‐critical crack growth allows rocks to deform and fail at stresses well below their short‐term failure strength, and even at constant applied stress (“brittle creep”). Here we provide a micromechanical model describing time dependent brittle creep of water‐saturated rocks under triaxial stress conditions. Macroscopic brittle creep is modeled on the basis of microcrack extension under compressive stresses due to sub‐critical crack growth. The incremental strains due to the growth of cracks in compression are derived from the sliding wing crack model ofAshby and Sammis(1990), and the crack length evolution is computed from Charles' law. The macroscopic strains and strain rates computed from the model are non linear, and compare well with experimental results obtained on granite, low porosity sandstone and basalt rock samples. Primary creep (decelerating strain) corresponds to decelerating crack growth, due to an initial decrease in stress intensity factor with increasing crack length in compression. Tertiary creep (accelerating strain as failure is approached) corresponds to an increase in crack growth rate due to crack interactions. Secondary creep with apparently constant strain rate arises as an inflexion between those two end‐member phases. The minimum strain rate at the inflexion point can be estimated analytically as a function of model parameters, effective confining pressure and temperature, which provides an approximate creep law for the process. The creep law is used to infer the long term strain rate as a function of depth in the upper crust due to the action of the applied stresses: in this way, sub‐critical cracking reduces the failure stress in a manner equivalent to a decrease in cohesion. We also investigate the competition with pressure solution in porous rocks, and show that the transition from sub‐critical cracking to pressure solution dominated creep occurs with increasing depth and decreasing strain rates.

Multiscale prediction of viscoelastic properties of softwood under constant climatic conditions

This paper covers the development and validation of a multiscale homogenization model for linear viscoelastic properties of wood. Starting point is the intrinsic structural hierarchy of wood, which is accounted for by several homogenization steps. Using the correspondence principle, an existing homogenization model for the prediction of elastic properties of wood is adapted herein for upscaling of viscoelastic characteristics. Accordingly, self-consistent, Mori–Tanaka, and unit-cell-based techniques are employed, leading to pointwise defined tensorial creep and relaxation functions in the Laplace-Carson domain. Subsequently, these functions are back-transformed into the time domain by means of the Gaver-Stehfest algorithm. With this procedure the orthotropic macroscopic creep behavior of wood can be derived from the isotropic shear behavior of the lignin-hemicellulose phase. A comparison of model predictions for viscoelastic properties of softwood with corresponding experimentally derived values yields very promising results and confirms the suitability of the model.

High Temperature Mechanical Spectroscopy Study of 3 mol% Yttria Stabilized Tetragonal Zirconia Reinforced with Carbon Nanotubes

Composites containing 3 mol% yttria stabilized tetragonal zirconia (3Y-TZP) reinforced with multiwalled carbon nanotubes (CNTs) with various amounts of CNTs (3Y-TZP / X wt% CNT, X= 0, 0.5, 1.5, 3 and 5) were processed by spark plasma sintering. Microscopic analysis proves that CNTs were well dispersed and embedded in grain boundaries of the sintered body. High temperature mechanical properties have been investigated using mechanical spectroscopy and low stress (6 MPa) creep. The isothermal spectrum (measured at 1600 K) consists of a mechanical loss peak at a frequency of about 0.1 Hz, which is superimposed on an exponential increase at low frequency. The absence of a well-marked peak in monolithic 3Y-TZP is justified considering that restoring force decreases at low frequencies or high temperatures due to the elasticity of neighboring grains. Therefore, strain is no more restricted and the mechanical loss increases exponentially, which is correlated to macroscopic creep. However, with CNT additions the mechanical loss decreases and a better resolved peak was observed. In parallel, the results have shown that the creep rate drastically decreases with CNT additions. These results can be interpreted by the pinning effect of CNTs which can hinder grain boundary sliding at high temperatures, resulting in a creep resistance improvement.

