engleski

A REVIEW OF MATHEMATICAL TOOLS FOR MODELLING OF HARDNESS AND HARDENABILITY OF STEELS

The paper presents a review of the methods of modelling the hardness and hardenability of steel. Among the various numerical methods there were presented method of multiple regression, artificial neural networks, fuzzy systems genetic programming and Finite Element Method. In the case of regression analysis, it has been only mentioned well-known methods and models proposed in the literature. While for the other three computational tools the results of own work indicating the possibility of their use for hardenability modelling were presented. The developed neural network model can also be employed for simulations of the relationship between hardness at a given distance from the Jominy specimen face and the chemical composition of steel. This can be done in the entire range of concentrations of the main alloying elements occurring in constructional alloy steels. The fuzzy system deals very well with data on which it was created - in cases outside the scope of the model results were very different. The systems are a good tool to approximate inference what is possible because of previously created if-then rules, which describe the phenomenon that is otherwise hard to describe. This computer tool, which was used in materials science for structural steels for quenching and tempering, could be successfully used for other materials and their properties. The results of calculations obtained using genetic programming looks very promising, considering, that the loaded set of data ignored other alloying elements that have influence on hardness of steel. Genetic programming is a very useful tool for solving problems like that. This problem is particularly important when there are more factors affecting the investigated phenomenon. What is the main advantage of genetic programming is to release the investigator from the problem of predicting the correct form of a model describing the phenomenon investigated. GP method accomplishes this task autonomously. The established FEM models can be applied in mathematical modelling of microstructure transformations and hardness distribution, as well as, stress and strain generaton. One of the most important factors for efficient simulation of hardening is the proper selection and use of representative cooling phenomena that is relevant for microstructure transformation. The structure transformations and hardness distribution can be estimated based on time relevant for structure transformation. Hardness at different location of quenched steel specimen can be estimated by the conversion of the calculated cooling time t8/5 to the hardness. It can be done by using both, the relation between cooling time, t8/5 and Jominy distance and the Jominy hardenability curve

hardenability, hardness, modelling, steels, chemical composition.

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