Nouvelle loi phénoménologique de l’adoucissement d’un acier à outil au cours du revenu. Application en fatigue thermique

New phenomenological law of the softening of a tool steel during annealing. Application to thermal fatigue

Centre de Recherches Outillage, Matériaux et Procédés (CROMeP) - École des Mines d’Albi Carmaux

Résumé

L’équivalence temps-température est un concept général des cinétiques des processus thermiquement activés, qui s’appuie sur les formulations mathématiques maintenant bien connues des paramètres de traitement thermique, de type Hollomon et Jaffe ou de type Maynier. Mais, ces paramètres ne sont pas des fonctions explicites de la dureté, c’est-à-dire que nous ne connaissons pas de loi générale d’évolution de la dureté au cours du temps par revenu isotherme. De plus, cette équivalence établie en statique (sans contrainte) est parfois appliquée pour rechercher la température subie par un outil soumis à des sollicitations thermomécaniques à partir d’une évaluation du cycle thermique et d’une courbe maîtresse de revenu. Nous proposons et démontrons dans un cas particulier une nouvelle loi phénoménologique fondée sur l’équivalence temps-température, qui explicite la relation dureté-temps-température et qui unifie les écritures existantes. Cette loi permet de démontrer que l’évolution de la dureté en fatigue thermique ne peut pas être prévue par la seule résistance au revenu du matériau. Ainsi, évaluer le cycle thermique subi en peau par une éprouvette de fatigue thermique à partir de la dureté, de la durée d’exposition et de la résistance au revenu peut faire commettre une erreur de 200 °C.

Abstract

Among other loadings, hot-work tool steels are subjected to fast (few seconds) and large range (over 600 °C) temperature cycles. In addition to oxidation, this implies that mechanical evolutions are due to both thermomechanical fatigue and thermal softening. Among mechanical properties, hardness is widely used, as it is related to metallurgical characterisation of tool steels. For example, estimation of maximum temperature sustained by critical parts of tools is often done through measured hardness of a die associated with tempering resistance properties of the steel. This assumes that hardness evolution does not depend on mechanical straining. Furthermore, hardness is never expressed as an explicit function of time and temperature, thought it is supposed to be so.

In this paper, we suggest a new model which is such an explicit function. This model is based on the observation of evolutions of hardness during tempering. It is written thanks to four boundary conditions of the evolution of hardness with time and temperature, and the mathematical principles on which time-temperature equivalence is based. Direct experimental verifications lead then to a complete validation of the model in that particular case, that is the mathematical form of the function and values of the constants. The general shape of the model is :

[math]

It is verified in the case of the tempering of a 5% chromium steel with initial hardness 485 Hv :

[math]

Is it shown that constants have physical related values. Furthermore, the model we suggest leads to a formulation of the well known heat treatments parameters as functions of the desired hardness and the constants related to the thermoactivated processes like Jaffe’s one. For example,

[math]

means that all the couples of values (t,T) which implies the same value of

[math]

give the same heat treatment result, which is the hardness in that case. Thanks to our model, we can show that

[math]

with ΔHv₁ the desired evolution of hardness. Maynier parameter and Murry parameter are also shown to be such functions, but with particular shape. So, though the shape of this model has been suggested only by a phenomenological method, it can be seen that it is in agreement with existent parameters. In fact, it gives them a physical interpretation which tends to unify them all into a single model in any case where the model is proved to be valid. Using this model allows the evaluation of the maximum temperature sustained by the material assuming that only time and temperature are involved in the evolution of hardness. If one knows the thermal history (number of cycles N, exposure time per cycle Δt) and the measured hardness Hv₁, then the temperature at which it is necessary to heat the material is

[math]

Using this model makes it also possible to show that thermomechanical straining has a strong influence on the evolution of hardness. In the case of our thermal fatigue experiment, we show that a modification of the activation energy is not enough to explain the influence of thermal straining. If one would search for the maximum temperature sustained by the thermal fatigue specimens using only time-temperature process kinetic, the error made may be as great as 200 °C, though the experimental maximum temperature has been set to 650 °C.