Multi-step Creep Tests Research Articles

Multi-step creep tests of notched beams of silver fir (Abies alba) at different initial moisture contents

Silver fir is an important species for French timber engineering industry but its application faces drying issues. This paper presents the results of creep and ramp-loading bending tests on full-scale silver fir notched beams at different initial moisture contents. Initial moisture content showed no discernible impact on instantaneous maximum force, while dynamic compliance appeared to be proportional to this force, possibly due to the dowelling effect. Beam-theory equations are solved using finite differences with crack propagation assimilated to a height reduction, providing an estimation of the compliance and that total deflection primarily results from creep rather than crack. No correlation is observed between the maximum relative compliance and the initial moisture content. Besides this maximum value never reaches the deformation factor for serviceability design in Eurocode 5, suggesting oversizing for green wood. The discrepancy between experimental and theoretically derived crack openings highlights limitations in traditional beam theory, especially concerning fracture mechanics analysis and non-linear effects. For all tests upward crack trajectories towards compression zone are observed and physically discussed. These findings contribute to a better understanding of the mechanical behaviour of wood, particularly regarding creep and crack propagation, with implications for structural design and material characterisation.

Damage evolution in flax fibre composite under creep load

This work aims to reveal the damage mechanisms and evolution in unidirectional flax fibre biocomposites when subjected to creep load. X-ray micro computed tomography and acoustic emission (AE) was used to monitor the failure progress during flexural creep tests. A correlation between the event clusters and directly observed damage modes was established based on coupons with expected failure mechanisms and then validated by computed tomography observations. The damage initiated from matrix cracking in the primary creep stage, and then fibre–matrix interface debonding combined with fibre pull-out occurred sequentially during the steady creep stage. In the tertiary creep stage, the explosive fibre fracture emerged and eventually triggered catastrophic failure. Considerably more AE events were detected during creep tests compared to those in quasi-static tests, which indicates that intensive damage is generated under creep load, and therefore causes the strength degradation. A good agreement was observed between the cumulative number of AE events and the increasing damage volume fraction over time determined by X-ray micro computed tomography during multi-step creep tests.

Study on Shear Creep Characteristics of the Discontinuities with Different 3D Morphologies

The rheological phenomenon of rock mass affects the long-term safety of rock mass engineering. In this study, gneiss samples with different 3D morphologies are prepared by splitting tests and are tested through multi-step creep tests. The long-term strength of rock discontinuities is determined by using several methods. The test results show that as the 3D morphological parameter increases, the creep deformation, creep rate, and the duration of failure all decrease. The long-term strength of rock discontinuities is linearly related to the 3D morphological parameter. Based on the principle of damage mechanics for rock mass, a damage variable is introduced in the creep model, and an improved non-linear Burgers model is established. Research results are of great theoretical significance and practical value for the design, construction, and long-term safety of rock mass engineering.

A Constitutive Model of Time-Dependent Deformation Behavior for Sandstone

Considering sandstone's heterogeneity in the mesoscale and homogeneity in the macroscale, it is very difficult to describe its time-dependent behavior under stress. The mesoscale heterogeneity can affect the initiation and propagation of cracks. Clusters of cracks have a strong influence on the formation of macroscale fractures. In order to investigate the influence of crack evolution on the formation of fractures during creep deformation, a time-dependent damage model is introduced in this paper. First, the instantaneous elastoplastic damage model of sandstone was built based on the elastoplastic theory of rock and the micro-heterogeneous characteristics of sandstone. A viscoelastic plastic creep damage model was established by combining the Nishihara model and the elastoplastic damage constitutive model. The proposed models have been validated by the results of corresponding analytical solutions. To help back up the model, some conventional constant strain rate tests and multi-step creep tests were carried out to analyze the time-dependent behavior of sandstone. The results show that the proposed damage model can not only reflect the time-dependent viscoelastic deformation characteristics of sandstone, but also provide a good fit to the viscoelastic plastic deformation characteristics of sandstone's creep behavior. The damage model can also reproduce the propagation process of mesoscopic cracks in sandstone upon the damage and failure of micro-units. This research can provide an effective tool for studying the propagation of microscopic cracks in sandstone.

