Showing papers on "Viscoplasticity published in 2019"

A soft soil model that accounts for creep

Abstract: The well-known logarithmic creep law for secondary compression is transformed into a differential form in order to include transient loading conditions. This 1-D creep model for oedometer-type strain conditions is then extended towards general 3-D states of stress and strain by incorporating concepts of Modified Cam-Clay and viscoplasticity. Considering lab test data it is shown that phenomena such as undrained creep, overconsolidation and aging are well captured by the model.

Time-resolved dynamics of the yielding transition in soft materials

Abstract: A rigorously-defined method that maps and quantifies the time-resolved dynamical yielding process of elastoviscoplastic materials is proposed and investigated. Building on the foundations of linear viscoelastic theory for oscillatory deformations, the method utilizes the motion of an instantaneous phase angle between the stress and strain of the rheological response within deformation space to quantify the yielding transition. Principal component analysis demonstrates that this phase angle velocity is based on the natural description for a material response in deformation space. The response of the Carreau model with constitutive parameters selected to correspond to a regularized viscoplastic fluid that undergoes an apparent yielding transition at a critical shear rate, and of a Carbopol microgel are investigated as canonical examples of theoretical and experimental model yield stress fluids. Calculation of the phase angle velocity clearly identifies the yield transition as being gradual. This approach provides a physically-motivated understanding of the dynamical processes occurring during yielding of elastoviscoplastic materials.

A constitutive relation of AZ80 magnesium alloy during hot deformation based on Arrhenius and Johnson–Cook model

Abstract: In order to understand the constitutive behavior of as-cast AZ80 with large grain size, the uniaxial hot compression tests were carried out over a series of isothermal upsetting experiments. The maximum deformation degree was 65%. The experimental temperatures were 523 K, 573 K, 623 K and 673 K and the strain rate was 0.001 s(-1), 0.01 s(-1), 0.1 s(-1), and 1 s(-1). The stress-strain curves can be divided into three stages which are work hardening stage, softening stage, and steady-state stage at low strain rate and high temperature, while the steady-state stage cannot be observed at low forming temperature and high strain rate because of incomplete dynamic recrystallization. The Arrhenius type relation predicts the peak stress with high accuracy but cannot satisfy the strain relevant requirement. The Johnson-Cook model shows an inappropriate ability to describe the constitutive behavior in this case. Therefore, a new mathematic model (a segmented model) with high prediction accuracy based on the modified Arrhenius type relation (including strain rate) and Johnson-Cook model is proposed. The modified Arrhenius type relation is used to reflect the constitutive behavior before the peak strain and the modified Johnson-Cook model is aimed at showing the stages after peak strain.

Multi-axial creep-fatigue life prediction considering history-dependent damage evolution: A new numerical procedure and experimental validation

Abstract: In this paper, a new numerical procedure based on a cycle-by-cycle analysis has been constructed for creep-fatigue behavior and life prediction of high-temperature structures under multi-axial stress states. Within this framework, a modified unified viscoplastic constitutive model with isotropic hardening and modified kinematic hardening rules is developed to simulate the cycle-by-cycle stress-strain responses. Moreover, the newly constructed creep-fatigue approach calculates fatigue and creep damage variables using the critical plane method (CPM) and the modified strain energy density exhaustion (SEDE) model, respectively. The multi-axial ductility factor and elastic follow-up factor are also introduced into the modified SEDE model to accommodate the special multi-axial and mixed controlled modes, which are widely existed in practical structures. In order to validate the feasibility of the proposed numerical procedure, a series of creep-fatigue tests of notched specimens made from nickel-based GH4169 superalloy were carried out at 650 °C. The predicted numbers of cycles to crack initiation agree well with the experimental data. Evidence of crack initiation under various loading conditions was observed via the electron backscatter diffraction (EBSD) technique, indicating location-dependent crack initiations depending on loading conditions. In detail, the crack initiation sites shifting from surface to subsurface with increasing hold times can be well simulated by the proposed numerical procedure due to a reasonable description of the creep-fatigue damage evolution.

