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Modelling of brittle damage nucleation by means of

Nowak K.

Computer Methods in Materials Science

2007

Vol. 7, No. 1

150-155

The main goal of the paper is to motivate damage nucleation in metals, subjected to creep conditions, on the level of material structure. In classical approach of mechanics it is achieved by introducing a scalar (or tensorial) parameter called damage variable and postulating its phenomenological evolution equation. Such an approach has been successfully used in analysis of structures under different loading circumstances, giving rise to the formation of special branch of mechanics “Continuum Damage Mechanics” (CDM). This approach reflects neither physical process that is underlying macroscopically observed phenomena, nor material structure. On the other hand, in metallurgy, the process of brittle damage formation is well recognized and described. In brief, it consists of microcraking and voids formation initiating in the triple-points and developing along grain boundaries. Therefore, it is essential to associate any description of damage formation with modelling of material structures. In the paper, it was achieved by associating deformation process with changing states of CA cells. To model time dependent behaviour of representative volume element (RVA) of material a 3D cellular automaton was developed. The process of damage formation consists of two steps in each time increment. In the first one, the tension (or compression) of RVE over an increment of deformation mesh was supposed, and then projected onto cellular automaton cells. In the second step the damage formation is controlled by the rules of an automaton. These probabilistic rules change the state of mass cell to empty for specific combination of neighbouring cells, provided this cell corresponds to grain boundary. Above procedure allows to forms microvoids or microcracs. The main rule governing cellular automaton is the mass conservation law, which enforced the number of empty cells in RVE. As the outcome from CA the damage variable is calculated as a percentage of entire damage of RVE. The entire damage is assumed to happen when the voids form a surface spanning two opposite borders of element. The procedures developed in the paper are used to modify standard FE programs through incorporating results of CA-based microstructural analysis according to the CAFE methodology. For each Gauss point of finite element the CA is running and values of state variables are exchanged between FE and CA. Strains obtained from FE are used to calculate deformation of the borders of RVE. In turn, the damage variable calculated from CA modifies the value of stress used in FE solution. In such a way multiscale description of phenomenon is proposed to obtain solution of engineering problems with sound physical background. As an example, a plate under uniform pressure working in creep condition is analysed using HKS Abaqus. Results obtained are compared with numerical solution of CDM.

Zaproponowano opis nukleacji uszkodzeń dla metali pracujących w warunkach pełzania na poziomie mikrostruktury. Opisując to zjawisko w klasycznym podejściu do mechaniki wprowadza się skalarny (lub tensorowy) parametr nazywany uszkodzeniem i postuluje fenomenologiczne prawo jego rozwoju. Takie podejście jest z powodzeniem używane w analizie konstrukcji w różnych warunkach obciążenia tworząc specjalną gałąź mechaniki zwaną kontynualną mechaniką uszkodzeń. Pomimo rozwiązania szeregu ważnych technicznych problemów, takich jak oszacowanie czasu do pojawienia się pierwszego makroskopowego uszkodzenia a także dalszego rozwoju procesu pękania, podejście to nie odzwierciedla ani procesu fizycznego leżącego u podstaw makroskopowo obserwowanych zjawisk, ani struktury materiału. W niniejszej pracy proponuje się podejście wieloskalowe poprzez połączenie rozwiązania numerycznego na poziomie makroskopowym z opisem zachowania się struktury materiału na poziomie mikro przy pomocy automatów komórkowych. Otrzymane rozwiązania porównane