Time-dependent Creep Deformation Research Articles

Fractional cyclic cohesive zone model for time-dependent fatigue behavior of soft adhesives under mode-II loading

Soft adhesives exhibit nonlinear viscoelastic behavior during cyclic loading, suggesting that their cycle-dependent fatigue behavior can be significantly affected by the time-dependent deformation behavior. Soft adhesives are frequently subject to various cyclic conditions in practical applications, presenting potential safety risks. This paper has proposed a fractional cyclic cohesive zone model (CZM) to characterize the time-dependent fatigue behavior of soft adhesives. To capture the nonlinear evolution of fatigue damage under asymmetric stress-controlled cyclic loading, a fatigue damage model that considers the contribution of in-situ stress/strain was incorporated into fractional-order viscoelastic model. The proposed CZM was validated through single-lap shear creep tests at various stress levels and fatigue tests at various stress amplitudes and loading periods. Furthermore, the impacts of stress ratio and peak stress level on fatigue failure under different loading periods were investigated using the proposed CZM. The results indicate that under a short loading period, the failure of the soft adhesives is primarily influenced by cycle-dependent fatigue damage, while under a long loading period, it is primarily affected by time-dependent creep deformation. Overall, this work offers a numerical strategy to describe the fatigue failure of nonlinear viscoelastic soft adhesives and to understand their time-dependent fatigue failure mechanism, with implications for product design and optimization.

Strength and creep characteristics of methane hydrate-bearing clayey silts of the South China Sea

Natural gas hydrates are abundantly detected in the clayey-silty deposits of the South China Sea (SCS). The long-term hydrate extraction process may trigger creep deformation and failure of the clayey-silty reservoir. Hence, it is essential to evaluate the creep properties of the clayey-silty hydrate reservoir for safe production. Current research mainly focused on rapid failure, while neglecting time-dependent creep deformation of the clayey-silty hydrate reservoir. In this study, a number of triaxial shear and creep experiments were carried out on methane hydrate-bearing clayey silts (HBCSs) in the SCS in order to investigate their strength and creep deformation characteristics. The results indicated that: (1) the increase of effective stress enhances the shear strength and deformation, and the presence of hydrates enhances the shear strength while reducing the deformation; (2) the creep strain and strain rate increase as the creep stress ratio and effective stress rise; (3) the accelerated creep stage only occurs at higher effective stress in HBCSs and not in hydrate-free clayey silts (HFCSs), and the creep strain and strain rate of the HBCSs are lower than those of the HFCSs. The experimental data will contribute to the construction and verification of creep constitutive models for HBCSs in the SCS.

A coupled model of wellbore-formation thermal phenomena and salt creep in offshore wells

The present work proposes a mathematical framework for calculating heat transport and annular pressure buildup (APB) in petroleum wells, taking into account salt creep in uncemented annular segments. To achieve this, we propose a Laplace Transform-based semi-analytic method to calculate transient heat flow in the wellbore. To estimate wellbore closure due to creep, we developed a Finite Element Method (FEM) formulation to handle the three deformation components that affect salt displacement. In addition to the time-dependent creep deformation of the rock, the model initially considers the elastic deformation of the rock due to geomechanical loads and pressure changes in the exposed annulus. The model was compared against field data from a well that contained an 800-m long uncemented second annulus exposed to halite. Regarding APB, considering creep in the salt layer resulted in a 2.55-MPa increase (approximately 15%) in annulus pressure. The thermal expansion of the salt rock did not significantly affect APB but significantly increased the computational cost of the simulations.

Crack driving forces under creep conditions in presence of material inhomogeneity

ABSTRACT Under time-dependent creep deformation in metallic materials in the presence of a crack, the driving force is influenced at a distance in the presence of a zone (such as an interlayer, interface, hole, etc.) which deforms differently in reference configuration. This influence may increase or decrease the crack driving force based on the type of inhomogeneity (elastic, plastic, creep). The nature and extent of influence of material inhomogeneity are studied in this work with a configurational force-based rate of crack driving force definition for a crack in the presence of dissimilar metal weld zone, HAZ and second base metal.

