Elasto-viscoplastic Material Research Articles

Modelling of Glulam beams pre-stressed by compressed wood

Finite element models were, in the first time, developed to simulate the pre-stressing behaviour of Glulam beams with insertion of compressed wood blocks, which were further used to simulate the structural behaviour of the pre-stressed beams subjected to subsequent destructive bending. Here, both the Glulam and compressed wood were modelled as orthotropic elasto-viscoplastic materials. The moisture-dependent, including spring back, swelling of the compressed wood block and the creep of the Glulam were considered in the modelling. The models developed were validated against the corresponding experimental results, with reasonably good correlation in terms of the free swelling, the precamber, initial stress state of the Glulam beams reinforced and load-deflection relationships. With validated models, further studies were then undertaken to investigate effects of the thickness, depth and spacing of compressed wood blocks on the precamber, initial bending stiffness and ultimate load carrying capacity of the beams pre-stressed. The results indicate that there are significant enhancements on the precamber (up to 1/288 of the deflection/span ratio), the initial bending stiffness (up to 23.8%) and the ultimate load carrying capacity (up to 10.4%).

A nonlinear dynamical system approach for the yielding behaviour of a viscoplastic material.

A nonlinear dynamical system model that approximates a microscopic Gibbs field model for the yielding of a viscoplastic material subjected to varying external stresses recently reported in R. Sainudiin, M. Moyers-Gonzalez and T. Burghelea, Soft Matter, 2015, 11(27), 5531-5545 is presented. The predictions of the model are in fair agreement with microscopic simulations and are in very good agreement with the micro-structural semi-empirical model reported in A. M. V. Putz and T. I. Burghelea, Rheol. Acta, 2009, 48, 673-689. With only two internal parameters, the nonlinear dynamical system model captures several key features of the solid-fluid transition observed in experiments: the effect of the interactions between microscopic constituents on the yield point, the abruptness of solid-fluid transition and the emergence of a hysteresis of the micro-structural states upon increasing/decreasing external forces. The scaling behaviour of the magnitude of the hysteresis with the degree of the steadiness of the flow is consistent with previous experimental observations. Finally, the practical usefulness of the approach is demonstrated by fitting a rheological data set measured with an elasto-viscoplastic material.

Нелинейная модель вязкоупругопластичности типа Максвелла: моделирование влияния температуры на кривые деформирования, релаксации и ползучести

Исследуются область применимости, арсенал возможностей и способы идентификации и настройки нелинейного определяющего соотношения типа Максвелла для вязкоупругопластичных материалов с двумя произвольными материальными функциями и двумя параметрами (в случае одноосного изотермического нагружения). Оно нацелено на описание комплекса основных реологических эффектов, типичных для реономных материалов, обладающих наследственностью, высокой скоростной чувствительностью и разносопротивляемостью, для которых характерны установившаяся ползучесть, стадия течения при постоянном напряжении и возрастание податливости, скоростей диссипации, релаксации, ползучести и рэтчетинга и скоростной чувствительности с увеличением температуры. К ним относятся, в частности, многие полимеры, их расплавы и растворы, композиты, твердые топлива, асфальтобетоны, титановые и алюминиевые сплавы, углеродные и керамические материалы при высоких температурах и др. Для учета влияния температуры на механическое поведение материалов (при изотермических процессах) два материальных параметра модели (коэффициент вязкости и «модуль упругости») рассматриваются как функции температуры. Найдены ограничения на свойства этих функций, необходимые и достаточные для адекватного описания качественных характеристик влияния температуры на экспериментальные кривые ползучести, релаксации, деформирования с постоянными скоростями, ползучести при ступенчатом нагружении, на касательный модуль и предел текучести, скоростную чувствительность и скорость накопления пластической деформации, типичных для стабильных вязкоупругопластичных материалов в изотермических квазистатических испытаниях. Они получены в результате аналитического изучения свойств кривых релаксации, ползучести и деформирования, порождаемых определяющим соотношением типа Максвелла с произвольными материальными функциями, и их сопоставления с типичными свойствами экспериментальных кривых реономных материалов. Доказано, что коэффициент вязкости, «модуль упругости» и их отношение (время релаксации ассоциированной линейной модели Максвелла) должны быть убывающими функциями температуры, и это обеспечивает адекватное качественное описание десятка наблюдаемых базовых термомеханических эффектов, свидетельствующих о возрастании податливости материалов (в частности, убывании касательного модуля и предела текучести), скоростей релаксации, ползучести и рэтчетинга и скоростной чувствительности с ростом температуры.

