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1
Content available remote Simulations of concrete response to impact loading using two regularized models
Wosatko Adam, Winnicki Andrzej, Pamin Jerzy
Computer Assisted Methods in Engineering and Science
|
2020
|
Vol. 27, no. 1
27--60
EN
This paper focuses on a comparison of two regularized continuum models for concrete in the simulations of selected benchmarks of response to impact loading. Their overview is performed in the context of application in dynamics. The first one is the Hoffman viscoplastic consistency model, where the strain rate activates regularization. The second model is derived from the scalar damage theory enhanced by an averaging equation incorporating the Laplacian of an averaged strain measure. Both models are implemented in the FEAP package. The results of some standard wave propagation tests are discussed, considering discretization sensitivity and predicted failure modes. Three examples are pre- sented: the direct tension of a plain and reinforced concrete bar, the split test of a cylinder, and the four-point bending of a reinforced concrete beam. The ability of both models to simulate impact loading is assessed.
2
Content available remote Modelling of superplastic deformation for metallic alloys using a cavity based approach
Marzbali M. H.
Journal of Achievements in Materials and Manufacturing Engineering
|
2017
|
Vol. 81, nr 2
61--96
EN
Purpose: In this study, modeling of superplastic deformation characteristic for metallic alloys was investigated using GTN failure criteria in viscoplastic framework. Design/methodology/approach: The proposed model studied the simultaneous effects of cavitation and deformation parameter and considered the effects of strain hardening, static and dynamic recoveries, and hydrostatic stress. This cavity based model was then implemented in a creep subroutine in ABAQUS 6.12 finite element software. Findings: Experimental results of Aluminum 5083 from different studies were used to verify the model and evaluate its reliability. Afterwards, numerical simulations for uniaxial tension were performed, and good agreement between experimental and modeling results was obtained. Research limitations/implications: This study showed that using a viscoplastic framework with a cavity criterion ensures more precise pressure-time algorithm, lower deformation time and better failure predictions. These capabilities provides forming more complex parts and different geometries. Accordingly, applying this model is recommended to predict the behaviour of other metallic superplastic alloys.
3
Content available Basic flows of generalized second grade fluids based on a Sisko model
Walicka A.
International Journal of Applied Mechanics and Engineering
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2017
|
Vol. 22, no. 4
1019--1033
EN
The present investigation is concerned with basic flows of generalized second grade fluids based on a Sisko fluid. After formulation of the general equations of motion three simple flows of viscoplastic fluids of a Sisko type or fluids similar to them are considered. These flows are: Poiseuille flow in a plane channel, Poiseuille flow in a circular pipe and rotating Couette flow between two coaxial cylinders. After presentation the Sisko model one was presented some models of fluids similar to this model. Next it was given the solutions of equations of motion for three flows mentioned above.
4
Content available Towards viscoplastic constitutive models for Cosserat rods
Dörlich V., Linn J., Scheffer T., Diebels S.
Archive of Mechanical Engineering
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2016
|
Vol. LXIII, nr 2
215--230
EN
Flexible, slender structures like cables, hoses or wires can be described by the geometrically exact Cosserat rod theory. Due to their complex multilayer structure, consisting of various materials, viscoplastic behavior has to be expected for cables under load. Classical experiments like uniaxial tension, torsion or three-point bending already show that the behavior of e.g. electric cables is viscoplastic. A suitable constitutive law for the observed load case is crucial for a realistic simulation of the deformation of a component. Consequently, this contribution aims at a viscoplastic constitutive law formulated in the terms of sectional quantities of Cosserat rods. Since the loading of cables in applications is in most cases not represented by these mostly uniaxial classical experiments, but rather multiaxial, new experiments for cables have to be designed. They have to illustrate viscoplastic effects, enable access to (viscoplastic) material parameters and account for coupling effects between different deformation modes. This work focuses on the design of such experiments.
