Showing papers on "Viscoplasticity published in 2016"

Nonlinear regularization operators as derived from the micromorphic approach to gradient elasticity, viscoplasticity and damage.

Abstract: The construction of regularization operators presented in this work is based on the introduction of strain or damage micromorphic degrees of freedom in addition to the displacement vector and of their gradients into the Helmholtz free energy function of the constitutive material model. The combination of a new balance equation for generalized stresses and of the micromorphic constitutive equations generates the regularization operator. Within the small strain framework, the choice of a quadratic potential w.r.t. the gradient term provides the widely used Helmholtz operator whose regularization properties are well known: smoothing of discontinuities at interfaces and boundary layers in hardening materials, and finite width localization bands in softening materials. The objective is to review and propose nonlinear extensions of micromorphic and strain/damage gradient models along two lines: the first one introducing nonlinear relations between generalized stresses and strains; the second one envisaging several classes of finite deformation model formulations. The generic approach is applicable to a large class of elastoviscoplastic and damage models including anisothermal and multiphysics coupling. Two standard procedures of extension of classical constitutive laws to large strains are combined with the micromorphic approach: additive split of some Lagrangian strain measure or choice of a local objective rotating frame. Three distinct operators are finally derived using the multiplicative decomposition of the deformation gradient. A new feature is that a free energy function depending solely on variables defined in the intermediate isoclinic configuration leads to the existence of additional kinematic hardening induced by the gradient of a scalar micromorphic variable.

Yielding the yield-stress analysis: a study focused on the effects of elasticity on the settling of a single spherical particle in simple yield-stress fluids

Abstract: The sedimentation of a single particle in materials that exhibit simultaneously elastic, viscous and plastic behavior is examined in an effort to explain phenomena that contradict the nature of purely yield-stress materials. Such phenomena include the loss of the fore-and-aft symmetry with respect to an isolated settling particle under creeping flow conditions and the appearance of the “negative wake” behind it. Despite the fact that similar observations have been reported in studies involving viscoelastic fluids, researchers conjectured that thixotropy is responsible for these phenomena, as the aging of yield-stress materials is another common feature. By means of transient calculations, we study the effect of elasticity on both the fluidized and the solid phase. The latter is considered to behave as an ideal Hookean solid. The material properties of the model are determined under the isotropic kinematic hardening framework via Large Amplitude Oscillatory Shear (LAOS) measurements. In this way, we are able to predict accurately the unusual phenomena observed in experiments with simple yield-stress materials, irrespective of the appearance of slip on the particle surface. Viscoelasticity favors the formation of intense shear and extensional stresses downstream of the particle, significantly changing the entrapment mechanism in comparison to that observed in viscoplastic fluids. Therefore, the critical conditions under which the entrapment of the particle occurs deviate from the well-known criterion established theoretically by Beris et al. (1985) and verified experimentally by Tabuteau et al. (2007) for similar materials under conditions that elastic effects are negligible. Our predictions are in quantitative agreement with published experimental results by Holenberg et al. (2012) on the loss of the fore–aft symmetry and the formation of the negative wake in Carbopol with well-characterized rheology. Additionally, we propose simple expressions for the Stokes drag coefficient, as a function of the gravity number, Yg (related to the Bingham number), for different levels of elasticity and for its critical value, under which entrapment of particles occurs. These criteria are in agreement with the results found in the recent work by Ahonguio et al. (2014). Finally, we propose a method to quantify experimentally the elastic effects in viscoplastic particulate systems.

Viscoplastic dimensionless numbers

Abstract: In the present paper we analyze the dimensionless numbers that concern the flow of viscoplastic materials. The Bingham material is used to conduct the main discussion but the ideas are generalized to more complex viscoplastic models at the end of the article. Although one can explore the space of solutions with a set of dimensionless numbers where only one of them takes into account the yield stress, like the Bingham number for example, we recommend that the characteristic stress should be defined as the extra-stress intensity evaluated at a characteristic (maximum) deformation rate. Such a definition includes the yield stress in every dimensionless number that is related to viscous effects like the Reynolds number, the viscosity ratio, and the Rayleigh number. This procedure was shown to be more effective on collapsing data into master curves and to provide a fairer comparison with the Newtonian case. This happens because a more representative viscous effect is taken into account, concentrating the plastic effects into a single parameter. The plastic number, the ratio of the yield stress to the maximum stress of the domain, is shown to better capture plastic effects than the usual Bingham number. The analysis of problems where a characteristic stress, but not a characteristic velocity, is provided, indicates that a more representative characteristic velocity should be defined with respect to the driving potential for the motion, i.e., the difference between the characteristic and yield stresses. This method is in contrast to the majority of the literature, where for Bingham materials, the dimensionless numbers are maintained in the same form as the original Newtonian ones, replacing the Newtonian viscosity by the viscous parameter of the Bingham model.

