Viscoplastic Strain Research Articles

Influence of field aging on viscoelastoplastic performance of rubberized asphalt mixtures incorporating reclaimed asphalt pavement in arid urban climate

This study investigates the effects of reclaimed asphalt pavement (RAP) and crumb rubber-modified asphalt (CRMA) on the viscoelastoplastic properties of asphalt mixtures under a range of aging conditions. Six asphalt mixtures, with varying RAP contents (0 %, 30 %, and 50 %) and CRMA modifications, were evaluated through dynamic modulus (|E*|) and flow number (FN) analyses. The specimens were subjected to authentic field-aging conditions for periods of 0, 3, 6, and 9 months. The results reveal that increasing RAP content enhances volumetric properties, Marshall stability, and rutting resistance. CRMA significantly improves fatigue performance and further bolsters rutting resistance, although some detrimental effects are observed at lower temperatures. Aging has a pronounced impact on the mixtures’ performance, particularly on |E*|, Prony series coefficients, viscoelastic strain (εve), and viscoplastic strain (εvp). Newly proposed aging indices, the dynamic modulus aging index (DMAI) and viscoplastic aging index (VPAI), effectively capture the changes in viscoelastoplastic behavior under different aging durations. These findings underscore the potential of RAP and CRMA to enhance pavement durability, prolong service life, and contribute to the development of sustainable and resilient infrastructure. The research offers valuable insights into the performance of asphalt mixtures incorporating RAP and CRMA under real-world conditions.

Verification of time-temperature superposition principle for viscoplastic strains of asphalt mixtures obtained from creep-recovery tests in the low-strain regime

The creep compliances, total, and viscoplastic (VP) strains of various asphalt mixtures were determined from creep-recovery tests at different temperatures to construct their master curves. In order to ensure the reliability of the obtained results, the agreement between quantities in the time and frequency domain as well as sources of bias in testing were investigated. A viscoelastic and a VP model were used to respectively characterise the reversible and irreversible deformation of the materials. The behaviour of the specimens exerted by a constant stress at various temperatures were then predicted using independent values of the viscoelastic and VP reduced times. Owing to the good agreement between prediction and measurement, the time-temperature superposition principle in the VP domain was verified. In general, the shift factors were uncorrelated with each other. However, at elevated temperatures, the gaps between them became unimportant, enabling the extension of viscoelastic shift factors into the VP domain.

Deformation behaviour of concrete with different moisture contents subjected to compressive creep and cyclic loading

The expected long-term deformations of concrete structures are calculated using creep models, derived from experiments performed with constant mechanical loads. However, in the majority of real structures, such as bridges, constant creep loads are superimposed with cyclic loads of substantial magnitude. Additionally, such structures are subject to changes in environmental conditions (temperature and humidity). Deformation measurements of existing bridges have shown significant underestimations by established creep models, which might be traced back to the superimposition of cyclic loads and different moisture contents. Therefore, the developments of strains, viscoplastic strains and modulus of elasticity under creep and cyclic loading of a normal strength concrete have been comparatively investigated for two different pore moisture contents (approx. 100 and 75%). The results show that viscous strains due to cyclic loading are significantly higher than those due to creep loading at the mean stress level of cyclic loading. Furthermore, the strains are higher for the higher moisture content. The differences in the development of the modulus of elasticity and viscoplastic strains of both load types give clear indication for load type dependent microstructural deformation mechanisms. The results obtained concerning the influence of the load type and the moisture content need to be considered for the improvement of existing models.