PL
Giętkie, smukłe struktury, takie jak kable, rury lub druty, mogą być opisane przez geometrycznie ścisłą teorię prętów Cosserata. Biorąc pod uwagę, że omawiane obiekty mają skomplikowaną, wielowarstwową strukturę i składają się z wielu różnych materiałów, można oczekiwać, że pod obciążeniem będą wykazywać właściwości lepkoplastyczne. Klasyczne eksperymenty, takie jak rozciąganie jednoosiowe, skręcanie lub zginanie trójpunktowe, pokazały, że np. kable zachowują się jak ciała lepkoplastyczne. Odpowiednie, konstytutywne prawo opisujące obserwowany przypadek obciążenia jest niezwykle istotne dla realistycznej symulacji odkształcenia takiego obiektu. Tak więc, celem pracy było znalezienie lepkoplastycznego konstytutywnego prawa sformułowanego z uwzględnieniem właściwości poszczególnych sekcji pręta Cosserata. Ponieważ klasyczne eksperymenty, w których głównie stosuje się obciążenie jednoosiowe, nie reprezentują właściwie zachowania kabli w zastosowaniach praktycznych, należy zaprojektować nowe eksperymenty, z obciążeniem wieloosiowym. Powinny one zilustrować efekty lepkoplastyczne, umożliwić identyfikację (lepkoplastycznych) parametrów materiału i wyjaśnić efekty sprzężeń pomiędzy różnymi trybami odkształceń. W pracy skoncentrowano się na projektowaniu takich eksperymentów.
5
Content available remote Multiscale Constitutive Modelling of the Influence of Anisotropy E?ects on Fracture Phenomena in Inelastic Solids
Perzyna P. P.
Engineering Transactions
|
2012
|
Vol. 60, iss. 3
225-225
EN
The main objective of the present paper is the consistent development of the thermodynamical theory of elasto-viscoplasticity within the framework of a unique constitutive materialstructure. The focus of attention on the description of the influence of anisotropy effects on fracture phenomena is proposed. In the first part a general principle of determinism is formulated and a unique constitutive material structure is developed. The original conception of the intrinsic state of a particle X during motion of a body B has been assumed. A notion of the method of preparation of the deformation-temperature con?guration of a particle X has been proposed as a simple way of the gathering information for the description of the internal dissipation. As the basis of the thermodynamical requirements the dissipation principle in the form of the Clausius-Duhem inequality is assumed. By particular assumption of the method of preparation space for a unique constitutive material structure the internal state variable material structure has been constructed. In the second part the thermodynamical theory of elasto-viscoplasticity within the framework of the internal state variable material structure is formulated. Introduction of a finite set of the internal state variables is based on multiscale considerations in analysis of the physical foundations of inelastic solids and experimental observation results. Particular attention is focused on the determination of the evolution laws for the introduced internal state variables. Fracture criterion based on the evolution of the anisotropic intrinsic microdamage is proposed.
6
Content available Lepkoplastyczne związki konstytutywne dla specjalnych struktur granulowanych
Zalewski R.
Acta Mechanica et Automatica
|
2009
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Vol. 3, no. 2
118-121
PL
W pracy podjęto próbę opisu nieliniowych zachowań specjalnych struktur granulowanych za pomocą lepkoplastycznych związków konstytutywnych zbudowanych dla metali. Specjalne struktury granulowane budowane są na bazie luźnego granulatu umieszczonego w szczelnej przestrzeni, w której w następnym etapie wytwarza się podciśnienie. Wartość zadanego podciśnienia wewnętrznego determinuje globalne właściwości fizyczne tak utworzonego konglomeratu. W procesie modelowania zastosowano prawo Chaboche’a oraz Bodnera-Partoma. Dokonano weryfikacji zidentyfikowanych modeli konstytutywnych z bezpośrednimi wynikami eksperymentalnymi.
EN
Presented work is the next stage of considerations related to innovative semi-intelligent structures composed on the basis of granular materials. Loose granular material is initially placed in a hermetic plastomers envelope, where in the next step so called “underpressure” is generated.
7
Content available remote Methods of Material Parameters Identification for Isotropic Damage in Viscoplastic Flow Conditions
Kłosowski P., Pyrzowski Ł., Woźnica K.