Creep characteristics and prediction of creep failure of rock discontinuities under shearing conditions

Shear creep is one of the most important mechanical behaviors of rock discontinuities. The creep mechanism and prediction of starting point of the accelerating creep stage are vital for establishing the creep model and predicting creep failure. In this study, a series of multi-step creep tests are conducted. The three creep stages of shear creep tests are investigated in detail, and a method for predicting the accelerating creep stage is proposed. Distinct nonlinear and local fluctuations caused by cracking are observed in the creep curve. To describe the transition creep stage and steady creep stage, an empirical creep model is established, and the creep characteristics related to the joint roughness coefficient (JRC) and the normal stress are explored in detail using the model’s parameters. The creep process can be described as involving the JRC resistance weakening and frictional resistance compensation, and a model also established to describe this process. The frictional resistance cannot compensate for the loss of JRC resistance; consequently, creep failure occurs. The starting point of the accelerating creep stage can be predicted by combining the JRC weakening and frictional mobilization model and the empirical creep model. A new method for determining long-term strength is also proposed based on the relationships between the starting point creep deformation and the shear creep stress.

Gas permeability evolution mechanism during creep of a low permeable claystone

Clayey rocks, due to its low permeability and self-sealing ability, have been selected as a privilege candidate host rock for underground radioactive waste repository in many countries. The gas permeability evolution is very sensitive to the deformation process in such rocks and can be used as a good indicator of microstructure changes such as the growth of micro-cracks. In this work, the mechanism of gas permeability evolution in the Callovo-Oxfordian (Cox) claystone during a creep deformation is investigated. Firstly, multi-step creep tests with different confining pressures are carried out to characterize gas permeability evolutions under different levels of the deviatoric stress. Secondly, in order to minimize effects of multiple deviatoric loading steps, one-step creep tests are also realized. Throughout all creep tests, the gas permeability is measured by a transient pulse decay method in together with the axial and radial strains. It is first found that the gas permeability of the claystone significantly decreases with the confining pressure or hydrostatic stress. The gas permeability in multi-step creep tests can exhibit a four-stage evolution with the progressive increase of deviatoric stress level, composed of a rapid decrease, a gentle decrease, a gentle increase and a rapid increase. However, the gas permeability is continuously decreasing during one-step creep tests. The permeability change in a one-step creep test can be well correlated with the volumetric strain variation by a logarithmic function. Effects of loading orientation with respect to claystone bedding planes are also investigated.

Acoustic emission hysteresis effect of polyvinylchloride under multi-step mechanical loads

Multi-step creep tests and multi-step stress relaxation tests were performed on polyvinylchloride samples. Acoustic emission signals were monitored to assess the damage evolution in the tested samples, and an interesting phenomenon, named here as the ‘acoustic emission hysteresis effect’, was found in both the multi-step creep tests and multi-step stress relaxation tests. The observed acoustic emission behaviour indicates that the damage in polymers is time dependent, and the acoustic emission hysteresis effect is attributed to the viscoelasticity and time-dependent damage in the material. The more marked the viscoelasticity of the material, the greater the acoustic emission hysteresis effect.