Ballistic Response of 2024 Aluminium Plates Against Blunt Nose Projectiles

Numerical investigations were carried out on 1.27, 3.18, 6.35, 12.7and 19.05 mm thick 2024-O aluminum target against blunt nose steel projectiles of 12.7 mm diameter and 37.7 gram mass. Three-dimensional numerical simulations of the problem are carried out using finite element code ABAQUS. The ABAQUS/Explicit finite element code in conjunction with Johnson-Cook elasto-viscoplastic material model proposed by Leuser[1] was employed to perform the simulations. The present studyis concerned with the measurement of ballistic limit of deformable projectiles. The results obtained were compared with the experimental results conducted by [3,4] and a close correlation between the two was found. The failure mode of the target was also found in good agreement. The results obtained showed a consistent increase in the ballistic resistance of target with an increase in the target thickness.

Influence of Target Span and Boundary Conditions on Ballistic Limit of Thin Aluminum Plate

A collective study was performed to probe the influence of projectile nose shape, target span and target boundary condition on ballistic limit of thin aluminium plates. 1 mm thick 1100-H12 aluminium target plates were normally impacted by ogive and blunt nosed projectiles of 19 mm diameter and 50.8 mm length. The target span was varied as 95, 190, 285, 380, 475, 570, 665 and 760 mm whereas the target boundary condition was studied by varying the fixity at the target circumference region as 100%, 75%, 50% and 25%. ABAQUS/Explicit finite element code using Johnson-Cook elasto-viscoplastic material model were employed to carry out the numerical simulation. To validity of numerical results are revealed by experiments performed on pressure gun in the sub-ordnance velocity regime.The numerical as well as experimental study revealed that the ballistic limit of thin target plate was significantly affected by target span as well as target circumference fixity. The ballistic limit increases with increase in target span diameter while opposite trend was observed with increase in the region of fixity.

ON ACCOUNT OF VISCOUS PROPERTIES OF MATERIALS IN THE THEORY OF LARGE ELASTOPLASTIC STRAINS

A geometrically and thermodynamically consistent mathematical model of large strains of materials with elastic, viscous and plastic properties is proposed. It is believed that at the stage of a strain, which precedes the plastic flow and during unloading, the viscous material properties provide the creep process and thus a slow growth of irreversible strains. While rapid growth of irreversible strains under plastic flow conditions, viscous properties act as a mechanism that retards the flow. The accumulation of irreversible strains, therefore, occurs successively: initially, in the creep process, then under plastic flow and, finally, again due to creep of the material (during unloading). On the elastoplastic boundaries advancing along the deformable material, there is a change in the growth mechanism of irreversible strains from creep to plasticity and vice versa. Such a change is possible only under conditions of continuity of irreversible strains and their change rates, which imposes the requirement of consistency in the definitions of irreversible stress distribution rates, i.e., the laws of creep and plasticity. Changing the production mechanisms of irreversible strains means various setting up of the source in the differential equation of the change (transfer) of these strains, hence irreversible strains are not divided into plastic strains and creep strains. To maximize the visibility of the model’s correlations, the hypothesis on the independence of thermodynamic potentials (internal energy, free energy) on irreversible strains is accepted. As a consequence of the hypothesis, an analog of the Murnaghan formula is obtained, the classical position of the elastoplasticity is that the stresses in the material are completely determined by the level and distribution of reversible strains. The main provisions of the proposed model are illustrated by the solution in its framework of the boundary value problem of the elastoviscoplastic material motion in a pipe due to a varying pressure drop.