Machine Dynamics Problems
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2008
|
Vol. 32, No. 3
44-50
EN
The paper presents three methods of damage parameters identification in viscous flow conditions. Constitutive relations including damage are used according to the Chaboche and Lemaitre concept. The authors propose also their own modifications of identification algorithm. All algorithms are compared in the identification process for aluminum alloys.
8
Content available remote A Dynamic Piezoelectric Contact Problem
Barboteu M., Sofonea M.
Machine Dynamics Problems
|
2008
|
Vol. 32, No. 1
23-32
EN
We consider a mathematical model, which describes the dynamic process of contact between a piezoelectric body and an electrically conductive foundation. The material's behavior is modeled with a nonlinear electro-viscoelastic constitutive law; the contact is frictionless and is described with the normal compliance condition and a regularized electrical conductivity condition. We state the variational formulation for the problem, and then we introduce a fully discrete scheme, based on the finite element method to approximate the spatial variable and the backward Euler scheme to discretize the time derivatives. We implement this scheme in a numerical code and, in order to verify its accuracy, we present numerical simulations in the study of a two-dimensional test problem.
9
Izotropic damage in viscoplastic flow conditions
Pyrzowski Ł.
Zeszyty Naukowe. Budownictwo / Politechnika Śląska
|
2007
|
z. 112
275-282
EN
The damage mechanics is a very important branches of solid mechanics. Although it is still developing, it has already been applied to many engineering problems. This paper includes information about the viscoplastic type of constitutive modeling, the presentation of mechanical representation of damage by variable D, effective stress concept, equations of the chosen damage model and the Chaboche viscoplastic constitutive model including damage effects. Also the identification procedure of damage parameters with practical example and MES applications in the commercial program MSC.Marc is presented.
PL
Mechanika zniszczenia jest obecnie jedną z ważniejszych gałęzi mechaniki ciał stałych. Jest to cały czas rozwijająca się dziedzina nauki, która znalazła swoje zastosowania w problemach inżynierskich. W artykule zaprezentowano podstawowe informacje na temat lepkoplastyczności i jej zastosowania, koncepcję mechanicznej reprezentacji zniszczenia przez zmiermą D, koncepcję naprężeń efektywnych, równania opisujące zniszczenie oraz lepkoplastyczny model Chaboche'a z uwzględnieniem zniszczenia. Ponadto, w artykule przedstawiono procedurę identyfikacji parametrów zniszczenia dla przyjętej koncepcji wraz z przykładem praktycznym oraz przykład prezentujący wykorzystanie przedstawionych praw w MES w programie MSC.Marc.
10
Konsystentny, sprężysto-lepkoplastyczny model opisujący odpowiedź gruntu na złożone ścieżki obciążenia
Łupieżowiec M.
Prace Naukowe Instytutu Geotechniki i Hydrotechniki Politechniki Wrocławskiej. Konferencje
|
2007
|
Vol. 76, nr 42
431-439
PL
W pracy przedstawiono model sprężysto-lepkoplastyczny, który jest w stanie realistycznie symulować odpowiedź gruntu zarówno na złożone ścieżki obciążenia, jak i na prędkość, przy jakiej są one realizowane. Omawiany model jest rozwinięciem teorii stanu krytycznego. Rozbudowane zostało równanie powierzchni ograniczającej, prawo wzmocnienia oraz opis zachowania w stanie prekonsolidacji. Szczególnie istotna jest ostatnia z modyfikacji, która umożliwia opis silnej zmienności sztywności materiału w zakresie małych odkształceń. Po przedstawieniu równań modelu, w dalszej części podane zostały wyniki testów numerycznych trójosiowego ściskania z uniemożliwionym drenażem oraz analizy rozszerzania się cylindrycznej pustki w masywie gruntowym. Uzyskane rezultaty wykazały bardzo dobrą zgodność z doświadczeniami.
EN
In paper the elasto-viscoplastic model was proposed. It is capable to realistically simulate the answer to both complex load paths and velocity, which are realised. Discussed model is a generalisation of critical state theory. It developed the bounding surface equation, the hardening rule and the description of the behaviour in over Consolidated state. Particularly essential is the last modification, which enables the description of a strong variable of a materiał stiffness in a smali strain rangę. After presented model equations, then it has given results of numerical tests of the triaxial compression without drainage and analysis of spreading the cylindrical emptiness in soil medium. Obtained results show a very good conformity with experimcnts.
