Internal Variable and Cellular Automata-Finite Element Models of Heat Treatment
Heat treatment is one of the most important process es in advanced steel products manufacturing. While production processes are still being optimised, numerical modelling of heat treatment is very useful. Finite Elements Method (FEM) is widely used in these cases, due to its proved potential fo r modelling of continuous, macroscopic phenomena. However, its capability to simulate microscale and noncontinuous processes is very limited. Introducing e mpirical model of phase changes into FEM, usually based on Internal Variable Method (IVM) is useful when the information about volume fraction of the phases in the domain a nd stresses due to phase change satisfies the requirements. Notwithstanding, it is difficult to obtain information in-depth about microstructure during heat treatment, because it requires more sophisticated description of phase change process. Those problems can be resolved with multiscale modelling. One of the current approaches in this fi eld employs FEM for computing of temperature, stress and strain fields, while non-co ntinuous, microscale model is based on Cellular Automata (CA) method [1]. Recently, several CA models concerning phase transformation have been proposed, e.g. [2]. In th is paper Cellular Automata ‐ Finite Elements (CAFE) is applied for modelling of both macroscopic and microscopic influence of heat treatment. It also takes into acc ount a stochastic character of processes, which is hard to obtain in typical FEM or IVM solut ion. The advantage of CAFE model ensues from direct representation of microstructure. Although the current microstructural CA model is two-dimensional, it reproduces topological and morphological relations between components of microstructure. The state of CA cells is updated synchronically in cons ecutive time steps. Every cell includes state vector representing fractions of all phases. Thermodynamics of phase transition is a base for a rule-based knowledge rep resentation in the CA model. However, the nondeterministic definition of neighbo urhood and probabilistic energy
Modeling with FCA-based model of microstructure evolution in ultra-thin wires of MgCa0.8 alloy during hot drawing
Magnesium alloys are widely applied in medicine due to their high biocompatibility and solubility in human body. For example, they could be applied for surgical threads used for integration of tissue [1,2]. This application requires wires diameter of 0.1 mm and smaller. A new manufacturing process of thin wires, including drawing in heated dies, was developed by Authors [3,4] for biocompatible Mg alloys. An occurrence of recrystallization is the main condition of such a process, which does not use intermediate annealing between the deformations. Because the trial and error method is very expensive and ineffective, a numerical modeling was applied for process design and its optimization. A model of recrystallization of MgCa0.8 alloy in macro scale was developed previously [5]. This model allows for prediction and optimization of drawing process parameters. However, basing on the results of the study [5], we conclude that some microstructural phenomena should be additionally considered in the case of ultra-thin wire drawing in the heated tools. An analysis of the effect of the wire diameter on recrystallization kinetics was an object of interest, especially when wire diameter is comparable with grain size. Study of influence of such a geometrical parameter was fulfilled with use of FCA-based model. The modelling shows that an approaching of the wire diameter to the grain size elongates the recrystallization process with other conditions the same. For example, a decrease of the diameter from 200 to 20 µm extends the recrystallization time by 30%. From the practical point of view, the results detached such a geometrical parameter can be implemented into simpler models of recrystallization, e.g. JMAK-based models.
Britain, the Commonwealth and Europe : the Commonwealth and Britain's applications to join the European Communities
Preface Notes on the Contributors Britain, The Commonwealth and Europe: An Overview D.Maitland 'The Jolly Old Empire': Labour, the Commonwealth and Europe, 1945-51 D.Russell Britain, the Commonwealth and Europe in the 1950s W.Nicoll The Australian Department of Trade and the EEC, 1956-61 J.O'Brien The Commonwealth in British European Policy: Politics and Sentiment, 1956-63 G.Wilkes 'Commonwealth or Europe?': Macmillan's Dilemma, 1961-63 A.May Commonwealth International Financial Arrangements and Britain's First Application to Join the EEC M.Kandiah & G.Staerck The Labour Government, Commonwealth Policy, and the Second Application to Join the EEC, 1964-67 P.R.Alexander The EEC and the Erosion of the Old Commonwealth Relationship S.Ward Index