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1
Content available remote The Identfication Procedure for The Constitutive Model of Elasto-Viscoplasticity Describing the Behaviour of Nanocrystalline Titanium
Nowak Z., Perzyna P.
Engineering Transactions
|
2014
|
Vol. 62, iss. 3
221--240
EN
The main objective of the present paper is the description of the behaviour of the ultrafinegrained (UFG) titanium by the constitutive model of elasto-viscoplasticity with the development of the identification procedure. We intend to utilize the constitutive model of the thermodynamical theory of elasto-viscoplasticity for description of nanocrystalline metals presented by Perzyna [21]. The identification procedure is based on experimental observation data obtained by Jia et al. [11] for ultrafine-grained titanium and by Wang et al. [25] for nanostructured titanium. Hexagonal close-packed (hcp) ultrafine-grained titanium processed by sever plastic deformation (SPD) has gained wide interest due to its excellent mechanical properties and potential applications as biomedical implants.
2
Content available remote On consequences of the principle of stationary action for dissipative bodies
Kosiński W., Perzyna P.
Archives of Mechanics
|
2012
|
Vol. 64, nr 1
95-106
EN
The aim of this note is to show possible consequences of the principle of stationary action formulated for dissipative bodies. The material structure with internal state variables is considered for those bodies. The appropriate action functional is proposed for a typical dissipative body. Possible variations of fields of dependent state variables are introduced together with a non-commutative rule between operations of taking variations of the field and their partial time derivatives. Assuming vanishing of the first variation of the functional, the balance of linear momentum in differential form is received together with evolution equations for internal state variables and stress boundary condition.
3
Content available remote Micromechanics of localized fracture phenomena in inelastic solids generated by impact-loaded adiabatic processes
Perzyna P.
Engineering Transactions
|
2011
|
Vol. 59, iss. 4
299-348
EN
The main objective of the present paper is to discuss very efficient procedure of the numerical investigation of localized fracture in inelastic solids generated by impact-loaded adiabatic processes. Particular attention is focused on the proper description of a ductile mode of fracture propagating along the shear band for high impact velocities. This procedure of investigation is based on utilization the finite difference method for regularized thermo-elasto-viscoplastic constitutive model of damaged material. A general constitutive model of thermo-elasto-viscoplastic damaged polycrystalline solids with a finite set of internal state variables is used. The set of internal state variables consists of two scalars, namely 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 relaxation time is used as a regularization parameter. Fracture criterion based on the evolution of microdamage is assumed. As a numerical example we consider dynamic shear band propagation and localized fracture in an asymmetrically impact-loaded prenotched thin plate. The impact loading is simulated by a velocity boundary condition which are the results of dynamic contact problem. The separation of the projectile from the specimen, resulting from wave reflections within the projectile and the specimen, occurs in the phenomenon. A thin shear band region of finite width which undergoes significant deformation and temperature rise has been determined. Its evolution until occurrence of final fracture has been simulated. Shear band advance, microdamage and the development of the temperature field as a function of time have been determined. Qualitative comparison of numerical results with experimental observation data has been presented. The numerical results obtained have proven the usefulness of the thermo-elasto-viscoplastic theory in the investigation of dynamic shear band propagations and localized fracture.
4
Content available Effect of strain rate on ductile fracture. A new methodology
Nowacki W. K., Nowak Z., Perzyna P., Pęcherski R. B.
Journal of Theoretical and Applied Mechanics
|
2010
|
Vol. 48 nr 4
1003-1026
EN
The aim of our study is to discuss a new methodology to account for the effect of strain rate on ductile fracture phenomena. Theory of inelastic materials accounting for the effects of microshear bands and microdamage is presented. The influence of microshear bands is explained by means of a function describing the instantaneous contribution of shear banding in the total rate of plastic deformation. The experimental investigations of the effect of strain rate on ductile fracture with use of the results of a dynamic double shear test of DH-36 steel with thermographic observations are reported. The registration of temperature evolution during the deformation process can provide additional data for the identification of the shear banding contribution function and the onset of ductile fracture.
PL
W pracy przedstawiono nowy sposób analizy zjawiska zniszczenia ciągliwego metali z uwzględnieniem wpływu prędkości odkształcenia. Przedstawiono teorię materiałów niesprężystych z uwzględnieniem efektu pasm ścinania i mikrouszkodzeń. W opisie zjawiska płynięcia plastycznego uwzględniono wpływ mikropasm ścinania przez wprowadzenie funkcji opisującej chwilowy udział mikropasm ścinania w całkowitej prędkości deformacji plastycznej. Przedstawiono wyniki badań doświadczalnych określających wpływ prędkości odkształcenia na zniszczenie i sposób wykorzystania obserwacji termograficznych w dynamicznej próbie podwójnego ścinania dla stali DH-36. Pomiary zmian temperatury podczas procesu deformacji dostarczają dodatkowych danych ułatwiających zidentyfikowanie funkcji udziału mikropasm ścinania dla danego materiału.