11
Content available remote On micro-damage in hot metal working. P. 2 Constitutive modelling
Lin J., Foster A. D., Liu Y., Farrugia D. C., Dean T. A.
Engineering Transactions
|
2007
|
Vol. 55, iss. 1
43-60
EN
Damage constitutive equations are formulated to model the evolution of grain boundary and plasticity-induced damage for free-cutting steels under hot forming conditions. During high temperature, high strain rate deformation, material degradation has characteristics of both creep damage at grain boundaries, and ductile damage surrounding hard inclusions. This has been experimentally observed and is reported in the companion paper. This paper describes the development of unified viscoplastic-damage constitutive equations, in which the nucleation and growth of both damage types are considered independently. The effects of deformation rate, temperature, and material microstructure on damage evolution are modelled. The proposed damage evolution equations are combined with a viscoplastic constitutive equation set, enabling the evolution of dislocation hardening, recovery, recrystallisation, grain size, and damage to be modelled. This set of unified, mechanism-based, viscoplastic damage constitutive equations is determined from experimental data of a freemachining steel for the temperature range 1173- 1373 K. The fitted model is then used to predict damage and failure features of the same material tested using a set of interrupted constant strain rate tests. Close agreement between the predicted and experimental results is obtained for all the cases studied.
12
Content available remote Description of viscoplastic flow accounting for shear banding
Nowak Z., Perzyna P., Pęcherski R. B.
Archives of Metallurgy and Materials
|
2007
|
Vol. 52, iss. 2
217-222
EN
The subject of the study is concerned with ultra fine grained (ufg) and nanocrystalline metals (nc-metals). Experimental investigations of the behaviour of such materials under quasistatic as well as dynamic loading conditions related with microscopic observations show that in many cases the dominant mechanism of plastic strain is multiscale development of shear deformation modes – called shear banding. The comprehensive discussion of these phenomena in ufg and nc-metals is given in [1], [2] and [3], where it has been shown that the deformation mode of nanocrystalline materials changes as the grain size decreases into the ultrafine region. For smaller grain sizes (d < 300 nm) shear band development occurs immediately after the onset of plastic flow. Significant strain-rate dependence of the flow stress, particularly at high strain rates was also emphasized. Our objective is to propose a new description of viscoplastic deformation, which accounts for the observed shear banding. Viscoplasticity model proposed earlier by P e r z y n a [4], [5] was extended in order to describe the shear banding contribution. The shear banding contribution function, which was introduced formerly by P e c h e r s k i [6], [7] and applied in continuum plasticity accounting for shear banding in [8] and [9] as well as in [10] and [11] plays pivotal role in the viscoplasticity model. The derived constitutive equations were identified and verified with application of experimental data provided in paper [2], where quasistatic and dynamic compression tests of ufg and nanocrystalline iron specimens of a wide range of mean grain size were reported. The possibilities of the application of the proposed description for other ufg and nc-metals are discussed.
