Macroscopic Creep Behavior Research Articles

From micro to macro: Creep behaviour and closed-form expression of viscoelastic parameters for a rheological particle assembly

This study is devoted to analytically establish macro–micro quantitative relationships for creep characteristics of a rheological particle assembly, contributing to a more comprehensive insight into the interplay between different scales. To represent the various rheological behaviour in microscopic for a hexagonal close-packed (HCP) circular particle assembly, the contact responses are assumed as viscoelastic models. By extending the traditional homogenization method to the Laplace domain, the macroscopic one/two-dimensional creep equations of the rheological particle assembly, expressed with the microscopic contact parameters in a closed-form manner, are innovatively identified. It is found that the macroscopic creep behaviour is not always consistent with the microscopic one and in general exhibits more complex creep characteristics. The parametric analysis presents the quantitative influence of contact parameters on macroscopic creep behaviour. Extending the one-dimensional case to three dimensions (3D), the relaxation moduli as well as creep compliance, expressed in closed-form by contact parameters, are obtained in 3D viscoelastic constitutive equations. Distinct viscoelastic behaviours are observed for macroscopic shear and bulk responses. The proposed macro–micro quantitative relations of creep characteristics in this study benefit to deeply understand the macro–micro relations of viscoelastic properties, providing an alternative approach to calibrate microscopic parameters when involving the DEM simulations.

Viscoelastic behavior of softwood based on a multiscale computational homogenization

In the present study, a numerical multiscale model is made to show how the hierarchical structure of softwood affect its macroscopic viscoelastic properties. The performance of the model is demonstrated for two softwood species — Norway spruce and Japanese cypress, whose creep behavior has been characterized experimentally. The results show that by using the same transversely isotropic viscous properties of the cell wall for both species, it is possible to predict creep deformation relatively close to experimental creep measurements for both species. Assuming that the variability is larger on the microstructural level (density, cell-wall geometry, microfibril angle, composition of wood tissues) than on the cell-wall level, it is possible to predict the macroscopic creep behavior based on the microstructural parameters alone. Such predictions can potentially save cost and time, since creep characterization in all material directions is demanding.

Exploring the correlation between microscopic mechanisms and macroscopic behaviour in creep of a directionally solidified tungsten-free γ/γ′ CoNi-base superalloy

We describe in detail the deformation micromechanisms operative during the compressive creep of a directionally solidified (DS) tungsten-free γ/γ' Cobalt-base superalloy across a range of stresses and temperatures and their manifestation on the macroscopic creep behaviour. Creep experiments were carried out at 800 °C, 850 °C, and 900 °C under different stress levels between 200 MPa and 500 MPa. We observe two low and high-stress domains with stress exponent values of 2.3–3.2 and 6.8–9.5, and the estimated activation enthalpies of ∼352 KJ/mol (at 200 MPa) and ∼657 KJ/mol (at 400 MPa), respectively. Transmission electron microscopy and atom probe tomography were used to understand operative micromechanisms. In the low-stress regime, dislocations are confined to the γ matrix channels and form γ/γ' interface networks with enrichment of Mo solute at the dislocation cores implying that a viscous drag may influence dislocation bow out processes from the interface network leading to a stress exponent of 2–3. The high-stress regime is characterized by γ′ precipitate shearing along with the formation of superlattice-extrinsic stacking faults and micro-twins at 800 °C. Compositional analysis reveals segregation at these faults and twin boundaries. At higher temperatures (850 °C and 900 °C), γ' shearing is dominated by the formation of antiphase boundaries rich in Co and depleted in Mo. Accordingly, we identify three distinct deformation mode domains within the stress versus temperature space associated with interface network formation and low stress exponent creep, γ′ precipitate shearing by SESFs/micro-twinning, and shearing by APB.