5
Content available remote The thermodynamical theory of elasto-viscoplasticity for description of nanocrystalline metals
Perzyna P.
Engineering Transactions
|
2010
|
Vol. 58, iss. 1/2
15-74
EN
The main object of the present paper is the development of thermodynamical elasto-viscoplaslic constitutive model describing the behaviour of nanocrystalline metals. Only fcc, bcc and hcp metals will be covered in this description, because they are the classes of metals for which systematic experimental observation data sets are available. Investigation of the deformation mechanisms is important for understanding, controlling and optimizing of the mechanical properties of nanocrystalline metals. Strengthening with grain size refinement in metals and alloys, with an average grain size of 100 nm or larger, has been well characterized by the Hall-Petch (H-P) relationship, where dislocation pile-up against grain boundaries, along with other transgranular dislocations mechanisms, are the dominant strength-cont rolling processes. When the average, and entire range of grain sizes is reduced to less than 100 nm. the dislocation operation becomes increasingly more difficult and grain boundary-mediated processes become increasingly more important. The principal short-range barrier, the Peierls-Nabarro stress. Is important for ultrafine crystalline bcc metals, whereas in ultrafine crystalline fcc and hcp metals, forest dislocations are the primary short-range barriers at lower temperatures. Experimental observations have shown that nanosized grains rotate during plastic deformation and can coalesce along directions of shear, creating larger paths for dislocation movement. The model is developed within the thermodynamic framework of the rate-type covariance constitutive structure with a finite set of the internal state variables. 1 he thermodynamic restrictions have been satisfied and the rate-type constitutive equations have been determined. Fracture criterion based on the evolution of the anisotropic intrinsic microdamage is formulated. The fundamental features of the proposed constitutive theory have been carefully discussed.
6
Content available The thermodynamical theory of elasto-viscoplasticity accounting for microshear banding and induced anisotropy effects
Perzyna P.
Mechanics / AGH University of Science and Technology
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2008
|
Vol. 27, no. 1
25-42
EN
The main objective of the present paper is the development of thermo-elasto-viscoplastic constitutive model of a material which takes into consideration induced anisotropy effects as well as observed contribution to strain rate effects generated by microshear banding. Physical foundations and experimental motivations for both induced anisotropy and microshear banding effects have been presented. The model is developed within the thermodynamic framework of the rate type covariance constitutive structure with a finite set of the internal state variables. A set of internal state variables consists of one scalar and two tensors, namely the equivalent inelastic deformation e/p the second order microdamage tensor [symbol] with the physical interpretation that ([formula]) defines the volume fraction porosity and the residual stress tensor (the backstress) alpha. The equivalent inelastic deformation [symbol] describes the dissipation effects generated by viscoplastic flow phenomena, the microdamage tensor [symbol] takes into account the anisotropic intrinsic microdamage mechanisms on internal dissipation and the back stress tensor alpha aims at the description of dissipation effects caused by the kinematic hardening. To describe suitably the influence of both induced anisotropy effects and the stress triaxiality observed experimentally the new kinetic equations for the microdamage tensor [symbol] and for the back stress tensor alpha are proposed. The relaxation time Tm is used as a regularization parameter. To describe the contribution to strain rate effects generated by microshear banding we propose to introduce certain scalar function which affects the relaxation time Tm in the viscoplastic flow rule. Fracture criterion based on the evolution of the anisotropic intrinsic microdamege is formulated. The fundamental features of the proposed constitutive theory have been carefully discussed. The purpose of the development of this theory is in future applications for the description of important problems in modem manufacturing processes, and particularly for meso-, micro-, and nano-mechanical issues. This description is needed for the investigation by using the numerical methods how to avoid unexpected plastic strain localization and localized fracture phenomena in new manufacturing technology.
