Anisotropic time-dependent behaviors of shale under direct shearing and associated empirical creep models

Understanding the anisotropic creep behaviors of shale under direct shearing is a challenging issue.In this context,we conducted shear-creep and steady-creep tests on shale with five bedding orientations (i.e.0°,30°,45°,60°,and 90°),under multiple levels of direct shearing for the first time.The results show that the anisotropic creep of shale exhibits a significant stress-dependent behavior.Under a low shear stress,the creep compliance of shale increases linearly with the logarithm of time at all bedding orientations,and the increase depends on the bedding orientation and creep time.Under high shear stress conditions,the creep compliance of shale is minimal when the bedding orientation is 0°,and the steady-creep rate of shale increases significantly with increasing bedding orientations of 30°,45°,60°,and 90°.The stress-strain values corresponding to the inception of the accelerated creep stage show an increasing and then decreasing trend with the bedding orientation.A semilogarithmic model that could reflect the stress dependence of the steady-creep rate while considering the hardening and damage process is proposed.The model minimizes the deviation of the calculated steady-state creep rate from the observed value and reveals the behavior of the bedding orientation's influence on the steady-creep rate.The applicability of the five classical empirical creep models is quantitatively evaluated.It shows that the logarithmic model can well explain the experimental creep strain and creep rate,and it can accurately predict long-term shear creep deformation.Based on an improved logarithmic model,the variations in creep parameters with shear stress and bedding orientations are discussed.With abovementioned findings,a mathematical method for constructing an anisotropic shear creep model of shale is proposed,which can characterize the nonlinear dependence of the anisotropic shear creep behavior of shale on the bedding orientation.

Generic creep behavior and creep modeling of an aged surface support liner under tension

Polymer-based materials have been motivated to be an alternative support system element in the mining/tunneling industry due to their logistic and geotechnical benefits.Thin spray-on liner(TSL),a term to define the application of the material on the rock surface with a layer ranging from 2 mm to10 mm in thickness,shows some promising results.TSLs are mainly composed of plastic,polymer,or cement-based ingredients to a certain proportion.This study intends to reveal the time-dependent response of TSL specimens,cured throughout 500 d,under four constant stress levels for stable laboratory conditions.The results were correlated using two interrelated equations to predict the material’s service life(creep-rupture envelopes).The proposed correlations offered an insight into both the effective permanent support time and the strain amount at the liner failure.The time-dependent deformation of TSL,whose performance is highly responsive to creep behavior,was obtained so that the design engineers may use the findings to avoid the severe problems of material creep.Experimental data were also used to develop a Burgers(four-element)creep model.Since the liner has a nonlinear time-dependent behavior,creep models were built for each stress level separately.Subsequently,a generic equation was obtained using the nonlinear parametric dependencies.There is a good agreement between the proposed model and the experimental results.The proposed model can be used as a basis for future numerical studies related to the support behavior of aged surface support liners.

Experimental investigation on the nanoindentation viscoelastic constitutive model of quartz and kaolinite in mudstone

The creep behaviors in deep underground engineering structures,especially in soft rocks,have a remarkable impact on the long-term stability of the excavations,which finally leads to the high risk and failure of it.Accordingly,it is essential to recognize the time-dependent deformation through the investigation of this phenomenon.In this study,the creep behaviors of soft rocks were examined to help understand the underlying mechanism of the extended time-dependent deformation.Due to the limited results about the time-dependent properties of the constituents of the rock that reveal their heterogeneity,the targeting nanoindentation technique(TNIT),was adopted to investigate the viscoelastic characteristics of kaolinite and quartz in a two-constituent mudstone sample.The TNIT consists of identifications of mineralogical ingredients in mudstone and nanoindentation experiments on each identified constituent.After conducting experiments,the unloading stages of the typical indentation curves were analyzed to calculate the hardness and elastic modulus of both elements in mudstone.Additionally,the 180 s load-holding stages with the peak load of 50 mN were transformed into the typical creep strain-time curves for fitting analysis by using the Kelvin model,the standard viscoelastic model,and the extended viscoelastic model.Fitting results show that the standard viscoelastic model not only can perfectly express the nanoindentation creep behaviors of both kaolinite and quartz but also can produce suitable constants used to measure their creep parameters.The creep parameters of kaolinite are much smaller than that of quartz,which causes the considerable time-dependent deformation of the soft mudstone.Eventually,the standard viscoelastic model was also verified on the quartz in a sandstone sample.

Primary-transient creep and anelastic backflow of pure copper deformed at low temperatures and ultra-low strain rates

Creep and anelastic backflow behaviors of pure copper （4N Cu） with grain size dg=40 μm were investigated at low temperatures of T〈0.3Tm （Tm is melting point） and ultra-low creep rates of ε≤1×10^-10 s^-1 by a high strain-resolution measurement （the helicoid spring specimen technique）. Analysis of creep data was based on the scaling factors of creep curves instead of the conventional extrapolated steady-state creep rate. Power-law creep equation is suggested to be the best for describing the primary transient creep behavior, because the pre-parameter does not apparently change with elapsed time. The observed anelastic strains are 1/6 of the calculated elastic strains, and linear viscous behavior was identified from the logarithm plot of the anelastic strain rate versus anelastic strain （slope equals 1）. Therefore, the creep anelasticity is suggested to be due to the unbowing of there-dimensional network of dislocations.