Temperature-dependent creep damage mechanism and prediction model of fiber-reinforced phenolic resin composites

Carbon fiber-reinforced phenolic resin (CF/PF) and glass fiber-reinforced phenolic resin (GF/PF) composites are crucial for thermal insulation and load-bearing capabilities in the aerospace industry. Understanding their creep behavior at various temperatures is essential. This study investigates the impact of temperature on the bending creep properties of CF/PF and GF/PF composites, focusing on deformation response, damage mechanisms, and prediction models. Results reveal that the decrease in creep properties at elevated temperatures is mainly attributed to the increased viscoplastic strain. At room temperature, CF/PF composite demonstrates exceptional creep properties. CF/PF composite exhibits heightened sensitivity to elevated temperatures, undergoing creep rupture at 210 °C and 240 °C with failure strains of 0.48 % and 0.49 %, respectively. High-temperature damage mechanisms have been analyzed in depth using a combination of thermal stress finite element simulation and microscopic characterization. Thermal stress is directly related to the difference in thermal expansion between the fibers and the resin. The influence of fiber distribution and geometry results in the interface being subjected to both normal and shear stresses. The accumulation of interfacial damage increases the plastic deformation and degrades creep performance. Additionally, an advanced temperature-dependent Burgers model has been developed and effectively predicted the creep curves under different temperatures and loads. This model demonstrated great potential as a general predictive model.

A three-dimensional viscoelastic–viscoplastic and viscodamage constitutive model for unidirectional fibre-reinforced polymer laminates

A novel 3D viscoelastic–viscoplastic and viscodamage constitutive model is proposed to predict the viscous effects due to dynamic loading conditions of unidirectional carbon fibre-reinforced polymer laminates at the meso-scale level. The present model is developed under continuum damage mechanics and the thermodynamics of irreversible processes framework. The viscoelastic response is modelled using the generalised Maxwell model, while an overstress model is employed to address the viscoplastic strain. The onset of the viscodamage mechanisms is based on experimental expressions, and their propagation is defined as a function of the corresponding fracture toughness. The mechanical response of the present constitutive model under pure longitudinal shear loading conditions at different strain rates is presented. The higher the strain rate is, the stiffer the responses in the viscoelastic and viscoplastic regions are. Additionally, the onset of viscodamage increases with higher strain rates. Off-axis compressive experimental data at two different strain rates are employed to demonstrate the capabilities of the present model with good predictions being obtained.

Creep characteristics and long-term strength of underground water reservoirs’ coal pillar dam specimens under different osmotic pressures

Overlying rock pressure and stored water seepage notably affect coal pillar dam creep and long-term strength in underground water reservoirs. However, the current understanding of the seepage-creep coupling effects on coal pillar dam behavior is unclear, necessitating targeted research. Therefore, This Paper conducted experiments on coal pillar dam samples under various osmotic pressures to study their creep behavior and long-term strength. The results indicate that seepage fluids, with their softening, dissolving, lubricating, and flow carrier effects, significantly notably promote the creep behavior of coal samples. Viscoelastic creep in coal decreases with increasing osmotic pressure, whereas the viscoplastic creep strain increases with increasing time and stress. This Paper proposes employing the critical stress at the steady state viscoplastic creep rate threshold as the long-term strength of coal. These findings indicate an inverse link between long-term strength and osmotic pressure, with osmotic pressure going from 0 to 6 MPa, strength drops from 23.2 to 8.5 MPa. Therefore, when designing and ensuring the long-term stability of coal pillar dams, it is crucial to consider the impact of stored water seepage.

New accelerated rock creep model considering nonstationary viscosity coefficient

Accelerated creep models are popular research topics in rock mechanics. By analyzing the variation in the viscosity coefficient in the accelerated creep stage and defining the viscoplastic internal variable, a general evolution law for the viscosity coefficient was revealed, and a widely applicable accelerated creep model was proposed. First, the creep test data of 24 rock types were collected and analyzed. Subsequently, the contrast between the strength decrease in the accelerated creep-subsequent failure stage and the post-peak strength decrease in the elastoplastic process was evaluated, and the viscoplastic internal variable in the accelerated creep stage was defined. Subsequently, the evolution function between the normalized viscosity coefficient and the viscoplastic internal variable was established. Based on the test data for different rocks, the predicted curves accurately captured the evolution of the normalized viscosity coefficient with the viscoplastic strain increment and confining pressure in the accelerated creep stage. A new accelerated creep model was constructed by modifying the linear viscoplastic part of the Nishihara model using an established evolution model of the viscosity coefficient. The model demonstrated agreement with the experimental data for different rocks and yielded results close to the monitored tunnel convergence data.

