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1

Accounting for the random character of nucleation in the modelling of phase transformations in steels

Poloczek Łukasz, Kuziak Roman, Foryś Jakub, Szeliga Danuta, Pietrzyk Maciej

Computer Methods in Materials Science

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2023

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Vol. 23, No. 2

17--28

EN

In our earlier work, a stochastic model of multi-stage deformation at elevated temperatures was developed. The model was applied to calculate histograms of dislocation density and grain size at the onset of phase transformation. The histograms were used as input data for the simulation of phase transitions using the traditional deterministic model. Following this approach, microstructural inhomogeneity was predicted for different cooling conditions. The results obtained, showing the effect of dislocation density and inhomogeneity of austenite grain size on the microstructural inhomogeneity of the final product, can be considered reliable as they are based on material models determined in previous publications and validated experimentally. The aim of the present work was to extend the model by taking into account the stochastic nature of nucleation during phase transitions. The analysis of existing stochastic models of nucleation was performed, and a model for ferritic transformation in steels was proposed. Simulations for constant cooling rates as well as for industrial cooling processes of steel rods were performed. In the latter case, uncertainties in defining the boundary conditions and segregation of elements were also considered. The reduction of the computing costs is an important advantage of the model, which is much faster when compared to full field models with explicit microstructure representation.

2

Tribological properties of hybrid aluminium matrix composites reinforced with boron carbide and ilmenite particles for brake rotor applications

Gupta Rahul, Nanda Tarun, Pandey O. P.

Archives of Civil and Mechanical Engineering

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2023

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Vol. 23, no. 1

art. no. e47, 2023

EN

In the present study, stir casting process was employed to incorporate a blend mixture of ilmenite (FeTiO3) and boron carbide (B4C) particles in the matrix of LM13 base alloy. The study demonstrated the effect of individual reinforcement, weight percentage and mixing proportion on wear behaviour of LM13 alloy for brake rotor applications. Composite with 15 wt.% of reinforcement having 75% proportion of boron carbide (15BI-31 composite) shows change in silicon morphology to globular and highest refinement of silicon structure. Highest wear resistance, highest hardness, lowest coefficient of thermal expansion and lowest friction coefficient values were obtained for 15BI-31 composites. The addition of ilmenite particles enhances the properties of BI composites by making the strong interfacial bonding and enhancing the oxidation rate of sliding surface. However, the increase in dislocation density by boron carbide particles helps in enhancing the hardness of composites which contributes in providing the stability to mechanical mixed layer. The comparable wear property (17% higher wear rate), low processing cost and low material cost of 15BI-31 composite make it a suitable material for brake rotor applications. The predominant wear mechanism for composites was observed to be abrasive wear and delamination wear. However, the severity of wear mechanism changes as the applied load increases.

3

Internal Friction Study on the Influence of Pre-Deformation on Hydrogen Embrittlement Sensitivity of Dual-Phase Steel

Pang Qihang, Geng Cong, Wang Jiaji, Li Weijuan, Guo Jing, Yu Xiaoming

Archives of Metallurgy and Materials

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2022

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Vol. 67, iss. 4

1315--1324

EN

In this study, an electrochemical method was used to permeate hydrogen through annealed DP590 steel under various pre-strain conditions (0-15%). Stress-strain and internal friction-temperature curves of the dual phase (DP) steel were obtained from slow strain-rate tensile tests and internal friction measurements, respectively. The diffusion of interstitial atoms, formation of Cottrell atmospheres, and embrittlement mechanism of DP steel were investigated under different prestress conditions before and after hydrogen permeation. The results show that the tensile strength of DP steel first decreases and then increases and the elongation sharply decreases with increasing pre-strain. The strength and ductility present similar trends with changes in pre-strain before and after hydrogen charging, however, after hydrogen charging, an obvious increase in tensile strength and decrease in elongation are observed. Furthermore, the γ peak amplitude decreases and the Snoek-Ke-Koster (SKK) peak amplitude increases with increasing internal pre-strain according to the friction-temperature curve. The γ peak and SKK peak exhibit the same trends with increasing pre-strain before and after hydrogen charging and both the γ peak and SKK peak decrease with hydrogen charging. The dislocation density in DP steel increases after hydrogen charging.

