Showing papers on "Viscoplasticity published in 2018"

Nonlinear viscoplasticity in ASPECT : Benchmarking and applications to subduction

Abstract: . ASPECT (Advanced Solver for Problems in Earth's ConvecTion) is a massively parallel finite element code originally designed for modeling thermal convection in the mantle with a Newtonian rheology. The code is characterized by modern numerical methods, high-performance parallelism and extensibility. This last characteristic is illustrated in this work: we have extended the use of ASPECT from global thermal convection modeling to upper-mantle-scale applications of subduction. Subduction modeling generally requires the tracking of multiple materials with different properties and with nonlinear viscous and viscoplastic rheologies. To this end, we implemented a frictional plasticity criterion that is combined with a viscous diffusion and dislocation creep rheology. Because ASPECT uses compositional fields to represent different materials, all material parameters are made dependent on a user-specified number of fields. The goal of this paper is primarily to describe and verify our implementations of complex, multi-material rheology by reproducing the results of four well-known two-dimensional benchmarks: the indentor benchmark, the brick experiment, the sandbox experiment and the slab detachment benchmark. Furthermore, we aim to provide hands-on examples for prospective users by demonstrating the use of multi-material viscoplasticity with three-dimensional, thermomechanical models of oceanic subduction, putting ASPECT on the map as a community code for high-resolution, nonlinear rheology subduction modeling.

Comparison of Short-Term and Long-Term Creep Experiments in Shales and Carbonates from Unconventional Gas Reservoirs

Abstract: We carried out a series of long-term creep experiments on clay- and carbonate-rich shale samples from unconventional gas reservoirs to investigate creep over both relatively short-term (4-h) and long-term (4-week) periods. Results from each set of experiments were compared to evaluate the ability to predict the long-term behavior of reservoir rocks using relatively short-term creep experiments. The triaxial deformation experiments were performed in a time-cycling pattern, which included a series of four stages of loading, creep, unloading and recovery experiments conducted over different time spans. The loading conditions (tens of MPa) reflect current reservoir conditions and were far below the strength of the samples. Experiments were conducted on both horizontal and vertical shale samples to address anisotropy introduced by the bedding. A power-law model was fitted to the creep data to predict the long-term behavior of shale samples. Regardless of the applied loading history, results of the experiments show that the shale samples follow a single trend representing their creep behavior through time. We show that the simple power-law model is capable of describing creep over multiple time periods. Additionally, the value of the creep compliance factor is consistent over different creep testing periods and it is possible to characterize the behavior of these samples from relatively short-term (1 day) creep experiments.

A multimode structural kinetics constitutive equation for the transient rheology of thixotropic elasto-viscoplastic fluids

Abstract: To predict the complex transient rheology of thixotropic elasto-viscoplastic (TEVP) fluids, we generalize a previous scalar thixotropic-only “multilambda” (ML) model [Wei et al., J. Rheol. 60(6), 1301–1315 (2016)] and combine it with the isotropic kinematic hardening (IKH) model [C. J. Dimitriou and G. H. Mckinley, Soft Matter 10(35), 6619–6644 (2014)]. This new constitutive equation, which we call ML-IKH model, has the following features: (1) Multiple thixotropic structure parameters that collectively exhibit a stretch-exponential thixotropic relaxation in step tests; (2) nonlinear thixotropic kinetic equations in both the shear rate or stress and the structure parameters; (3) incorporation of the Armstrong-Frederick kinematic hardening rule [C. O. Frederick and P. Armstrong, Mater. High Temp. 24(1), 1–26 (2007)] for the evolution of yield stress; and (4) viscoelasticity. We evaluate this 12-parameter model, discuss its four key features, and compare its predictions with those of the ML, IKH, and modified Delaware thixotropic models [Armstrong et al., J. Rheol. 60(3), 433–450 (2016)] for two sets of experimental data [Wei et al., J. Rheol. 60(6), 1301–1315 (2016); Armstrong et al., J. Rheol. 60(3), 433–450 (2016)] of a TEVP fumed silica suspension. The shear-rate histories include steady state, step shear rate, step stress, intermittent shear, flow reversal, and large amplitude oscillatory shear (LAOS). We show that in step tests the thixotropic and viscoelastic evolutions are dominant, while intermittent shear tests the multiple thixotropic timescales, and flow reversal tests the viscoelastic and plastic evolutions. The rheological responses in LAOS tests are more complex and involve all aspects of TEVP rheology. The four features quantitatively capture different aspects of TEVP rheology. We also provide a tensorial formulation of the ML-IKH model that is frame-invariant, obeys the second law of thermodynamics, and can reproduce the predictions of the scalar version.To predict the complex transient rheology of thixotropic elasto-viscoplastic (TEVP) fluids, we generalize a previous scalar thixotropic-only “multilambda” (ML) model [Wei et al., J. Rheol. 60(6), 1301–1315 (2016)] and combine it with the isotropic kinematic hardening (IKH) model [C. J. Dimitriou and G. H. Mckinley, Soft Matter 10(35), 6619–6644 (2014)]. This new constitutive equation, which we call ML-IKH model, has the following features: (1) Multiple thixotropic structure parameters that collectively exhibit a stretch-exponential thixotropic relaxation in step tests; (2) nonlinear thixotropic kinetic equations in both the shear rate or stress and the structure parameters; (3) incorporation of the Armstrong-Frederick kinematic hardening rule [C. O. Frederick and P. Armstrong, Mater. High Temp. 24(1), 1–26 (2007)] for the evolution of yield stress; and (4) viscoelasticity. We evaluate this 12-parameter model, discuss its four key features, and compare its predictions with those of the ML, IKH, and modifie...