Modeling the rheology of thixotropic elasto-visco-plastic materials

Abstract: To describe the macroscopic rheological behavior of thixotropic elasto-visco-plastic (TEVP) materials, phenomena that take place in their microstructure must be accounted for. To this end, we couple the tensorial constitutive model by Saramito for EVP materials with thixotropy, extending the ideas of isotropic hardening, and with kinematic hardening (KH), to account for back stresses. We use a scalar variable that describes the level of structure at any instance and a modified Armstrong–Frederick KH equation, thus providing rules governing the dynamics of the apparent yield stress. The material viscosity, yield stress, and back stress modulus feature a nonlinear dependence on the structural parameter, enabling the model to make accurate predictions with a single structural parameter. To avoid unphysical stress evolution in both shear and extensional flows, we propose a modified back stress constitutive equation that keeps the components of the stress tensor bounded. The predictions of the new model are compared to experimental data and predictions of previously proposed TEVP models in simple rheometric flows, including steady and step-shear tests, flow reversal, intermittent step tests, small amplitude oscillatory shear (SAOS) and large amplitude oscillatory shear. In most cases, the proposed model reproduces more accurately these experimental data than the other models, highlighting its predictive capabilities. Moreover, SAOS illustrates that introducing viscoplasticity via the Saramito model necessarily reduces G″ to zero in the linear strain regime. This calls for model adjustments in the solid state. Finally, we examined the proposed model in uniaxial elongation and concluded that it is important to include this flow in the rheological characterization and modeling of such systems.To describe the macroscopic rheological behavior of thixotropic elasto-visco-plastic (TEVP) materials, phenomena that take place in their microstructure must be accounted for. To this end, we couple the tensorial constitutive model by Saramito for EVP materials with thixotropy, extending the ideas of isotropic hardening, and with kinematic hardening (KH), to account for back stresses. We use a scalar variable that describes the level of structure at any instance and a modified Armstrong–Frederick KH equation, thus providing rules governing the dynamics of the apparent yield stress. The material viscosity, yield stress, and back stress modulus feature a nonlinear dependence on the structural parameter, enabling the model to make accurate predictions with a single structural parameter. To avoid unphysical stress evolution in both shear and extensional flows, we propose a modified back stress constitutive equation that keeps the components of the stress tensor bounded. The predictions of the new model are co...

A canonical framework for modeling elasto-viscoplasticity in complex fluids

Abstract: A comprehensive framework for modeling elasto-viscoplasticity in complex fluids is discussed. It is based on the plasticity mechanism of kinematic hardening, which is widely accepted in solid mechanics and accounts for transient yielding processes. We discuss a simple one dimensional variant of the model, as well as a fully three-dimensional, frame-invariant and thermodynamically admissible version of the model. Predictions for several canonical rheometric test protocols are provided. We also discuss possible extensions to account for additional rheological complexities exhibited by real fluids, such as thixotropy, nonlinear elasticity and normal stress differences. We find that this framework has several advantages over the more commonly used elastic Bingham-like or elastic Herschel Bulkley models for describing elasto-viscoplasticity. First, the model can account for behavior over a much wider range of viscometric test conditions. Second, it eliminates the flow/no flow criterion inherent in Bingham-like constitutive laws, which frequently requires regularization. Third, it is a flexible framework and allows for implementation of additional complexities, including thixotropic behavior and other nonlinear rheological features.