Enthalpy of anelasticity and rejuvenation of metallic glasses

Elastostatic loading and cryogenic thermal cycling are known to be capable of increasing the enthalpy of metallic glasses and improving their mechanical properties, effects of particular interest as these treatments operate in the nominally elastic regime. The increases in volume and stored energy induced by these treatments are studied for two prototypical (Pd- and Zr-based) bulk metallic glasses. The energy increase induced by elastostatic loading is associated with unrecovered anelastic strain, and not with viscoplastic strain as previously proposed. This energy increase decays similarly to that induced by thermal cycling, implying a storage mechanism that is similar for these two treatments and distinct from that operating under plastic deformation. For different as-cast and annealed states of metallic glasses, increased energy shows a linear correlation with increased volume. Property changes induced by elastostatic loading and thermal cycling also show a linear correlation, but with a different gradient, indicating greater excess volume for a given energy. It is proposed that the changes induced by treatments within the elastic limit do not constitute ‘rejuvenation’ of a metallic glass, but rather structural excitation localized at shear-transformation zones. The energetics of such excitation are analysed.

The UTUH model: a time-dependent unified hardening constitutive model for unsaturated soils

AbstractAn advanced constitutive framework for unsaturated soils, the UTUH model, is proposed in this paper, which considers the joint effect of time, suction and overconsolidation within the framework of sub-loading surface plasticity. A reference line, namely the instantaneously normal compression line (INCLs) for unsaturated soils, is introduced from a conceptual framework drawn from constant rates of strain test results to determine creep time and overconsolidation states of unsaturated soils. Subsequently, an isotropic elasto-viscoplastic constitutive model for unsaturated soils is produced by combining viscous deformation with mechanical and hydraulic deformation through overconsolidation parameter. Net stress, suction and time are adopted as fundamental constitutive variables and time-dependent loading collapse yield surface is derived to characterize the relationship between yield stress, suction, and time. Then, an extension to a triaxial stress state is built in the space of mean effective stress, suction, deviator stress and time variable. The hardening of yield surface and sub-loading surface is controlled by viscoplastic volumetric strain and unified hardening parameter. The performance of the proposed UTUH model is addressed through four numerical studies, and the proposed model is validated against experimental data from the literature.

A viscoplastic constitutive model for unsaturated soils based on nonstationary flow surface theory

AbstractA viscoplastic constitutive model is developed to describe the viscoplastic behavior of unsaturated soils. The proposed model accounts for the stain‐rate and suction effects on yield by adopting an unsaturated isotach concept. The nonstationary flow surface theory (NSFS) is applied for modeling the viscoplastic behavior, with the yield surface which can evolve with the viscoplastic strain, viscoplastic strain rate and suction. Meanwhile, the progressively hardening concept is adopted for reproducing the viscoplastic behavior of soil at an over‐consolidated state. For the validation, a series of loading conditions are considered based on the data from the literature. Results show that the proposed model is able to reproduce the main viscoplastic behaviors of unsaturated highly compacted Gaomiaozi (GMZ) bentonite, Glenroy silt and Qianjiangping landslide (QL) soil, including CRS compression tests, rate‐dependent triaxial shear tests, and triaxial creep tests.

