Prof. Piotr Perzyna, Ph.D., Dr. Habil., Eng. |

##### Doctoral thesis

1959 | Fale naprężenia w ośrodkach niesprężystych
| 21 |

##### Habilitation thesis

1962 | Wpływ prędkości odkształcenia i niejednorodności materiału na rozprzestrzenianie się fal naprężenia w ośrodkach plastycznych | 740 |

##### Professor

1971 | Title of professor |

##### Supervision of doctoral theses

1. | 1999 | Drabik Aldona | Mikromechanika zniszczenia materiałów niesprężystych | ||

2. | 1998 | Korbel Katarzyna | Analiza wpływu struktury wewnętrznej kryształu na zjawiska lokalizacji deformacji plastycznych | ||

3. | 1988 | Nowak Zdzisław | Zagadnienie lokalizacji deformacji lepkoplastycznych w tarczy kołowej wszechstronnie rozciąganej | ||

4. | 1985 | Dłużewski Paweł | Zastosowanie teorii poślizgów do opisu procesów deformacji niesprężystych | ||

5. | 1983 | Frischmuth Kurt | Zagadnienia modelowania konstytutywnego i stabilności ciał dyssypatywnych | ||

6. | 1980 | Rońda Jacek | Rozwiązania dynamicznych zagadnień początkowo-brzegowych w teorii lepkoplastyczności | ||

7. | 1979 | Pęcherski Ryszard | Teoretyczny opis wpływu napromieniowania neutronami na właściwości lepkoplastyczne miękkiej stali | ||

8. | 1979 | Wołoszyńska Katarzyna | Zagadnienia falowe w sprzężonej termolepkoplastyczności | ||

9. | 1972 | Kosiński Witold | Liniowa teoria materiałów reologicznych z wewnętrznymi zmianami strukturalnymi | ||

10. | 1971 | Pabjanek Anna | Analiza lepkoplastycznych powłok walcowych | ||

11. | 1969 | Pielorz Amalia | Porównanie metod przybliżonego rozwiązywania problemów falowych w ośrodkach niesprężystych | ||

12. | 1967 | Baltow Angel | Płaskie zagadnienia w lepkoplastyczności | ||

13. | 1967 | Wojno Włodzimierz | Termodynamika materiałów sprężystolepkoplastycznych | ||

14. | 1966 | Bejda Józef | Rozwiązanie falowego problemu sprężysto-lepko-plastycznych belek | ||

15. | 1965 | Wierzbicki Tomasz | Dynamika sztywno-lepko-plastycznych płyt kołowych |