4

Use of computer modeling for defect engineering in Czochralski silicon growth

Artemyev Vladimir, Smirnov Andrey, Kalaev Vladimir, Mamedov Vasif, Sid'ko A., Wejrzanowski Tomasz, Grybczuk Mateusz, Dold Peter, Kunert Roland

Journal of Power Technologies

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2019

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Vol. 99, nr 2

163--169

EN

The yield and quality of silicon wafers are mostly determined by defects, including grain boundaries, dislocations, vacancies, interstitials, and vacancy and oxygen clusters. Active generation and multiplication of dislocations during Czochralski monosilicon crystal growth is almost always followed by a transition to multicrystalline material and is called structure loss. Possible factors in structure loss are related to high thermal stresses, fluctuations of local crystallization rate caused by melt flow turbulence, melt undercooling and incorporation of solid particles from the melt into the crystal. Experimental analysis of dislocation density distributions in grown crystals contributes to an understanding of the key reasons for structure loss: particle incorporation at the crystallization front and strong fluctuations of crystallization rate with temporal remelting. Comparison of experimental dislocation density measurements and modeling results calculated using the Alexander-Haasen model showed good agreement for silicon samples. The Alexander-Haasen model provides reasonably accurate results for dislocation density accompanying structure loss phenomena and can be used to predict dislocation density and residual stresses in multicrystalline Czochralski silicon ingots, which are grown for the purpose of manufacturing polysilicon rods for Siemens reactors and silicon construction elements.

5

Flow stress under cyclic deformation conditions – modelling possibilities

Graca P., Muszka K., Majta J.

Computer Methods in Materials Science

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2013

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Vol. 13, No. 3

275--281

EN

This paper presents and discusses some aspects of the computer modelling of mechanical response of the high strength low alloy steels subjected to deformation processes where significant cyclic strain path changes exist. The proper choice of the work hardening model for the cyclic plastic deformation is essential for predicting the inhomogeneities occurring during metal forming. Aim of the current work is to discuss the differences between various hardening models with respect to their capabilities in capturing complex deformation models. Application of such models to simulate various simple plastometric tests, such as cyclic compression/tension and cyclic torsion are presented. Finally, based upon results obtained in both of the analyzed simulations, conclusions regarding the possibilities of potential application of the investigated tests in the identification process of hardening model parameters, trough the inverse analysis, are drawn.

PL

W pracy omówiono aspekty dotyczące modelowania komputerowego podczas odkształcania stali mikrostopowej o podwyższonych własnościach wytrzymałościowych przeprowadzanych z wykorzystaniem procesów charakteryzujących się zmienną ścieżką odkształcenia. Właściwy dobór modelu naprężenia uplastyczniającego do opisu zachowania się materiału podczas odkształceń cyklicznych jest niezbędny do właściwego przewidywania niejednorodności odkształcenia spowodowanej występowaniem zmiennej ścieżki odkształcania. Celem pracy jest omówienie różnic pomiędzy modelami umocnienia w odniesieniu do ich możliwości w zakresie prawidłowego odzwierciedlenia realnych procesów obejmujących zastosowanie odkształceń cyklicznych. W artykule zostało przedstawione zastosowanie tego typu modeli do symulacji prostych testów plastometrycznych, takich jak: cykliczne skręcanie próbki oraz cykliczne ściskanie/ rozciąganie próbki. Wyniki wszystkich symulacji poddano szczegółowej analizie I na tej drodze sformułowano wnioski dotyczące wykorzystania prezentowanych testów podczas identyfikacji parametrów modeli umocnienia dla odkształceń cyklicznych z wykorzystaniem analizy odwrotnej.

6

Rozwój modelu naprężenia uplastyczniającego opartego na zmiennych wewnętrznych

Nowak J., Svyetlichnyy D., Łach Ł., Pidvysotskyy V.

Rudy i Metale Nieżelazne

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2011

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R. 56, nr 11

617-623

PL

W artykule przedstawiono model naprężenia uplastyczniającego opierającego się na teorii dyslokacji z uwzględnieniem rekrystalizacji. Model składa się z dwóch części: klasycznego modelu rozwoju dyslokacji oraz modelu rekrystalizacji. Druga część bierze pod uwagę różne rodzaje rekrystalizacji i rozpatruje te procesy jako jeden, który zawiera procesy zarodkowania nowych ziaren oraz ich rozrost. Wyniki identyfikacji parametrów modelu oraz symulacje pokazano w artykule. Rozważono wady modelu i przedstawiono propozycje poprawek do modelu. Zaprezentowano również wyniki wstępnych symulacji.