PL
Przedmiotem studiów są drobnoziarniste oraz nanokrystaliczne metale. Badania doświadczalne zachowania się takich materiałów w warunkach obciążeń quasistatycznych oraz dynamicznych, w powiązaniu z obserwacjami mikroskopowymi, wykazują, że w wielu wypadkach dominującym mechanizmem odkształcenia plastycznego jest wieloskalowy rozwój form ścinania – zwany zwojem pasmami ścinania. Wyczerpująca dyskusja tych zjawisk zawarta jest w [1], [2] i [3], gdzie wykazano, że forma odkształcenia w materiałach drobnoziarnistych zmienia się, kiedy rozpatrujemy materiały o coraz mniejszym ziarnie. Dla materiałów o średniej wielkości ziarna mniejszej niż 300 nm obserwuje się rozwój pasm ścinania zaraz po inicjacji odkształcenia plastycznego. Podkreślono także znaczący wpływ prędkości odkształcenia na naprężenie płynięcia. Naszym celem jest propozycja nowego opisu odkształcenia lepkoplastycznego, w którym uwzględnia się udział obserwowanego rozwoju pasm ścinania. Model lepkoplastyczności proponowany wcześniej przez P e r z y n e [4], [5] został rozszerzony z wykorzystaniem opisu udziału pasm ścinania. Podstawową rolę w proponowanym modelu lepkoplastyczności odgrywa funkcja udziału pasm ścinania wprowadzona przez P e c h e r s k i e g o [6], [7] i zastosowana w kontynualnej teorii plastyczności z udziałem pasm ścinania w [8] i [9] oraz w [10] i [11]. Dokonano identyfikacji oraz weryfikacji wyprowadzonych równań konstytutywnych z zastosowaniem danych doświadczalnych otrzymanych w testach quasistatycznego i dynamicznego ściskania dla serii próbek wykonanych z drobnoziarnistego i nanokrystalicznego żelaza o szerokim zakresie średniej wielkości ziarna [2]. Przedyskutowano możliwości zastosowania proponowanego opisu do innych metali o budowie drobnoziarnistej i nanokrystalicznej.
13
Physical and numerical aspects of dispersion phenomenon in solids under impact loading
Glema A.
Foundations of Civil and Environmental Engineering
|
2006
|
No. 7
127-146
EN
Dispersion as the material property is discussed in the paper. The definition, origination and dispersion analysis are presented. The dispersive and non-dispersive constitutive models are studied. The mechanical problem of inelastic deformation of solids is considered. The evolution of viscoplastic flow describes material hardening and softening with formation of strain localization zone. Wave character and dispersion are recognized as fundamental elements in formulation and solution in dynamic, rate dependent processes with strain localization and shear band propagation. The physical and numerical aspects of dispersion clarify the development of deformation, stress or energy distribution and verify the solution procedure. The paper exposes the importance of dispersion phenomenon that should be carefully investigated in class of solid mechanics problems. The numerical results confirm the role of dispersion effects.
14
Content available remote On micro-damage in hot metal working. Part 1: Experimental investigation
Liu Y., Foster A. D., Lin J., Farrugia D. C. J., Dean T. A.
Engineering Transactions
|
2006
|
Vol. 54, iss. 4
271-287
EN
An experimental programme was defined and performed to investigate the characteristics of micro-damage for a plain CMn and a free machining steel under hot forming conditions. To investigate damage locations - at grain boundaries and around second phase inclusions - a series of constant strain rate tests were carried out on the free machining steel, which contained manganese sulphide inclusions. Specimens from both materials were strained to failure under tension using a Gleeble material simulator at a constant temperature of 1273 K, with strain rates = 0.01-10 s-1. The damage characteristics of the two different steel microstructures was analysed through microstructural examinations of the tested specimens. Particular attention is focussed on damage locations and features. To investigate the recovery of materials between the intervals of hot deformation, a series of two-step tensile tests were carried out at 1273 K and 10 s-1. The two-step specimens were initially deformed to a strain varying from 0.3-0.7, held for varying recovery periods of 0.3-10 s, then stretched to failure. Flow stress features and strains to failure during the second stage of deformation were analysed with respect to different recovery periods and strain levels at the first stage of deformation. The damage features discovered from the experimentation and microstructural examination provide theoretical evidence to form unified viscoplastic damage constitutive equations for hot forming of free machining steels, which are described in the companion paper.
15
Content available remote Investigation of macrocrack propagation along a bimaterial interface in adiabatic dynamic processes as a problem of mesomechanics
Dornowski W., Perzyna P.
