Elasto-viscoplastic Material Research Articles

Time-resolved dynamics of the yielding transition in soft materials

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.

Modeling of failure mode switching and shear band propagation using the correspondence framework of peridynamics

This study presents an approach to model dynamic failure mode switching and shear band propagation using the correspondence framework of state-based peridynamics. To effectively model spontaneous shear-band-to-crack switching phenomenon, which is of intrinsic complexity, a combined peridynamic nonlocal and classical local damage model for failure prediction is proposed. The concept of bond failure, often employed in the bond-based peridynamic modeling of brittle materials, is extended to the state-based peridynamics to model cleavage failure in elasto-viscoplastic materials so that the directional and progressive nature of damage can be readily handled. The classical constitutive relation for viscous fluid is adapted for use in non-ordinary state-based peridynamics to model stress collapsing state in shear bands. To show the effectiveness of the proposed approach, a comprehensive numerical study of a pre-notched plate subjected to asymmetric impact loading is conducted, including the phenomenon of shear-band-to-crack switching under an intermediate impact velocity and ductile failure under high impact velocity. A zero-energy mode suppression with an upper bound to avoid over-correction is introduced. By using the proposed modeling approach, dynamic failure mode switching and shear band propagation path are accurately captured.

Exchange flows between yield stress materials and Newtonian oils

We perform an experimental analysis of the exchange flow between an elasto-viscoplastic thixotropic material above a less dense Newtonian oil inside a vertical tube. This situation is usually found in cementing plug operations, performed in the oil industry when there is a need to abandon an oil well. The experiments show that three different flow regimes are observed, namely unstable, quasi-stable, and stable (no flow). The unstable regime is a wavy core-annular flow with the denser liquid in the core region. In the quasi-stable regime a slow plug flow starts after a time delay, which is a consequence of thixotropic and elastic effects. Through analysis of the experimental results it is possible to identify, for a given pair of fluids, the region in the governing parameter space, within which the exchange speed is sufficiently low (or zero).

Necking instabilities in elastoviscoplastic materials

Necking instabilities, in which tensile (extensional) deformation localizes into a small spatial region, are generic failure modes in elasto-viscoplastic materials. Materials in this very broad class --- including amorphous, crystalline, polycrystalline and other materials --- feature a predominantly elastic response at small stresses, plasticity onset at a rather well-defined yield stress and rate-dependence. Necking instabilities involve a unique coupling between the system's geometry and its constitutive behavior. We consider generic elasto-viscoplastic constitutive relations involving an internal-state field, which represents the structural evolution of the material during plastic deformation, and study necking in the long-wavelength approximation (sometimes termed the lubrication or slender-bar approximation). We derive a general expression for the largest time-dependent eigenvalue in an approximate WKB-like linear stability analysis, highlighting various basic physical effects involved in necking. This expression is then used to propose criteria for the onset of necking and more importantly for the emergence of strong localization. Applications to strain-softening amorphous plasticity, in the framework of the Shear-Transformation-Zone model, and to strain-hardening crystalline/polycrystalline plasticity, in the framework of the Kocks-Mecking model, are presented. These quantitative analyses of widely different material models support the theoretical predictions, most notably for the strong localization during necking.

Cвойства диаграмм нагружения и разгрузки, порождаемых нелинейным определяющим соотношением типа Максвелла для реономных материалов

В статье продолжены исследование и аттестация физически нелинейного определяющего соотношения типа Максвелла для нестареющих упруговязкопластичных материалов с двумя материальными функциями: комплекса моделируемых им реологических эффектов, области применимости, способов идентификации, настройки и дальнейшей модификации. Аналитически изучены общие качественные свойства семейства кривых нагружения и разгрузки с постоянными скоростями, порождаемых этим соотношением с произвольными материальными функциями в условиях одноосного квазистатического нагружения. Исследованы интервалы монотонности и выпуклости кривых и условия существования точек перегиба на участках нагрузки и разгрузки, величины максимальной деформации, скачков скорости деформации и пластической деформации за цикл нагрузки-разгрузки, их зависимость от максимального напряжения, скорости и длительности нагружения и разгрузки и от характеристик материальных функций. Обнаруженные свойства сопоставлены с типичными свойствами экспериментальных диаграмм нагружения и разгрузки классов реономных материалов с целью выявления феноменологических ограничений на материальные функции, арсенала возможностей и индикаторов (не)применимости определяющего соотношения.

