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1

Theoretical predictions on the influence of moisture on movements of wooden construction elements

Grobelny P., Dornowski W.

Biuletyn Wojskowej Akademii Technicznej

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2018

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Vol. 67, nr 1

175--184

EN

The paper presents a method for determining the creep function of wood. A key feature of this method is a constitutive relation which includes the continuous effect of wood moisture on creep. The method can be applied to improve the precision of design of wooden structures as well to assess the safety of biodegraded (biologically corroded) structural elements fabricated from wood.

PL

W artykule przedstawiono metodę wyznaczania funkcji pełzania dla drewna. Kluczową rolę w tej metodzie pełni relacja konstytutywna, uwzględniająca w sposób ciągły wpływ zmiany wilgotności drewna na pełzanie. Rozważana metoda może być wykorzystana w bardziej precyzyjnym projektowaniu konstrukcji drewnianych, jak również przy ocenie bezpieczeństwa elementów konstrukcyjnych skorodowanych biologicznie.

2

A general theoretical formulation of deformation of steel structures exposed to fire

Badowski A., Dornowski W.

Biuletyn Wojskowej Akademii Technicznej

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2018

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Vol. 67, nr 2

63--75

EN

This paper presents a proposal for the formulation of a mathematical model of a fire resistance testing process for steel beams subject to bending, carried out experimentally in a test furnace. The model for the formulation was created with a balance method by describing with the fundamental laws of thermomechanics the phenomena occurring during the experiment analysed for the formulation. The viscoplastic behave our of steel at high temperatures was described with constitutive relationships proposed by Perzyna (which form the so-called “overload model”). The general mathematical model of the experiment analysed, obtained in the form of a system of differential equations, is discussed. The authors considered the impact of known physical properties of the test material and the impact of the results of the observations made during the research on the behaviour of individual terms of the model’s equations. Based on these considerations, simplifications were proposed which optimized the mathematical description and facilitated its adaptation to a special case. As a result of the investigation, a system of equation was obtained which described the processes present during the fire resistance test. It is postulated here to accept the system of equations as the mathematical model.

PL

W artykule przedstawiono propozycję sformułowania modelu matematycznego procesu badania nośności ogniowej stalowych belek zginanych, przeprowadzanego w piecu ogniowym. W celu opracowania tego modelu posłużono się metodą bilansową, opisując zjawiska zachodzące w trakcie analizowanego eksperymentu za pomocą podstawowych praw termomechaniki. Zachowanie lepkoplastyczne stali w wysokich temperaturach zmiennych w czasie opisano, używając związków konstytutywnych zaproponowanych przez Perzynę (tzw. model „przeciążeniowy”). Uzyskany w postaci układu równań różniczkowych ogólny model matematyczny analizowanego eksperymentu poddano dyskusji. Rozważono wpływ znanych właściwości fizycznych materiału i wyników obserwacji dokonanych w czasie badań na zachowania poszczególnych składników równań modelu. W efekcie zaproponowano uproszczenia umożliwiające zoptymalizowanie opisu matematycznego i jego dostosowanie do rozważanego przypadku szczególnego. Jako rezultat przeprowadzonych dociekań uzyskano układ równań opisujący procesy zachodzące w badaniu ogniowym, który postuluje się przyjąć jako jego model matematyczny.

3

Analiza wzmocnionej belki drewnianej pod obciążeniem dynamicznym

Pogonowska S., Dornowski W.

Materiały Budowlane

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2017

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nr 7

61--62

PL

W artykule przedstawiono wybrane rezultaty numerycznej analizy drgań belki drewnianej wzmocnionej prętami stalowymi, poddanej obciążeniu dynamicznemu. Analizowano zakres tzw. umiarkowanie dużych ugięć. Zróżnicowane cechy mechaniczne materiału belki uwzględniono na etapie wyznaczania sił wewnętrznych, wprowadzając odpowiednie uwarstwienie przekroju. W analizie numerycznej wykorzystano metodę różnicową z jawnym schematem całkowania względem czasu. W przykładzie obliczeniowym analizowano wpływ zbrojenia na nośność i sztywność belki oraz na podstawowe parametry dynamiczne. W przypadku stali i drewna przyjęto sprężysto-idealnie plastyczny model materiału.

EN

This paper presents the solution of the numerical analysis for wooden beam reinforced with steel rods and loaded dynamically. The moderately large deformation is analyzed. The variation of material properties in the cross section is included during the integration of the internal forces. This effect was obtained by specification appropriate layers in the beam cross section. The finite difference method with explicit time integration scheme is used in the numerical analysis. The numerical example is given, in which the influence of the reinforcement for the load capacity and stiffness of the beam, as well as, the basic dynamic properties is analyzed. For both materials – reinforced steel and wood, the elastic perfectly plastic model is used.

