Cellular Automaton Finite Element Research Articles

Assessment of an instrumented Charpy impact machine

The dynamic responses of the standard Charpy impact machine were studied experimentally using strain gauges and accelerometer attached to the striker and the rotary position sensor fixed at the rotating axis and numerically with the finite element analysis. The fracture propagation was simulated with the cellular automata finite element approach developed earlier. A series of low velocity as well as full capacity Charpy tests were analysed. It was found that the strain gauge signal recorded close to the tup edge and the acceleration recorded at the back of the striker do not match. The energy calculated with the strain gauge data agrees well with the dial reading, while the energy calculated with the accelerometer signal is never near it. Frequencies close to the first natural \hbox{frequency} of the Charpy sample have high modal magnitudes in the acceleration signal but are effectively damped in the strain gauge response. Vibrations of the striker arm have highest modal magnitudes in the rotary position sensor. A low-pass filter is used to obtain the striker movements. The finite element analysis partly supports the experimental observations but also suggests that acceleration at the tup edge suffers higher oscillations than strain.

Application of cellular automaton–finite element model to the grain refinement of directionally solidified Al–4.15 wt% Mg alloys

Cellular automaton–finite element simulations and Bridgman experiments are used to study the grain refinement of directionally solidified Al–4.15 wt% Mg. The simulations can successfully map the conditions (velocity and temperature gradient) for columnar or equiaxed growth and account for variations in grain size in equiaxed structures. The simulations show that the latent heat released by dendritic solidification gives a quasi-isothermal zone interrupting the temperature gradient. This zone is important in limiting the degree of grain refinement which can be achieved, but also facilitates growth of equiaxed rather than elongated grains. The columnar-to-equiaxed transition is gradual, and its dependence on the addition level of refiner has been characterized. Hunt's model of the transition is supported by microstructural studies of quenched Bridgman samples.

Prediction Technology on Grain Structure Defects in Directional Solidification Casting. Application of Cellular Automaton Method for the Prediction of Solidification Grain Structures.

A method to predict grain structure defects in directional solidification precise casting has been developed based on a solidification process simulation with a three-dimensional CAFE (cellular automaton-finite element) model. In our paper we studied which parameters of the dendrite growth model in the CAFE model are important by sensitive analyses. Then, the dendrite growth model was advanced by evaluating quantitatively liquid diffusion coefficients dependent on temperature and liquidus slope dependent on liquid concentrations which have much effect on the growth model using molecular dynamics simulations and Thermo-Calc calculations. The method to forecast grain structure defects has been applied to directional solidification casting of a simple shape and a gas turbine blade, and has been verified with comparison between the simulated results and experimental results on locations or grain directions of defects, solidification microstructure. It was found that our method could predict a stray grain defect in directional solidification precise casting.

Stochastic modelling of dendritic grain structures

A three-dimensional cellular automaton-finite element model has been developed over the past five years for the prediction of macrostructures formed in casting. The present article briefly summarizes the growth algorithm of the model. Applications are then given for the prediction of the grain structure formed in a directionally solidified turbine blade produced by investment casting, a continuously cast cylinder and a near-net shape steel sheet obtained by twin-roll casting.

Stochastic modelling of dendritic grain structures

A three-dimensional cellular automaton–finite element model has been developed over the past five years for the prediction of macrostructures formed in casting. The present article briefly summarises the growth algorithm of the model. Applications are then given for the prediction of the grain structure formed in a directionally solidified turbine blade produced by investment casting, a continuously cast cylinder, and a near net shape steel sheet obtained by twin roll strip casting.

Stochastic Modeling of Dendritic Grain Structures

A three-dimensional cellular automaton-finite element model has been developed over the past five years for the prediction of macrostructures formed in casting. The present article briefly summarizes the growth algorithm of the model. Applications are then given for the prediction of the grain structure formed in a directionally solidified turbine blade produced by investment casting, a continuously cast cylinder and a near-net shape steel sheet obtained by twin-roll casting.