Practical applications analysis and economic efficiency of the method on assessment of the sealing action from the tracked mover on the soil layer

The article describes and evaluates the economic efficiency of applying a modern approach to solving the problem of soil compaction by tracked movers using a new method based on the theory of hereditary creep of elastoviscoplastic materials, taking into account new factors (the time of the impact of movers on the base, rheological properties of the soil, etc.), as well as using a new devices and techniques for determining the physico–mechanical characteristics of the soil layer and modern specialized software products.

On impact by a hard cone on elasto-viscoplastic material, leading to the generation of a conical crack

The destruction of solid physical objects is a complex process in which mechanical, chemical, thermobaric and other matter transformations take place. Under mechanical destruction is understood the violation of the integrity of the object due to the occurrence of cracks. High-speed impact of a solid body on deformable materials is accompanied by the spread of cracks and is of a wave nature. This article presents an analysis of the dynamic stress-strain state in an elastoviscoplastic (EVP) material near the leading edge of a moving crack, approximated by a zone of continuous deformation. An analysis of the distribution of the intensity of tangential stresses and plastic deformations that occur behind the front of the longitudinal and shear head waves of a spherical shape generated by the impact of the vertex of the solid cone is carried out on the model EVP of the medium by the ray method. It is shown that the presence of a maximum of the jump of the tangential velocity component on the shear wave leads to a development with time of a jump in the displacements of the tangents to the front of the shear wave. This can be interpreted as the moment of initiation of the head part of a crack running along with the front of the elastic wave with the velocity of shear waves.

Effect of porosity on infrared healing of fatigue damage in asphalt

Nowadays most of our roads are made of asphalt mixes, a complex visco-elastoplastic material with self-healing properties. The present paper explores the effect of air voids content and their interconnectivity on the capacity of asphalt mixtures to heal fatigue cracks when a thermal infrared treatment is applied. Results showed that the percolation of air voids is required to optimise healing results. In samples with a lower content, the thermal expansion of bitumen and its flow through cracks can exceed the pore network’s capacity. As a consequence, the internal pressure can increase enough to produce material damage instead of healing.

О СПОСОБНОСТИ НЕЛИНЕЙНОГО ОПРЕДЕЛЯЮЩЕГО СООТНОШЕНИЯ РАБОТНОВА ДЛЯ НАСЛЕДСТВЕННЫХ МАТЕРИАЛОВ МОДЕЛИРОВАТЬ ДИАГРАММЫ ДЕФОРМИРОВАНИЯ С ПАДАЮЩИМ УЧАСТКОМ

The Rabotnov physically non-linear constitutive equation with two arbitrary (increasing) material functions for elasto-viscoplastic materials is studied analytically in order to outline the set of basic rheological effects it can simulate, to clarify the material functions governing abilities, to indicate application field of the relation and to develop identification techniques.Under minimal primary restrictions on two material functions, the general equation of the stress-strain curves family produced by the model at constant strain rates is derived and analyzed in uniaxial case. The main qualitative properties of the stress-strain curves and their dependence on a strain rate and material functions are examined and compared to typical properties of test stress-strain curves of elasto-viscoplastic materials and to the properties of stress-strain curves generated by the Boltzmann - Volterra linear viscoelasticity theory (with arbitrary creep compliance). The last one have been generalized to formulate the Rabotnov relation and so the inherited properties and the new properties acquired due to the introduction of the second material function governing non-linearity are in the focus of attention. In particular, it is proved that the stress-strain curves family increases monotonously as strain rate parameter grow and converges to limit curve (instantaneous or equilibrium) as strain rate tends to zero or infinity. Two-sided bounds for stress-strain curves and conditions for their monotonicity with respect to strain or for existence of maximum are obtained. It is shown that the Rabotnov constitutive equation is able to simulate (qualitatively) deformation softening of materials, i.e. a non-monotone behavior and existence of a decreasing segment of stress-strain curves in tensile tests under constant strain rate condition. The linear viscoelasticity theory fails to do it as it generates only increasing and convex-up stress-strain curves.

On Finite Displacement of an Elastoviscoplastic Material in a Gap between Two Rigid Coaxial Cylindrical Surfaces

In the framework of the theory of large deformations, we obtain the solution of a boundary value problem on the flow of an elastoviscoplastic material in a gap between two rigid coaxial cylindrical surfaces under pressure drop changing with time. It is assumed that slip of the material is possible on both surfaces. We consider reversible deformation, the development of viscoplastic flow under the increasing and constant pressure drop, deceleration of the flow under the decreasing pressure drop, and the unloading of the medium.

