Micro- versus macro- modelling of creep damage

The results of creep damage tests in constant temperature for polycrystalline materials can be approximated by two straight lines on time-to-failure versus strain rate log-log graph. The steeper line at longer times-to-failure and lower strain rates is connected with brittle failure. The second line of reduced slope for short times and large strain rates represents ductile damage. In Continuum Damage Mechanics (CDM) brittle damage can be modelled using Kachanov equation and ductile damage using Hoff approach. To model the transition region the combination of these equations can be used. In present paper the continuous Kachanov equation is replaced by Cellular Automata (CA) model of damage development in microscale to back-up this complex phenomenon by microstructural changes. Microscopic observations show that, depending on loading and temperature levels, creep damage is affected heavily by material microstructure. For high loads and lower temperatures final failure is of ductile character, i.e. occurs mostly within material grains. In opposite case (low load and high temperature) inter-granular defects prevail causing brittle failure. For macroscopically observed transition region both micro-mechanisms come to interplay. Whereas the ductile failure can be well described by methods of continuum mechanics, the process of brittle deterioration exhibits more scatter as it is much more governed by microstructure of grain boundaries. In previous author?s work the technique of CA is developed for material structure modelling and brittle failure initiation. The same methodology is used in the present paper for conditions when both, ductile and brittle processes are of importance. The Hoff theory of ductile failure, based on the assumption of material incompressibility and power law for creep strain under constant load, is implemented in Abaqus package and coupled with CA model of brittle failure proposed earlier. Thus, the proposed description falls into category of CAFE methodology pursued recently in metallurgy. Concurrent running of both models yields effectively transition points on log-log diagram of time to failure. The results of above descriptions are compared with experimental observations.

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W pracy kontynualne podejście do modelowania przejścia pomiędzy kruchym a ciągliwym zniszczeniem w warunkach pełzania zostało zastąpione poprzez użycie automatu komórkowego. Pozwoliło to na opis tego skomplikowanego zjawiska poprzez nawiązanie do zmian mikrostruktury materiału. W poprzednich pracach autora technika automatów komórkowych została zastosowana do modelowania struktury materiału i inicjalizacji zniszczenia kruchego. Ta sama metoda została użyta w obecnej pracy, w której zniszczenie kruche i ciągiwe są równouprawnione. Teoria zniszczenia ciągliwego Hoffa została zaimplementowana przy pomocy pakietu Abaqus i sprzężona z modelem zniszczenia kruchego realizowanym przez automat komórkowy. W ten sposób zaproponowana metoda zawiera się w klasie metod CAFE (Cellular Automata Finite Element). Równoległe uruchomienie obu modeli pozwala na efektywne wyznaczenie punktów przejściowych na wykresie logarytmicznym zależności czasu do zniszczenia od naprężenia. Wyniki są porównane z obserwacjami doświadczalnymi zamieszczonymi w literaturze.