155 巨視クリープ則と空孔拡散を融合した有限要素法による切欠き近傍のクリープ損傷解析(材料力学IV,一般講演)

155 巨視クリープ則と空孔拡散を融合した有限要素法による切欠き近傍のクリープ損傷解析(材料力学IV,一般講演)

In Situ Neutron-Diffraction Studies on the Creep Behavior of a Ferritic Superalloy

Precipitate strengthening effects toward the improved creep behavior have been investigated in a ferritic superalloy with B2-type (Ni,Fe)Al precipitates. In situ neutron diffraction has been employed to study the evolution of the average phase strains, (hkl) plane-specific lattice strains, interphase lattice misfit, and grain-orientation texture during creep deformation of the ferritic superalloy at 973 K (700 °C). The creep mechanisms and particle-dislocation interactions have been studied from the macroscopic creep behavior. At a low stress level of 107 MPa, the dislocation-climb-controlled power-law creep is dominant in the matrix phase, and the load partition between the matrix and the precipitate phases remains constant. However, intergranular stresses develop progressively during the primary creep regime with the load transferred to 200 and 310 oriented grains along the axial loading direction. At a high stress level of 150 MPa, deformation is governed by the thermally activated dislocation glide (power-law breakdown) accompanied by the accelerated texture evolution. Furthermore, an increase in stress level also leads to load transfer from the plastically deformed matrix to the elastically deformed precipitates in the axial direction, along with an increase in the lattice misfit between the matrix and the precipitate phases.

Multiscale poro-creep model for cement-based materials

SUMMARY Experimental observations clearly show that the relative humidity (hr) conditions influence significantly the creep behavior of cement-based materials, indicating that the water present within these materials plays a crucial role. This work presents a creep model for hardened cement pastes (HCP), based on a multiscale homogenization approach. It takes into account both free and adsorbed water contained in the porosity and investigates their effects on the HCP macroscopic creep behavior. The calcium silicate hydrate phase is assumed to be linear viscoelastic, and the Mori–Tanaka scheme is applied in the Laplace–Carson space to the composite formed of porosity, calcium silicate hydrate, and the other main hydrated compounds (which behavior is linearly elastic) by making use of the correspondence principle. With this model, estimations of the evolution of the macroscopic creep behavior of HCP submitted to constant external loading are examined under different hr and compared with available experimental data. Finally, a method for implementing the model in a finite element code is proposed, and simulations of standard creep tests are performed to assess its validity. Copyright © 2011 John Wiley & Sons, Ltd.

Brittle creep in basalt and its application to time-dependent volcano deformation

Time-dependent brittle deformation is a fundamental and pervasive process operating in the Earth's upper crust. Its characterization is a pre-requisite to understanding and unraveling the complexities of crustal evolution and dynamics. The preferential chemical interaction between pore fluids and strained atomic bonds at crack tips, a mechanism known as stress corrosion, allows rock to fail under a constant stress that is well below its short-term strength over an extended period of time; a process known as brittle creep. Here we present the first experimental measurements of brittle creep in a basic igneous rock (a basalt from Mt. Etna volcano) under triaxial stress conditions. Results from conventional creep experiments show that creep strain rates are highly dependent on the level of applied stress (and can be equally well fit by a power law or an exponential law); with a 20% increase in stress producing close to three orders of magnitude increase in creep strain rate. Results from stress-stepping creep experiments show that creep strain rates are also influenced by the imposed effective confining pressure. We show that only part of this change can be attributed to the purely mechanical influence of an increase in effective pressure, with the remainder interpreted as due to a reduction in stress corrosion reactions; the result of a reduction in crack aperture that restricts the rate of transport of reactive species to crack tips. Overall, our results also suggest that a critical level of crack damage is required before the deformation starts to accelerate to failure, regardless of the level of applied stress and the time taken to reach this point. The experimental results are discussed in terms of microstructural observations and fits to a macroscopic creep law, and compared with the observed deformation history at Mt. Etna volcano.