PL
Głównym celem obecnej pracy jest opracowanie termo-sprężysto-lepkoplastycznego modelu konstytutywnego materiału, który uwzględnia efekty indukowanej anizotropii, jak również wpływ na wrażliwość materiału, prędkość deformacji spowodowanej tworzeniem się mikropasm ścinania. Przedstawiono fizykalne podstawy oraz eksperymentalne motywacje dla efektów wywołanych przez obydwa rodzaje indukowanych anizotropii oraz przez tworzenie się mikropasm ścinania. Model materiału został opracowany w ramach termodynamicznej, kowariantnej struktury konstytutywnej typu prędkościowego ze skończonym zbiorem parametrów wewnętrznych. Przyjęto, że zbiór parametrów wewnętrznych składa się z jednej wielkości skalarnej i dwóch tensorów, mianowicie z ekwiwalentnej niesprężystej deformacji e/p, tensora mikrouszkodzeń drugiego rzędu [symbol] (z fizykalną interpretacją, że ([wzór]) definiuje objętościowy udział porowatości) oraz tensora naprężeń resztkowych alfa. Ekwiwalentna niesprężysta deformacja [symbol] opisuje efekty dyssypacji generowane przez zjawisko lepkoplastycznego płynięcia, tensor mikrouszkodzeń [symbol] uwzględnia anizotropowe mechanizmy wewnętrznego mikrouszkodzenia w opisie wewnętrznej dyssypacji, natomiast tensor alfa opisuje efekty dyssypacji wywołane kinematycznym wzmocnieniem materiału. Aby opisać wpływ efektów obydwu indukowanych anizotropii i uwzględnienia efektów trójosiowości stanu naprężenia zaobserwowanych doświadczalnie zaproponowano nowe równanie kinetyczne dla tensora mikrouszkodzenia [symbol] i dla tensora naprężeń resztkowych alfa. Czas relaksacji Tm został wykorzystany jako parametr regularyzacji. Aby opisać udział wrażliwości materiału na prędkość deformacji generowanego przez tworzenie się mikropasm ścinania, zaproponowano wprowadzenie pewnej funkcji skalarnej, która wpływa na czas relaksacji Tm w procesie płynięcia lepkoplastycznego. Sformułowano kryterium zniszczenia bazujące na ewolucji anizotropowego wewnętrznego mikrouszkodzenia. Przeprowadzono szczegółową analizę wszystkich podstawowych cech zaproponowanej teorii konstytutywnej. Opracowana teoria może być wykorzystana w przyszłości do opisu ważnych problemów związanych z technologicznymi procesami, w szczególności dla zbadania zjawisk w meso-, micro-, i nanomechanice. Te opisy są potrzebne do szczegółowego zbadania za pomocą metod numerycznych jak uniknąć niepotrzebnych plastycznych lokalizacji oraz zjawiska zlokalizowanego zniszczenia w nowych procesach technologicznych.
7
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.
8
Numerical investigation of localized fracture phenomena in inelastic solids
Dornowski W., Perzyna P.
Foundations of Civil and Environmental Engineering
|
2006
|
No. 7
79-116
EN
The main objective of the present paper is to discuss a very efficient procedure of the numerical investigation of localized fracture in inelastic solids generated by impact-loaded adiabatic processes. Particular attention is focused on the proper description of a ductile mode of fracture propagating along the shear band for high impact velocities. This procedure of investigation is based on the utilization of the finite difference method for regularized thermo-elasto-viscoplastic constitutive model of damaged material. A general constitutive model of thermo-elasto-viscoplastic damaged polycrystal-line solids with a finite set of internal variables is used. The set of internal state variables consists of two scalars, namely 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 relaxation time is used as a regularization parameter. Fracture criterion based on the evolution of microdamage is assumed. As a numerical example we consider dynamic shear band propagation and localized fracture in an asymmetrically impact-loaded prenotched thin plate. The impact loading is simulated by a velocity boundary condition which are the results of dynamic contact problem. The separation of the projectile from the specimen, resulting from wave reflections within the projectile and the specimen, occurs in the phenomenon. A thin shear band region of finite width which undergoes significant deformation and temperature rise has been determined. Its evolution until occurrence of final fracture has been simulated. Shear band advance as a function of time, the evolution of the Mises stress, equivalent plastic deformation, temperature, the microdamage and the crack path in the fracture region have been determined. Qualitative comparison of numerical results with experimental observation data has been presented. The numerical results obtained have proven the usefulness of the thermo-clasto-viscoplastic theory in the investigation of dynamic shear band propagations and localized fracture.
9
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.
10
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.
11
Content available remote Localization of plastic deformations as a result of wave interaction
Glema A., Łodygowski T., Perzyna P.