A semi-analytical solution for one-dimensional elasto-viscoplastic consolidation of layered soft clay

Abstract The threshold yield stress plays a key role in controlling the rheological consolidation behaviour of soft clay. A semi-analytical theory combining numerical and analytical methods is introduced that excludes the effects of clay self-weight. The governing equations assume the clay is an elasto-viscoplastic material. Approximate solutions as well as computational programme to surface loading for two drainage boundary conditions are obtained, while the clay profile is separated into material which is overconsolidated and normally consolidated. The effects of threshold yield stress and time-dependent loading on the rheological behaviour of soft clays are explored using the solutions developed.

Elasto-viscoplastic analysis for negative through-the-thickness Poisson’s ratio of woven laminate composites based on homogenization theory

In this study, the negative through-the-thickness Poisson’s ratios of [±θ] woven laminates were analyzed based on the homogenization theory for elasto-viscoplastic materials. A [±θ] woven laminate model with the fiber bundle cross angle ±θ was considered and its diamond-shaped domain of analysis was defined. The elasto-viscoplastic homogenization analysis was performed to investigate the negativity of the through-the-thickness Poisson’s ratios for the [±θ] carbon fiber/epoxy and glass fiber/epoxy woven laminates. The through-the-thickness Poisson’s ratio of the [±30°] carbon fiber/epoxy woven laminate was negative in both the elastic and viscoplastic regions. However, that of the [±30°] glass fiber/epoxy woven laminate was positive in the elastic region but became negative in the viscoplastic region. The negative through-the-thickness Poisson’s ratios of the [±30°] woven laminates were caused by the compressive stress with respect to the in-plane direction and the viscoplastic deformation of the matrix.

Origin of the onset of Rayleigh-Bénard convection in a concentrated suspension of microgels with a yield stress behavior

In this paper, we propose to explore experimentally the origin of the onset of motion in a well-known Carbopol gel, a concentrated suspension of microgels, when submitted to a vertical temperature gradient, namely, the Rayleigh-Bénard Convection (RBC). We consider three possible scenarios: (i) the gel behaves as an elasto-viscoplastic material, (ii) the gel presents a low-stress viscosity μ+ below the yield stress τy, and (iii) the gel can be considered as a two phase system, say the microgels and the solvent, i.e., a porous medium. We propose a complete rheological characterization of Carbopol 940. Creep measurements lead to obtain an instantaneous viscosity plateau μ+∼tm with m≈1. For the first time, we measure and provide permeability values k in the Carbopol gels. We show that k = O(10−14) m2 and k∝τy0.2. Our study focuses on the reference case of the RBC with no-slip conditions at walls, and new results are provided. The results lead to the conclusion that the control parameter is the (inverse) of the yield number Y, ratio between the yield stress and the buoyancy stress, and they show that the critical value is 1/Yc≈80 for no-slip conditions. One shows that both scenarios (i) and (ii) lead to recover 1/Y as the control parameter. By considering the Carbopol gels as porous media [scenario (iii)], one finds that the critical porous Rayleigh-Darcy number is Rap = O(10−4).

Structural analysis of a prestressed segmented girder using contact elements in ANSYS

Studying the structural behavior of prestressed segmented girders is quite important due to the large use this type of solution in viaducts and bridges. Thus, this work presents a nonlinear three-dimensional structural analysis of an externally prestressed segmented concrete girder through the Finite Element Method (FEM), using a customized ANSYS platform, version 14.5. Aiming the minimization of the computational effort by using the lowest number of finite elements, a new viscoelastoplastic material model has been implemented for the structural concrete with the UPF customization tool of ANSYS, adding new subroutines, written in FORTRAN programming language, to the main program. This model takes into consideration the cracking of concrete in its formulation, being based on fib Model Code 2010, which uses Ottosen rupture surface as the rupture criterion. By implementing this new material model, it was possible to use the three-dimensional 20-node quadratic element SOLID186 to model the concrete. Upon validation of the model, an externally prestressed segmented box concrete girder that was originally lab tested by Aparicio et al. (2002) has been computationally simulated. In the discretization of the structure, in addition to element SOLID186 for the concrete, unidimensional element LINK180 has been used to model the prestressing tendons, as well as contact elements CONTA174 and TARGE170 to simulate the dry joints along the segmented girder. Stresses in the concrete and in the prestressing tendons are assessed, as well as joint openings and load versus deflection diagrams. A comparison between numerical and experimental data is also presented, showing a good agreement.