Numerical Investigations on the Impact of Hemi Spherically Tipped Projectiles on Thin Plates

Numerical investigations were carried out on 1.27mm thick 2024-O aluminum plates against hemi spherically tipped nose, steel projectiles, of 12.7mm diameter and 37.7 gram mass. Three-dimensional numerical simulations of the problem were carried out using finite element code ABAQUS. The ABAQUS/Explicit finite element code, in conjunction with Johnson-Cook elasto-viscoplastic material model, proposed by Lesuer [1] was employed to perform the simulation. The present studies are concerned with the measurement of impact forces and permanent deflections produced by rigid projectiles during contact and perforation of the plates. The numerical results thus obtained were compared with the experimental results obtained by Levy and Goldsmith [2] and a close correlation between the two was found. The results obtained showed a consistent increase in the ballistic resistance of target with an increase in the incidence velocity. The failure mode of the target was also found to be affected by a change in the incidence velocity.

Numerical Investigations on Impact of Ogive Nosed Projectiles on Thin Plates

Objectives: Numerical investigations were carried out on 1mm thick aluminum plates against ogive-nosed steel projectiles of 15mm diameter and 55g mass. The finite element code ABAQUS was used to perform Three-dimensional and two-dimensional axisymmetric numerical simulations for the conducted experiment. Methods: The ABAQUS/Explicit finite element code in conjunction with a elasto-viscoplastic material model employed by Johnson-Cook model was used to perform the simulation study. The material model takes in various factors: yielding, linear thermo-elasticity, strain rate hardening, softening due to adiabatic heating, plastic flow, fracture effects and isotropic strain hardening. Both the rigid and deformable projectiles were considered to study their influence on the failure mechanism. Findings: The numerical results thus obtained, when compared with the available experimental results are found to be similar at high incidence velocities. However, at low incidence velocities the numerical results are found to be under predicted. Almost same ballistic resistance was offered by the target plate irrespective of the rigidity of projectile. The residual velocities of aluminum targets obtained using 2D and 3D deformable and rigid projectile curves became almost thesame. Improvements: Based on these studies, the influence of deformable projectile on thin targets was not significant but the energy absorption by the projectile on thick target is to be studied further.

Properties of a nonlinear viscoelastoplastic model of Maxwell type with two material functions

General qualitative properties of quasistatic curves for creep, relaxation, strain, and others are studied analytically. These curves are obtained on the basis of a one-dimensional constitutive relation of Maxwell type. Some constraints are proposed for the material functions to adequately describe the typical properties of experimental curves for a wide class of viscoelastoplastic materials. The applicability of the proposed model to describe, in particular, the superplastic deformation is analyzed. The effects that cannot be described in the framework of this model are found and its applicability range is revealed.

Transient motions of elasto-viscoplastic thixotropic materials subjected to an imposed stress field and to stress-based free-surface boundary conditions

In the present work, we present an approach to handle transient flows of elasto-viscoplastic thixotropic (EVPT) materials under the action of the gravity force field and subjected to free-surface boundary conditions that are stress-based. This kind of conditions are common in problems where the motion is unknown a priori, i.e. the motion is treated as a consequence while the forces are the cause. The model for the EVPT material employed is within the scope of a recently developed thermodynamic backbone for elasto-viscoplastic thixotropic materials. The finite difference Marker and Cell method is used to investigate effects of elasticity, thixotropy, and plasticity varying the Weissenberg number, the dimensionless thixotropic equilibrium time, and the yield number, respectively. The Cartesian Poiseuille flow is used to test the main features of the numerical scheme. The evolution in time of an initially square and fully-structured block is captured. The structure level and shape evolutions of the block reveal the capability of the present numerical approach to handle the complexity of the material and the free-surface motion.