A modified Johnson-Cook model for 10%Cr steel at elevated temperatures and a wide range of strain rates

Abstract: A modified J-C model of 10%Cr steel, based on the original J-C model, is further developed to consider not only the coupling effects of strains, strain rates and temperatures, but also the mechanism of the hardening and the flow softening during whole deformation processes. The model can simulate multi-deformation processes including work hardening, recovery and recrystallization at the high temperature for use as the nuclear power equipments. To establish this new model, the compression tests at different temperatures (950–1250 °C) and strain rates (0.001 s−1−0.01 s−1) were conducted and the observations of microstructure under various conditions were performed. The results indicate that the influences of the strain, strain rate and temperature on the strain hardening of material are not independent of each other, while many of them interact. Moreover, Compared with the original J-C model and experimental data, the modified J-C model has good predictability of the hot deformation behavior of material.

Identifiability of material parameters in solid mechanics

Abstract: Material parameter identification using constitutive models of elasticity, viscoelasticity, rate-independent plasticity and viscoplasticity has a long history with regard to homogeneous and inhomogeneous deformations. For example, uniaxial tensile tests, pure shear tests, torsion experiments of thin-walled tubes or biaxial tensile tests are used to obtain the material parameters by solving the inverse problem. Frequently, the parameters are determined by numerical optimization tools. In this paper, we investigate some very basic single- and two-layered examples regarding identifiability, because these tests are the basis for more complex geometrical and physical nonlinear problems. These simple examples are the uniaxial tensile/compression case, biaxial tensile tests of a cruciform specimen, torsion of a thin-walled tube, a thick-walled tube under internal pressure and the indentation test. For the thick-walled tube under internal and external pressure with an axial pre-strain with several layers, an analytical solution is provided directly suitable for programming. The aim is to get an understanding whether some problems lead to non-identifiable parameters.

Topology optimization of finite strain viscoplastic systems under transient loads

Abstract: A transient finite strain viscoplastic model is implemented in a gradient-based topology optimization framework to design impact mitigating structures. The model's kinematics relies on the multiplicative split of the deformation gradient, and the constitutive response is based on isotropic hardening viscoplasticity. To solve the mechanical balance laws, the implicit Newmark-beta method is used together with a total Lagrangian finite element formulation. The optimization problem is regularized using a partial differential equation filter and solved using the method of moving asymptotes. Sensitivities required to solve the optimization problem are derived using the adjoint method. To demonstrate the capability of the algorithm, several protective systems are designed, in which the absorbed viscoplastic energy is maximized. The numerical examples demonstrate that transient finite strain viscoplastic effects can successfully be combined with topology optimization. (Less)

A new constitutive model for polymeric matrices: Application to biomedical materials

Abstract: Semi-crystalline polymeric composites are increasingly used as bearing material in the biomedical sector, mainly because of their specific mechanical properties and the new advances in 3D printing technologies that allows for customised devices. Among these applications, total or partial prostheses for surgical purposes must consider the influence of temperature and loading rate. This paper proposes a new constitutive model for semi-crystalline polymers, commonly used as matrix material in a wide variety of biomedical composites, that enables reliable predictions under a wide range of loading conditions. Most of the recent models present limitations to predict the non-linear behaviour of the polymer when it is exposed to large deformations at high strain rates. The proposed model takes into account characteristic behaviours of injected and 3D printed thermoplastic polymers such as material hardening due to strain rate sensitivity, thermal softening, thermal expansion and combines viscoelastic and viscoplastic responses. These viscous-behaviours are relevant for biomedical applications where temperature evolution is expected during the deformation process due to heat generation induced by inelastic dissipation, being essential the thermo-mechanical coupling consideration. The constitutive model is formulated for finite deformations within a thermodynamically consistent framework. Additionally, the model is implemented in a finite element code and its parameters are identified for two biomedical polymers: ultra-high-molecular-weight-polyethylene (UHMWPE) and high density polyethylene (HDPE). Finally, the influence of viscous behaviours on dynamic deformation of semi-crystalline polymeric matrices is analysed. This constitutive model predicts the mechanical behaviour of semi-crystalline polymeric matrices for a wide range of strain rate and temperature conditions, allowing for the optimisation of new composite materials potentially used as effective joint replacement prostheses.