The “avalanche effect” of an elasto-viscoplastic thixotropic material on an inclined plane

The so-called avalanche effect is one of the fingerprints of thixotropic materials. This self-reinforcing process where the decrease in viscosity, due to a rejuvenation process triggered by a stress field, induces a motion which in turn contributes to decrease the viscosity again, is well exemplified by the inclined plane problem. In this situation, the material in its fully-structured state is placed on an inclined plane with respect to the gravity force which is responsible for the beginning of the breakdown process. These thixotropic systems generally have a yield stress, a strength that must be overcome in order to induce rejuvenation. In addition, they exhibit elastic features, especially in the pre-yield state. In the present work we numerically solve the transient evolution of an elasto-viscoplastic thixotropic material subjected to the action of gravity on an inclined plane. In order to handle with the moving free-surface boundary condition encountered in the avalanche effect, we have used a combination of the Marker-And-Cell (MAC) method with the front-tracking scheme. This formulation was successfully employed for this kind of material in the recent paper of Oishi et al. (2016) [28]. In the present work, we have adapted our finite difference formulation to analyze the effects associated with an extended Herschel–Bulkley model in the simulation of a transient complex free surface flow. Concerning the parameters of the flow curve, it is shown that the dimensionless yield stress (plastic number) is the most significant one. However, for a fixed plastic number, different combinations of dimensionless consistency index and dimensionless Newtonian viscosity plateau can lead to a diversity of responses. The thixotropic equilibrium time had a significant impact on shifting the instant when the flow regime changes from an accelerating (when the front part of the material accelerates) to a retardation one (when this front part decelerates). Higher elasticity, as captured by the Weissenberg number, led to longer distances covered by the material.

The yielding and the linear-to-nonlinear viscoelastic transition of an elastoviscoplastic material

Elastoviscoplastic materials present a transition from a gel-like to a liquidlike state induced by shearing: While the first is primarily elastic, the second is predominantly viscous. The point that characterizes this transition is usually known as the yield point, which is associated to critical quantities such as yield stress and/or yield strain. Another characteristic of elastoviscoplastic materials is the transition from linear to nonlinear viscoelasticity. In the current work, a commercial hair gel, which is an elastoviscoplastic material, was tested in two rotational rheometers in order to evaluate these two transition points. Stress oscillatory amplitude sweeps at different frequencies were performed and a Fourier-Transform analysis was applied to the results in order to determine the linear viscoelastic limit. The linear viscoelastic limit stresses and strains at different frequencies were then compared to quantities that are usually associated to the yield point: The extrapolated zero-shear-rate stress obtained from the equilibrium flow curve, the minimum stress required to start up flows in creep experiments, the stress overshoot reached in constant shear rate experiments and the G′-and-G″ crossover stress determined through oscillatory amplitude sweeps. The results showed that the stresses and strains obtained as the linear viscoelastic limits were smaller than the critical quantities associated to the yield point for all evaluated cases. Although the critical quantities depend on the experimental condition, the linear viscoelastic limit strain was remarkably constant. Additionally, the linear viscoelastic limit strain was found to be in the same order of magnitude of the strain that characterizes the onset of plastic behavior in recovery experiments. This suggests that the beginning of the transition from a completely structured state of elastoviscoplastic materials to an unstructured state might be associated to the threshold of nonlinear viscoelasticity.

Effect of initial orientation on subgrain formation in nickel single crystals during equal channel angular pressing

This study deals with the development of the microstructure and grain refinement of nickel single crystals during the Equal Channel Angular Pressing (ECAP) process. In the experimental study, the electron backscattered diffraction data reveal that during the forming process the microstructure is modified and subgrains are developed. The microstructure is characterized by both low and high angle grain boundaries. Also, the (111) pole figures show that after the ECAP process the orientation is scattered, and the deformation process is heterogeneous. In the numerical work, a rate-dependent elasto-viscoplastic material model based on the theory of materials with isomorphic elastic ranges is applied. The identification of the material parameters has been performed by using the least square method with the Levenberg-Marquardt algorithm. A three-dimensional model of the ECAP process has been implemented in the finite element software Abaqus/Standard. The initial and final orientations after a single pass of the ECAP process are evaluated to study the subgrain formation under large deformations. The agreement between the simulated and experimental response in terms of stress-strain response and (111) pole figures are investigated. The analysis of the misorientation distribution reveals that the grain fragmentation has occurred with both high and low angle grain boundaries. The reconstruction of the microstructure after the deformation shows that the initial orientation has a significant influence on the microstructural evolution and grain refinement after a single pass ECAP extrusion.