Modeling and simulation framework for dynamic strain localization in elasto-viscoplastic metallic materials subject to large deformations

This paper describes a theoretical and computational framework for the treatment of adiabatic shear band formation in rate-sensitive polycrystalline metallic materials. From a computational perspective, accurate representation of strain localization behavior has been a long-standing challenge. In addition, the underlying physical mechanisms leading to the localization of plastic deformation are still not fully understood. The proposed framework is built around an enhanced-strain finite element formulation, designed to alleviate numerical pathologies known to arise in localization problems, by allowing a localization band of given finite width (weak discontinuity) to be embedded within individual elements. The mechanical threshold strength (MTS) model is used to represent the temperature and strain rate-dependent viscoplastic response of the material. This classical flow stress model employs an internal state variable to quantify the effect of dislocation structure evolution (work hardening and recovery). In light of growing evidence suggesting that the softening effect of dynamic recrystallization may play a significant role, alongside thermal softening, in the process of shear band formation and growth, a simple dynamic recrystallization model is proposed and cast within the context of the MTS model with the aid of the aforementioned internal state variable. An initiation criterion for shear localization in rate and temperature-sensitive materials is introduced and used in the present context of high-rate loading, where material rate-dependence is pronounced and substantial temperature increases are achieved due to the dissipative nature of viscoplastic processes. In addition, explicit time integration is adopted to facilitate treatment of the dynamic problems under consideration, where strain rates in excess of 104 s−1 are typically attained. Two series of experiments are conducted on AISI 316L stainless steel, employing the commonly used top-hat sample geometry and the Split-Hopkinson Pressure Bar dynamic test system. Axi-symmetric finite element simulation results are compared to cross-sectional micrographs of recovered samples and experimental load–displacement results, in order to examine the performance of the proposed framework and demonstrate its effectiveness in treating the initiation and growth of adiabatic shear banding in dynamically loaded metallic materials. These comparisons demonstrate that thermal softening alone is insufficient to induce shear localization behaviors observed in some materials, such as stainless steel, and support the hypothesis that dynamic recrystallization and/or other softening mechanisms play an essential role in this process.

Startup flow of elasto-viscoplastic thixotropic materials in pipes

Waxy crude oils transportation is one of the main challenges in offshore oil industry, specially after long shutdown periods when the flow has to be restarted. From the reservoir to the platform, the high-temperature crude oil undergoes a sudden temperature drop. As a consequence of cooling, the paraffin molecules precipitate forming a gel-like structure that can obstruct the tube completely. Under these conditions, the pressure required to startup the flow can be higher than usual operating pressure. Hence, the correct prediction of the minimum pressure required is of great importance. The aim of this work is to investigate the startup flow of yield stress materials being displaced by a Newtonian fluid in pipes. To this end, a flow-loop was developed and rheological tests were performed. Aqueous solutions of Carbopol® were used as a model fluid to mimic the waxy crude oil viscoplastic behavior. A polyester resin pipe with a threaded inner wall was used in order to avoid wall slip. The test section was validated with Hagen-Poiseuille law and with a Herschel-Bulkley analytical result. Applying different entrance pressures rates, the minimum pressure required to restart the flow was identified. An elasto-viscoplastic thixotropic behavior was observed through a delayed start up and the avalanche effect. Moreover, an increase in dimensionless entrance pressure rate results in a decrease in delay and clearance times. It is seen that the higher the viscosity of incoming fluid the lower the displacement velocity. A Herschel-Bulkley relationship between the dimensionless entrance pressure rate and the dimensionless shear stress required to start the flow is observed.

A phase field model for damage in elasto-viscoplastic materials

A phase field method for brittle fracture is formulated for a finite strain elasto-viscoplastic material using a novel obstacle phase field energy model. The obstacle energy model results in a crack profile with compact support, and thus gives a physically realistic description of the material behaviour at the vicinity of the crack tip. The resulting variational inequality is discretised by a finite element method, and is efficiently solved using a reduced space Newton method. The solution accuracy and numerical performance of this method is compared with a conventional phase field energy model for brittle fracture through representative examples, and a significant reduction in the numerical solution cost is demonstrated.