Nonlinear Creep Damage Constitutive Model of Concrete Based on Fractional Calculus Theory

Abstract: Concrete creep has become one of the major problems that threatens concrete structural development and construction. However, a reasonable and accurate calculation model for numerical analysis is the key to control and solve the creep deformation of concrete. To better describe the concrete nonlinear creep damage evolution rule, the visco-elasticity Plasticity Rheological Theory, Riemann Liouville Theory and Combined Model Theory are quoted, and the Able dashpot is used to reconstruct fractional-order soft-body composite elements to propose the expression of the stress-strain relationship of the elastomer, visco-elasticity plasticity body, and Viscoplasticity body, considering the evolution of the concrete compression damage process. A nonlinear creep damage constitutive model of concrete, based on fractional calculus theory, is conducted, and the parameters of the specific calculation method of the model are given. The influence of stress level σ, fractional order n and material parameter α on the concrete creep process is determined by a sensitivity analysis of the model parameters. The creep process and deformation amount of concrete in practical engineering can be effectively controlled by the results of the proposed sensitivity analysis. The research results can be used to provide guidance and reference for the safe construction of concrete engineering in actual practice.

A thermo-elasto-viscoplastic constitutive model for polymers

Abstract: Tensile tests conducted at different temperatures and strain rates on a low density cross-linked polyethylene (XLPE) have shown that increasing the strain rate raises the yield stress in a similar manner as when the temperature is decreased. The locking stretch also increases as a function of the strain rate, but not to the same extent as by decreasing the temperature. The volumetric straining and self-heating of the specimens were also measured in the experimental campaign: at room temperature the material was close to incompressible, while at the lower temperatures it was found to be moderately compressible. At the lowest strain rate isothermal conditions was observed, while adiabatic heating was seen at the highest strain rate. In this study, a thermo-elasto-viscoplastic model is developed for XLPE in an attempt to describe the combined effects of temperature and strain rate on the mechanical stress-strain response but also on the thermodynamical response. The proposed model consists of two parts. On one side, Part A models the thermoelastic and thermoviscoplastic response, and incorporates an elastic Hencky spring in series with two Ree-Eyring dashpots. The two Ree-Eyring dashpots represent the effects of the main α relaxation and the secondary β relaxation processes on the plastic flow. Part B, on the other side, consists of an eight chain spring capturing the entropic strain hardening due to alignment of the polymer chains during deformation. The constitutive model was implemented in a nonlinear finite element (FE) code using a semi-implicit stress update algorithm combined with sub-stepping and a numerical scheme to calculate the consistent tangent operator. After calibration to available experimental data, FE simulations with the constitutive model are shown to successfully describe the stress-strain curves, the volumetric strain, the local strain rate and the self-heating observed in the tensile tests. In addition, the FE simulations adequately predict the global response of the tensile tests, such as the force-displacement curves and the deformed shape of the tensile specimen.

The analysis of dates obtained from long-term creep tests to determine creep coefficients of rock salt

Abstract: Failure to properly characterize time-dependent behavior (i.e. creep) of rocks and the use of inappropriate behavior models when analyzing stability of underground spaces such as mining drifts and stopes, road tunnels, different types of caverns and reservoirs for storing natural gas, petroleum fluids, and compressed air energy as well as nuclear waste disposal caverns will end up with costly losses. The most important factors affecting creep behavior of rock masses include composition of the minerals composing the rock, size of the grains or crystals of which the rock is composed, humidity, temperature, time, loading scheme, loading rate, strain rate and loading frequency. On this basis, in order to attain a proper understanding of creep behavior of rocks, it is necessary to determine creep coefficients of rocks via in-lab experiments. In the present research, rock salt samples were prepared in the form of cylinders at length-to-diameter ratios of greater than 2. Performed experiments in this study were long-term creep (LTC) tests at 6 stress levels of 5.5, 7.5, 10, 12, 14.02, and 18 MPa and stepwise short-term creep (STC) tests (each at 3 stress levels, namely 4.4, 10.1, and 11.9 MPa, and 7.5, 12, and 17 MPa, respectively). The tests were performed at ambient conditions at a constant temperature of 22 °C and relative humidity of 23%. Then, according to Burger’s rheological model and the Lubby 2 constitutive model and analyzing the obtained information from the tests, Kelvin’s viscoelastic coefficient and shear modulus as well as Maxwell’s elastic and viscoplastic coefficients were calculated. Also, obtained creep coefficients were improved using linear and nonlinear regression analysis of experiment dates.