Micromechanical modelling of the anisotropic creep behaviour of granular medium as a fourth-order fabric tensor

The main objective of the present work is to develop a micromechanics approach to predict the macroscopic anisotropic creep behaviour of granular media. To this end, the linear viscoelastic behaviour of the inter-particle interaction at contact is adopted, and the contact distribution is characterized by a fourth-order fabric tensor in the local scale. Then, fourth-order tensor fabric-based micromechanical approaches based on Voigt and Reuss localization assumptions are applied to granular media in the Laplace–Carson space. With help of the inverse Laplace–Carson transformation of these obtained models, the macroscopic anisotropic creep behaviour of granular media submitted to a constant external loading is examined. Finally, the obtained results by specializing the Burgers model into the obtained models are compared with the numerical simulations in the particle flow code (PFC2D) to illustrate the validation and the accuracy of the analytical models for the macroscopic anisotropic creep behaviour of granular media.

Microstructure evolution under [110] creep in Ni-base superalloys

Microstructure evolutions in Ni-base superalloys are investigated during [110] creep loading using 3D and 2D phase field simulations. A recently developed phase field model coupled to a crystal plasticity model based on dislocation densities is employed. The model uses a storage-recovery law for the dislocation density of each glide system and a hardening matrix to account for the short-range interactions between dislocations. We show that small misorientations of the tensile axis strongly modify the evolution: rafting is observed for small deviations, as opposed to a microstructure made of rod-like precipitates when loading is performed along a perfectly aligned [110] direction. Depending on the precise direction of the mechanical load, different evolutions are obtained accompanied by strong modification of the macroscopic creep behavior, explaining the variety of results observed experimentally. The relative role of inhomogeneous and anisotropic elastic and plastic driving forces is also investigated, plasticity being the main driving force for rafting in the considered case. In addition, our calculations show that the initial dislocation density slightly modifies the precipitates morphology but the creep curve is significantly impacted.

Creep behaviour of two-phase lamellar TiAl: Crystal plasticity modelling and analysis

Two-phase (α2Ti3Al+γTiAl) fully lamellar TiAl alloys show highly anisotropic creep behaviour. Depending on lamellar orientations, locally in the TiAl phases hard and easy deformation modes are active, which significantly influence the creep behaviour at a global scale. To obtain comprehensive understanding how the locally activated crystallographic deformation modes influence the macroscopic creep behaviour, a crystal plasticity (CP) model with modified hardening behaviour is proposed in this work. For this purpose, a softening parameter is introduced in the model that phenomenologically describes the threshold stresses for material softening depending on pile-up dislocation lengths during creep deformation. The model allows us to interpret the cause of creep anisotropy at macro-scale deformation based on the orientation dependent activation and interactions of slip systems at the TiAl phases. Comprehensive study was performed to validate the model and to predict creep parameters under different temperature and stress loading conditions. Comparing the experimental data with simulation results, we found that the proposed CP model captures creep behaviour in primary, secondary, and tertiary regime for all the lamellar orientations with good accuracy. This model can be further used for investigating microstructure-sensitive creep behaviour of a wide range of TiAl alloys.

Influence of geochemical reactions on the creep behavior of Mt. Simon sandstone

The capture and subsurface storage of carbon dioxide is a sustainable option that is currently pursued worldwide to mitigate greenhouse gas effect. However, predicting the long-term mechanical integrity of CO2 underground storage systems remains a challenge. To address that question, it is essential to understand the influence of fluid-rock chemo-mechanical interactions on the long-term and on the time-dependent mechanical properties. In turn, the long-term mechanical response and the time-dependent mechanical behavior can be represented by the creep response. We investigate the impact of CO2-induced geochemical reactions on the creep response of Mt. Simon sandstone with a 50–400 μm grain size. We perform static and dynamic flow experiments on Mt. Simon sandstone specimens under geological conditions, at a temperature of T=50–53 °C and for CO2 pressures of P=8.62, 17.2 MPa under both static flow and dynamic flow-through conditions. After aging, we employ creep indentation testing, high-resolution SEM-EDS, computer vision, machine learning, and micromechanics modeling to probe changes on the microstructure and mechanical properties. Following both static and dynamic flow-through experiments, we observe a 10–22% decrease in quartz volume fraction and an increase in both the microporosity (7–28%) and nanoporosity (60–65%). Additional CO2-induced microstructural changes include an enlargement of pore throats and the formation of channels. These observations point to the presence of CO2-induced K-feldspar dissolution and clay dissolution reactions. The macroscopic creep behavior is logarithmic and the macroscopic creep modulus varies depending on the microporosity and the relative quartz and feldspar content. As a result of these geochemical reactions and of the related microstructural changes, a 55–60% decrease in the macroscopic logarithmic creep modulus is predicted.