An assessment of the creep behaviour of Brazilian salt rocks using the multi-mechanism deformation model

Salt rocks are geomaterials that exhibit several peculiarities, which require a particular approach in rock mechanics. In the field, those rocks are usually found in layered/bedded deposits and in domes or similar structures. Creep is one of the main deformation mechanisms associated with salt rocks, and this phenomenon is highly dependent on the stress state, temperature and mineralogy. Salt rock mechanics for engineering applications requires the definition of a powerful constitutive model and this is an ongoing challenge. Among the many available models, one of the most sophisticated physical constitutive models for salt rocks is the multi-mechanism deformation creep model (MD model). The main contribution of this work is to present a first effort in the use of the MD model for Brazilian salt rocks. Material-sensitive parameters have been calibrated for the Brazilian halite through two methodologies. Salt is modelled as an elasto-viscoplastic material. Numerical simulations using the finite element method have been carried out for triaxial creep tests, Pre-salt wellbore closure and mining gallery convergence in order to validate the parameter set and the methodologies. Excellent results have been observed in most of the applications for validation. Even so, validation efforts should continue to consolidate the parameters and identify possible limitations.

CALCULATION OF PAVEMENT PERMANENT DEFORMATION USING PERZYNA’S ELASTO-VISCOPLASTIC MODEL

In this work, a method for calculation of pavement permanent deformation due to traffic loading is presented. The mechanics behavior of asphalt concrete layer is considered as Perzyna’s elasto-viscoplastic material. The pavement permanent deformation is incrementally calculated using nonlinear finite element method. Model parameters are determined using Hamburg Wheel Tracking Test result.

Experimental observations and modelling of cyclic and relaxation behaviour of the Ni-based superalloy Haynes 282

In this paper, the high temperature cyclic and relaxation behaviour of Ni-based superalloy Haynes 282 is investigated. Low-cycle fatigue (LCF) tests with and without hold time have been performed at two elevated temperatures, 650 and 730°C. The test results are presented and analysed with respect to the cyclic behaviour and the stress relaxation behaviour. Based on this analysis, a Chaboche type of elasto-viscoplastic material model is formulated and calibrated with respect to the cyclic experimental data. Furthermore, the effect of the scatter, observed in the initial yield stresses of the LCF tests, is considered in the calibration of the material model. Finally, a Golos–Ellyin strain energy density fatigue criterion is used to predict the fatigue life and how the scatter in the LCF tests influences the predicted fatigue lives is studied. Moreover, to account for the reduction in fatigue life due to stress relaxation, a frequency modification of the Golos–Ellyin fatigue criterion is proposed and evaluated.

On Modelling of Creep and Plasticity in a Problem of Viscosimetric Flow of a Material

This paper considers a deformation process of an incompressible elastoviscoplastic material placed between two coaxial rigid cylinders. The material is deformed when the internal cylinder rotates around its axis while the external one is fixed. The adhesion conditions are set on both boundary surfaces. The theory of large elastoviscoplastic deformations is used to solve the problem. The mathematical model is constructed in cylindrical coordinates.

A comparative numerical study of time-dependent structured fluids in complex flows

This study is concerned with the modelling of thixotropic and viscoelastoplastic material systems, contrasting two approaches in the development of such constitutive models. Accordingly, departure from Oldroyd-B-like behaviour is engineered through, first, a new micellar viscoelastic–thixotropic model (NM_τ p _ABS), under the Bautista–Manero framework, and second, a De Souza model. This NM_τ p _ABS model, is based on the energy dissipated by a micellar material to change its internal structure, whilst equivalently, the De Souza model employs the second invariant of stress. These models are compared and contrasted in their response through counterpart numerical solutions for axisymmetric contraction–expansion flow. Here, solution features of yielded–unyielded regions, total pressure drop, stress fields and vortex dynamics are analysed under scaling based on the second-Newtonian viscosity-plateau (η s ). With the NM_τ p _ABS model, yield-stress features are identified through solvent-fraction β-variation. In contrast, for the De Souza model, counterpart yield-stress features are exposed through yield-stress τ 0d -variation. With either yield-stress increase or rise in elasticity, NM_τ p _ABS solution response appears symmetrical about the contraction-plane axis, whilst De Souza patterns prove asymmetrical. Under solvent-fraction decrease, NM_τ p _ABS response provides yielded-region shrinkage, upstream and downstream vortex suppression, and non-zero N 1-region growth. Moreover, under elasticity rise, fading non-zero N 1-regions, size-invariant yield-fronts and non-zero N 1-regions are observed. In contrast under τ 0d increase or rise in elasticity, De Souza solutions manifest enhancement in vortex activity, and non-zero N 1-region-intensification and expansion. Furthermore, τ 0d -rise provokes De Souza yielded-region shrinkage, whilst elasticity does the opposite. On total pressure drop (Δp), for NM_τ p _ABS and with polymeric-fraction increase at fixed Wi, both monotonic rise at low-Wi and decline at higher-Wi are gathered. In contrast, only a monotonic rising trend is recorded with De Souza Δp-solutions for fixed Wi under τ 0d -rise. Furthermore, with Wi-rise and at any fixed τ 0eff-level, both models concur in a declining Δp-trend.

