Tamás Réti

Computer simulation of steel quenching process using a multi-phase transformation model

A phenomenological kinetic model has been developed for the description of diffusional austenite transformations in low-alloy hypoeutectoid steels during cooling after austenitization. A fundamental property of the model consisting of coupled differential equations is that by taking into account the rate of austenite grain growth, it permits the prediction of the progress of ferrite, pearlite, upper bainite and lower bainite transformations simultaneously. To demonstrate the applicability of the model, experiments have been performed on the DIN 34 Cr 4 steel. Investigations based on computer simulation verified that the coupled multi-phase model can be applicable to predicting the CCT diagrams of low-alloy steels and calculating the microstructure and hardness distribution after quenching.

Simulation of Phase Transformations in Steel Parts Produced by Laser Powder Deposition

Multilayer laser powder deposition is being used for the rapid manufacturing of fully dense near net shape components in a wide variety of materials. In this process parts are built by overlapping consecutive layers of a laser melted material. As a result of this overlapping, the material in each layer will undergo successive thermal cycles as new layers are deposited. Despite their short duration, these thermal cycles can activate solid-state transformations that lead to progressive modification of the microstructure and properties of the material. Since the thermal history of the material in the deposited part will differ from point to point, the part will present a complex and heterogeneous microstructure, and properties that differ from point to point. Given that the microstructure and property distribution in steel parts produced by laser powder deposition can only be predicted by modelling, a three-dimensional thermo-kinetic finite element model of laser powder deposition of tool steels was developed. In the present work this model was applied to the study of the influence of substrate size on the microstructure and properties of a six-layer wall of AISI 420 tool steel. The results show that the temperature field depends significantly on the size of the substrate, leading to distinct microstructures and properties in the final part. Introduction Laser powder deposition (LPD) [1-4] is a very promising technique for the rapid manufacture of fully dense steel components. Although the advantages of this flexible manufacturing process are widely recognised [1-5], there are still some factors restraining its wide acceptance by industry. Controlling and tailoring the material properties of the final part is one such factor. These properties are significantly affected by the solid-state transformations that may occur during deposition, induced by the consecutive thermal cycles created by successive layer overlapping. The lack of detailed understanding of these transformations and of their influence on the final properties of the deposited part may lead to irreproducible results. In order to ensure that the final part possesses an appropriate microstructure, one must know the effect of the processing parameters and part build-up strategy on the thermal cycle and microstructural changes. This knowledge cannot be obtained by trial and error, due to the large number of processing parameters that must be considered. Also, the results of such an approach might not be directly applicable to all cases because the specific geometry of individual parts strongly affects the thermal field in the part and its time evolution. A more satisfactory approach relies on computer aided engineering techniques, such as finite element analysis [6-9]. This approach requires a model describing the time evolution of the thermal field in the part during the deposition process, as well as a detailed knowledge of the solid-state phase transformations that occur in laser processed steels. The latter information is available in the work of several authors [10-15] on laser processed tool steels. In particular, Colaço et. al [11] showed that, due to their fast solidification and cooling rates, laser processed tool steels may contain

A Simplified Semi-Empirical Method to Select the Processing Parameters for Laser Clad Coatings

A semi-empirical method for selecting the processing parameter s of laser cladding is proposed. This phenomenological approach uses simple mathematical formulae, derived from a statistical analysis of measured data, to relate the laser cladding parameters with the geometric features of the clad track. Given the prescribed clad height and avai lable laser beam power, the proposed method allows to calculate values of the scanning speed and powder feed rate which are required to obtain low dilution, pore free coatings, fusion bonded to the substra te. To illustrate the application of this method, variable powder feed rate laser cladding e xperiments were carried out with Stellite 6 powder on mild steel substrates. In this technique t he laser beam power and radius and the processing speed are kept constant, while the powder feed rate is varied along a single track length according to a specified linear function. The expressions derive d from the model allowed to plot the experimental data in a coherent manner, revealing the combine d role of the different processing parameters.