EN

In the paper a flow stress model based on the dislocation theory in consideration of the recrystallization is briefly presented. The model consists of two parts: the classic model of the dislocation evolution and recrystallization model. The latter deal with various types of recrystallization as the same process rooted in nucleation and grain growth. The results of the model parameters identification and the simulation are presented in this paper. Then disadvantages of the model are considered and new proposal for improvement the model are presented. The results of preliminary simulation are presented as well.

7

Modelowanie zmian struktury podczas odkształcania plastycznego na gorąco metodą automatów komórkowych

Kuc D., Gawęd J.

Hutnik, Wiadomości Hutnicze

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2009

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Vol. 76, nr 8

601-603

PL

W artykule przedstawiono model wieloskalowy (CAFE), który opisuje zmiany struktury w warunkach ciągłego odkształcenia oraz umożliwia obliczenie krzywych płynięcia. Do opracowania modelu zmian struktury wykorzystano metodę automatów komórkowych CA. Model zmian naprężenia uplastyczniającego bazuje na średniej gęstości dyslokacji wyznaczonej z siatki CA. Opracowany model zweryfikowano w oparciu o wyznaczone krzywe płynięcia wyznaczone dla stali austenitycznej X3CrNi18-9 i badania struktury z wykorzystaniem mikroskopii świetlnej i zaawansowanych technik mikroskopii elektronowej – transmisyjnej oraz EBSD. Naprężenie uplastyczniające zostało obliczone z wykorzystaniem metody inverse na podstawie danych uzyskanych z prób osiowosymetrycznego ściskania.

EN

The paper is focused on application of multi-scale 2D method. Model approach consists of Cellular Automata (CA) model of microstructure development and the thermal-mechanical finite element (FE) code. Dynamic recrystallization phenomenon is taken into account in 2D CA model which takes advantage of explicit representation of microstructure, including individual grains and grain boundaries. Flow stress is the main material parameter in mechanical part of FE and is calculated on the basis of average dislocation density obtained from CA model. The results attained from the model were validated with the experimental data. In the present study, austenitic steel X3CrNi18-9 was investigated. Light microscopy and EBSD analyses were performed for the initial and final microstructures of the samples. Compression forces were recorded during the tests and flow stresses were determined using inverse method.

8

Effective dislocation lines in continuously dislocated crystals. III. Kinematics

Trzęsowski A.

Journal of Technical Physics

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2008

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Vol. 49, no 2

79-99

EN

A class of congrunces of principal Volterra-type effective dislocation lines associated with a dislocation density tensor is distinguished in order to investigate the kinematics of continuized defective crystals in terms of their dislocation densities (tensorial as well as scalar). Moreover, it is shown, basing oneself on a formula defining the mean curvature of glide surfaces for principal edge effective dislocation lines, that the considered kinematics of continuized defective crystals is consistent with some relations appearing in the physical theory of plasticity (e.g. with the Orowan-type kinematic relations and with treatment of the shear stresses as driving stresses of moving dislocations).

9

Effective dislocation lines in continuously dislocated crystals. II. Congruences of effective dislocations

Trzęsowski A.

Journal of Technical Physics

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2008

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Vol. 49, no 1

53-74

EN

The notion of a congruence of effective dislocation lines endowed with the nonvanishing local Burgers vector is introduced. Particularly, the class of congrunces of principal Volterra-type effective dislocation lines associated with the dislocation densities (tensorial as well as scalar) is distinguished in order to investigate the geometry of continuized defective crystals in terms of these densities. It is shown that effective dislocation lines can be endowed with the dislocation line tension and with a finite self-energy.

10

Effective dislocation lines in continuously dislocated crystals. I. Material anholonomity

Trzęsowski A.

Journal of Technical Physics

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2007

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Vol. 48, no 3-4

193-214

EN

A continuous geometric description of Bravais monocrystals with many dislocations and secondary point defects created by the distribution of these dislocations is proposed. Namely, it is distinguished, basing oneself on Kondo and Kröner's Gedanken Experiments for dislocated bodies, an anholonomic triad of linearly independent vector fields. The triad defines local crystallographic directions of the defective crystal as well as a continuous counterpart of the Burgers vector for single dislocations. Next, the influence of secondary point defects on the distribution of many dislocations is modeled by treating these local crystallographic directions, as well as Burgers circuits, as those located in such a Riemannian material space that becomes an Euclidean 3-manifold when dislocations are absent. Some consequences of this approach are discussed.

