Institute of Fundamental Technological Research

The problems of quenching-stress analysis are critically reviewed and an adequate simple theory is discussed. The theory accounts for both plasticity and volumetric changes due to phase transformation accompanying the thermal-hardening of a group of simple steels that are characterized by C-shaped time-temperature-transformation diagrams. The volume dilatation in the absence of stress is assumed to be a linear function of the separate specific volumes and weight fractions of the constituents (pearlite, austenite and martensite). With use of the classical relationships of a formal theory of transformation kinetics, the amounts of pearlite and martensite are expressed in terms of the temperature and the temperature-history. The specific forms of such functions are given. In order to account for the influence of phase transformation on plastic properties, the non-isothermal plastic flow-rule is generalized, and a thermal-hardening parameter is introduced which is identified with the amount of pearlite. Variational principles and bounding inequalities associated with the fundamental rate-problem are considered. As an example, the problem for a rapidly, uniformly-cooled half-space is solved. The variations of the residual stress and the final amount of martensite with distance from the outer surface are given, for several values of the rate-of-cooling. The results suggest that the residual stress vanishes on the plane containing approximately 30–35 per cent of martensite.

Kinetics of phase transformations in steel during quenching is presented. The transformations form austenite to pearlite and to martensite are characterized as a function of thermal history, and the volumetric change of an element is discussed. A plastic flow rule including such effects of structural changes is proposed in the second part of this paper. A numerical example is shown for a semi-infinite body cooled at the surface from an eutectoid temperature.