##### Recent publications

1. | Nowak Z., Perzyna P., The Identﬁcation Procedure for The Constitutive Model of Elasto-Viscoplasticity Describing the Behaviour of Nanocrystalline Titanium, ENGINEERING TRANSACTIONS (ROZPRAWY INŻYNIERSKIE), ISSN: 0867-888X, Vol.62, No.3, pp.221-240, 2014Abstract:The main objective of the present paper is the description of the behaviour of the ultrafine- grained (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 Keywords:elasto-viscoplasticity, nanocrystalline titanium, uniaxial compression Affiliations:
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2. | Kosiński W., Perzyna P., On consequences of the principle of stationary action for dissipative bodies, ARCHIVES OF MECHANICS, ISSN: 0373-2029, Vol.64, No.1, pp.95-106, 2012Abstract: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. Keywords:dissipative bodies, principle of stationary action, Lagrangian, non-commutative rule, internal state variables Affiliations:
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3. | Perzyna P., Multiscale Constitutive Modelling of the Influence of Anisotropy Effects on Fracture Phenomena in Inelastic Solids, ENGINEERING TRANSACTIONS (ROZPRAWY INŻYNIERSKIE), ISSN: 0867-888X, Vol.60, No.3, pp.225-284, 2012Abstract: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 material structure. 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 configuration 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. Affiliations:
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4. | Frąś T., Nowak Z., Perzyna P., Pęcherski R.B., Identification of the model describing viscoplastic behaviour of high strength metals, INVERSE PROBLEMS IN SCIENCE AND ENGINEERING, ISSN: 1741-5977, DOI: 10.1080/17415977.2010.531474, Vol.19, No.1, pp.17-30, 2011Abstract:Ultrafine grained (UFG) and nanocrystalline metals (nc-metals) are studied. 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 a multiscale development of shear deformation modes. The comprehensive discussion of these phenomena in UFG and nc-metals is given in M.A. Meyers, A. Mishra and D.J. Benson [Mechanical properties of nanocrystalline materials, Progr. Mater. Sci. 51 (2006), pp. 427–556], 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 identify the parameters of Perzyna constitutive model, a new description of viscoplastic deformation, which accounts for the observed shear banding. The viscoplasticity model proposed earlier by Perzyna [Fundamental problems in viscoplasticity, Adv. Mech. 9 (1966), pp. 243–377] was extended in order to describe the shear banding contribution in Z. Nowak, P. Perzyna, R.B. Pecherski [Description of viscoplastic fow accounting for shear banding, Arch. Metall. Mater. 52 (2007), pp. 217–222]. The shear banding contribution function, which was introduced formerly by Pe¸cherski [Modelling of large plastic deformation produced by micro-shear banding, Arch. Mech. 44 (1992), pp. 563–584] and applied in continuum plasticity accounting for shear banding in R.B. Pecherski [Macroscopic measure of the rate of deformation produced by micro-shear banding, Arch. Mech. 49 (1997), pp. 385–401] plays pivotal role in the viscoplasticity model. The derived constitutive equations were identified and verified with the application of experimental data provided in the article by D. Jia, K.T. Ramesh and E. Ma [Effects of nanocrystalline and ultrafne grain sizes on constitutive behavior and shear bands in iron, Acta Mat. 51 (2003), pp. 3495–3509], where quasistatic and dynamic compression tests with UFG and nanocrystalline iron specimens of a wide range of mean grain size were reported. Numerical simulation of the compression of the prismatic specimen was made by the ABAQUS FEM program with UMAT subroutine. Comparison with experimental results proved the validity of the Keywords:Ultra fine grained metals, nanocrystalline metals, viscoplastic deformation, shear banding, shear banding contribution function, numerical simulation of compression test, identification of the model parameters Affiliations:
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5. | Nowacki W.K., Nowak Z., Perzyna P., Pęcherski R.B., Effect of strain rate on ductile fracture. A new methodology, JOURNAL OF THEORETICAL AND APPLIED MECHANICS, ISSN: 1429-2955, Vol.48, No.4, pp.1003-1026, 2010Abstract: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. Keywords:Effect of strain rate, ductile fracture, dynamic double shear test, DH-36 steel, thermographic observation Affiliations:
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6. | Glema A.^{♦}, Łodygowski T.^{♦}, Perzyna P., Numerical investigation of dynamic shear bands in inelastic solids as a problem of mesomechanics, COMPUTATIONAL MECHANICS, ISSN: 0178-7675, DOI: 10.1007/s00466-007-0180-z, Vol.41, No.2, pp.219-229, 2008Abstract:The main objective of the present paper is to discuss very efficient procedure of the numerical investigation of the propagation of shear band in inelastic solids generated by impact-loaded adiabatic processes. This procedure of investigation is based on utilization the finite element method and ABAQUS system for regularized thermo-elasto-viscoplastic constitutive model of damaged material. A general constitutive model of thermo-elasto-viscoplastic polycrystalline solids with a finite set of internal state variables is used. The set of internal state variables is restricted to only one scalar, namely equivalent inelastic deformation. The equivalent inelastic deformation can describe the dissipation effects generated by viscoplastic flow phenomena. Affiliations:
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7. | Glema A.^{♦}, Łodygowski T.^{♦}, Sumelka W.^{♦}, Perzyna P., Numerical Analysis of the Intrinsic Anisotropic Microdamage Evolution in Elasto-Viscoplastic Solids, INTERNATIONAL JOURNAL OF DAMAGE MECHANICS, ISSN: 1056-7895, DOI: 10.1177/1056789508097543, Vol.18, No.3, pp.205-231, 2008Abstract:The objective of the present article is to show the formulation for elastic-viscoplastic material model accounting for intrinsic anisotropic microdamage. The strain-induced anisotropy is described by the evolution of the intrinsic microdamage process — defined by the second-order microdamage tensor. The first step of the possibility of identification procedure (calibration of parameters) are also accounted and illustrated by numerical examples. Keywords:microdamage, anisotropy Affiliations:
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8. | Perzyna P., The thermodynamical theory of elasto-viscoplasticity accounting for microshear banding and induced anisotropy effects, MECHANICS, ISSN: 1734-8927, Vol.27, No.1, pp.25-42, 2008Abstract: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. Keywords:thermodynamical theory of elasto-viscoplasticity, microshear banding, induced anisotropy, microdamage, fracture phenomena Affiliations:
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9. | Nowak Z., Perzyna P., Pęcherski R.B., Description of viscoplastic flow accounting for shear banding, ARCHIVES OF METALLURGY AND MATERIALS, ISSN: 1733-3490, Vol.52, No.2, pp.217-222, 2007Abstract: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 ę 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. Keywords:Viscoplastic flow, shear banding, micro-shear bands, nanocrystalline metals, nc-metals, ultra fine grain (ufg) metals Affiliations:
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10. | Woelke P.^{♦}, Voyiadjis G.Z.^{♦}, Perzyna P., Elasto-plastic finite element analysis of shells with damage due to microvoids, INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, ISSN: 0029-5981, DOI: 10.1002/nme.1711, Vol.68, No.3, pp.338-380, 2006Abstract:This paper presents a non-linear finite element analysis for the elasto-plastic behaviour of thick/thin shells and plates with large rotations and damage effects. The refined shell theory given by Voyiadjis and Woelke (Int. J. Solids Struct. 2004; 41:3747–3769) provides a set of shell constitutive equations. Numerical implementation of the shell theory leading to the development of the C0 quadrilateral shell element (Woelke and Voyiadjis, Shell element based on the refined theory for thick spherical shells. 2006, submitted) is used here as an effective tool for a linear elastic analysis of shells. The large rotation elasto-plastic model for shells presented by Voyiadjis and Woelke (General non-linear finite element analysis of thick plates and shells. 2006, submitted) is enhanced here to account for the damage effects due to microvoids, formulated within the framework of a micromechanical damage model. The evolution equation of the scalar porosity parameter as given by Duszek-Perzyna and Perzyna (Material Instabilities: Theory and Applications, ASME Congress, Chicago, AMD-Vol. 183/MD-50, 9–11 November 1994; 59–85) is reduced here to describe the most relevant damage effects for isotropic plates and shells, i.e. the growth of voids as a function of the plastic flow. The anisotropic damage effects, the influence of the microcracks and elastic damage are not considered in this paper. The damage modelled through the evolution of porosity is incorporated directly into the yield function, giving a generalized and convenient loading surface expressed in terms of stress resultants and stress couples. A plastic node method (Comput. Methods Appl. Mech. Eng. 1982; 34:1089–1104) is used to derive the large rotation, elasto-plastic-damage tangent stiffness matrix. Some of the important features of this paper are that the elastic stiffness matrix is derived explicitly, with all the integrals calculated analytically (Woelke and Voyiadjis, Shell element based on the refined theory for thick spherical shells. 2006, submitted). In addition, a non-layered model is adopted in which integration through the thickness is not necessary. Consequently, the elasto-plastic-damage stiffness matrix is also given explicitly and numerical integration is not performed. This makes this model consistent mathematically, accurate for a variety of applications and very inexpensive from the point of view of computer power and time. Affiliations:
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11. | Glema A.^{♦}, Łodygowski T.^{♦}, Perzyna P., Localization of plastic deformations as a result of wave interaction, Computer Assisted Mechanics and Engineering Sciences, ISSN: 1232-308X, Vol.10, No.1, pp.81-91, 2003Abstract: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. Affiliations:
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12. | Dornowski W.^{♦}, Perzyna P., Numerical analysis of macrocrack propagation along a bimaterial interface under dynamic loading processes, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 0020-7683, DOI: 10.1016/S0020-7683(02)00405-5, Vol.39, No.19, pp.4949-4977, 2002Abstract:Advances in computing as well as measurement instrumentation have recently allowed for the investigation of a wider spectrum of physical phenomena in dynamic failure than previously possible. With increasing demand for specialized lightweight, high strength structures, failure of inhomogeneous solids has been receiving increased attention. Such inhomogeneous solids include structural composites such as bonded and sandwich structures, layered and composite materials as well as functionally graded solids. Many of such solids are composed of brittle constituents possessing substantial mismatch in wave speeds, and are bonded together with weak interfaces, which may serve as sites for catastrophic failure (Rosakis and Ravichandran (2000)). Keywords:Propagation of macrocrack, Bimaterial interface, Thermo-elasto-viscoplastic material, Adiabatic dynamic processes, Localized fracture Affiliations:
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13. | Dornowski W.^{♦}, Perzyna P., Localized fracture phenomena in thermo-visco-plastic flow processes under cyclic dynamic loadings, ACTA MECHANICA, ISSN: 0001-5970, DOI: 10.1007/BF01176245, Vol.155, No.3-4, pp.233-255, 2002Abstract:The main objective of the paper is the investigation of 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 depend 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. Affiliations:
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14. | Dornowski W.^{♦}, Perzyna P., Analysis of various effects in dynamic cyclic fatigue damage, ARCHIVE OF APPLIED MECHANICS, ISSN: 0939-1533, DOI: 10.1007/s00419-002-0217-x, Vol.72, No.6, pp.418-438, 2002Abstract:The objective of the paper is the analysis of various effects in fatigue damage in plastic flow of solids under dynamic cyclic loading. Attention is focused on the investigation of the following effects: (i) influence of the shape of the loading pulse; (ii) softening generated by thermomechanical coupling; (iii) softening generated by microdamage; (iv) plastic strain-induced anisotropy caused by kinematic hardening; (v) plastic spin; (vi) strain-rate sensitivity; (vii) covariant terms. Keywords:Cyclic fatigue, Damage, Dynamic loading, Adiabatic process, Thermal coupling, Elasto-viscoplasticity, Microdamage Affiliations:
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15. | Glema A.^{♦}, Łodygowski T.^{♦}, Perzyna P., Interaction of deformation waves and localization phenomena in inelastic solids, COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, ISSN: 0045-7825, DOI: 10.1016/S0045-7825(99)00215-7, Vol.183, No.1-2, pp.123-140, 2000Abstract:The main objective of this 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 developed. An adiabatic inelastic flow process is considered. The Cauchy problem is investigated and the conditions for well-posedness are examined. Discussion of fundamental features of rate-dependent plastic medium is presented. This medium has dissipative and dispersive properties. Mathematical analysis of the evolution problem (the dynamical initial-boundary value problem) is presented. The dispersion property implies that in the viscoplastic medium any initial disturbance can break up into a system of group of oscillations or wavelets. On the other hand, the dissipation property causes the amplitude of a harmonic wavetrain to decay with time. 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. Affiliations:
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16. | Dornowski W.^{♦}, Perzyna P., Localization phenomena in thermo-viscoplastic flow processes under cyclic dynamic loadings, Computer Assisted Mechanics and Engineering Sciences, ISSN: 1232-308X, Vol.7, No.1, pp.117-160, 2000Abstract: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. Affiliations:
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17. | Dornowski W.^{♦}, Perzyna P., Constitutive modeling of inelastic solids for plastic flow processes under cyclic dynamic loadings, Journal of Engineering Materials and Technology, ISSN: 0094-4289, DOI: 10.1115/1.2812368, Vol.121, No.2, pp.210-220, 1999Abstract:The main objective of the paper is the description of the behavior and fatigue damage of inelastic solids in plastic flow processes under dynamic cyclic loadings. Experimental motivations and physical foundations are given. Recent experimental observations for cycle fatigue damage mechanics at high temperature of metals suggest that the intrinsic microdamage process does very much depend on the strain rate effects as well as on the wave shape effects. The microdamage process has been treated as a sequence of nucleation, growth and coalescence of microcracks. 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; (iv) thermomechanical coupling (thermal plastic softening and thermal expansion); (v) rate sensitivity. 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, a dynamic, adiabatic and isothermal, cyclic loading processes for a thin steel plate with small rectangular hole located in the centre. Small two 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. Affiliations:
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18. | Perzyna P., Korbel K.^{♦}, Analysis of the influence of various effects on criteria for adiabatic shear band localization in single crystals, ACTA MECHANICA, ISSN: 0001-5970, DOI: 10.1007/BF01379649, Vol.129, No.1-2, pp.31-62, 1998Abstract:The paper aims at the investigation of the influence of various effects on criteria for shear band localization in inelastic single crystals. This investigation is based on an analysis of acceleration waves and takes advantage of a notion of the instantaneous adiabatic acoustic tensor. Particular attention is focussed on the analysis of the effects as follows: (i) spatial covariance and plastic spin; (ii) thermomechanical coupling; (iii) non-Schmid; (iv) evolution of substructure; (v) nondissipative thermal term; (vi) cooperative phenomena (synergetic). The theory of thermoviscoplasticity of inelastic single crystals is presented within a framework of the rate type covariance constitutive structure with a finite set of the internal state variables. By assuming that the mechanical relaxation time is equal to zero the thermo-elasto-plastic (rate independent) response of single crystals is accomplished. An adiabatic inelastic flow process of the single crystal is formulated and investigated. Symmetric double slip and single slip processes are considered. The formulation of macroscopic adiabatic shear bands is investigated. The criteria for adiabatic shear band localization for a single slip process are presented in exact analytical form. For a symmetric double slip process these criteria are estimated numerically. The discussion of the influence of various effects is presented, and the comparison of the results obtained with available experimental observations is given. Affiliations:
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19. | Duszek-Perzyna M.K., Perzyna P., Analysis of anisotropy and plastic spin effects on localization phenomena, ARCHIVE OF APPLIED MECHANICS, ISSN: 0939-1533, DOI: 10.1007/s004190050171, Vol.68, No.5, pp.352-374, 1998Abstract: The main objective of the paper is the investigation of the influence of the anisotrophy and plastic spin effects on criteria for adiabatic shear band localization of plastic deformation. A theory of thermoplasticity is formulated within a framework of the rate-type covariance material structure with a finite set of internal state variables. The theory takes into consideration such effects as plastic non-normality, plastic-induced anisotropy (kinematic hardening), micro-damage mechanism, thermomechanical coupling and plastic spin. Keywords:plastic-induced anisotropy, plastic spin, localization, micro-damage, stress triaxiality Affiliations:
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20. | Łodygowski T.^{♦}, Perzyna P., Numerical modelling of localized fracture of inelastic solids in dynamic loading processes, INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, ISSN: 0029-5981, DOI: 10.1002/(SICI)1097-0207(19971130)40:22<4137::AID-NME260>3.0., Vol.40, pp.4137-4158, 1997Abstract:The main objective of the paper is the investigation of adiabatic shear band localized fracture phenomenon in inelastic solids during dynamic loading processes. This kind of fracture can occur as a result of an adiabatic shear band localization generally attributed to a plastic instability implied by microdamage and thermal softening during dynamic plastic flow processes. Keywords:viscoplasticity, localization, regularization, micro-damage, localized fracture Affiliations:
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21. | Łodygowski T.^{♦}, Perzyna P., Localized fracture in inelastic polycrystalline solids under dynamic loading processes, INTERNATIONAL JOURNAL OF DAMAGE MECHANICS, ISSN: 1056-7895, DOI: 10.1177/105678959700600402, Vol.6, No.4, pp.364-407, 1997Abstract:The main objective of the paper is the investigation of adiabatic shear band localized fracture phenomenon in inelastic solids during dynamic loading processes. This kind of fracture can occur as a result of an adiabatic shear band localization generally attributed to a plastic instability implied by micro-damage and thermal softening during dynamic plastic flow processes. Affiliations:
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22. | Perzyna P., Korbel K.^{♦}, Analysis of the influence of the substructure of a crystal on shear band localization phenomena of plastic deformation, MECHANICS OF MATERIALS, ISSN: 0167-6636, DOI: 10.1016/S0167-6636(96)00032-4, Vol.24, No.2, pp.141-158, 1996Abstract:The main objective of the present paper is the discussion of the influence of the evolution of the substructure of single crystal on the shear band localization phenomena. A constitutive model of an inelastic crystal within the thermodynamic framework of the rate type covariance constitutive structure with internal state variables is developed. Thermomechanical couplings are considered and internal heating generated by the rate of internal dissipation is described. It has been proved that the description of a rate independent adiabatic single slip process in elasto-plastic single crystal is reduced to one fundamental evolution equation for the Kirchhoff stress tensor. Using the analysis of acceleration waves the necessary condition for a localized plastic deformation region to be formed is obtained. The criteria for adiabatic shear band localization are presented in an exact analytical form. Numerical estimations for the critical hardening modulus rate and the direction of the macroscopic shear band are given. The influence of various effects on shear band localization criteria is investigated. It has been found that the influence of the dislocation substructure is combined with the thermomechanical coupling and leads to distinct synergetic effect. The possibility of deviation from the Schmid rule of the critical resolved shear stress is also investigated. Comparison of the numerical results with available experimental data is presented. Affiliations:
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23. | Duszek-Perzyna M.K., Perzyna P., Adiabatic shear band localization of inelastic single crystals in symmetric double-slip process, ARCHIVE OF APPLIED MECHANICS, ISSN: 0939-1533, DOI: 10.1007/BF00803672, Vol.66, No.6, pp.369-384, 1996Abstract:The main objective of the present paper is the development of a viscoplastic regularization procedure valid for an adiabatic dynamic process for multi-slips of single crystals. The next objective is to focus attention on the investigation of instability criteria, and particularly on shear band localization conditions. Keywords:shear band localization, viscoplasticity, adiabatic process, crystal slip Affiliations:
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24. | Perzyna P., Instability phenomena and adiabatic shear band localization in thermoplastic flow processes, ACTA MECHANICA, ISSN: 0001-5970, DOI: 10.1007/BF01213561, Vol.106, No.3-4, pp.173-205, 1994Abstract:The main objective of the paper is the development of the viscoplastic regularization procedure valid for a broad class of thermodynamic plastic flow processes in damaged solids. The additional aim is to investigate instability phenomena and adiabatic shear band localization criteria when spatial covariance, thermomechanical coupling, strain induced anisostropy and micro-damage softening effects are taken into consideration. This investigation is based on an analysis of acceleration waves and takes advantage of a notion of the instantaneous adiabatic acoustic tensor. In the first part of the paper the formulation of an inelastic flow process is given and particular attention is focussed on the thermomechanical coupling effects. The thermodynamic theory of elastic-viscoplastic damaged solids is presented within a framework of the rate type covariance material structure with a finite set of the internal state variables. A notion of covariance is understood in the sense of invariance under an arbitrary spatial diffeomorphism. Rate sensitivity effect is introduced by the assumption of the viscoplastic overstress conception. A notion of a relaxation time has been used to control the description of mechanical as well as thermal disturbances. By the assumption that the mechanical relaxation time is equal to zero the thermo-elastic-plastic (rate independent) response of the damaged material is accomplished. In the second part of the paper the existence of a solution to the initial-boundary value problem is examined and its stability property is investigated based on the application of nonlinear semi-group methods and an analysis of continuity of evolution operators. For an adiabatic process the investigation of acceleration waves is given. The determination of eigenvalues of the appropriate acoustic tensor is presented. This helps to assess the well-posedness of the initial-value problems which describe the thermodynamic plastic flow processes. Differences for two constitutive assumptions, namely for rate dependent and rate independent responses, are examined. In the case of an adiabatic process and elastic-viscoplastic response of a material the conditions for the existence, uniqueness and well-posedness of the initial value problem have been investigated. Affiliations:
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25. | Perzyna P., Micromechanics of localized fracture in inelastic solids under dynamic loading processes, ACTA MECHANICA, ISSN: 0001-5970, DOI: 10.1007/BF01213561, Vol.106, No.3-4, pp.173-205, 1994Abstract:The main objective of the paper is the development of the viscoplastic regularization procedure valid for a broad class of thermodynamic plastic flow processes in damaged solids. The additional aim is to investigate instability phenomena and adiabatic shear band localization criteria when spatial covariance, thermomechanical coupling, strain induced anisostropy and micro-damage softening effects are taken into consideration. This investigation is based on an analysis of acceleration waves and takes advantage of a notion of the instantaneous adiabatic acoustic tensor. In the first part of the paper the formulation of an inelastic flow process is given and particular attention is focussed on the thermomechanical coupling effects. The thermodynamic theory of elastic-viscoplastic damaged solids is presented within a framework of the rate type covariance material structure with a finite set of the internal state variables. A notion of covariance is understood in the sense of invariance under an arbitrary spatial diffeomorphism. Rate sensitivity effect is introduced by the assumption of the viscoplastic overstress conception. A notion of a relaxation time has been used to control the description of mechanical as well as thermal disturbances. By the assumption that the mechanical relaxation time is equal to zero the thermo-elastic-plastic (rate independent) response of the damaged material is accomplished. In the second part of the paper the existence of a solution to the initial-boundary value problem is examined and its stability property is investigated based on the application of nonlinear semi-group methods and an analysis of continuity of evolution operators. For an adiabatic process the investigation of acceleration waves is given. The determination of eigenvalues of the appropriate acoustic tensor is presented. This helps to assess the well-posedness of the initial-value problems which describe the thermodynamic plastic flow processes. Differences for two constitutive assumptions, namely for rate dependent and rate independent responses, are examined. In the case of an adiabatic process and elastic-viscoplastic response of a material the conditions for the existence, uniqueness and well-posedness of the initial value problem have been investigated. Affiliations:
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26. | Duszek-Perzyna M.K., Perzyna P., Adiabatic shear band localization in elastic-plastic single crystals, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 0020-7683, DOI: 10.1016/0020-7683(93)90132-Q, Vol.30, No.1, pp.61-89, 1993Abstract:The main objective of the paper is the investigation of shear band localization criteria for finite elastic-plastic deformations of a single crystal subjected to an adiabatic process. The next objective is to focus attention on the temperature dependent plastic behaviour of the single crystal considered. A constitutive model is developed within the thermodynamic framework of the rate type covariance constitutive structure i.e. it is invariant with respect to diffeomorphism. To achieve this aim a multiplicative decomposition of the deformation gradient is adopted and the Lie derivative is used to define all objective rates for introduced vectors and tensors. Thermomechanical couplings are investigated and a method is developed which allows us to use the standard bifurcation procedure in the examination of the adiabatic shear band localization. The general evolution equation for the Kirchhoff stress tensor is obtained. The fundamental matrix in this evolution equation describes thermomechanical couplings as well as local lattice deformation and rotation. For the particular elastic properties of the single crystal and for some simplified case of the coupling effects the criteria for adiabatic shear band localization are obtained in their exact analytical form. The influence of two important thermal effects, namely thermal expansion and thermal plastic softening on the criteria of localization is investigated. The similar influence of spatial covariance effects (which arise from the difference between the Lie derivative and the material rate of the Kirchhoff stress tensor) is also examined. Affiliations:
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27. | Duszek M.K., Perzyna P., Stein E.^{♦}, Adiabatic shear band localization in elastic-plastic damaged solids, International Journal of Plasticity, ISSN: 0749-6419, DOI: 10.1016/0749-6419(92)90055-H, Vol.8, No.4, pp.361-384, 1992Abstract:The main objective of the paper is the investigation of shear band localization conditions for finite elastic-plastic rate independent deformations of a damaged solid body subjected to an adiabatic process. For the kind of process considered, the thermal effects may play a dominating role. The next objective of the paper is to focus attention on temperature-dependent plastic behaviour of the body considered. Thermomechanical couplings are investigated, and a method is developed that allows application of the standard bifurcation procedure in examination of the shear band localization criteria when influence of thermomechanical couplings and thermal softening effects, together with hardening and micro-damage effects, are taken into consideration. Particular attention is focused on the coupling phenomena generated by the heat resulting from internal dissipation. A set of the coupled evolution equations for the Kirchhoff stress tensor and for temperature is considered. The assumption that the thermodynamic process is adiabatic permits elimination of the rate of temperature and permits us to obtain the general evolution equation for the Kirchhoff stress tensor. The fundamental matrix in this evolution equation describes thermomechanical couplings. For the particular elastic properties of the material and for some simplified cases of the coupling effects the criteria for shear band localization have been obtained in exact analytical form. Affiliations:
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28. | Duszek M.K., Perzyna P., The localization of plastic deformation in thermoplastic solids, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 0020-7683, DOI: 10.1016/0020-7683(91)90040-M, Vol.27, No.11, pp.1419-1443, 1991Abstract:The main objective of this paper is the investigation of the influence of thermomechanical couplings and thermal softening effects on adiabatic shear band localization criteria for finite rate-independent deformation of an elastic-plastic body. The constitutive equations for thermoelastic-plastic J2-flow theory are formulated within a framework of the rate type covariance structure with internal state variables. Two alternative descriptions are presented. Both constitutive structures formulated are invariant with respect to diffeomorphisms and are materially isomorphic. Particular attention is focused on the coupling phenomena generated by the internal heat resulting from internal dissipation. An identification procedure has been developed which permits the determination of the exact form of the evolution equation for the internal state variable vector. A set of coupled evolution equations for the Kirchhoff stress tensor and for temperature is investigated. The assumption that the thermodynamic process considered is adiabatic permits the elimination of the rate of temperature and gives the fundamental cvolution equation for the Kirchhoff stress tensor. This important result allows the use of the standard bifurcation method in the examination of the adiabatic shear band localization criteria. For the particular clastic properties of the material and for some simplified case of the coupling effects the criteria for adiabatic shear band localization are obtained in exact analytical form. Discussions of the influence of thermomechanical couplings, thermal expansion, thermal plastic softening effects and the covariance terms on the localization criteria are presented. Affiliations:
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29. | Duszek-Perzyna M.K., Perzyna P., On combined isotropic and kinematic hardening effects in plastic flow processes, International Journal of Plasticity, ISSN: 0749-6419, DOI: 10.1016/0749-6419(91)90009-N, Vol.7, No.5, pp.351-363, 1991Abstract:Attention is focused on the description of the combined isotropic and kinematic hardening effects in plastic solids. It has been found that making use of the simple geometrical relation permits us to determine the coefficient in the evolution equation describing the kinematic hardening of the Ziegler type in such a way that the evolution law is consistent with the loading criterion and satisfies the time independence requirement. On the other hand this method leaves room for the identification procedure for the material constants based on available experimental results. General constitutive and evolution equations for plastic solids are formulated. The plastic potential is assumed different than the yield criterion. Simplifications for the associated flow rule are also investigated. A new evolution law for the anisotropic hardening is discussed. This law represents the linear combination of the Prager and Ziegler kinematic hardening rules. Application of the theory developed to the description of the plastic behavior of damaged solids is given. A particular example is considered. The discussion and the interpretation of the isotropic and anisotropic hardening moduli are presented. Affiliations:
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30. | Perzyna P., Drabik A., Description of micro-damage process by porosity parameter for nonlinear viscoplasticity, ARCHIVES OF MECHANICS, ISSN: 0373-2029, Vol.41, No.6, pp.895-908, 1989Abstract:The main purpose of this paper is to investigate the contribution implied by additional terms arising in the nonlinear viscoplastic response for the growth mechanism of microvoids in ductile solids. The dissipative mechanisms suggested by dynamics of dislocations are discussed. Experimental data are reviewed and compared. The evolution equation for the porosity parameter for the general nonlinear overstress viscoplastic theory is derived. Three different particular overstress functions are investigated, namely - logarithmic, power and linear. The approximation procedure for the three types of the evolution equation obtained shows that a description of the dynamic fracture phenomenon for dissipative solids can be the same in the case of logarithmic and linear functions. Affiliations:
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31. | Duszek M.K., Perzyna P., Plasticity of damaged solids and shear band localization, Ingenieur-Archiv, ISSN: 0020-1154, DOI: 10.1007/BF00534357, Vol.58, No.5, pp.380-392, 1988Abstract:The main objective of the paper is the investigation of shear band localization conditions for finite elastic-plastic rate independent deformations of damaged solids. The first part of the paper is devoted to the formulation of the constitutive relations for elastic-plastic solids when isotropic and kinematic hardening effects and the micro-damage process are taken into consideration. The isotropic work-hardening effect is incorporated in the theory directly by defining the work-hardening-softening material function while the kinematic hardening effect and the softening effect generated by the micro-damage process are described by means of the internal state variable method. The second part of the paper aims at the investigation of the localization of plastic deformations. Different effects on the localization phenomenon are investigated. Particular attention is focused on kinematic hardening and micro-damage effects. It has been found that the influence of these two cooperative phenomena on the onset of localization within shear bands has synergetic nature. The results obtained are in good agreement with recent experimental observations. Affiliations:
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32. | Perzyna P., Temperature and rate dependent theory of plasticity of crystalline solids, Revue de Physique Appliquée (Paris), ISSN: 0035-1687, DOI: 10.1051/rphysap:01988002304044500, Vol.23, No.4, pp.445-459, 1988Abstract:The paper shows a new approach for formulation of temperature and rate dependent models of plastic behaviour of crystalline solids. It has several particular objectives. The first is to give a very brief overview of recent developments of large strain constitutive laws for crystalline rate dependent plasticity.The second is to investigate how the main mechanisms on crystalline slip system can be incorporated in the general framework of continuum rate dependent large plastic deformation constitutive structure. The internal state variables have been precisely interpreted. Based on main mechanisms for crystalline slip system the evolution equations for the internal state variables introduced are proposed. The third objective is to illustrate how to include additional features such as work hardening, thermal softening etc. in constitutive structure proposed. Next objective is to focus attention on temperature dependence of plastic behaviour. The final goal is the discussion how these propositions can be extended to develop theories for large deformation,temperature and rate dependent, polycrystalline behaviour. Keywords:slip, plasticity, plastic behaviour, crystalline solids, strain constitutive laws, slip systems, plastic deformation, internal state variables, work hardening, thermal softening Affiliations:
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33. | Duszek M.K., Perzyna P., Plasticity of damaged solids and shear band localization, Revue de Physique Appliquée (Paris), ISSN: 0035-1687, DOI: 10.1051/rphysap:01988002304069400, Vol.23, No.4, pp.694, 1988Keywords:crystallographic shear, plasticity, work hardening, damaged solids, shear band localization, elastic plastic rate independent deformations, isotropic work hardening, kinematic hardening, porous solid Affiliations:
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34. | Perzyna P., Internal state variable description of dynamic fracture of ductile solids, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, ISSN: 0020-7683, DOI: 10.1016/0020-7683(86)90123-X, Vol.22, No.7, pp.797-818, 1986Abstract:The paper aims at the description of ductile fracture phenomenon in dynamic processes in inelastic solids by means of internal state variable structure. Dynamical test data for aluminum and copper have been discussed. Particular attention is given to postshot photomicrographic observations of the residual porosity and on investigation of fracture mechanisms and spalling phenomenon. Spalling process has been described as a sequence of the nucleation, growth and coalescence of microvoids. Heuristic considerations of the growth and nucleation of microvoids are presented Affiliations:
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35. | Perzyna P., Nowak Z., Równanie ewolucji pustek w obszarze szyjki, Prace IPPT - IFTR Reports, ISSN: 2299-3657, No.24, pp.1-23, 1985 | |||||||||||||