Thermoelastic creep evolution in a variable thickness functionally graded piezoelectric rotating annular plate considering convection and radiation heat transfer

The thermoelastic time-dependent creep progress of a rotating annular plate with nonuniform thickness made of functionally graded piezoelectric material considering convection heat transfer and solar radiation was investigated. The nonlinear differential equation of heat transfer considering conduction, convection, and solar radiation was solved using the differential transformation method. Then, the differential equation of equilibrium for the annular plate containing creep strains was derived. Firstly, the differential equation was solved analytically for the zero time . Then, the stress and strain rates were achieved using Norton’s law with Prandtl–Reuss equations. Finally, the time-dependent creep stresses and deformation redistributions were obtained employing an iterative method.

A micromechanical fatigue damage model for quasi-brittle rocks subjected to triaxial compressive cyclic loads

This paper is devoted to a novel micromechanics-based damage constitutive model for describing the mechanical behavior of quasi-brittle rocks under cyclic loading considering the effects of confining pressure. The proposed model is successfully employed to simulate cyclic loading tests under various confining pressures and upper limit stresses. Inspired by previous studies that focus on time-dependent creep deformation of quasi-brittle materials, the number of cyclic loading is regarded as equivalent to time scale. In the same spirit, the scalar-valued internal damage variable used to describe the degradation of rock materials is decomposed into two parts, namely an instantaneous component due to monotonic loading, and a fatigue-related component attributed to cyclic loading. Within the framework of irreversible thermodynamics, we present a Coulomb-type friction criterion and a strain energy release rate-based damage criterion. To describe the evolution of fatigue damage, we also propose a damage criterion based on the microstructure evolution. By the use of returning mapping procedure, the constructed model is applied to simulate two representative quasi-brittle rocks, namely sandstone and argillaceous quartz siltstone, and successfully captures all significant behavior features.

Moisture and short-term time-dependent behavior of Norway spruce clear wood under compression perpendicular to the grain and rolling shear

ABSTRACT Material properties of wood under compression perpendicular to the grain and rolling shear are important for the engineering design of timber structures. This regards the short-term stiffness and strength, their dependence on the moisture content of wood, as well as the time-dependent behavior. Norway spruce clear wood properties in the transverse plane of wood were studied in an experimental campaign exploiting an earlier developed biaxial test setup. The moisture dependence of the stiffness and strength and the short-term time-dependent creep deformations under compression in the radial direction and under rolling shear were characterized. Loading and unloading stiffness, as well as the strength, were determined in quasi-static tests at five different moisture contents from 4% to 29%. The elastic and viscous stiffnesses were identified in creep tests at three compressive stress levels of 0.50, 0.75, and 1.00 N/mm 2 , and at two rolling shear stress levels of 0.33 and 0.50 N/mm 2 . The test data complements the existing experimental database, especially with novel data regarding the moisture dependence of the rolling shear strength, which showed less moisture dependence than the compressive strength perpendicular to the grain. The results of the creep tests revealed different material properties for the different loading and material directions of wood.

Potential Loss in Prestressing Tendon Forces under Long-Term Service Conditions: Cross-Laminated Timber Shear Wall Applications

The seismic performance of post-tensioned cross-laminated timber (CLT) shear walls depends on the existing prestressing tendon force. The prestressing force will change over time because of the time-dependent elastic, creep, and environmental deformation of timber. In this study, post-tensioned CLT shear walls under three different prestressing force levels were monitored over 540 days to study the prestressing force loss under varied environments. The long-term experimental results of temperature and relative humidity, moisture content, prestressing force, and timber strain were carefully recorded and analyzed. Subsequently, a comprehensive numerical model was established which includes four modules: moisture diffusion analysis, time-dependent elastic deformation analysis, time-dependent creep and environmental deformation analysis, and prestressing force updating. The long-term experimental results were used to validate the established model. Good agreement between the simulated and the experimental results was achieved. Lastly, the validated numerical model was implemented to predict the potential loss of prestressing force in post-tensioned CLT shear walls during a service life of 50 years. The loss percentage under three different stress levels in uncontrolled environment scenario were 26.8%, 25.2%, and 21.1%. This information can be used to support the life cycle design of post-tensioned CLT structures ensuring the long-term structural safety.