11

Simulation of dynamic recrystallization using random grid cellular automata

Yazdipour N., Davies C., Hodgson P.

Computer Methods in Materials Science

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2007

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Vol. 7, No. 1

175-181

EN

Computer simulation is a powerful tool to predict microstructure and its evolution in dynamic and post-dynamic recrystallization. CAFE proposed as an appropriate approach by combining finite element (FE) method and cellular automata (CA) for recrystallization simulation. In the current study, a random grid cellular automaton (CA), as micro-scale model, based on finite element (FE), as macro-scale method, has been used to study initial and evolving microstructural features; including nuclei densities, dislocation densities, grain size and grain boundary movement during dynamic recrystallization in a C-Mn steel. An optimized relation has been established between mechanical variables and evolving microstructure features during recrystallization and grain growth. In this model, the microstructure is defined as cells located within grains and grain boundaries while dislocations are randomly dispersed throughout microstructure. Changes of dislocation density during deformation are described considering hardening, recovery and recrystallization. Recrystallization is assumed to initiate near grain boundaries and nucleation rate was considered constant (site-saturated condition). The model produced a mathematical formulation which captured the initial and evolving microstructural entities and linked their effects to measurable macroscopic variables (e.g. stress).

PL

Symulacje komputerowe są doskonałym narzędziem umożliwiającym przewidywanie rozwoju mikrostruktury podczas rekrystalizacji dynamicznej. Automaty komórkowe są jedną z najbardziej efektywnych metod symulowania zjawisk fizycznych zachodzących podczas rekrystalizacji i rozrostu ziaren. W niniejszym artykule obydwa wymienione zjawiska zostały zamodelowane przy wykorzystaniu dwuwymiarowej siatki automatów komórkowych. Dane takie jak czas, wstępna wielkość ziaren oraz wstępna gęstość zarodkowania zostały wykorzystanie do walidacji modelu jako zmienne modelu JMAK (Johnson, Mehl, Avrami, i Kolmogorov). Zgodnie z przyjętymi założeniami, automaty komórkowe okazały się być dogodnym narzędziem symulacji zjawiska dynamicznej rekrystalizacji.

12

Effect of high strain rate on the dislocation structure of microalloved and if steels

Stefańska-Kądziela M., Majta J., Dymek S., Muszka K.

Archives of Metallurgy and Materials

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2007

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Vol. 52, iss. 2

223-229

EN

The problem of quality and quantity evaluation of dislocation structure under very high strain rates was analyzed. The investigation was performed for two steels of common application: high strength microalloyed Nb(Y) steel and interstitial free (IF) steel. Investigation of microalloyed steel allowed the analysis of dislocation structure evolution in strengthened material (both via precipitations and solid solution). In such conditions, the dislocation movement is difficult and forming substructures are significantly different from those observed in IF steel. In present studies, for suitable evaluation of dislocation structure, an attempt of modification of existing relationships was made. Bergstr¨om’s proposition was utilized and relationships between dislocation cell size and mean dislocation density were determined. The axisymmetrical compression tests were performed with different strain rates at room temperature using static and dynamic testing machines and dropweight. The analysis of microstructure of deformed materials was also performed using transmission electron microscopy (TEM). The estimation of the effect of strain rate on microstructure evolution and, first of all, on dislocation cell structure, was made. It was observed that dislocation structure evolution depends on thermomechanical history of deformed material, strain and strain rate. On the basis of measurements and characteristics of dislocation structure and using B e r g s t r ¨o m’s model it is possible to determine the total dislocation density, taking into account basic process parameters including strain rate under dynamic loading conditions. Obtained results showed a good accuracy of established model to estimate dislocation density on the basis of dislocation cell size.