4

Reakcja dynamiczna belek drewnianych wzmocnionych prętami stalowymi w zakresie umiarkowanie dużych ugięć

Pogonowska S., Dornowski W.

Inżynieria i Budownictwo

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2017

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R. 73, nr 2

67--71

PL

W analizie zróżnicowanie właściwości odkształceniowych materiału w przekroju belki uwzględniono na etapie całkowania sił wewnętrznych, wprowadzając odpowiednie uwarstwienie przekroju. Wykorzystano metodę różnicową z jawnym schematem całkowania względem czasu. Podano kryterium oszacowania wartości krytycznej kroku czasowego. W przykładzie obliczeniowym analizowano wpływ zbrojenia na nośność i sztywność belki oraz na podstawowe parametry dynamiczne.

EN

In the analysis the variation of material properties in the cross section is included during the integration of internal forces. This effect was obtained by specification appropriate layers in the beam cross section. The finite difference method with explicit time integration scheme is used in the numerical analysis. Due to the conditional stability of the proposed method, the criterion for estimating the value of the critical time step is applied. The numerical example is given, in which the influence of the reinforcement for the load capacity and stiffness of the beam, as well as, the basic dynamic properties is analyzed.

5

Opis konwekcyjny kinematyki sprężysto-plastycznych deformacji skończonych

Dornowski W.

Biuletyn Wojskowej Akademii Technicznej

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2016

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Vol. 65, nr 1

69--87

PL

W pracy przedstawiono opis konwekcyjny kinematyki sprężysto-plastycznych deformacji skończonych. Proponowane podejście jest bardzo użyteczne z punktu widzenia zastosowań numerycznych [4]. Podano reguły transformacyjne dla przestrzennych pól tensorowych obiektywnych ze względu na zmianę konfiguracji aktualnej opisaną odwzorowaniem dyfeomorficznym. Przy definiowaniu miar odkształceń niesprężystych wykorzystano pojęcie konfiguracji odciążonej. Zdefiniowany w tej konfiguracji tensor metryczny jest miarą deformacji plastycznej. Wykazano, że transformacje tego tensora do innych konfiguracji prowadzą do innych miar deformacji, lecz zawsze plastycznych. W ramach koncepcji obiektywności względem całkowitego ruchu ośrodka ciągłego wykazano tożsamość multiplikatywnego rozkładu gradientu deformacji sprężysto-plastycznej z addytywnymi rozkładami innych miar odkształcenia i prędkości odkształcenia sprężysto-plastycznego. Posługując się pojęciem funkcji energii swobodnej, zaproponowano pewne sformułowanie postulatu obiektywności materialnej dla struktury konstytutywnej z parametrami wewnętrznymi. Wykorzystując ten postulat, przedstawiono ogólną postać struktury konstytutywnej typu prędkościowego.

EN

The convective description of kinematics of finite elasto-plastic deformations is presented. From the numerical application point of view, such an approach is very useful [4]. It also leads to clear interpretation of the geometrical sense of tensor transformation. Transformation rules for the spatial tensor field objective at superposed spatial diffeomorphism are given. The local notion of the tangent space unloaded elastically is introduced. The metric tensor defined in this space is the purely plastic deformation measure. It is shown that transformation of this tensor to any other configuration leads to other deformation measures but ever plastic one. Within the limits of the concept of covariance it is shown that the additive decompositions, in which strains and their rates decompose additively into elastic and plastic parts, can be derived from the multiplicative decomposition of the deformation gradient. Using the free energy function, the formulation of material objectivity of the constitutive structure with a finite set of internal variables is proposed. Making use of this formulation, the general form of the rate type constitutive structure is presented.

6

Analiza falowa tarczy w płaskim stanie naprężenia metodą ruchomych, najmniejszych kwadratów

Dornowski W.

Biuletyn Wojskowej Akademii Technicznej

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2014

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Vol. 63, nr 3

189-206

PL

W pracy rozwiązano zadanie początkowo-brzegowe propagacji płaskiej fali naprężenia w tarczy stalowej metodą ruchomych najmniejszych kwadratów. Stosowano różne siatki węzłów. W przypadku siatek z węzłami generowanymi losowo istotne znaczenie ma wybór węzłów sąsiedztwa aproksymacyjnego. Przyjęto kryterium topologiczne wynikające z triangulacji zbioru węzłów, która minimalizuje łączną długość krawędzi triangulacji. Stwierdzono, że triangulacyjny sposób wyboru otoczenia aproksymacyjnego i wygładzanie siatki nieregularnej metodą Laplace’a znacznie poprawia dokładność rozwiązania. Efekt odbicia fali naprężenia od brzegu swobodnego modelowano przez wprowadzenie węzłów fikcyjnych (poza obszarem tarczy). Otrzymane rezultaty porównano z wynikami obliczeń metodą różnicową, stwierdzając ich zgodność jakościową i ilościową.