The effects of internal stresses on the creep deformation investigated using in-situ synchrotron diffraction and crystal plasticity modelling

In this study we investigated the evolution of meso-scale internal stresses and those effects on local deformation behaviour during incremental plastic and creep deformation in type 316H stainless steel at 550 °C, using in-situ X-ray synchrotron diffraction and crystal plasticity modelling. Owing to the fast data accusation rate of synchrotron diffraction technique, for the first time, the transient behaviour of different grain families was captured during initial fast stress relaxation period of the displacement-controlled creep dwells. Significantly it is found that the evolution of internal stresses during time independent plastic deformation is distinct from that during time dependent creep deformation. During plastic deformation, lattice strains in the {311} grain family exhibit linear behaviour whereas during creep deformation it exhibits non-linear behaviour, instead the {111} grain family exhibit linear behaviour. A novel unified constitutive law was devised within crystal plasticity framework based on the theoretical physics; the model successfully predicts the macroscopic deformation behaviour as well as the distinction between the evolution of meso-scale internal stresses during plastic and creep deformation, therefore, correctly accounting for the effect of internal stresses generated during plastic deformation on the subsequent creep deformation. The validated model has elucidated the grain-neighbouring effects on individual grain deformations.

Altered Envelope Structure and Nanomechanical Properties of a C-Terminal Protease A-Deficient Rhizobium leguminosarum

(1) Background: Many factors can impact bacterial mechanical properties, which play an important role in survival and adaptation. This study characterizes the ultrastructural phenotype, elastic and viscoelastic properties of Rhizobium leguminosarum bv. viciae 3841 and the C-terminal protease A (ctpA) null mutant strain predicted to have a compromised cell envelope; (2) Methods: To probe the cell envelope, we used transmission electron microscopy (TEM), high performance liquid chromatography (HPLC), mass spectrometry (MS), atomic force microscopy (AFM) force spectroscopy, and time-dependent AFM creep deformation; (3) Results: TEM images show a compromised and often detached outer membrane for the ctpA mutant. Muropeptide characterization by HPLC and MS showed an increase in peptidoglycan dimeric peptide (GlcNAc-MurNAc-Ala-Glu-meso-DAP-Ala-meso-DAP-Glu-Ala-MurNAc-GlcNAc) for the ctpA mutant, indicative of increased crosslinking. The ctpA mutant had significantly larger spring constants than wild type under all hydrated conditions, attributable to more highly crosslinked peptidoglycan. Time-dependent AFM creep deformation for both the wild type and ctpA mutant was indicative of a viscoelastic cell envelope, with best fit to the four-element Burgers model and generating values for viscoelastic parameters k1, k2, η1, and η2; (4) Conclusions: The viscoelastic response of the ctpA mutant is consistent with both its compromised outer membrane (TEM) and fortified peptidoglycan layer (HPLC/MS).

Mechanical creep of tea leaves.

Tea processing involves fermentation, withering, steaming or pan-firing, rolling, baking, and drying. Some of these steps are performed at a high temperatures. At such temperatures the creep of the tea leaves plays an important role in the quality of tea. In materials science, creep is the tendency of a tea leaf to move slowly or defom permanently under a constant load. There has been much research on the mechanical properties of the outmost cuticular layer of leaves but there are few reports addressing the mechanical properties of whole leaves. We cut tea leaf into specimen of dog-bone shape and measure the time-dependent creep deformation using a dynamic mechnical analyzer. Three different tea leaves grown in Taiwan were examined. The nonlinear Burgers model is proposed to describe the creep deformation of the tea leaves. The creep of the tea leaves consists of primary and steady states, and the creep deformation is accurately described by the Kelvin representation of the nonlinear Burgers model. The viscosities in the primary stages satisfied the Arrhenius equation, and the activation energies were determined. The stress exponents for the creep of the tea leaves were less than unity. The Maxwell representation of the Burgers model is mathematically equivalent to the Kelvin representation of the Burgers model and can also be used to explain the creep of tea leaves. © 2020 Society of Chemical Industry.

Inelastic design for type 316L stainless steel at ambient and 600 °C under uniaxial loading

This study aims to determine the safe elastoplastic shakedown limit of type 316L stainless steel at room temperature and at an elevated temperature of 600°C. Components made of type 316L stainless steel are commonly subjected to combined thermomechanical loads in various engineering applications. Shakedown based designs can be used to expand the feasible design space under combined thermomechanical cyclic loading conditions compared to conventional yield-limited designs. Extensive experimental and numerical effort has been made to model ratchetting and cyclic hardening/softening of stainless steels under uniaxial cyclic loading but a very limited number of studies have focused on determining the shakedown limit. In this work, shakedown limits are determined experimentally and numerically. A numerical model that combines time-dependent creep deformation and time-independent hardening is used to develop Bree load-interaction diagrams. It is found that shakedown occurs at room temperature at stress levels up to two times the linear elastic limit of the material and is limited by the time-dependent creep deformation. At 600oC, an enhanced shakedown behavior is observed that expands the feasible design space up to 4 times the linear elastic limit.