Analytical and 3D numerical analysis of the thermoviscoelastic behavior of concrete-like materials including interfaces

We investigate in this paper analytically and numerically by means of 3D simulations the viscoelastic behavior of concrete and mortar subjected to creep loading and moderate temperatures at mesoscale. These heterogeneous materials are assumed to be composed of thermoelastic aggregates distributed in a linear thermoviscoelastic matrix; moreover, the Interfacial Transition Zones (ITZ) between aggregates and matrix, whose behavior is also considered as linear thermoviscoelastic, are explicitly introduced. The numerical specimens consist in unstructured periodic meshes containing polyhedral aggregates with various size and shapes randomly distributed in a box. Zero-thickness interface finite elements are introduced between aggregates and matrix to model the ITZ. Macroscopic response and averaged stresses and strains in the matrix and aggregate phases are compared to analytical estimations obtained with classical mean-field approximation schemes applied in the Laplace–Carson space, in which the ITZ are introduced via imperfect interfaces modeled with the Linear Spring Model (LSM). The effects of ITZ thickness, aggregate shape and uniform temperature increase are then studied to evaluate their respective influence on the local and macroscopic creep behavior of mortar and concrete. Globally, it is found that the model response is in relatively good agreement with numerical simulations results, and that as expected while the ITZ do not affect significantly the concrete behavior, they have a non-negligible impact on the mortar one.

A dual-scale approach to model time-dependent deformation, creep and fracturing of brittle rocks

A physically-motivated dual-scale modeling approach is proposed to model the time-dependent damage, deformation and fracturing behavior of heterogeneous brittle rocks during creep. The proposed model uses a microcrack-based damage constitutive law established at the elemental scale, in which the time-dependent degradation of elastic stiffness and damage-induced anisotropy are directly linked to microcrack growth. The evolution of mechanical heterogeneity is based on a Weibull distribution that captures the transition from distributed damage to localized failure. The key feature of the proposed model is to establish an adequate prediction of macroscopic creep behavior based on the microscopic kinetics of microcrack growth rather than the phenomenological material degradation laws adopted in previously-developed statistical models. The general capabilities of the proposed model are illustrated with numerical simulations of biaxial creep tests. The influences of differential stresses, heterogeneities and microscopic element sizes on creep behavior in brittle rocks are also examined. Results from such analyses indicate that the proposed model not only accurately replicates the trimodal phases of creep deformation and the associated temporal evolution of acoustic emission but also follows the progressive evolution of fracture modes and morphology commonly observed. Thus, subject to suitable calibration, this model provides an attractive virtual experimental tool to probe process-based understanding of complex long-term problems related to structures on an in geologic media.