Кривые длительной прочности нелинейной модели вязкоупругопластичности типа Максвелла и правило суммирования поврежденности при ступенчатых нагружениях

Исследуется нелинейное определяющее соотношение типа Максвелла для вязкоупругопластичных материалов с двумя произвольными материальными функциями одного аргумента с целью выявления арсенала его возможностей и области применимости, в частности, возможности подключения к нему критериев для описания разрушения при ползучести с постоянным или кусочно-постоянным напряжением. При минимальных первичных ограничениях на материальные функции выведены уравнения теоретических кривых длительной прочности, порожденных соотношением типа Максвелла в сочетании с деформационными и энергетическим (диссипативным) критериями разрушения, а также с интегральными критериями, учитывающими историю деформирования. Аналитически изучены и сопоставлены общие свойства этих кривых. Показано, что они адекватно описывают типичные свойства экспериментальных кривых длительной прочности вязкоупругопластических материалов. Для найденных зависимостей времен разрушения от напряжения проверено выполнение правила линейного накопления поврежденности при ступенчатом нагружении и выведены формулы для величины (и знака) отклонений от него. В частности доказано, что для нелинейного соотношения типа Максвелла в сочетании с диссипативным критерием разрушения всегда в точности выполняется правило линейного накопления поврежденности при любом ступенчатом нагружении, а для деформационного критерия оно, наоборот, никогда не выполняется, но дает оценку сверху или снизу для времени разрушения в зависимости от знака скачка напряжения.

КРИВЫЕ ПОЛЗУЧЕСТИ И РЕЛАКСАЦИИ НЕЛИНЕЙНОГО ОПРЕДЕЛЯЮЩЕГО СООТНОШЕНИЯ Ю.Н. РАБОТНОВА ДЛЯ ВЯЗКОУПРУГОПЛАСТИЧНЫХ МАТЕРИАЛОВ

General qualitative properties of the theoretic creep curves and relaxation curves produced by the Rabotnov nonlinear hereditary constitutive relation with two arbitrary material functions are studied analytically in uni-axial case. Necessary restrictions that should be imposed on the material functions to provide an adequate description of typical test relaxation, creep and recovery curves of viscoelastoplastic materials are revealed and clearly formulated. The Rabotnov constitutive relation is proved to be able to simulate the basic rheological phenomena related to creep, relaxation and recovery which are typical to a wide class of viscoelastoplastic materials. In particular, it is capable to produce creep curves with flexure point and convex down arcs, it can simulate primary, secondary and tertiary creep, creep failure, tension compression asymmetry, complete and incomplete recovery, fading memory property and so on. A number of effects are pointed out that the model can't simulate whatever material functions are taken (e.g. strain dependence of relaxation curve shape and relaxation spectrum). The capabilities of the Rabotnov nonlinear constitutive relation and its applicability scope are elucidated and compared to capabilities of the Boltzmann - Volterra linear viscoelasticity equation which is the particular case the Rabotnov's relation. Keywords: viscoelastîplasticity, nonlinear constitutive equation, theoretic creep curves, creep rate, recovery, relaxation curves, tension compression asymmetry. &nbsp