Modelling the viscoplastic behaviour of Callovo-Oxfordian claystone with consideration of damage effect

In order to evaluate the performance of deep geological disposal of radioactive waste, an underground research laboratory (URL) was constructed by Andra in the Callovo-Oxfordian (COx) claystone formation at the Meuse/Haute-Marne (MHM). The construction of URL induced the excavation damage of host formations, and the ventilation in the galleries desaturated the host formation close to the gallery wall. Moreover, it is expected that the mechanical behaviour of COx claystone is time-dependent. This study presents a constitutive model developed to describe the viscoplastic behaviour of unsaturated and damaged COx claystone. In this model, the unsaturation effect is considered by adopting the Bishop effective stress and the van Genuchten (VG) water retention model. In terms of the viscoplastic behaviour, the nonstationary flow surface (NSFS) theory for unsaturated soils is used with consideration of the coupled effects of strain rate and suction on the yield stress. A progressive hardening law is adopted. Meanwhile, a non-associated flow rule is used, which is similar to that in Barcelona basic model (BBM). In addition, to describe the damage effect induced by suction change and viscoplastic loading, a damage function is defined based on the crack volume proportion. This damage function contains two variables: unsaturated effective stress and viscoplastic volumetric strain, with the related parameters determined based on the mercury intrusion porosimetry (MIP) tests. For the model validation, different tests on COx claystone under different loading paths are simulated. Comparisons between experimental and simulated results indicated that the present model is able to well describe the viscoplastic behaviour of damaged COx claystone, including swelling/shrinkage, triaxial extension and compression, and triaxial creep.

A Computationally Efficient IGBT Lifetime Prediction Method Based on Successive Initiation Technique by Iteratively Using Clech Algorithm

Thermal-mechanical coupled models built by finite element analysis (FEA) software are attractive due to its excellent capability to calculate thermal/mechanical behaviors of the material interfaces inside the power module. However, these FEA-based approaches will consume enormous computational resources, resulting in unacceptably long simulation times. Herein, a computationally efficient and accurate IGBT lifetime prediction method enabling explicit emulation of solder layer degradation is proposed with the assistance of Clech algorithm. The variation of assembly stiffness <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> and imposed strain <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</i> in Clech algorithm with the geometrical variation during the solder layer degradation is particularly considered. A look-up table of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</i> changing with crack propagation is established to calculate viscoplastic strain energy density Δ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">W</i> (VSED) of the critical elements across the crack path. This improved process is applied for lifetime consumption calculation of each successive run. It remarkably reduces the simulation costs compared to that based on FEA. Finally, two sets of experimental results verify high prediction accuracy and low time-consuming cost of the proposed method.

Effect of Soil Creep on the Bearing Characteristics of Soil Slope Reinforced with CFRP and Anti-Slide Piles

In order to research the displacement characteristics and stability of a soil slope reinforced with carbon-fiber-reinforced plastic (CFRP) and anti-slide piles, the displacement composition, aging deformation and failure mode of a soil mass were analyzed. According to the Mohr–Coulomb strength criterion, a new nonlinear, accelerated creep model of soil mass was founded with the addition of a self-building M-C plastic element. Furthermore, a viscoplastic strain analytical formula of an M-C plastic element was obtained, and the tensile deformation characteristics of a CFRP sheet were also discovered under a landslide thrust creep load. According to the environmental conditions of the anti-slide pile, the CFRP was arranged along the load-bearing side of the pile to control deformation. Combining the calculation example, it is shown that the horizontal displacement of the soil slope’s composite structure decreases by approximately 40% with CFRP reinforcement. Furthermore, for the first two calculation conditions, after one year, the maximum horizontal displacement decreased by 50% and increased by 10%, respectively. Simultaneously, the overall safety factor increased by 31.3% without soil creep properties. On the contrary, the overall safety factor was reduced, and the slope has a tendency toward unstable failure. Moreover, there is no through plastic zone in the slope. The stability of the reinforced slope and the bearing capacity of the pile are related to the CFRP method. Simultaneously, the structure can reduce the costs and construction difficulty of anti-slide piles in a complex environment surrounded by the soil creep effect.