Engineering Transactions
|
2006
|
Vol. 54, iss. 4
289-321
EN
The main objective of the present paper is the investigation of macrocrack propagation along a bimaterial interface in adiabatic dynamic processes. The investigation has been generated by very recent experimental observation (cf. Rosakis, Samudrala and Coker [34], Guduru, Rosakis and Ravichandran [13], Guduru, Zehnder, Rosakis and Ravichandran [14]). A general constitutive model of elastic-viscoplastic damaged polycrystalline solids has been developed within the thermodynamic framework of the rate-type covariance material structure with a finite set of internal state variables. This set of internal state variables will be assumed and interpreted so that the theory developed has been taken into account the effects as follows: (i) plastic non-normality; (ii) softening generated by microdamage mechanisms; (iii) thermomechanical coupling (thermal plastic softening and thermal expansion); (iv) strain-rate sensitivity. It is noteworthy to stress that viscosity introduces implicitly a length-scale parameter into the dynamical initial boundary value problem. In order to describe in a constitutive model all the previously mentioned properties and incorporate their respective effects, it is intended to introduce a particular set of internal state variables, which consists of the equivalent inelastic deformation and volume fraction porosity. The equivalent inelastic deformation can describe the dissipation effects generated by viscoplastic flow phenomena and the volume fraction porosity takes into account the microdamage evolution effects. The kinetics of microdamage plays a very important role in this constitutive model. Fracture criterion based on the evolution of microdamage is assumed. The relaxation time is viewed either as a microstructural parameter to be determined from experimental observations, or as a mathematical regularization parameter. By assuming that the relaxation time tends to zero, the rate-independent elastic-plastic response can be obtained. The identification procedure is developed basing on the experimental observations. We consider isothermal and adiabatic processes in the thin flat specimen made of two identical elements (material A) and the cohesive band (material B). The width of the cohesive band is 1 žm, so it is a mesoscale size range. In this cohesive band the initial notch is localized symmetrically. It is assumed that the boundary conditions are modelled by the speed of the upper edge of the specimen, while the lower edge is clamped. The initial conditions of the problem are homogeneous. Both materials of the specimen are modelled as elastic-viscoplastic. A two-dimensional, plane stress, finite-difference model of the entire specimen is applied. The numerical algorithm satisfies the material objectivity, i.e. is invariant with respect to any diffeomorphism (any motion). Particular attention is focused on the investigation of interaction of stress waves on the propagation of macrocrack within the interface band. The macrocrack-tip speed history and the evolution of the transient macrocrack-tip temperature fields are obtained.
16
Content available remote Adaptive analysis of inelastic problems with Bodner-Partom constitutive model
Cecot W.
Computer Assisted Mechanics and Engineering Sciences
|
2006
|
Vol. 13, No. 4
513-521
EN
The Bodner-Partom elastic-visco-plastic constitutive eąuations [4] were used for numerical analysis of inelastic problems. This rate-dependent model makes it possible to describe elastic, plastic and viscous processes in metals, including temperaturę and continuum damage effects. The adaptive finite element method [9] was applied to approximate solution of the governing eąuations with two a posteriori error es-timates that control accuracy of time and space discretization of displacements and internal variables. The paper addresses a further development of the methodology proposed by the author in previous works [7, 8] and used in [6]. We present here certain additional theoretical background and propose a novel strategy of adaptation as well as verify the method of solution transfer.
17
Content available remote The thermodynamical theory of elasto-viscoplasticity
Perzyna P.
Engineering Transactions
|
2005
|
Vol. 53, iss. 3
235-316
EN
The main objective of this paper is to survey some recent developments in the constitutive modelling of inelastic polycrystalline solids, which may be used for the description of important problems in modern manufacturing processes, and particularly for mesomechanical issues. This description is needed for the investigation by using the numerical methods how to avoid unexpected plastic strain localization and fracture phenomena in manufacturing technology. Since modern manufacturing processes lead to very complex states of stress and deformation for a solid body under consideration, then in the description we have to take into account the influence of stress triaxiality and plastic spin effects. In this paper emphasis is laid on experimental and physical foundations as well as on mathematical constitutive modelling for the description of localization of plastic deformation and various modes of fracture phenomena in polycrystalline solids. The description of kinematics of finite deformations and the stress tensors is given. The development of a thermo-elasto-viscoplastic model within the thermo-dynamic framework of the rate-type covariance constitutive structure with finite set of the internal state variables is presented. Particular attention is focused on the determination of the evolution laws for the internal state variables. Fracture criterion based on the evolution of microdamage is formulated. By assuming that the mechanical relaxation time is equal to zero, the thermo-elasto-plastic (rate-independent) response of the damaged material can be accomplished.
