Metoda identyfikacji w mechanice materiałów ciągliwych z uszkodzeniami

• Autorzy: Nowak Z.
• Języki publikacji: PL

Abstrakty

PL

Mechanika materiałów niejednorodnych służy przewidywaniu ich właściwości makroskopowych na podstawie badania ich mikrostruktury i mechanizmów deformacji. Nowe metody badawcze dostarczają informacji o zachowaniu się materiałów w skali mikroskopowej i nanometrycznej. Opis złożonego zachowania się materiałów przy różnych obciążeniach wymaga wprowadzenia do modeli konstytutywnych funkcji i parametrów materiałowych, które trzeba określić eksperymentalnie. Jednak nie dla wszystkich wielkości dysponujemy bezpośrednimi danymi doświadczalnymi. Wszechstronne badania materiałów przy różnych obciążeniach są zbyt kosztowne, a w wielu przypadkach niemożliwe do przeprowadzenia. Konieczne staje się, zatem dokonanie wyboru najistotniejszych efektów danego zjawiska, cech badanego materiału i określenie w miarę prostego, ale wszechstronnego modelu konstytutywnego. Podstawowym celem pracy jest opracowanie metody identyfikacji wykorzystującej funkcję strat odporną na błędy pomiarów oraz określeniu metod porównywania i wyboru najlepszego modelu z kilku nieliniowych modeli konstytutywnych. Wykorzystanie miary odległości informacyjnej Kullbacka-Leiblera między modelami lub między odpowiedzią modelu a danymi doświadczalnymi, pozwala określić, który z modeli lepiej dopasowuje się do danych rzeczywistych. Opracowaną metodę użyto w analizie zaawansowanych deformacji plastycznych osiowosymmetrycznego rozciągania próbek cylindrycznych i jest treścią rozdziału 9. W pierwszej części rozprawy, w rozdziałach 2-7 przedstawiono różne sposoby opisu złożonego zachowania się metali przy ąuasi-statycznych i dynamicznych obciążeniach. Przedstawiono zagadnienie modelowania rozwoju mikrouszkodzeń i mikropustek podczas deformacji ciała stałego. Przedyskutowano sposoby doboru modelu konstytutywnego i wpływ metody identyfikacji na postać użytych funkcji materiałowych. Zbadano zjawisko zaawansowanych odkształceń plastycznych i wpływ rozwoju mikrouszkodzeń na zachowanie materiału jako agregatu (osnowa i cząstki drugiej fazy). Przedstawiono opis płynięcia plastycznego materiału z mikrouszkodzeniami. Zachowanie materiału w procesach ąuasistatycznych opisano z wykorzystaniem modelu plastyczności, w którym uwzględniono izotropowe wzmocnienie plastyczne, a osłabienie opisano przez ewolucję mikrouszkodzeń. Przeprowadzono systematyczną analizę numeryczną ąuasistatycznego rozciągania próbek stalowych. Zbadano problem lokalizacji odkształceń plastycznych w ramach teorii lepkoplastyczności. Zastosowano opis płynięcia plastycznego z pasmami ścinania w numerycznej analizie procesu kucia matrycowego. Modyfikację klasycznej metody najmniejszych kwadratów do oszacowania parametrów materiałowych w celu uniezależnienia się od błędów pomiarowych przedstawiono w rozdziale 8. Użyto różnych odpornych funkcji celu do porównania ich wpływu na oszacowanie stałych materiałowych dla różnych modeli materiału z mikropustkami. Następnie przedstawiono zmodyfikowaną metodę optymalizacji globalnej i opisano algorytmy obliczeniowe użyte do identyfikacji funkcji materiałowych. Zagadnienia opisane w pracy dotyczą dwóch dziedzin: mechaniki materiałów ciągliwych z ewolucją mikrouszkodzeń oraz metod identyfikacji funkcji materiałowych w modelach nieliniowych, z koniecznością porównywania i wyboru najlepszego modelu. Wspólne ujęcie obu dziedzin w niniejszej rozprawie pozwoliło na opracowanie narzędzi do prawidłowego modelowania konstytutywnego i poszerzyło zakres analizowanych opisów materiałów z mikropustkami. Wspólną cechą wszystkich analizowanych przypadków jest problem identyfikacji stałych materiałowych w oparciu o dane doświadczalne. W pracy zbadano naturę powstawania mikrouszkodzeń i wykazano, że ewolucja mikrouszkodzeń oraz interakcje między pustkami mają decydujący wpływ na przebieg deformacji oraz na lokalizację odkształceń plastycznych i sposób zniszczenia. Wykorzystano przy tym modele obliczeniowe: jednowymiarowe, dwuwymiarowe (osiowosymetryczne) i trójwymiarowe. Stwierdzono, że ewolucja mikropustek jest przyczyną niejednorodnego stanu odkształcenia i naprężenia, która bez jakichkolwiek imperfekcji geometrycznych i termicznych prowadzi do lokalizacji odkształceń plastycznych i przyczynia się w końcowej fazie do całkowitego zniszczenia. Zbadano wpływ parametrów konstytutywnych, lokalnych zmian własności mechanicznych materiału osnowy na przebieg deformacji, rozkład stanu odkształcenia i naprężenia oraz rozwój strefy lokalizacji odkształceń plastycznych w postaci 'szyjki'. Przedstawiono podstawowe cechy zjawiska powstawania i wzrostu mikrouszkodzeń, przyczyny ich kierunkowego rozwoju i przeprowadzono analizę wzajemnego oddziaływania mikrouszkodzeń. Wykazano decydującą rolę struktury materiału osnowy i wynikającego z niej losowego charakteru zjawiska zniszczenia. Otrzymane wyniki w pełni potwierdzają konieczność użycia odpornych funkcji celu do identyfikacji stałych materiałowych w oparciu o doświadczenie oraz potrzebę stosowania testów statystycznych do wyboru najlepszego modelu.

Słowa kluczowe

PL

mechanika; mechanika materiałów; materiały niejednorodne

EN

mechanics

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Prace Instytutu Podstawowych Problemów Techniki PAN
• Rocznik: 2006
• Tom: nr 5
• Strony: 3--213
• Opis fizyczny: bibliogr. 249 poz.

Twórcy

autor

Nowak Z.

• Instytut Podstawowych Problemów Techniki PAN

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