Yielding and Flow of Soft-Jammed Systems in Elongation.

Abstract: So far, yielding and flow properties of soft-jammed systems have only been studied from simple shear and then extrapolated to other flow situations. In particular, simple flows such as elongations have barely been investigated experimentally or only in a nonconstant, partial volume of material. We show that using smooth tool surfaces makes it possible to obtain a prolonged elongational flow over a large range of aspect ratios in the whole volume of material. The normal force measured for various soft-jammed systems with different microstructures shows that the ratio of the elongation yield stress to the shear yield stress is larger (by a factor of around 1.5) than expected from the standard theory which assumes that the stress tensor is a function of the second invariant of the strain rate tensor. This suggests that the constitutive tensor of the materials cannot be determined solely from macroscopic shear measurements.

Rising bubbles in yield stress materials

Abstract: We present an experimental investigation of bubbles rising in elasto-viscoplastic media. The effects of medium rheology and bubble size on the bubble velocity and shape are investigated. In addition, a discussion regarding the influence of the stress history on the bubble path is presented. Experimental tests are performed using yield stress materials which also present elastic behavior. Despite the difficulty in determining the relative importance of the different forces that are present in this flow, the results obtained illustrate the effect of yield stress, inertia, elasticity, and buoyancy on the dynamics and shape of the bubble.

The yield stress tensor

Abstract: Yield stress materials are known to possess a certain threshold property, a strength , that must be overcome in order for flow to occur. This strength is commonly conceived as a scalar representation of the stress tensor at the yielding point, here called the yield stress tensor . The recognition of the importance of elastic, thixotropic, and other effects not predicted by ideal viscoplastic models is becoming more and more present in the study of yield stress materials. Nevertheless, the paradigm built by the theoretical analysis of inelastic viscoplastic models has a strong influence in the literature. For example, the common denomination of the shear component of the stress tensor at the yielding point as the yield stress of the material . This nomenclature is so spread in the literature that is explicitly employed even in articles where elastic effects are investigated. Viscometric rheometry is the most widely imposed kinematics used to probe the material, and the flow curve is considered the most useful single information about the material related to flow. However, even for this fixed kinematics, the conditions at the yielding point are not uniquely determined by the shear stress component. Although the existence of normal stress differences are known to be present in a variety of yield stress materials, and virtually all yielding criteria are dependent on the invariants of the deviatoric stress tensor at the yield point, the components of the yield stress tensor other than the yield shear stress are ignored altogether. In the present work, we measure not only the shear stress component of the yield stress tensor, but also the normal stress differences at the yielding point for eight yield stress materials, in order to determine the full deviatoric yield stress tensor in viscometric flow. To this end, besides creep tests performed to find the yield shear stress, cone-plate as well as plate-plate geometries are employed to determine, respectively, the first normal stress difference, N 1 , and the difference of normal stress differences, N 1 − N 2 . A low-slope shear stress ramp is imposed and the normal stress differences are plotted as a function of the shear stress, in order to determine their values at the yield shear stress. In most of the cases, it is found that the normal stresses of the deviatoric yield stress tensor are significant when compared to the yield shear stress component. Therefore, in general all the yield stress tensor components can contribute significantly to the composition of a yield criterion. This fact imposes the need for reliable measurements to determine the full yield stress tensor of the material.

A Cosserat crystal plasticity and phase field theory for grain boundary migration

Abstract: The microstructure evolution due to thermomechanical treatment of metals can largely be described by viscoplastic deformation, nucleation and grain growth. These processes take place over different length and time scales which present significant challenges when formulating simulation models. In particular, no overall unified field framework exists to model concurrent viscoplastic deformation and recrystal-lization and grain growth in metal polycrystals. In this work a thermodynamically consistent diffuse interface framework incorporating crystal viscoplasticity and grain boundary migration is elaborated. The Kobayashi–Warren–Carter (KWC) phase field model is extended to incorporate the full mechanical coupling with material and lattice rotations and evolution of dislocation densities. The Cosserat crystal plasticity theory is shown to be the appropriate framework to formulate the coupling between phase field and mechanics with proper distinction between bulk and grain boundary behaviour.