Oblique impact on single, layered and spaced mild steel targets by 7.62 AP projectiles

The ballistic performance of monolithic and multi-layered in contact and spaced mild steel target plates has been studied at normal and oblique impact against 7.62 AP projectiles with an objective to ascertain the effect of angle of obliquity. Numerical simulations have been performed on ABAQUS/Explicit finite element code and typical results obtained have been validated by earlier experimental results, Gupta and Madhu [1,2]. The Johnson–Cook elasto-viscoplastic material model calibrated by the authors for mild steel was employed in the numerical simulations. Close correlation of typical experimental and numerical results validated the numerical procedure and the calibrated model.Ballistic limits of monolithic mild steel targets of thicknesses 4.7, 6, 10, 12 and 16mm each impacted at 0, 30 and 45ᵒ obliquity were numerically computed. The ballistic limits of in contact layered and spaced targets of equivalent thickness 10mm (3.33 + 3.33 + 3.33mm) were also computed at 0, 30 and 45° obliquity. For 60° angle of obliquity, the monolithic target experienced project ricochet, in contact layered target, projectile embedment, and the spaced target, projectile perforation. At low angles of obliquity, the difference between the ballistic performance of monolithic, layered in contact and spaced targets was not significant. As the angle of obliquity increased, each studied configuration was found to have distinct ballistic performance.Simulations were also done for three layered target of 4.7 and 6mm thick plate and spacing was varied to study its effect on their ballistic resistance. The variation of spacing at normal impact was found to have influence as long as the spacing was smaller than the projectile length.

Model-based control of dynamic frictional contact problems using the example of hot rolling

We consider hot forming processes, in which a metal solid body is deformed by several rolls in order to obtain a desired final shape. To minimize cutting scrap and to ensure that this shape satisfies the required tolerances as precisely as possible, we formulate an optimal control problem where we use the trajectories of the rolls as control functions. The deformation of the solid body is described through the basic equations of nonlinear continuum mechanics, which are here coupled with an elasto-viscoplastic material model based on a multiplicative split of the deformation gradient. We assume that the deformations of the rolls can be neglected, thus we add unilateral frictional contact boundary conditions, resulting in an evolutionary quasi-variational inclusion. The associated control-to-observation map is non-differentiable due to changes of state between elastic and plastic material behavior, contact and separation and stick and slip motion, yet we still want to apply gradient-based methods to solve the optimal control problem and therefore have to make sure that derivatives of cost functional and constraints exist. To resolve this issue, we first regularize all non-differentiabilities and subsequently apply the direct differentiation method to obtain sensitivity information. Finally, we formulate a suitable algorithm and discuss numerical results for a real-world example to illustrate its capability.

Ballistic resistance of 2024 aluminium plates against hemispherical, sphere and blunt nose projectiles

Numerical investigation has been carried out on 2024 aluminium plate targets against 12.7mm diameter hardened steel projectiles. The ballistic resistance of 1.27mm thick target was studied against a spherical ball as well as the hemispherical and blunt nosed cylindrical projectiles. The simulations were performed on ABAQUS/Explicit finite element code by modelling the target as deformable and the projectiles as rigid three dimensional surface. The Johnson-Cook (JC) elasto-viscoplastic material model was employed to predict the flow and fracture behaviour of the target. The objective of the study was to investigate the efficiency of the JC model to numerically reproduce the maximum target deflection and peak impact force caused by three distinct shaped projectiles during target perforation. Three different sets of JC parameters calibrated by different authors [20,21] for 2024 aluminium alloy were considered to simulate the performance of the target against each projectile and the results thus obtained were compared and validated through available experiments [24]. The failure mode, deflection and impact force obtained have been noticed to have significant influence of the material models. The ballistic limit of 1.27mm thick target was numerically computed against each of the three projectiles and validated through the Recht-Ipson model. The effective span and target thickness were also varied to investigate the influence on the maximum deflection and peak impact force.