Influence of microstructure on local intra- and intergranular deformations during creep of a nickel-based superalloy at 700 °C

Several microstructural parameters of the NR6 nickel-based superalloy were varied by applying four heat treatment procedures. Tensile creep tests were performed in air at 700°C and 700MPa on specimens exhibiting different grain sizes, strengthening γ′ precipitate sizes and distributions and grain boundary morphologies. Flat creep specimens were instrumented thanks to a dedicated microextensometry technique to analyze the local intra- and intergranular deformations after tensile creep under vacuum at 700°C. Tertiary γ′ precipitate dissolution, grain boundary serration and larger grain size reduce grain boundary sliding contribution to overall strain. These effects are attributed to the promotion of Orowan by-passing instead of shearing of the γ′ strengthening particles by matrix dislocations, increase of grain boundary resistance or decrease of grain boundary fraction. Relationships between local deformations and macroscopic creep behavior have been evidenced.

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.

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.

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.

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.

Modeling Large-deformation-induced Microflow in Soft Biological Tissues

The homogenization approach to multiscale modeling of soft biological tissues is presented. The homogenized model describes the relationship between the macroscopic hereditary creep behavior and the microflow in a fluid-saturated dual-porous medium at the microscopic level. The micromodel is based on Biot’s system for quasistatic deformation processes, modified for the updated Lagrangian formulation to account for coupling the fluid diffusion through a porous solid undergoing large deformation. Its microstructure is constituted by fluid-filled inclusions embedded in the porous matrix. The tangential stiffness coefficients and the retardation stress for the macromodel are derived for a time-stepping algorithm. Numerical examples are discussed, showing the strong potential of the model for simulations of deformation-driven physiological processes at the microscopic scale.

Fluencia de materiales compuestos de matriz metálica reforzados con fibras cortas bajo deformaciones en cizalla

A new model is proposed which described the creep behaviour of metal matrix composites randomly reinforced by short fibers. The internal damage of the composite during creep due to fiber fragmentation is introduced by assigning a heuristic non-linear stress-strain relationship to the fiber. The macroscopic creep behaviour is simulated for composites deformed in shear for different fiber distribution.

Creep of multidirectionally fibre-reinforced composites

A model for the creep of metal matrix composites multidirectionally reinforced by short fibres is proposed. The reinforcement is described by the effective stiffness tensor of a multidirectional arrangement of continuous fibres and the internal damage of the composite during creep due to fibre fragmentation is introduced by assigning a heuristic nonlinear stress–strain relationship to the fibres. Based on the model, the load partitioning between matrix and fibres is computed. The macroscopic creep behaviour is simulated for composites exhibiting different fibre orientation distributions and different heuristic nonlinear stress–strain functions. The computational results rationalize the creep behaviour of multidirectional fibre-reinforced composites. For a two-dimensional random orientation distribution, a good qualitative match between simulation and experimental results is obtained for compressive loading and for in-plane tensile loading. For loading normal to the reinforcement plane, the model overestimates the creep resistance. In this case, the formation and growth of cavities seems to govern the creep deformation of the composite.

A new constitutive creep-damage model for rocksalt

A physically-motivated dual-scale modeling approach is proposed to model the time-dependent damage, deformation and fracturing behavior of heterogeneous brittle rocks during creep. The proposed model uses a microcrack-based damage constitutive law established at the elemental scale, in which the time-dependent degradation of elastic stiffness and damage-induced anisotropy are directly linked to microcrack growth. The evolution of mechanical heterogeneity is based on a Weibull distribution that captures the transition from distributed damage to localized failure. The key feature of the proposed model is to establish an adequate prediction of macroscopic creep behavior based on the microscopic kinetics of microcrack growth rather than the phenomenological material degradation laws adopted in previously-developed statistical models. The general capabilities of the proposed model are illustrated with numerical simulations of biaxial creep tests. The influences of differential stresses, heterogeneities and microscopic element sizes on creep behavior in brittle rocks are also examined. Results from such analyses indicate that the proposed model not only accurately replicates the trimodal phases of creep deformation and the associated temporal evolution of acoustic emission but also follows the progressive evolution of fracture modes and morphology commonly observed. Thus, subject to suitable calibration, this model provides an attractive virtual experimental tool to probe process-based understanding of complex long-term problems related to structures on an in geologic media.