A new kinetic model for anisothermal metallurgical transformations in steels including effect of austenite grain size

The two main effects of stress on phase transformation, kinetics modification and transformation plasticity, are reviewed for both diffusional and non-diffusional transformations. Results for these interactions during the pearlitic and martensitic transformation of steels under uniaxial tensile stress are analysed from a metallurgical point of view. These results are used to produce a model for a triaxial stress state, and in a finite element program for calculating internal stresses during quenching. Transformation plasticity is introduced in the calculation of internal stresses as an additional strain related to the stress state and to the progress of transformation, and the kinetics of martensitic transformation are also related to the stress state. The calculated results show that these phenomena have important consequences on the stress and plastic strain histories during quenching.MST/9

Stress–phase-transformation interactions – basic principles, modelling, and calculation of internal stresses

A study has been made of constitutive relations for a time–dependent inelastic material within the framework of continuum thermodynamics, and of the heat conduction equation and transformation kinetics for processes involving phase transformations. Calculations of the stress, temperature, and structures of a half–spaced body, heated and cooled from the surface have been made using the finite element method, and are presented as an illustrative example. The effects of coupling between stress, temperature, and metallic structures, and of time dependence on the constitutive model for melting during welding are evaluated.MST/14

Coupling between stress, temperature, and metallic structures during processes involving phase transformations

In this paper, the various interactions between the different parameters involved during quenching, i.e. temperature, phase transformation, and stress–strain, are investigated and a constitutive model of the material during the process is presented and discussed. The influence of the parameters has been studied, by computer calculations using a constitutive model, for three steel cylinders, and the results indicate that in some cases the constitutive model seems important. In none of the cases studied in the paper is the influence of the stress state on the transformation kinetics very great.MST/11

Interactions and constitutive models for calculating quench stresses in steel

n this paper, the kinetics of anisothermal structural transformations are first discussed. Classical models are shown to raise difficulties because they do not take into account the existence of a temperature–dependent equilibrium proportion of the phases. A very simple model incorporating this factor is proposed and shown to lead to a good correlation between experimental and theoretical results it is also shown to be compatible with the thermodynamics of irreversible processes. The model can be extended to include the possibility of isothermal kinetics of the Johnson–Mehl type, as well as the influence of austenite grain size. The influence of the transformations on plastic behaviour (transformation plasticity) is next discussed. A simple model is described using first purely heuristic considerations, then a more microscopic and physical approach. Possible improvements to this model are suggested, especially the inclusion of the fact that the microscopic plasticity generated by volume differenc...

Mathematical models of anisothermal phase transformations in steels, and predicted plastic behaviour

The first part of the paper deals with the constitutive relations of thermoelastic-plastic bodies during heat treatment when considering phase transformation on the basis of continuum thermodynamics. Interaction between temperature and metallic structures is carefully discussed to obtain the heat conduction equation including latent heat due to phase transformation. Applications of the theory to the cases of quenching and low-temperature-tempering are also presented. Structure and temperature distributions are numerically calculated by a finite element technique after determining the physical properties from the data of dilatation-temperature-time diagrams. Variations of stress and strain are also analysed. Calculated results of the transformation kinetics and residual stress are compared with experimental data for plain carbon and chromium steels measured by micrographs and both method of X-ray diffraction and Sachs' boring out technique, respectively.

S. Nagaki

Papers

Description of transformation kinetics, heat conduction and elastic-plastic stress in the course of quenching and tempering of some steels