The inherent strain rate method for thermo‐mechanical simulation of directed energy deposition additive manufacturing

AbstractTo reduce the computational time of thermo‐mechanical simulation of additive manufacturing by directed energy deposition, a new method is proposed, consisting in linearizing the transient standard thermomechanical simulation, by taking advantage of the strong concentration of strain rates around the deposition zone. In practice, a predictor/corrector algorithm is developed. The predictor step consists of a linearized mechanical resolution, which is obtained by considering the scalar generalized viscoplastic strain rate as an inherent strain rate, deduced from resolutions performed during previous time steps. The corrector step consists of a local (e.g., in each finite element) reconstruction of the effective stress field by solving a local nonlinear scalar equation. This predictor/corrector strategy is employed to deal with the dynamic evolution of strain rates and stress, during the distinct stages of the process: deposition, inter‐layer dwell time, and final cooling. With the proposed method, a time gain of around 5 is obtained for both a single wall and a curved turbine blade mock‐up, while the results (distortion and stress) of the full nonlinear thermomechanical resolution are replicated with an excellent accuracy. This makes the new inherent strain rate method a very promising tool for additive manufacturing simulation.

Low strain rate yield characteristics and failure modes of solid composite propellant

Solid motor propellant grain is in low strain rate creep state under long-term storage condition. To analyze the yield characteristics and failure modes of HTPB (hydroxyl-terminated polybutadiene) propellant under different strain rate conditions, the constant speed tensile test of 2.38 × 10−5 s−1～2.38 × 10−2 s−1, 12-week long-term relaxation test and 4-week long-term creep test were carried out. The dynamic yield function of elastic-viscoplastic model was proposed, and the function parameters were fitted and verified by experimental data. The results show that the mechanical properties of the propellant show obvious rate dependence under lower strain rate, and the breaking strength and maximum elongation decrease significantly with the decrease of strain rate. The propellant starts to yield after strain reaching 15.0%, and the meso-structure enters an unstable state. The matrix and particle interface dewetting gradually becomes serious, developing into large particle shedding and matrix tearing, and finally causing macroscopic failure. The dynamic yield function can well describe the relationship between the dynamic yield strength, viscoplastic strain rate and static yield strength. The static yield strength of the propellant was analyzed and obtained as 0.06 MPa. The obtained yield strain and static yield strength can support the establishment of structural integrity failure criteria for long-term storage solid rocket motor.

Multiscale identification and NTFA reduction of the elasto-viscoplastic polycrystalline behaviour of uranium dioxide (UO2) for wide range of loading conditions

This numerical study presents a micromechanical modelling of the behaviour of uranium dioxide fuel (UO2), a polycrystalline ceramic used in nuclear power plants, for loading condition typical of a reactivity initiated accident (RIA). Above a specific temperature, UO2 has an elasto-viscoplastic behaviour with strain hardening depending on both temperature and macroscopic strain rate (T,ε¯˙).In a first step, via a full-field approach, an inverse identification of the local single crystal evolution law is performed based on experimental data obtained at the macroscopic scale [4,5]. Beyond the macroscopic behaviour of the fuel pellet, it is sometimes necessary to go down in scale to study local phenomena. A first approach would be to perform a Finite Element Method squared to two (FEM2) resolution [37]. It consists to solve a thermomechanical problem on a first mesh defined at the pellet scale where at each integration point is solved another thermomechanical problem on a Representative Volume Element. The full-field approach guarantees access to the local field at the expense of relatively high computational time. It is not conceivable within industrial codes.In a second step it appeared necessary to replace the second full-field resolution by a model reduction method based on the Nonuniform Transformation Field Analysis (NTFA) approach. This method allows access to macroscopic quantities and local fields while drastically reducing the computational time. The NTFA model [21] with tangent second order (TSO) approximation [24,21] is developed and applied to the problem at hand. Two decompositions of the hardening variable are studied. It is taken as in the reference [21], as uniform per grain or taken as decomposed, like modes associated with the viscoplastic strain tensor. Then, work is done to integrate the specific loading conditions, i.e. temperatures and strain rates of the RIA, into the NTFA model while keeping the number of internal variables as low as possible. Finally, the results from the experimental, full-field and NTFA TSO models are compared. It is checked that the numerical results are not deteriorated either macroscopically or locally at the macroscopic and local scales for uniaxial and triaxial loading.