Two-stage wetting deformation behaviour of rock-fill material

Combined loading–creep–wetting tests were performed to investigate the wetting deformation behaviours of rock-fill material by using a modified triaxial apparatus. Results show that the wetting deformation of rock-fill material can be classified into two components, namely, instantaneous wetting deformation and time-dependent wet-state creep deformation. The former occurs simultaneously with rock-fill wetting and possesses the characteristics of parallelism and non-hardening; the latter occurs over time after the rock-fill is wetted and exhibits features similar to those of general creep deformations in rock-fill material. Wetting deformation is induced by the physical-state weakening of the wetted rock-fill material; the wetting can be intuitively considered as a generalised load. Then, a new constitutive model of two-stage wetting deformation for rock-fill material is proposed. In the model, the instantaneous shear wetting strain is in a hyperbolic relationship with the stress level; the instantaneous volumetric wetting strain is described by the dilatancy equation of conventional triaxial loading; and the time-dependent wet-state creep strain is calculated using a general rock-fill creep model. The new model was also used to simulate triaxial wetting tests of rock-fill material, and its validity and practicability were further evaluated.

Effect of the silicon-carbide micro- and nanoparticle size on the thermo-elastic and time-dependent creep response of a rotating Al–SiC composite cylinder

The history of stresses and creep strains of a rotating composite cylinder made of an aluminum matrix reinforced by silicon carbide particles is investigated. The effect of uniformly distributed SiC micro- and nanoparticles on the initial thermo-elastic and time-dependent creep deformation is studied. The material creep behavior is described by Sherby’s constitutive model where the creep parameters are functions of temperature and the particle sizes vary from 50 nm to 45.9 μm. Loading is composed of a temperature field due to outward steady-state heat conduction and an inertia body force due to cylinder rotation. Based on the equilibrium equation and also stress-strain and strain-displacement relations, a constitutive second-order differential equation for displacements with variable and time-dependent coefficients is obtained. By solving this differential equation together with the Prandtl–Reuss relation and the material creep constitutive model, the history of stresses and creep strains is obtained. It is found that the minimum effective stresses are reached in a material reinforced by uniformly distributed SiC particles with the volume fraction of 20% and particle size of 50 nm. It is also found that the effective and tangential stresses increase with time at the inner surface of the composite cylinder; however, their variation at the outer surface is insignificant.

A time-dependent anisotropic model for argillaceous rocks. Application to an underground excavation in Callovo-Oxfordian claystone

The paper presents a constitutive model for argillaceous rocks, developed within the framework of elastoplasticity, that includes a number of features that are relevant for a satisfactory description of their hydromechanical behaviour: anisotropy of strength and stiffness, behaviour nonlinearity and occurrence of plastic strains prior to peak strength, significant softening after peak, time-dependent creep deformations and permeability increase due to damage. Both saturated and unsaturated conditions are envisaged. The constitutive model is then applied to the simulation of triaxial and creep tests on Callovo-Oxfordian (COx) claystone. Although the main objective has been the simulation of the COx claystone behaviour, the model can be readily used for other argillaceous materials. The constitutive model developed is then applied, via a suitable coupled hydromechanical formulation, to the analysis of the excavation of a drift in the Meuse/Haute-Marne Underground Research Laboratory. The pattern of observed pore water pressures and displacements, as well as the shape and extent of the damaged zone, are generally satisfactorily reproduced. The relevance and importance of rock anisotropy and of the development of a damaged zone around the excavations are clearly demonstrated.

Compression creep test on expanded polystyrene (EPS) geofoam

Expanded polystyrene (EPS) geofoam is vulnerable to time-dependent creep deformation when a constant magnitude stress level is applied. In the present study, an attempt has been made to understand the behavior of compression creep of EPS geofoam using stress controlled loading frames. The test has been carried out on EPS geofoam samples of three different densities, 12, 15, and 20 kg m−3 under the applied pressure of 65% of the compressive strength. Cube samples of 50 and 100 mm sizes were tested for the investigation. The test results showed that with the increase in density of EPS geofoam, creep deformation value decreases, whereas on low density of EPS geofoam, the effects of creep deformations were more pronounced. Small size samples tend to overestimate creep deformations of EPS geofoam because of end effects and more noticeable seating error.