Stochastic Modeling of Dendritic Grain Structures

A three-dimensional cellular automaton-finite element model has been developed over the past five years for the prediction of macrostructures formed in casting. The present article briefly summarizes the growth algorithnt of the model. Applications are then given for the prediction of the grain structure formed in a directionally solidified turbine blade produced by investment casting, a continuously cast cylinder and a near-net shape steel sheet obtained by twin-roll casting.

A three-dimensional cellular automation-finite element model for the prediction of solidification grain structures

A three-dimensional (3-D) model for the prediction of dendritic grain structures formed during solidification is presented. This model is built on the basis of a 3-D cellular automaton (CA) algorithm. The simulation domain is subdivided into a regular lattice of cubic cells. Using physically based rules for the simulation of nucleation and growth phenomena, a state index associated with each cell is switched from zero (liquid state) to a positive value (mushy and solid state) as solidification proceeds. Because these physical phenomena are related to the temperature field, the cell grid is superimposed to a coarser finite element (FE) mesh used for the solution of the heat flow equation. Two coupling modes between the microscopic CA and macroscopic FE calculations have been designed. In a so-called “weak” coupling mode, the temperature of each cell is simply interpolated from the temperature of the FE nodes using a unique solidification path at the macroscopic scale. In a “full” coupling mode, the enthalpy field is also interpolated from the FE nodes to the CA cells and a fraction of solid increment is computed for each mushy cell using a truncated Scheil microsegregation model. These fractions of solid increments are then fed back to the FE nodes in order to update the new temperature field, thus accounting for a more realistic release of the latent heat (i.e., the solidification path is no longer unique). Special dynamic allocation techniques have been designed in order to minimize the computation costs and memory size associated with a very large number of cells (typically 107 to 108). The potentiality of the CAFE model is demonstrated through the predictions of typical grain structures formed during the investment casting and continuous casting processes.

Analytical and numerical predictions of dendritic grain envelopes

An analytical model is developed for the prediction of the shape of dendritic grain envelopes during solidification of a metallic alloy in a Bridgman configuration (i.e. constant thermal gradient and cooling rate). The assumptions built into the model allow a direct comparison of the results with those obtained from a previously developed cellular automaton-finite element (CAFE) model. After this comparison, the CAFE model is applied to the study of the extension of a single grain into an open region of liquid after passing a re-entrant corner. The simulation results are compared with experimental observations made on a directionally solidified succinonitrile-acetone alloy. Good agreement is found for the shape of the grain envelopes when varying the orientation of the primary dendrites with respect to the thermal gradient direction, the velocity of the isotherms or the thermal gradient.

A coupled finite element-cellular automaton model for the prediction of dendritic grain structures in solidification processes

A new algorithm based upon a 2-dimensional Cellular Automaton (CA) technique is proposed for the simulation of dendritic grain formation during solidification. The CA model takes into account the heterogeneous nucleation, the growth kinetics and the preferential growth directions of the dendrites. This new CA algorithm, which applies to non-uniform temperature situations, is fully coupled to an enthalpybased Finite Element (FE) heat flow calculation. At each time-step, the temperature at the cell locations is interpolated from those at the FE nodal points in order to calculate the nucleation-growth of grains. The latent heat released by the cells and calculated using a Scheil-type approximation is fed back into the FE nodal points. The coupled CA-FE model is applied to two solidification experiments, the Bridgman growth of an organic alloy and the one-dimensional solidification of an Al-7wt% Si alloy. In the first case, the predicted boundaries between grains are in good agreement with experiment, providing the CA cell size is of the order of the dendrite spacing. For the second experiment, the quality of the coupled CA-FE model is assessed based upon grain structures and cooling curves. The columnar-to-equiaxed transition and the occurrence of a recalescence are shown to be in good agreement with the model.