The thermodynamical theory of elasto-viscoplasticity accounting for microshear banding and induced anisotropy effects

• Autorzy: Perzyna P.

Warianty tytułu

PL

Termodynamiczna teoria sprężysto-lepkoplastyczności uwzględniająca efekty mikropasm ścinania oraz indukowanej anizotropii

• Języki publikacji: EN

Abstrakty

EN

The main objective of the present paper is the development of thermo-elasto-viscoplastic constitutive model of a material which takes into consideration induced anisotropy effects as well as observed contribution to strain rate effects generated by microshear banding. Physical foundations and experimental motivations for both induced anisotropy and microshear banding effects have been presented. The model is developed within the thermodynamic framework of the rate type covariance constitutive structure with a finite set of the internal state variables. A set of internal state variables consists of one scalar and two tensors, namely the equivalent inelastic deformation e/p the second order microdamage tensor [symbol] with the physical interpretation that ([formula]) defines the volume fraction porosity and the residual stress tensor (the backstress) alpha. The equivalent inelastic deformation [symbol] describes the dissipation effects generated by viscoplastic flow phenomena, the microdamage tensor [symbol] takes into account the anisotropic intrinsic microdamage mechanisms on internal dissipation and the back stress tensor alpha aims at the description of dissipation effects caused by the kinematic hardening. To describe suitably the influence of both induced anisotropy effects and the stress triaxiality observed experimentally the new kinetic equations for the microdamage tensor [symbol] and for the back stress tensor alpha are proposed. The relaxation time Tm is used as a regularization parameter. To describe the contribution to strain rate effects generated by microshear banding we propose to introduce certain scalar function which affects the relaxation time Tm in the viscoplastic flow rule. Fracture criterion based on the evolution of the anisotropic intrinsic microdamege is formulated. The fundamental features of the proposed constitutive theory have been carefully discussed. The purpose of the development of this theory is in future applications for the description of important problems in modem manufacturing processes, and particularly for meso-, micro-, and nano-mechanical issues. This description is needed for the investigation by using the numerical methods how to avoid unexpected plastic strain localization and localized fracture phenomena in new manufacturing technology.

PL

Głównym celem obecnej pracy jest opracowanie termo-sprężysto-lepkoplastycznego modelu konstytutywnego materiału, który uwzględnia efekty indukowanej anizotropii, jak również wpływ na wrażliwość materiału, prędkość deformacji spowodowanej tworzeniem się mikropasm ścinania. Przedstawiono fizykalne podstawy oraz eksperymentalne motywacje dla efektów wywołanych przez obydwa rodzaje indukowanych anizotropii oraz przez tworzenie się mikropasm ścinania. Model materiału został opracowany w ramach termodynamicznej, kowariantnej struktury konstytutywnej typu prędkościowego ze skończonym zbiorem parametrów wewnętrznych. Przyjęto, że zbiór parametrów wewnętrznych składa się z jednej wielkości skalarnej i dwóch tensorów, mianowicie z ekwiwalentnej niesprężystej deformacji e/p, tensora mikrouszkodzeń drugiego rzędu [symbol] (z fizykalną interpretacją, że ([wzór]) definiuje objętościowy udział porowatości) oraz tensora naprężeń resztkowych alfa. Ekwiwalentna niesprężysta deformacja [symbol] opisuje efekty dyssypacji generowane przez zjawisko lepkoplastycznego płynięcia, tensor mikrouszkodzeń [symbol] uwzględnia anizotropowe mechanizmy wewnętrznego mikrouszkodzenia w opisie wewnętrznej dyssypacji, natomiast tensor alfa opisuje efekty dyssypacji wywołane kinematycznym wzmocnieniem materiału. Aby opisać wpływ efektów obydwu indukowanych anizotropii i uwzględnienia efektów trójosiowości stanu naprężenia zaobserwowanych doświadczalnie zaproponowano nowe równanie kinetyczne dla tensora mikrouszkodzenia [symbol] i dla tensora naprężeń resztkowych alfa. Czas relaksacji Tm został wykorzystany jako parametr regularyzacji. Aby opisać udział wrażliwości materiału na prędkość deformacji generowanego przez tworzenie się mikropasm ścinania, zaproponowano wprowadzenie pewnej funkcji skalarnej, która wpływa na czas relaksacji Tm w procesie płynięcia lepkoplastycznego. Sformułowano kryterium zniszczenia bazujące na ewolucji anizotropowego wewnętrznego mikrouszkodzenia. Przeprowadzono szczegółową analizę wszystkich podstawowych cech zaproponowanej teorii konstytutywnej. Opracowana teoria może być wykorzystana w przyszłości do opisu ważnych problemów związanych z technologicznymi procesami, w szczególności dla zbadania zjawisk w meso-, micro-, i nanomechanice. Te opisy są potrzebne do szczegółowego zbadania za pomocą metod numerycznych jak uniknąć niepotrzebnych plastycznych lokalizacji oraz zjawiska zlokalizowanego zniszczenia w nowych procesach technologicznych.

Słowa kluczowe

EN

thermodynamical theory of elasto-viscoplasticity; micro-shear banding; induced anisotropy; microdamage; fracture phenomena

PL

termodynamiczna teoria sprężysto-lepkoplastyczności; mikropasma ścinania; indukowana anizotropia; zjawiska zniszczenia

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Mechanics / AGH University of Science and Technology
• Rocznik: 2008
• Tom: Vol. 27, no. 1
• Strony: 25--42
• Opis fizyczny: Bibliogr. 80 poz., rys., wykr.

Twórcy

autor

Perzyna P.

• Institute of Fundamental Technological Research, Polish Academy of Sciences, Warsaw, Poland

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