Computer Assisted Mechanics and Engineering Sciences
|
2003
|
Vol. 10, No. 1
81-91
EN
The main objective of the paper is the investigation of the interaction and reflection of elastic-viscoplastic waves which can lead to localization phenomena in solids. The rate type constitutive structure for an elastic-viscoplastic material with thermomechanical coupling is used. An adiabatic inelastic flow process is considered. Discussion of some features of rate dependent plastic medium is presented. This medium has dissipative and dispersive properties. In the evolution problem considered in such dissipative and dispersive medium the stress and deformation due to wave reflections and interactions are not uniformly distributed, and this kind of heterogeneity can lead to strain localization in the absence of geometrical or material imperfections. Numerical examples are presented for a 2D specimens subjected to tension, with the controlled displacements imposed at one side with different velocities. The initial-boundary conditions which are considered reflect the asymmetric (single side) tension of the specimen with the opposite side fixed, which leads to non-symmetric deformation. The influence of the constitutive parameter (relaxation time of mechanical perturbances) is also studied in the examples. The attention is focused on the investigation of the interactions and reflections of waves and on the location of localization of plastic deformations.
12
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].
13
Content available remote Thermodynamical theory of inelastic single crystals
Perzyna P.
Engineering Transactions
|
2002
|
Vol.50, iss.3
107-164
EN
The paper aims at the development of the thermodynamic theory of elasto-viscoplasticity of single crystals which takes account of the evolution of the dislocation substructure. The next objective is the application of the theory developed for the investigation of the adiabatic shear-band formation in single crystals under dynamic loading processes. The description of the kinematics of finite elasto-viscoplastic deformations of single crystal is based on notions of the Riemannian space of manifolds and the tangent space. A multiplicative decomposition of the deformation gradient is adopted and the Lie derivative is used to define all objective rates for the introduced vectors and tensors. A general constitutive model is developed within the thermodynamic framework of the rate-type covariance constitutive structure with finite set of the internal state variables, and takes account of the effects as follows: (i) thermomechanical coupling; (ii) influence of covariance terms, lattice deformations and rotations and plastic spin; (iii) evolution of the dislocation substructure; (iv) deviation from the Schmid rule of a critical resolved shear stress for slip; (v) rate sensitivity (viscosity). A notion of covariance is understood in the sense of invariance under arbitrary spatial diffeomorphisms. The developed thermoviscoplasticity theory of single crystals is based on the axioms as follows: (i) existence of the free energy function; (ii) invariance with respect to any diffeomorphism (any superposed motion); (iii) assumption of the entropy production inequality; (iv) assumption of the evolution equations for the internal state variables in the particular rate-dependent form. To describe the evolution of the dislocation substructure, a finite set of the internal state variables is interpreted as follows: the density of mobile dislocations, the density of obstacle dislocations and the concentration of the point defects. Physical foundations and experimental motivations are given. Two fundamental constitutive equations of the rate-type for the Kirchhoff stress tensor and temperature are formulated. To show that the thermodynamic theory of viscoplasticity of single crystals takes account of all the mentioned effects, an analysis of the thermomechanical couplings and internal dissipation is presented. Particular attention is focused on synergetic effects, generated by cooperative phenomena of thermomechanical couplings and the influence of the evolution of the dislocation substructure. The initial boundary value problem (the evolution problem) for rate-dependent elasto-plastic single crystal has been proved to be well posed. Criteria for adiabatic shear-band localization of plastic deformation are obtained by assuming that some eigenvalue of the instantaneous adiabatic acoustic tensor for rate-independent response is equal to zero. The formation of the adiabatic shear-band is investigated. It has been found that the synergetic effects generated by cooperative phenomena of thermomechanical couplings and the influence of the evolution of the dislocation substructure play a fundamental role in the inception of localization. The results obtained are compared with available experimental observations.
14
Content available remote Localization phenomena in thermo-viscoplastic flow processes under cyclic dynamic loadings
Dornowski W., Perzyna P.
Computer Assisted Mechanics and Engineering Sciences
|
2000
|
Vol. 7, No. 1
117-160
EN
The main objective of the paper is the investigation of localization 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 microdamage kinetics interacts with thermal and load changes to make failure of solids a highly rate, temperature and history dependent, nonlinear process. A general constitutive model of elasto-viscoplastic damaged polycrystalline solids is developed within the thermodynamic framework of the rate type covariance 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. By assuming that the relaxation time tends to zero, the rate independent elastic-plastic response can be obtained. The viscoplastic regularization procedure assures the stable integration algorithm by using the finite difference method. Particular attention is focused on the well-posedness of the evolution problem (the initial-boundary value problem) as well as on its numerical solutions. The Lax-Richtmyer equivalence theorem is formulated and conditions under which this theory is valid are examined. 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, namely dynamic, adiabatic and isothermal, cyclic loading processes for a thin steel plate with small rectangular hole located in the centre. To the upper edge of the plate the normal and parallel displacements are applied while the lower edge is supported rigidly. Both these displacements change in time cyclically. Small two asymmetric regions which undergo significant deformations and temperature rise have been determined. Their evolution until occurrence of final fracture has been simulated. 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 wave shape of the assumed loading cycle.
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