Prediction of as-quenched hardness after rapid austenitization and cooling of surface hardened steels

Abstract A new phenomenological model and computational method is outlined for estimating the as-quenched hardness of steel after rapid austenitization and quenching. The model is based upon the concept of a complex transformation parameter derived from a differential equation characterizing the progress of the “non-isothermal transformations”. A fundamental property of this complex transformation parameter is that it depends not only on the temperature, but also on the rate of temperature change. The applicability of this new approach is demonstrated on the basis of computer simulation and laser hardening experiments with a low alloy hypoeutectoid steel.

Shape characterization of particles via generalized Fourier analysis

A general method for shape characterization of two‐dimensional (2‐D) microscopical particles is presented. The proposed procedure based on Fourier analysis techniques can be regarded as a generalization and further development of methods described in the literature. The geometry of the particles is characterized by a set of shape functions which is invariant under translation, rotation and dilation. Shape descriptors generated from the Fourier coefficients are used for shape evaluation. Similarity between particles has been evaluated using an appropriately defined distance measure. The method is demonstrated by an application using a collection of 2‐D objects.

Prediction of Fullerene Stability Using Topological Descriptors

In recent years, several attempts have been made to characterize the geometric structure of fullerenes by means of topological shape factors in order to predict their physical properties and stability. In this paper, we present a simple method to estimate the stability of fullerenes on the basis of quantitative topological criteria. This approach is based on the concept of the generalized combinatorial curvatures defined on the set of simple graphs embedded on a closed surface without boundary (sphere, torus, projective plane, Klein bottle). It is shown that starting with the computed generalized combinatorial curvatures several novel topological indices can be generated. From computations performed on a set of C40 and C60 fullerenes, we concluded that the four topological shape factors tested (Λ(-1), (-1), Λ(1) and (1)) could be successfully used to preselect the most stable fullerene isomers.

Local Combinatorial Characterization of Fullerenes

We present a general method which enables a possible classification of fullerenes by means of local topological invariants. In this study fullerenes are considered as bifaced simple (trivalent) polyhedra. The method proposed is based on the combinatorial analysis of the first neighbor environments (coronas) of vertices and/or edges of bifaced simple polyhedra. For this purpose, we used the so-called line-corona detectors (LC detectors) which are simple connected acyclic graphs (trees) having only 1- and 3-valent vertices. It is demonstrated that by performing certain matching operations with appropriately defined LC detectors, a finite set of local, algebraically independent topological invariants can be obtained by which various fullerene structures can be partitioned into disjoint classes of equivalence. We found also linear interdependencies between similar parameters previously defined in the scientific literature. Discriminating performance of computed topological descriptors have been tested on the set of C40 fullerene isomers.

Evaluation of Cooling Characteristics of Quenchants by Using Inverse Heat Conduction Methods and Property Prediction

A sequential numerical method for characterization of hardening performance of quenchants applied for steel quenching is outlined here. This novel method is based on the specific processing of measured time–temperature samples performed as a result of cooling curve tests. The heat transfer coefficient, as a function of surface temperature, characterises the heat transfer during cooling and is calculated using an iterative inverse algorithm. The heat transfer coefficient is used for calculation of the microstructural constituents and the hardness profile of cylindrical samples of arbitrary diameters. The hardening performance of the media is evaluated by the estimated hardness of the specimen obtained by heat treatment.

On the Topological Characterization of 3-D Polyhedral Microstrutures

To characterize topologically the polycrystalline microstructure of single-phase alloys computer simulations are performed on 3-dimensional cellular models. These infinite periodic cellular systems are constructed from a finite set of space filling convex polyhedra (grains). It is shown that the appropriately selected topological shape factors can be successfully used for the quantitative characterization of computer-simulated microstructures of various types.

Numerical Methods for Safeguarding the Performance of the Quenching Process

A new numerical technique for testing and evaluation of quenching media and quenching systems is outlined. The measured time-temperature samples as a result of cooling curve test are analyzed by the new software developed, in order to characterize quantitatively the quenchants. The method applied is based on Fourier analysis. Examples for evaluation and comparison of cooling performance of quenchants are presented the applicability of the computational technique.