CREEP BEHAVIOUR OF T300/5222(C/E)COMPOSITE LAMINATEWITH CROSS-PLY

A study is conducted on the creep behaviour of T300/5222 compositelaminate by expenmental and theoretical researches. Experimental results of creep,stress relaxation and historydependent stress-strain curves at different temperaturelevels are reported. Both loading and unloading processes are included. The locally av-eraged constitutive functionals are established on the basis of rational theimodynamics.Finally, a non-linear creep constitutive equation is constructed using the experimentaldata.

Time-dependent behavior and permeability evolution of limestone under hydro-mechanical coupling

Excessively high pore water pressure presents unpredictable risks to the safety of rock tunnels in mountainous regions that are predominantly composed of limestone. Investigating the creep characteristics and permeability evolution of limestone under varying hydrated conditions is crucial for a better understanding of the delayed deformation mechanisms of limestone rock tunnels. To this end, this paper initially conducts a series of multi-stage triaxial creep tests on limestone samples under varying pore water pressures. The experiment examines how pore water pressure affects limestone’s creep strain, strain rate, long-term strength, lifespan, and permeability, all within the context of hydraulicmechanical(HM) coupling. To better describe the creep behavior associated with pore water pressure, this paper proposes a new nonlinear fractional creep constitutive model. This constitutive model depicts the initial, steady-state, and accelerated phases of limestone’s creep behavior. Finally, the proposed model is applied to the numerical realization of deformation in limestone tunnel, validating the effectiveness of the proposed constitutive model in predicting tunnel’s creep deformation. This research enhances our understanding of limestone’s creep characteristics and permeability evolution under HM coupling, laying a foundation for assessing the longterm stability of mountain tunnels.

A Constitutive Model of Granite Shear Creep under Moisture

Previous constitutive models of granite shear creep have two limitations：（1） although moisture greatly affects granite shear creep behavior, currently there are no constitutive models that include this factor;（2） there are also no models that include an acceleration stage. This paper presents an improved Burgers constitutive model with the addition of a damage parameter to characterize the moisture effect and uses a nonlinear relation equation between stress and strain for inclusion as the acceleration stage. The damage parameter is determined from granite creep experiment under four different moisture contents（0%, 0.22%, 0.49%, and 0.79%）. The nonlinear relation equation is obtained by fitting a dataset of stain versus time under five different loading stages. To verify the presented model, a creep experiment was conducted on other granite samples and the results show that the model agrees well with the experimental observation data.

FEM analysis of vacuum hot bulge forming of Hastelloy C-276 thin-walled cylindrical workpiece

A stress relaxation test has been carried out for Hastelloy C-276 at temperature of 800 ~C and initial stress level of 250 MPa. Based on the experimental stress relaxation curve, the relationship between creep strain rate and stress has been derived. Then, a set of creep constitutive equations has been built and the values of constants arising in the constitutive equations have been determined by fitting the creep strain rate-stress curve. Close agreement between computed results and experimental ones is obtained for stress relaxation data. The creep constitutive equation set has been integrated with the commercial FE （finite element） solver MSC.Marc via the user defined subroutine, CRPLAW, for the vacuum hot bulge forming process modelling of Hastelloy C-276 thin-walled cylindrical workpiece. The temperature field, the radius-direction displacement field and the stress-strain field are calculated and analyzed. Furthermore, the bulging dimension and the final internal diameter of workpiece are predicted and the test results verify the reliability of the finite element method.

EBSD parameter assessment and constitutive models of crept HR3C austenitic steel

Creep damage and evolution of HR3C steel at 650℃ were investigated using electron backscatter diffraction(EBSD),and EBSD-based parameter assessments were conducted.EBSD analyses show that the grain size is almost unchanged and no obvious texture formed after creep at different creep rates.The lowest proportion of low Σ coincidence site lattice grain boundaries under 150 MPa implies that the primary twin structures are preserved under the low stress level,while some twin structures evolved into general grain boundaries at the high creep level.Two main damage features of microcracks and cavities can be seen along the grain boundaries:the former emerged at higher stress levels,while the latter appeared at the lower stress level,and both were shown under medium stress.Band contrast shows that the most severe creep damage is present at 170 MPa.It implies that the creep mechanism differs distinctly under different stress levels,and the transition point is around 170 MPa.Kernel average misorientation is better to describe the local plastic deformation related to the strain distribution while grain reference orientation deviation describes the inhomogeneous strain distribution.Creep lifetime prediction models including the isothermal method,Larson-Miller parameter method and Monkman–Grant relation were evaluated by the experimental data and literature data,and they are valid for predicting creep behavior.