36. | Perzyna P., Stability of flow processes for dissipative solids with internal imperfections, ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK ZAMP, ISSN: 0044-2275, DOI: 10.1007/BF00945448, Vol.35, No.6, pp.848-867, 1984Abstract:In the paper the description of the postcritical behaviour of dissipative solids is presented. A simple model of an elastic-viscoplastic material with internal imperfections is proposed. This model is justified by physical mechanisms of polycrystalline matter flow in some regions of temperature and strain rate changes. Affiliations:
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37. | Perzyna P., Constitutive Modeling of Dissipative Solids for Postcritical Behavior and Fracture, Journal of Engineering Materials and Technology, ISSN: 0094-4289, DOI: 10.1115/1.3225739, Vol.106, No.4, pp.410-419, 1984Abstract:The paper aims at the description of the postcritical behavior and fracture of dissipative solids during tensile test. The ductile fracture is understood as the final stage of the necking process and is preceded by the nucleation and growth of voids mostly due to plastic deformations and yield stress state and by the linkage of voids. An elastic-viscoplastic model of solids with internal imperfections parameter interpreted as the void volume fraction is postulated. Elastic-plastic response of the matetrial is also discussed. The material functions and constants are determined based on available mechanical test data as well as on metallurgical observation results. The theory of ductile fracture based on the evolution of internal imperfections is presented. Influence of different effects is examined and synergetic nature of fracture phenomenon is investigated. The criterion of fracture is deduced. The initial-boundary-value problem is discussed. Affiliations:
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38. | Perzyna P., Stability of flow processes for dissipative solids with internal imperfections, Prace IPPT - IFTR Reports, ISSN: 2299-3657, No.27, pp.1-66, 1983 | |||||||||||||