Generalized approach to estimation of strains and stresses at blunt V-notches under non-localized creep

Abstract: Geometrical discontinuities such as notches need to be carefully analysed by engineers because of the stress concentration generated by them. Notches become even more important when the component is subjected, in service, to very severe conditions, such as high-temperature fatigue and imposed viscoplastic behaviour such as creep. The knowledge of strains and stresses in such stress concentration zones is essential for an efficient and safe design process. The aim of the paper is to present an improvement and extension of the existing notch-tip creep stress–strain analysis method developed by Nunez and Glinka, validated for U-notches only, to a wide variety of blunt V-notches. The key in obtaining the extension to blunt V-notches is the substitution of the Creager–Paris equations with the more generalized Lazzarin–Tovo solution, allowing a unified approach to the evaluation of linear elastic stress fields in the neighbourhood of both cracks and notches. Numerous examples have been analysed to date, and the stress fields obtained according to the proposed method were compared with appropriate finite element data, resulting in a very good agreement. In view of the promising results discussed in the paper, authors are considering possible further extension to sharp V-notches and cracks introducing the concept of the strain energy density.

Viscoplastic Deformation of the Bakken and Adjacent Formations and Its Relation to Hydraulic Fracture Growth

Abstract: We report laboratory studies of the time-dependent deformation of core samples from four different formations in the Williston Basin—the Lodgepole Formation, the Middle and Lower Bakken Formations, and Three Forks Formation. The laboratory tests reveal varying amounts of viscoplastic deformation in response to applied differential stress. The time-dependent deformation is generally greater in rocks with higher clay and organic content and can be described by a power-law function. Because the magnitude of the creep strain is linearly proportional to the applied differential stress, we can utilize viscoelastic theory and geophysical logs to estimate the degree to which tectonic stress is affected by viscoplastic stress relaxation. We suggest that viscoplastic stress relaxation results in the Upper and Lower Bakken Formations acting as frac barriers during hydraulic fracture stimulation in the Middle Bakken, but the Lodgepole and the Three Forks Formations are not frac barriers.

Anisotropic viscoplasticity and fracture of fine grained metallic aluminum foil used in Li-ion batteries

Abstract: Aluminum 1235-H18 foils with sub-micron grain dimensions are often used as current collectors in Li-ion batteries. Due to their contribution to the structural integrity of batteries under impact loading, their plastic and fracture response is investigated in detail. Using a novel micro-tensile testing device with a piezoelectric actuator, dogbone specimens with a 1.25 mm wide and 5.7 mm long gage section are tested for three different in-plane material orientations and for strain rates ranging from 10 −5 /s to 10 −2 /s. It was found that the stress at a proof strain of 2% increased by about 25% from 160 MPa to 200 MPa within this range of strain rates. Furthermore, pronounced in-plane anisotropy is observed as reflected by Lankford ratios variations from 0.2 to 1.5 . A material model is proposed which borrows elements of the anisotropic Yld2000-2d plasticity model and integrates these into a basic viscoplasticity framework that assumes the multiplicative decomposition of the equivalent stress into a strain and strain rate dependent contributions. The anisotropic fracture response is characterized for a strain rate of 10 −4 /s using notched tension and Hasek punch experiments. It is found that a simple stress-state independent version of the anisotropic MMC fracture initiation model provides a reasonable approximation of the observed experimental results.

Lattice Boltzmann modeling for multiphase viscoplastic fluid flow

Abstract: We present a lattice Boltzmann model to simulate multiphase viscoplastic fluid flow. It is an extended model based on the free-energy-based lattice Boltzmann method (LBM) for multiphase fluids with possible high-density and high-viscosity ratios by applying the Herschel-Bulkley constitutive relationship to account for the variable viscosity. The model shows good agreements between the simulation results and the corresponding theoretical solutions for different cases. Furthermore, the capability and effectivity of this model is tested by examples, including droplet(s) falling and interaction in Bingham fluid, and sessile viscoplastic droplet motion. The results illustrate that our model is able to catch the yield behavior well, and to distinguish various kinds of viscoplastic fluids effectively.

Rate-dependent size effects and material length scales in nanoindentation near the grain boundary for a bicrystal FCC metal

Abstract: This paper addresses the size effects encountered in nanoindentation experiments of a copper bicrystal specimen in close proximity to the grain boundary. The experimental results show that as the distance r between the indentations and the grain boundary decreases, the hardness of the tested specimen increases. The single grain boundary in the bicrystal specimen is believed to play an important role to the increase in the hardness. The impact of the distance r on the hardness can be considered as a new type of size effect. The strain rate dependency of the length scale is investigated by incorporating a strain rate variable in the expression of the length scale. A temperature and rate-dependent indentation size effect model is used in order to determine the material intrinsic length scale using the corresponding data from the experiments. Nanoindentation experiments with different strain rates are performed in order to investigate the effect of the strain rate. In order to obtain more robust simulation results, the required numerical analysis is performed using ABAQUS Explicit software with a VUMAT user-subroutine which gives the physically based viscoplastic constitutive relations for the tested material.

Two–dimensional viscoplastic dambreaks

Abstract: We report the results of computations for two–dimensional dambreaks of viscoplastic fluid, focusing on the phenomenology of the collapse, the mode of initial failure, and the final shape of the slump. The volume-of-fluid method is used to evolve the surface of the viscoplastic fluid, and its rheology is captured by either regularizing the viscosity or using an augmented-Lagrangian scheme. We outline a modification to the volume-of-fluid scheme that eliminates resolution problems associated with the no-slip condition applied on the underlying surface. We establish that the regularized and augmented-Lagrangian methods yield comparable results, except for the stress field at the initiation or termination of motion. The numerical results are compared with asymptotic theories valid for relatively shallow or vertically slender flow, with a series of previously reported experiments, and with predictions based on plasticity theory.