EN

A meshless method based on the moving least squares approximation is applied to stress wave propagation analysis. Two kinds of node meshes, the randomly generated mesh and the regular mesh are used. The nearest neighbours’ problem is developed from a triangulation that satisfies minimum edges length conditions. It is found that this method of neighbours’ choice significantly improves the solution accuracy. The reflection of stress waves from the free edge is modelled using fictitious nodes (outside the plate). The comparison with the finite difference results also demonstrated the accuracy of the proposed approach.

7

Numerical investigation of localized fracture phenomena in inelastic solids

Dornowski W., Perzyna P.

Foundations of Civil and Environmental Engineering

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2006

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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.

8

Investigation of macrocrack propagation along a bimaterial interface in adiabatic dynamic processes as a problem of mesomechanics

Dornowski W., Perzyna P.

Engineering Transactions

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2006

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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.

9

Numerical simulation of finite deformations of a dynamically loaded elasto-viscoplastic circular membrane

Dornowski W.

Engineering Transactions

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2003

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Vol. 51, iss.1

63-85

EN

The present paper deals with theoretical modeling and numerical simulation of a thin circular plate subjected to impulsive loading. To this end, the convective description is applied. The kinematical hypothesis used for theoretical description of the transient response includes membrane deformations only. This assumption is valid in the range of large deformations. The dynamical response of the material is described by Perzyna's elasto-viscoplastic constitutive relations. The theory is completed by an algorithm of the explicit finite difference method. With respect to the conditional stability of that method, the stability criterion is given. Basing on experimental data, an identification of material parameters is carried out. Some comparisons with the corresponding theoretical and experimental results are presented. Satisfactory agreement of the results has been found. Finally, an example of the plastic strain localization in a membrane is presented.

10

Localization and localized fracture phenomena in inealastic solids under cyclic dynamic loadings

Dornowski W., Perzyna P.

Foundations of Civil and Environmental Engineering

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2002

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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].

11

A new integration procedure for thermo-elasto-viscoplasticity

Dornowski W.

Archives of Mechanics

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2002

|

Vol. 54, nr 5-6

389-410

EN

A numerical integration algorithm for thermo-elasto-viscoplastic constitutive equations is presented. This algorithm satisfies the principle of material objectivity with respect to the total motion (translation, rotation and strain) of a material element. For this purpose, the properties of convective description are used. The explicit-implicit integration scheme for the plastic flow rule plays the crucial role in the proposed algorithm. The method of determining the stress state for inelastic deformations is based on the iterative solution of the dynamic yield condition with respect to the norm of the viscoplastic deformation rate tensor. The constitutive model being the subject of numerical analyses is described. Results of numerical calculations, which show an excellent performance of the proposed procedure, are presented.

12

Localization phenomena in thermo-viscoplastic flow processes under cyclic dynamic loadings

Dornowski W., Perzyna P.

Computer Assisted Mechanics and Engineering Sciences

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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.

13

Algorytm numerycznego całkowania równań konstytutywnych termo-sprężysto-lepkoplastyczności

Dornowski W.

Biuletyn Wojskowej Akademii Technicznej

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2000

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Vol. 49, nr 3

32-49

PL

W pracy przedstawiono algorytm numerycznego całkowania związków konstytutywnych termo-sprężysto-lepkoplastyczności, spełniający zasadę obiektywności materialnej z uwagi na całkowity ruch (translacja, obrót i odkształcenie) elementu konstrukcyjnego. Wykorzystano własności opisu konwekcyjnego. Istotą tego algorytmu jest mieszane ujęcie (jawno-niejawne) przyrostowego prawa płynięcia plastycznego. Sposób określania stanu naprężenia dla deformacji niesprężystej bazuje na iteracyjnym rozwiązaniu dynamicznego warunku plastyczności ze względu na normę tensora prędkości deformacji lepkoplastycznej. Omówiono model konstytutywny, który stanowi przedmiot analizy numerycznej. Zamieszczono rezultaty obliczeń numerycznych, ukazujące efektywność proponowanej procedury.

EN

In this paper a new numerical integration algorithm for thermo-elasto-viscoplastic constitutive equations is given. This algorithm satisfies the principle of material obiectivity with respect to the total motion (translation, rotation and strain) of a structural element. For this purpose, the properties of convective description are used. The explicit/implicit integration scheme for the plastic flow rule is the essential part of the proposed algorithm. The method of determining the stress state for inelastic deformations is based on the iterative solution of the dynamic vield condition with respect to the norm of the viscoplastic deformation rate tensor. The constitutive model being the subject of numerical analyses is described. Results of numerical calculations, which show an excellent performance of the proposed procedure, are included.