Material Constitutive Models for Creep and Rupture of SiC/SiC Ceramic-Matrix Composites (CMCs) Under Multiaxial Loading

Material constitutive models for creep deformation and creep rupture of the SiC/SiC ceramic-matrix composites (CMCs) under general three-dimensional stress states have been developed and parameterized using one set of available experimental data for the effect of stress magnitude and temperature on the time-dependent creep deformation and rupture. To validate the models developed, another set of available experimental data was utilized for each model. The models were subsequently implemented in a user-material subroutine and coupled with a commercial finite element package in order to enable computational analysis of the performance and durability of CMC components used in high-temperature high-stress applications, such as those encountered in gas-turbine engines. In the last portion of the work, the problem of creep-controlled contact of a gas-turbine engine blade with the shroud is investigated computationally. It is assumed that the blade is made of the SiC/SiC CMC, and that the creep behavior of this material can be accounted for using the material constitutive models developed in the present work. The results clearly show that the blade-tip/shroud clearance decreases and ultimately becomes zero (the condition which must be avoided) as a function of time. In addition, the analysis revealed that if the blade is trimmed at its tip to enable additional creep deformation before blade-tip/shroud contact, creep-rupture conditions can develop in the region of the blade adjacent to its attachment to the high-rotational-speed hub.

Derivation, parameterization and validation of a creep deformation/rupture material constitutive model for SiC/SiC ceramic-matrix composites (CMCs)

The present work deals with the development of material constitutive models for creep-deformation and creep-rupture of SiC/SiC ceramic-matrix composites (CMCs) under general three-dimensional stress states. The models derived are aimed for use in finite element analyses of the performance, durability and reliability of CMC turbine blades used in gas-turbine engines. Towards that end, one set of available experimental data pertaining to the effect of stress magnitude and temperature on the time-dependent creep deformation and rupture, available in the open literature, is used to derive and parameterize material constitutive models for creep-deformation and creep-rupture. The two models derived are validated by using additional experimental data, also available in the open literature. To enable the use of the newly-developed CMC creep-deformation and creep-rupture models within a structural finite-element framework, the models are implemented in a user-material subroutine which can be readily linked with a finite-element program/solver. In this way, the performance and reliability of CMC components used in high-temperature high-stress applications, such as those encountered in gas-turbine engines can be investigated computationally. Results of a preliminary finite-element analysis concerning the creep-deformation-induced contact between a gas-turbine engine blade and the shroud are presented and briefly discussed in the last portion of the paper. In this analysis, it is assumed that: (a) the blade is made of the SiC/SiC CMC; and (b) the creep-deformation behavior of the SiC/SiC CMC can be represented by the creep-deformation model developed in the present work.

A micromechanics-based creep damage model for brittle rocks

For brittle rocks, the essential non-linear mechanism of material degradation and structure failure can be related to cracking-induced inelastic deformation and damage evolution. This paper is devoted to modelling non-linear time-dependent mechanical behaviour of brittle rocks under compression. A micromechanics-based damage-friction coupling model is developed based on the linear homogenisation method and within the irreversible thermodynamics framework. Firstly, the free energy in the matrix-cracks representative volume is determined, from which are derived the thermodynamic forces associated with the inelastic strains and the damage. Under isotropic assumption, the evolutions of the two internal variables are calculated, respectively, using an associated Coulomb-type friction criterion and a strain energy release rate-based damage criterion. By accounting for subcritical cracking mechanism, the basic model is then extended to describe time-dependent creep deformation and applied to simulate triaxial compression tests and triaxial creep tests on granite. Comparisons of numerical predictions with experimental data are performed to show the predictive capacity and the advantage of the proposed model.

Prediction of Long – Term Creep Properties of Kenaf Fiber Unsaturated Polyester Composites

This research focuses on predicting long-term behavior of unsaturated polyester resin (UP) and kenaf unsaturated polyester composite. The objectives of these tests are to establish a relationship between stress, strain and time at constant loading and temperature. The results obtained from these tests are used in predicting the life and strength of the polymer material. Based on the 1,000 hours experimental data, curve fitting and Findley Power Law models are employed to predict long-term behavior of the material. The results showed that curve fitting model accurately predicted the non-linear time dependent creep deformation of these materials with acceptable accuracy.