Steady-State Creep of Rock Salt: Improved Approaches for Lab Determination and Modelling

Actual problems in geotechnical design, e.g., of underground openings for radioactive waste repositories or high-pressure gas storages, require sophisticated constitutive models and consistent parameters for rock salt that facilitate reliable prognosis of stress-dependent deformation and associated damage. Predictions have to comprise the active mining phase with open excavations as well as the long-term development of the backfilled mine or repository. While convergence-induced damage occurs mostly in the vicinity of openings, the long-term behaviour of the backfilled system is dominated by the damage-free steady-state creep. However, because in experiments the time necessary to reach truly stationary creep rates can range from few days to years, depending mainly on temperature and stress, an innovative but simple creep testing approach is suggested to obtain more reliable results: A series of multi-step tests with loading and unloading cycles allows a more reliable estimate of stationary creep rate in a reasonable time. For modelling, we use the advanced strain-hardening approach of Gunther–Salzer, which comprehensively describes all relevant deformation properties of rock salt such as creep and damage-induced rock failure within the scope of an unified creep ansatz. The capability of the combination of improved creep testing procedures and accompanied modelling is demonstrated by recalculating multi-step creep tests at different loading and temperature conditions. Thus reliable extrapolations relevant to in-situ creep rates ( $$10^{-9}$$ to $$10^{-13}$$ s $$^{-1}$$ ) become possible.

Experimental simulation of chemomechanical processes during deep burial diagenesis of carbonate rocks

Chemomechanical processes involved in the deep burial diagenesis of carbonate petroleum reservoirs are still poorly understood. To better understand these processes and explain how porosity and permeability can be preserved at the great depth of DBRs (deeply buried reservoirs), we developed an experimental device allowing both the simulation of high-pressure/stresses/temperature conditions (80°C, 60 MPa of confining pressure, and differential stress up to 40 MPa) of DBR and the circulation of different fluids in rock samples. We tested (triaxial multistep creep tests) four core samples of a cemented limestone and analyzed creep deformations, fluids chemistry, and petrographical and petrophysical properties of samples. Different flow conditions (no flow and flow through) and chemical compositions (natural meteoric water with and without phosphate ions) were considered. Our study showed that the precipitation of calcite on free pore walls of micrites blocks the microporosity between micrite crystals, thus rendering the microporosity inaccessible to fluids. Hence, the connected porosity decreased strongly after experimentation. This is due to the PSC (pressure solution creep) which is the main process implied in the porosity reduction of a carbonate rock during deep burial. The preservation of macropores during PSC allows the preservation of permeability. In addition, calcite solubility is positively dependent on mechanical parameters (axial compaction and axial stress), thus suggesting that calcite can precipitate during decompression of deep basinal fluids, resulting in changes in porosity. A comparison of experimental results with theoretical calculations showed that the integration of the PSC process into calculation databases would greatly improve the modeling of DBR.

The influence of different fluids on the static fatigue of a porous rock: Poro-mechanical coupling versus chemical effects

Characterization of time-dependent brittle deformation is important for estimating the long-term stability of rock structures in shallow environments such as underground mines which are exposed to water or in a water vapor environment. The poro-mechanical (pore pressure) and chemical (stress corrosion reactions) effects of fluids at crack tips are responsible for the subcritical propagation of microcracks. This brittle creep results in the weakening of porous rocks over time (i.e., static fatigue). The focus of this work was to characterize using very long duration uniaxial multi-step creep tests, both the fluids effects on subcritical stress corrosion cracking in a porous rock (oolithic iron ore). Different fluids with increasing levels of chemical influence (oil, ethanol and water) were tested and both acoustic and mechanical properties were investigated. The evolution of the cumulative number of AE (Acoustic Emission) events, which reproduces the shape of the creep curves very efficiently, and static elastic properties indicate that micro-cracking plays the main role in the creep process. The poro-mechanical effect, which is predominant under partially saturated (water or ethanol) conditions, decreases the rate of subcritical cracking through capillary attraction forces. These forces harden porous rocks by modifying the effective stress state, increasing the activation energy barrier of the stress corrosion process and the fracture toughness and decreasing the stress intensity factor. The chemical effect of fluids is related to minerals developing stress corrosion reactions at crack tips which enhance subcritical cracking. Immersion in water/ethanol annihilates capillary forces and decreases the activation energy of the chemical reactions, thus increasing dilatancy, the rate of stress corrosion cracking, AE activity and rock weakening. Under saturated conditions, the time-dependent strength and time to failure increase as the chemical influence of the interstitial fluid decreases but the cumulative number and energy of AE at failure do not seem to be influenced by the chemistry of fluids. The short-term strength and deformability are also influenced by the level of chemical influence of the interstitial fluid but to a less remarkable extent because of the slow rate of chemical reactions. Water is therefore the most effective chemical agent promoting stress corrosion of iron ore among the fluids tested in our study.