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.

Irradiation creep of SA 304L and CW 316 stainless steels: Mechanical behaviour and microstructural aspects. Part II: Numerical simulation and test of SIPA model

A cluster dynamic model has been adapted to test the Stress Induced Preferential Absorption of Defect (SIPA) on Frank loops hypothesis concerning irradiation creep, to reproduce quantitatively both microstructure evolution and its stress induced anisotropy and macroscopic creep rate. It is concluded that SIPA on Frank loops model can account for the observed defects structure, but is unable to reproduce quantitatively the creep rate.

Creep of a C-S-H gel: a micromechanical approach

Both clays and calcium silicate hydrates(the main hydration products of Portland cements) exhibit a microstructure made up of lamellar particles. The microscopic mechanism responsible for the macroscopic creep of such materials is often described as the relative sliding of the sheets. This paper proposes a micromechanical approach to estimate the macroscopic creep behavior rising from this microscopic mechanism. The asymptotic evolution of creep at both short- and long-term is especially investigated. More precisely, a non-vanishing initial elastic strain is retrieved. At long-term, a threshold on porosity appears. At lower porosities, the creep evolution admits an asymptotic strain. At higher porosities, it admits an asymptotic strain rate.

An activated energy approach for accelerated testing of the deformation of UHMWPE in artificial joints

The deformation behavior of ultrahigh molecular polyethylene (UHMWPE) is studied in the temperature range of 23–80 °C. Samples are examined in quasi-static compression, tensile and creep tests to determine the accelerated deformation of UHMWPE at elevated temperatures. The deformation mechanisms under compression load can be described by one strain rate and temperature dependent Eyring process. The activation energy and volume of that process do not change between 23 °C and 50 °C. This suggests that the deformation mechanism under compression remains stable within this temperature range. Tribological tests are conducted to transfer this activated energy approach to the deformation behavior under loading typical for artificial knee joints. While this approach does not cover the wear mechanisms close to the surface, testing at higher temperatures is shown to have a significant potential to reduce the testing time for lifetime predictions in terms of the macroscopic creep and deformation behavior of artificial joints.

Time‐dependent brittle creep in Darley Dale sandstone

The characterization of time‐dependent brittle rock deformation is fundamental to understanding the long‐term evolution and dynamics of the Earth's crust. The chemical influence of pore water promotes time‐dependent deformation through stress corrosion cracking that allows rocks to deform at stresses far below their short‐term failure strength. Here, we report results from a study of time‐dependent brittle creep in water‐saturated samples of Darley Dale sandstone (initial porosity, 13%) under triaxial stress conditions. Results from conventional creep experiments show that axial strain rate is heavily dependent on the applied differential stress. A reduction of only 10% in differential stress results in a decrease in strain rate of more than two orders of magnitude. However, natural sample variability means that multiple experiments must be performed to yield consistent results. Hence we also demonstrate that the use of stress‐stepping creep experiments can successfully overcome this issue. We have used the stress‐stepping technique to investigate the influence of confining pressure at effective confining pressures of 10, 30, and 50 MPa (while maintaining a constant 20 MPa pore fluid pressure). Our results demonstrate that the stress corrosion process appears to be significantly inhibited at higher effective pressures, with the creep strain rate reduced by multiple orders of magnitude. The influence of doubling the pore fluid pressure, however, while maintaining a constant effective confining pressure, is shown to influence the rate of stress corrosion within the range expected from sample variability. We discuss these results in the context of microstructural analysis, acoustic emission hypocenter locations, and fits to proposed macroscopic creep laws.