PL

W pracy podjęto problem oceny jakościowej i ilościowej struktury dyslokacyjnej powstałej w wyniku zastosowania bardzo dużych prędkości odkształcenia. Badania przeprowadzono dla dwóch szeroko stosowanych gatunków stali: mikrostopowej o podwyższonej wytrzymałości (Nb(Y)) oraz IF. Badanie stali mikrostopowej umożliwiło przeprowadzenie analizy rozwoju struktury dyslokacyjnej w materiale umocnionym wydzieleniowo oraz przez roztwór stały. W takich warunkach przemieszczanie się dyslokacji jest utrudnione, a tworzące się podstruktury różnią się znacząco od tych obserwowanych w stali IF. Dla właściwej oceny struktury dyslokacyjnej w obecnych badaniach podjęto próbę modyfikacji istniejących zależności. Wykorzystując propozycje Bergstr¨oma, wyznaczono związki pomiędzy wielkością komórek dyslokacyjnych a średnią wartością gęstości dyslokacji. Przeprowadzono testy osiowosymetrycznego spęczania z różnymi prędkościami odkształcenia, w temperaturze pokojowej przy użyciu statycznej i dynamicznej maszyny wytrzymałościowej oraz młota spadowego. Odkształcony materiał poddano badaniom mikrostruktury z wykorzystaniem mikroskopii elektronowej. Ocenie poddano wpływ prędkości odkształcenia na rozwój mikrostruktury, w tym przede wszystkim na strukturę komórkową. Zaobserwowano, że rozwój struktury dyslokacyjnej uzależniony jest od rodzaju odkształcanego materiału oraz wielkości i prędkosci odkształcenia. Na podstawie pomiarów i charakterystyki struktury dyslokacyjnej oraz wykorzystując wzór B e r g s t r ¨o m a można wyznaczyć całkowitą gśstość dyslokacji z uwzględnieniem podstawowych parametrów procesu, w tym z uwzględnieniem prędkości odkształcenia w dynamicznych warunkach obciążenia. Otrzymane wyniki wskazują na poprawność przyjętego modelu do oceny gęstości dyslokacji na podstawie pomiarów wielkości komórek dyslokacyjnych.

13

Porównanie modeli naprężenia uplastyczniającego

Svyetlichnyy D., Pidvysotskyy V.

Rudy i Metale Nieżelazne

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2005

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R. 50, nr 10-11

560-566

PL

W artykule przedstawiono dwa modele naprężenia uplastyczniającego. Pierwszy z nich opracowany został przez Sellarsa i jego współpracowników, zaś drugi, dwuczęściowy model, oparty jest na teorii dyslokacji oraz teorii rekrystalizacji Kołmogorowa-Johnsona-Mehla-Avra- miego. Są to modele naprężenia uplastyczniającego jak też powstawania mikrostruktury. Naprężenie uplastyczniające oblicza się w oparciu o znajomość gęstości dyslokacji. Model dyslokacyjny uwzględnia zjawiska utwardzenia, zdrowienia i rekrystalizacji zachodzące podczas odkształcania. Model rekrystalizacji nie bierze pod uwagę różnic typów rekrystalizacji, traktując je jako taki sam proces oparty na zarodkowaniu i rozroście ziaren. W artykule przedstawiono wyniki wyznaczania parametrów obydwu modeli naprężenia uplastyczniającego. Potrzebne do tego celu dane otrzymano z prób plastometrycznych przeprowadzonych w IMŻ w Gliwicach przy użyciu symulatora Gleeble-3800. Dokonano też porównania i analizy otrzymanych wyników.

EN

The paper deals with two models of flow stress. The first one is a model developed by Sellars with co-workers. The second one based on dislocation theory and Kolmogorov-Johnson-Mehl-Avrami recrystallization theory consists of two parts. They are models of flow stress and microstructure development. Flow stress is calculated using dislocation density. During the deformation process the dislocation model takes into account hardening, recovery and recrystallization. The recrystallization model does not distinguish different kinds of recrystallization. It considers them as the same process rooted in nucleation and grain growth. In the paper are presented results of identification of parameters of both flow stress models. Plastometric test data for identification were obtained using Gleeble-3800 simulator in IMŻ (Gliwice). Comparison and analysis of the results were carried out as well.

14

Dislocation dynamics and related electromagnetic excitation

Teisseyre R.

Acta Geophysica Polonica

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2001

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Vol. 49, nr 1

55-73

EN

Theory of stress and dislocation evolution is based on the equation of motion for the self-stresses on the slip-fault plane; this equation is supplemented with the source/sink function entering in a similar way as the body forces in the equation of motion for displacements. We present the effects of dislocation dynamics on generation of electric current and electromagnetic field emission.

15

Stress and dislocation field evolution and prediction problems of numerically simulated events

Teisseyre R., Yamashita T.