Estimation of the damage of a porous limestone using continuous wave velocity measurements during uniaxial creep tests

The damage of an oolitic limestone during quasi-instantaneous compressive tests and multi-step creep tests was studied using an experimental device which enabled the simultaneous and continuous measurement of strains and elastic wave velocities under mechanical loading and controlled hydrous conditions. The simultaneous measurements of five elastic wave velocities (3 P-waves and 2 S-waves) in different directions of propagation and polarisation allowed us to assess the acoustic tensor at any time during loading and thus continuously monitor the evolution of rock damage. The general trend observed in the experimental results was the strong influence of hydrous conditions on both the quasi-instantaneous and time dependent behaviour of this rock. As traditionally observed in the quasi-instantaneous behaviour of quasi-brittle rocks under deviatoric loading, typical anisotropic straining was observed, confirmed by the anisotropy of the wave velocity measured in axial and lateral directions. However, after full unloading, even if a decrease in all waves’s velocities and dynamic elastic moduli was observed, the quasi-isotropy of waves’s velocities was recovered. This recovery after unloading cycle was observed until stress levels close to the peak (i.e., failure) stress. A comparison of laboratory results with numerical predictions from micromechanical models showed that these observations could not be explained by traditional crack propagation theories and that other mechanisms of crack growth must therefore be considered. These trends were also observed during the loading/unloading stages between each creep step with one notable difference, namely that the anisotropy developed during the creep stage was not recovered during the full unloading. A combination of crack growth and crack nucleation combined with a mechanism of progressive crack sliding and closure seems to explain these unusual results. The nucleation of cracks is mostly related to fast loading while the crack propagation is mostly due to subcritical growth of favourable oriented cracks.

Creep behavior of Bure clayey rock

Clayey rock may be the host medium for a French long-term nuclear-waste storage facility. To gain better understanding of the delayed behavior of this potential host rock, we conducted a testing program that focused on creep tests. Fourteen tests were conducted: short-term multi-step creep tests (six at ambient temperature, four at T=80 °C and four on damaged samples); and four long-term mono-step creep tests (in which a constant load is applied for nearly 2 years). Experimental results are displayed and discussed.

Proposition d'une loi « hybride » modélisant l'écrouissage du sel gemme

The work presented in this paper is part of a research program dealing with the thermomechanical behaviour of rock salt. It consists of studying the deferred behaviour by means of multi-step creep tests with changes in deviator and temperature. The test results have revealed the strain-hardening character of rock salt superposed to the influence of temperature and stress. The interpretation of the test results with the model designed by J. Lemaitre, is not completely satisfactory for the entire set of test results because Lemaitre's model is used for the modeling of the viscoplastic behaviour of materials with only one strain hardening variable. Hence, a "hybrid" model introducing a double variable for strain hardening has been proposed. The validation of this model on the creep tests is very satisfactory and confirms the existence of two variables of strain hardening for rock salt behaviour.Key words: rock salt, multi-step creep, strain hardening, J. Lemaitre model.

Elevated Temperature Creep of Polyurethane under Nonlinear Torsional Stress with Step Changes in Torque

Constant stress experiments, recovery, and multi-step creep tests in torsion in the nonlinear range were performed at different temperatures up to 160 °F. It was found that the results could be described by a power function of time whose exponent was independent of stress and temperature. Most of the temperature effect and most of the nonlinearity were found in the coefficient of the time-dependent term. The nonlinearity was described by the multiple integral representation, and the changes in stress were adequately predicted by the modified superposition method, except at the highest temperatures.