An elasto-viscoplastic model for partially saturated geomaterials

Rainfall and reservoir water level changes lead to changes in pore water pressures and in turn to changes in effective stresses and thus to landslide deformations. This is also a time dependent process and creep may occur on top of it. To explore their creep mechanics, four groups of isotropic compression creep tests on unsaturated soils have been conducted. We found that the volumetric strain had a linear relationship with logarithmic time under a constant net confining pressure or suction. The gradient of the straight line is independent of the net confining pressure and has an exponential relationship with suction, indicating that the creep formula proposed by Yin and Graham can be employed to describe the strain in unsaturated soil; however, the creep parameters must be expressed by a function that considers suction. In this study, we established a creep model for unsaturated materials based on plastic and rheological theories. The hardening parameters of the yield stress include the plastic volumetric strain and viscous volumetric strain. We established a time-dependent yield surface equation for unsaturated soils by introducing a conversion time variable into the yield surface equation of the Barcelona Basic Model. Subsequently, based on the associated flow rule and the Perzyna theory, we derived a viscoplastic strain rate equation for unsaturated soil. To verify the model, a set of unsaturated shear and creep tests have been performed and recorded the volumetric, axial strains and stress over time. The values predicted by the model agreed with our experimental results, indicating the reliability of the new creep model for unsaturated soil.

One-dimensional elastic viscoplastic finite strain consolidation model for soft clay with uncertainty

One-dimensional elastic viscoplastic finite strain consolidation model for soft clay with uncertainty

Nonlinear viscoelastoplastic kinetics for high-temperature performance of modified asphalt binders

Modified additives are widely used to improve the high-temperature performance of asphalt binders. However, the high-temperature performance of modified asphalt binders cannot be well evaluated by the existing methods. To address this issue, this study aims to develop a new nonlinear viscoelastoplastic kinetics method to evaluate the high-temperature performance of modified asphalt binders. Styrene-butadiene-styrene (SBS), rubber modified asphalt binders and their aged materials are employed. First, the non-recoverable creep compliance from the standard and modified Multiple Stress Creep and Recovery (MSCR) tests are used to evaluate the high-temperature performance of asphalt binders. Then, the viscoplastic strain and activation energy from creep-recovery tests are adopted to evaluate the high-temperature performance of asphalt binders based on nonlinear viscoelastoplastic kinetics method. Results show that the high-temperature performance results from the standard and modified MSCR tests are inconsistent. The viscoplastic strain of unaged SBS modified asphalt binders shows different trends compared with other asphalt binders. It rapidly increases at the initial loading stage, then follows by a reinforcement period, and finally maintains a steady growth rate, while the reinforcement period will disappear after aging. The viscoplastic activation energy from the nonlinear viscoelastoplastic kinetics method can characterize the stable high-temperature performance of asphalt binders, avoiding controversy caused by the number of cycles in MSCR tests.

Macro-scale modeling of finite strain viscoplasticity in irradiated F/M steels: a continuum thermodynamic framework

The European reduced activation ferritic/martensitic steel Eurofer97 in irradiated states displays significant nonlinear material behavior involving irradiation hardening, loss of strain hardening, and uniform elongation, as well as irradiation-induced embrittlement. Nonlinear behavior of irradiated steel modeled on the continuum scale will help to estimate the maximum operating range of the irradiated components beyond the onset of localized plastic flow. In this work, a thermodynamic framework for modeling irradiation-influenced deformation is established based on irradiation defect density and a thermodynamically consistent finite strain formulation of an existing viscoplastic model using the Dual Variables concept is presented. The model is implemented in ABAQUS allowing the simulation of tensile tests conducted on irradiated and unirradiated materials which shows the model’s ability to capture the post-yield and post-necking behavior observed in experiments up to ductile failure.