39. | Perzyna P., Pęcherski R.B., Analiza wpływu prędkości odkształcenia na zniszczenie plastyczne metali, Prace IPPT - IFTR Reports, ISSN: 2299-3657, No.62, pp.1-27, 1979 | |||||||||||||

40. | Perzyna P., Coupling of Dissipative Mechanisms of Viscoplastic Flow, Prace IPPT - IFTR Reports, ISSN: 2299-3657, No.19, 1977 | |||||||||||||

41. | Olszak W., Perzyna P., Physical theory of viscoplasticity for small deformations, Mechanics Research Communications, ISSN: 0093-6413, DOI: 10.1016/0093-6413(74)90062-7, Vol.1, No.4, pp.187-190, 1974 | |||||||||||||

42. | Perzyna P., Sawczuk A., Problems of thermoplasticity, NUCLEAR ENGINEERING AND DESIGN, ISSN: 0029-5493, DOI: 10.1016/0029-5493(73)90017-4, Vol.24, No.1, pp.1-55, 1973Abstract:The problems of irreversible deformation of metallic structures have come to the very focus of interest in nuclear reactor technology. Affiliations:
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43. | Kosiński W., Perzyna P., Analysis of acceleration waves in rheological material, BULLETIN OF THE POLISH ACADEMY OF SCIENCES: TECHNICAL SCIENCES, ISSN: 0239-7528, Vol.20, No.4, pp.273-280, 1972Abstract:Acceleration waves in a rheological material in the case of a one-dimensional theory are investigated. It is assumed that the internal dissipation of a rheological material can be described by n internal scalar parameters. The basic theorems for a homothermal acceleration wave are proved. Affiliations:
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44. | Perzyna P., Memory effects and internal changes of a material, INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS, ISSN: 0020-7462, DOI: 10.1016/0020-7462(71)90006-0, Vol.6, No.6, pp.707-716, 1971Abstract:A thermodynamic theory of a material with memory and internal changes is proposed. A conception to treat such material as a generalized simple body is shown. Fading memory phenomenon is used to describe the rheological properties and internal state variables are introduced to describe the internal structural changes during plastic deformation. The application of this theory to the description of an elastic-viscoplastic material is given. The discussion of the behavior of an elastic-viscoplastic material during particular processes is presented. Affiliations:
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45. | Kosiński W., Perzyna P., Analiza fal przyśpieszenia w materiale reologicznym, Prace IPPT - IFTR Reports, ISSN: 2299-3657, No.59, pp.1-32, 1971 | |||||||||||||

46. | Olszak W., Perzyna P., On thermal effects in viscoplasticity, ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK ZAMP, ISSN: 0044-2275, DOI: 10.1007/BF01590623, Vol.20, No.5, pp.676-680, 1969 | |||||||||||||

47. | Perzyna P., Wojno W.^{♦}, Thermodynamics of a Rate Sensitive Plastic Material, Prace IPPT - IFTR Reports, ISSN: 2299-3657, No.10, pp.1-22, 1968 | |||||||||||||

48. | Perzyna P., On Physical Foundations on Viscoplasticity, Prace IPPT - IFTR Reports, ISSN: 2299-3657, No.28, pp.1-37, 1968 | |||||||||||||

49. | Olszak W., Perzyna P., Les equations constitutives et phenomenes de relaxation dans les milieux elasto/visco-plastiques, Rendiconti del Seminario Matematico e Fisico di Milano, ISSN: 0370-7377, DOI: 10.1007/BF02924479, Vol.38, No.1, pp.12-18, 1968Abstract:The paper consists of two parts. The first part is devoted to a discussion of the constitutive equations describing the dynamic properties of soils. In the second part, the relaxation problem in an elastic/visco-plastic soil is considered. Affiliations:
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50. | Perzyna P., On Thermodynamic Foundations of Viscoplasticity, Prace IPPT - IFTR Reports, ISSN: 2299-3657, No.17, pp.1-25, 1967 | |||||||||||||

51. | Perzyna P., On the propagation of stress waves in a rate sensitive plastic medium, ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK ZAMP, ISSN: 0044-2275, DOI: 10.1007/BF01601063, Vol.14, No.3, pp.241-261, 1963 | |||||||||||||

52. | Perzyna P., The constitutive equations for rate sensitive plastic materials, Quarterly of Applied Mathematics, ISSN: 1552-4485, DOI: 10.1090/qam/144536, Vol.20, No.4, pp.321-332, 1963Abstract:The principal aim of the present paper is to generalize the one-dimensional constitutive equations for rate-sensitive plastic materials to general states of stress. The dynamical yield conditions for elastic, visco-plastic materials are discussed and new relaxation functions are introduced. Solutions of the relaxation equations for such materials are given. Keywords:Plastics, Strain rate, Constitutive equations, Stress functions, Plasticity, Differential equations, Tensors, Stress relaxation, Mathematical functions, Stress tensors Affiliations:
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53. | Olszak W., Perzyna P., Variational theorems in general viscoelasticity, Ingenieur-Archiv, ISSN: 0020-1154, DOI: 10.1007/BF00536117, Vol.28, No.1, pp.246-250, 1959 |