14

Influence of finite deformations on the growth mechanism of microvoids contained in structural metals

Dornowski W.

Archives of Mechanics

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1999

|

Vol. 51, nr 1

71-86

EN

In this paper an analysis of the growth mechanism of the single microvoid for finite deformations is presented. A hollow sphere model is assumed. Such a model has been considered in many previous papers, however on the assumption that the strains remain small. The material surrounding the microvoid is assumed to be work-hardening, viscoplastic, described by the constitutive equations formulated by PERZYNA [l]. Quantitative and qualitative distinctions between the presented solution and geometrically linear solution are discussed. On the basis of the obtained solution, constitutive functions of a certain damage evolution equation for the complex stress state have been identified. A numerical example of the fracture analysis for a structural element is presented.

15

Wpływ deformacji skończonych na mechanizm wzrostu mikrouszkodzeń w metalach konstrukcyjnych

Dornowski W.

Biuletyn Wojskowej Akademii Technicznej

|

1998

|

Vol. 47, nr 9

23-39

PL

W pracy przedstawiono analizę mechanizmu wzrostu pojedynczego mikrouszkodzenia dla odkształceń skończonych. Podstawę analizy stanowi model pustki kulistej, zawartej w sferycznym otoczeniu materialnym. Model ten był przyjmowany do rozważań w wielu wcześniejszych pracach, jednak przy założeniu odkształceń infinitezymalnych. Przyjęto, że materialne otoczenie mikrouszkodzenia podlega prawu płynięcia lepkoplastycznego Perzyny oraz nieliniowemu wzmocnieniu izotropowemu. Przeprowadzono ilościowe i jakościowe porównania z rozwiązaniem geometrycznie zlinearyzowanym. Na podstawie otrzymanego rozwiązania zidentyfikowano funkcje konstytutywne dla pewnego równania ewolucji mikrouszkodzeń w złożonym stanie naprężenia. Przedstawiono przykład zastosowania rozważanej koncepcji opisu procesu wzrostu w numerycznej analizie zniszczenia elementu konstrukcyjnego.

EN

Analysis is presented of growth mechanism of a single microvoid for finite strains. The basis of the analysis is a spherical void in a spherical surrounding material. This model was accepted for analysis in many previous papers however at infinitesimal strain. It is assumed that a surrounding material behaves according to the Perzyna viscoplastic flow rule and non linear isotropic hardening. The qualitative and quantitative comparison was carried out with geometrically linearized solution. On the basis of the obtained solution the constitutive functions have been identified for a certain equation of microvoid evolution in the complex stress state. An example is presented for application the discussed conception of the growth in the numerical analysis of a structural element fracture.

16

Model konstytutywny dla cyklicznie obciążonego materiału sprężysto-plastycznego z mikrouszkodzeniami

Dornowski W.

Biuletyn Wojskowej Akademii Technicznej

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1998

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Vol. 47, nr 2

95-117

PL

Praca jest próbą wykorzystania pewnych elementów modelu konstytutywnego Gursoa dla materiału porowatego, do opisu wybranych efektów obserwowanych w metalach obciążonych cyklicznie. W ramach struktury konstytutywnej z parametrami wewnętrznymi podano podstawowe równania fizyczne dla cyklicznie obciążonego materiału sprężysto-plastycznego z mikrouszkodzeniami. Efekt wzmocnienia-osłabienia plastycznego opisano nieliniowymi prawami wzmocnienia-osłabienia izotropowego i wzmocnienia kinematycznego. Proces wewnętrznego uszkodzenia i w konsekwencji zniszczenia materiału potraktowano jako rezultat lokalizacji odkształceń na poziomie mikrostrukturalnym. W opisie zjawiska powstawania i kumulacji uszkodzenia wykorzystano koncepcję skalarnego parametru uszkodzenia. Podano algorytm numerycznego całkowania równań konstytutywnych. Przedstawiono przykłady numeryczne, które wskazują na jakościowo poprawny opis cyklicznego wzmocnienia, osłabienia, pełzania oraz cyklicznego zmęczenia i zniszczenia materiału.

EN

This work is an attempt of application of certain elements of the Gurson constitutive model for a porous material, for description of the selected observed effects in the cyclic loaded metals. In the frame of constitutive structure with internal parameters the fundamental constitutive equations are presented for the cyclic loaded elastic-plastic material with microdamages. The plastic hardening-softening effect is described by using the nonlinear rules of isotropic hardening-softening and kinematic hardening. The intrinsic damage process and as a result the material fracture was regarded as a result of localization of strains at the microstructure level. In the description of the appearance and cumulating of a damage the concept of the scalar damage parameter was used. The numerical integration algorithm for integration of constitutive equations is presented. The numerical examples are presented, which indicate the qualitative correctness of the cyclic hardening, softening, creep and cyclic fatigue and fracture of the material.