Nanogranular origin of concrete creep

Concrete, the solid that forms at room temperature from mixing Portland cement with water, sand, and aggregates, suffers from time-dependent deformation under load. This creep occurs at a rate that deteriorates the durability and truncates the lifespan of concrete structures. However, despite decades of research, the origin of concrete creep remains unknown. Here, we measure the in situ creep behavior of calcium-silicate-hydrates (C-S-H), the nano-meter sized particles that form the fundamental building block of Portland cement concrete. We show that C-S-H exhibits a logarithmic creep that depends only on the packing of 3 structurally distinct but compositionally similar C-S-H forms: low density, high density, ultra-high density. We demonstrate that the creep rate ( approximately 1/t) is likely due to the rearrangement of nanoscale particles around limit packing densities following the free-volume dynamics theory of granular physics. These findings could lead to a new basis for nanoengineering concrete materials and structures with minimal creep rates monitored by packing density distributions of nanoscale particles, and predicted by nanoscale creep measurements in some minute time, which are as exact as macroscopic creep tests carried out over years.

HOMOGENIZED CREEP BEHAVIOR OF CFRP LAMINATES AT HIGH TEMPERATURE

In this study, creep behavior of a CFRP laminate subjected to a constant stress is analyzed based on the time-dependent homogenization theory developed by the present authors. The laminate is a unidirectional carbon fiber/epoxy laminate T800H/#3631 manufactured by Toray Industries, Inc. Two kinds of creep analyses are performed. First, 45° off-axis creep deformation of the laminate at high temperature (100°C) is analyzed with three kinds of creep stress levels, respectively. It is shown that the present theory accurately predicts macroscopic creep behavior of the unidirectional CFRP laminate observed in experiments. Then, high temperature creep deformations at a constant creep stress are simulated with seven kinds of off-axis angles, i.e., θ = 0°, 10°, 30°, 45°, 60°, 75°, 90°. It is shown that the laminate has marked in-plane anisotropy with respect to the creep behavior.

A multiscale creep model as basis for simulation of early-age concrete behavior

A previously published multiscale model for early-age cement-based materials [Pichler, et al.2007. "A multiscale micromechanics model for the autogenous-shrinkage deformation of early-age cement-based materials." Engineering Fracture Mechanics, 74, 34-58] is extended towards upscaling of viscoelastic properties. The obtained model links macroscopic behavior, i.e., creep compliance of concrete samples, to the composition of concrete at finer scales and the (supposedly) intrinsic material properties of distinct phases at these scales. Whereas finer-scale composition (and its history) is accessible through recently developed hydration models for the main clinker phases in ordinary Portland cement (OPC), viscous properties of the creep active constituent at finer scales, i.e., calcium-silicate-hydrates (CSH) are identified from macroscopic creep tests using the proposed multiscale model. The proposed multiscale model is assessed by different concrete creep tests reported in the open literature. Moreover, the model prediction is compared to a commonly used macroscopic creep model, the so-called B3 model.

Multiscale Model for Creep of Shotcrete - From Logarithmic-Type Viscous Behavior of CSH at the μm-Scale to Macroscopic Tunnel Analysis

A previously published multiscale model for early-age cement-based materials [Pichler et al. 2007. “A multiscale micromechanics model for the autogenous-shrinkage deformation of early-age cement-based materials.” Engineering Fracture Mechanics, 74, 34-58] is extended towards upscaling of viscoelastic properties. The obtained model links macroscopic behavior, i.e., creep compliance of concrete samples, to the composition of concrete at finer scales and the (supposedly) intrinsic material properties of distinct phases at these scales. Whereas finer-scale composition (and its history) is accessible through recently developed hydration models for the main clinker phases in ordinary Portland cement (OPC), viscous properties of the creep active constituent at finer scales, i.e., calcium-silicate-hydrates (CSH) are identified from macroscopic creep tests using the proposed multiscale model. The proposed multiscale model is assessed by different concrete creep tests reported in the open literature. Moreover, the model prediction is compared to empirical creep models, such as the so-called B3 model. Finally, the developed multiscale model is incorporated in the macroscopic analysis of shotcrete tunnel linings. Hereby, the early-age properties of shotcrete are specified by the presented multiscale model, taking mix design, cement characteristics, and on-site conditions into account.