18
Lepkoplastyczność w gruntach - wrażliwość na prędkość odkształcenia
Łupieżowiec M.
Zeszyty Naukowe. Budownictwo / Politechnika Śląska
|
2002
|
z. 95
359-368
PL
W pracy przedstawiono opis modelu gruntu, który jest w stanie opisać wrażliwość materiału na prędkość jego odkształcania. Opis ten jest uogólnieniem bardzo często stosowanego w mechanice gruntów modelu Modified Cam Clay. Podano również wynik przeprowadzonego eksperymentu oraz jego symulację numeryczną.
EN
In the paper there is given description of soil model, which can describe material sensitivity to its strain rate. This description is the generalisation Modified Cam Clay Model that is often used in soil mechanic. There are also presented result of laboratory test and numerical simulation.
19
Localization and localized fracture phenomena in inealastic solids under cyclic dynamic loadings
Dornowski W., Perzyna P.
Foundations of Civil and Environmental Engineering
|
2002
|
No. 1
41-86
EN
The main objective of the paper is the investigation of localization and localized fatigue fracture phenomena in thermo-viscoplastic flow processes under cyclic dynamic loadings. Recent experimental observations for cycle fatigue damage mechanics at high temperature and dynamic loadings of metals suggest that the intrinsic microdamage process does very much dependent on the strain rate and the wave shape effects and is mostly developed in the regions where the plastic deformation is localized. The description of kinematics of finite deformations and the stress tensors is presented. The rates of the deformation tensor and the stress tensor are defined based on the Lie derivative. A general constitutive model of elasto-viscoplastic damaged polycrystalline solids is developed within the thermodynamic framework of the rate type covari-ance structure with finite set of the internal state variables. A set of the internal state variables is assumed and interpreted such that the theory developed takes account of the effects as follows: (i) plastic non-normality; (ii) plastic strain induced anisotropy (kinematic hardening); (iii) softening generated by microdamage mechanisms (nucleation, growth and coalescence of microcracks); (iv) thermomechanical coupling (thermal plastic softening and thermal expansion); (v) rate sensitivity; (vi) plastic spin. To describe suitably the time and temperature dependent effects observed experimentally and the accumulation of the plastic deformation and damage during dynamic cyclic loading process the kinetics of microdamage and the kinematic hardening law have been modified. The relaxation time is used as a regularization parameter. Fracture criterion based on the evolution of microdamage is formulated. Utilizing the finite difference method for regularized elasto-viscoplastic model, the numerical investigation of the three-dimensional dynamic adiabatic deformation in a particular body under cyclic loading condition is presented. Particular examples have been considered: (i) Dynamic, adiabatic and isothermal, cyclic loading processes for a thin steel plate with small rectangular hole located in the centre are considered. The accumulation of damage and equivalent plastic deformation on each considered cycle has been obtained. It has been found that this accumulation distinctly depends on the shape of the assumed loading cycle. (ii) A dynamic adiabatic cyclic loading process for a thin steel plate with sharp notch is investigated. The propagation of the macroscopic fatigue damage crack within the material of the plate is investigated. It has been found that the length of the macroscopic fatigue damage crack distinctly depends on the wave shape of the assumed loading cycle. The results obtained are in accord with the experimental observations performed by Sidey and Coffin [65].
20
Content available remote Visco-plasticity of polycrystalline tantalum - rational phenomenology in constitutive modeling
Klepaczko J. R.
Archives of Mechanics
|
2002
|
Vol. 54, nr 5-6
459-478
EN
Constitutive modeling based on the so-called rational phenomenology (materials science approach) has been applied to take into account strain hardening, strain-rate sensitivity, thermal effects and evolution of microstructure in a polycrystalline tantalum. A wide range of strain rate in shear ... and homologous temperature (0.05 < ... < 0.2) is considered. Behavior of tantalum is understood as an example for BCC polycrystalline metals. The constitutive modeling provided a possibility to determine all material constants via the experimental results obtained on thin tubular specimens using a fast hydraulic machine and a torsion Hopkinson bar. Finally, the model predictions are demonstrated by numerical simulations for different history paths in strain rate and temperature.
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