Acta Geophysica Polonica

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2000

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Vol. 48, nr 1

43-56

EN

Numerical simulations of the dislocation density evolution exhibit some perturbations which may be identified as seismic events. The influences of tidal stresses and random disturbances related to the material heterogeneities are analyzed. In relation to this analysis some problems of earthquake prediction and earthquake precursors are discussed. Occurrences of seismic events are very sensitive to small disturbances, while the great disturbances in tidal influence or in material properties cause the disappearance of the events.

16

Splitting stress motion equation into seismic wave and fault-related fields

Teisseyre R., Yamashita T.

Acta Geophysica Polonica

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1999

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Vol. 47, nr 2

135-137

EN

Considering elastic continuum with defects (strictly speaking: continuum with a continuous distribution of the self-strain nuclei, like in thermo-elastic or elasto-plastic bodies), we have to consider the elastic and self parts of the total strain and stress fields. Accordingly, we can split the motion equations (as expressed for stresses) into a wave field and a fault-related field, assuming that the self stresses play a decisive role on a fault. We show that the fault constitutive equation is a special case of the motion equation. The fault-related equation can be transformed into equation for dislocation density, identical with the 1D equation for evolution of dislocation field equivalent to the commonly considered fault slip constitutive equation. We discuss the fault equation as expressed in terms of dislocation field and we consider the static and dynamic approximations. Static approximation relates to the early phases: the infaltion phase from dislocation stress resistance to friction (phase characterized by an exponential decrease of stress resistance which corresponds to dislocation velocity increase in the expotential creep) and the fracture slip nucleation phase (governedby slip weakening law). Dynamic approximation relates to the slip propagation phase (governed by slipp velocity weakening law). Instead of the instability source introduced by the friction weakening laws for all these phases, we might introduce the source/sink function; such a function should first of all describe the coalescence processes between the dislocations of opposite sings (such an elementary process preserves material continuity) and also between the dislocation arrays of opposite sings (such a coalescence of the arrays can well describe a nucleation process of a crack-material fracturing, or/and a coalescence of two cracs).When the put this function proportional to a stress surface curvature, or equivalently a gradient of dislocation density on a fault, it will represent an inverse of a mean distance between the opposite dislocation groups; we image, in this way, and ability to create a coalescence process - and instability. Atraction forces between the opposite dislocations can effectively produce a weaking effect, making it easier for a dislocation (or crack) to propagate. Some exaples of the numerical solutions for stresses on a fault with the spontaneously simulated seismic events are discussed. From the fault solution we obtain an evolution pattern of a dislocation field; the respective values on a fault plane may then serve as the boundary conditions to slove the wave part equation for stresses in the 2D space and time domain.

17

Continuum theory of defects and gravity anomaly

Yamasaki K., Nagahama H.

Acta Geophysica Polonica

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1999

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Vol. 47, nr 3

239-257

EN

Based on the mathematical equivalence between the crack field and the continuous dislocation field, we briefly review continuum theory of defects from the view point of differential geometry. Then we derive a new differential geometric equation of static gravity change for anelastic effect due to the fault (dislocation) density. This equation shows that high gradient of dilatancy caused by the concentration of fault (dislocation) density accompanies high gradient of gravity change near the boundary between positive and negative gravity anomalies. This agrees with the characteristic distribution patterns; the distribution of short-wavelength gravity anomaly, active faults and shallow seismic activities overlap one another in the northeast Japan. Moreover, we discuss: (I) dynamic gravity anomaly related to earthquakes; (II) local gravity anomaly near the edges of an active fault; (III) differential geometric interpretation of gravity anomaly caused by the dislocation density; (IV) differential geometric relationship between gravity anomaly and magnetic anomaly (Poisson's relation).

18

Dislocation field evolution and dislocation source/sink function

Teisseyre R., Nagahama H.

Acta Geophysica Polonica

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1998

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Vol. 46, nr 1

13-33

EN

The evolution of dislocation density field depends on the source/sink function; this function describes the nucleation of new dislocations and the coalescence processes (mutual annihilation of dislocations having the opposite signs which is equivalent to coalescence of two neighbouring dislocated elements or coalescence of two co-planar cracks). In this paper we discuss the choice of this function, we present the solutions for dislocation field and stresses and we discuss the obtained results, especially the short period perturbations (seismic events) related to the extrema and sign changes of the source/sink function. General discussion on the source/sink function for dislocation fields closes this paper.