##### List of chapters in recent monographs

1. 64 | Perzyna P., Nowak Z., Mathematical methods in continuum mechanics, rozdział: , Technical University of Łódź, K. Wilmański, B. Michalak, J. Jędrysiak (Eds.), pp.63-88, The identification procedure for the constitutive model of elasto-viscoplasticity describing the behaviour of nanocrystalline iron during quasistatic and dynamic loading processes2011 | |

2. 487 | Perzyna P., Damage Mechanics and Micromechanics of Localized Fracture Phenomena in Inelastic Solids, rozdział: , Springer, CISM Courses and Lectures (ed. George Z. Voyiadjis), 525, pp.227-376, Application of the Thermodynamical Theory of Elasto-Viscoplasticity in Modern Manufacturing Processes2011 | |

3. 211 | Pęcherski R.B., Nowacki W.K., Nowak Z., Perzyna P., Workshop in Memory of Prof. J.R. Klepaczko: Dynamic Behaviour of Materials, rozdział: , LPMM, Metz, Rusinek A., Chevrier P. (Eds.), pp.65-73, Effect of strain rate on ductile fracture. A new methodology2009 | |

4. 546 | Perzyna P., Damage Mechanics in Engineering Materials, rozdział: , Elsevier B.V., series Studies in Applied Mechanics, 46, pp.183-202, Dynamic localized fracture in inelastic solids1998 | |

5. 547 | Perzyna P., Advances in Applied Mechanics, rozdział: , Elsevier B.V., G.G. Chernyi, H.L. Dryden, P. Germain, L. Howarth, W. Olszak, W. Prager, R.F. Probstein, H. Ziegler (Eds.), 9, pp.243-377, Fundamental Problems in Viscoplasticity1966 |

##### Conference papers

1. | Dornowski W.^{♦}, Perzyna P., Localized fatigue fracture in thermo-viscoplastic flow processes under cyclic dynamic loadings, JOURNAL DE PHYSIQUE IV, ISSN: 1155-4339, DOI: 10.1051/jp4:2000984, Vol.10, No.PR9, pp.503-508, 2000Abstract:The main objective of the paper is the investigation of localized fatigue fracture phenomena in thermo-viscoplastic flow processes under cyclic dynamic loadings. 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. 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 used in modified forms. 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. Fracture criterion based on the evolution of microdamage is formulated. Particular example has been considered, namely a dynamic adiabatic cyclic loading process for a thin plate with sharp notch. To the upper edge of the plate is applied cyclic constraint realized by rigid rotation of the edge of the plate while the lower edge is supported rigidly. Small localized region, distributed asymmetrically near the tip of the notch, which undergoes significant deformation and temperature rise has been determined. Its evolution until occurrence of fatigue fracture has been simulated. 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. Affiliations:
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2. | Glema A.^{♦}, Lodygowski T.^{♦}, Perzyna P., Wave propagation and strain localization in dynamically loaded specimen, JOURNAL DE PHYSIQUE IV, ISSN: 1155-4339, DOI: 10.1051/jp4:2000917, Vol.10, No.PR9, pp.99-104, 2000Abstract:The aim of the presentation is focused on two aspects which are the influance of the waves propagation in specimens on the choise of places of strain localization and the discussion of numerical models that serve the recognition of this phenomenon. There are some experimental tests which are under consideration (thin plate, axisymmetric bar, 3-D specimen) which are numericaly studied. The experiments are made in the Hopkinson tube with the typical velocity of deformations of order 104 s-1 so the processes could be treated as adiabatic. For ductile materials under such conditions to avoid the mathematical consequences due to thermal softening (ill-posedness) the viscoplastic constitutive description is used. In numerical simulations we have shown the well-posedness of the solution of governing equations by showing the insensitivity of the results to spatial discretization. The set of numerical examples proofs that it is possible to estimate the places of strain localization by observing the velocities of particles. Intensive plastic zones appear in the places where the local velocities are close to zero. In the formulation we have accepted the constitutive viscoplastic model, finite deformations and the evolution of porosity. The computations were performed in the environment of ABAQUS finite element program. Affiliations:
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3. | Olszak W., Perzyna P., On elastic/visco-plastic soils, IUTAM Symposia, Rheology and Soil Mechanics / Rhéologie et Mécanique des Sols, 1964-04-01/04-08, Grenoble (FR), pp.47-57, 1966 |

##### Conference abstracts

1. | Perzyna P., Nowak Z., The description of the behaviour of the ultrafine-grained titanium by the constitutive model of elasto-viscoplasticity, CMM 2013, 20th International Conference on Computer Methods in Mechanics, 2013-08-27/08-31, Poznań (PL), No.TS03, pp.23-24, 2013Abstract:The main objective of the present paper is the description of the behaviour of the ultrafine-grained (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 (2010)[1]. The identification procedure is based on experimental observation data obtained by Jia et al. (2001)[4] for ultrafine-grained titanium and by Wang et al. (2007) [5] 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. Keywords:Elasto-viscoplasticity, ultrafine-grained titanium, uniaxial compression Affiliations:
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2. | Nowak Z., Perzyna P., The Identification Procedure for the Constitutive Model of Elasto-Viscoplasticity Describing the Behaviour of Nanocrystalline Titanium, SolMech 2012, 38th Solid Mechanics Conference, 2012-08-27/08-31, Warszawa (PL), pp.94-95, 2012 | |||||||

3. | Nowak Z., Perzyna P., The identification procedure for the constitutive model of elasto–viscoplasticity with microdamage and dynamic grain growth mechanisms describing the behaviour of nanocrystalline iron, CMM 2011, 19th International Conference on Computer Methods in Mechanics, 2011-05-09/05-12, Warszawa (PL), pp.385-1-2, 2011 |