6. DISCUSSION
6.1 Prediction of the Thermal Stress and Strain Developed during Quenching
(i) Mathematical model without viscous processes: The mathematical model developed by Fletcher (99)
and Price' 7 has been used as a basis for the present work. These elastic-plastic calculations included
experimentally obtained data on the surface heat transfer coefficients of the quenchant used, and the mechanical and physical properties of the steel involved at various
temperatures during quenching from the stable high temperature austenitic condition, but did not include consideration of viscous effects. The characteristics of the stress and strain generation process as predicted by this model are exhibited at figure 98. At the onset of the quench, the surface cools faster than the centre, and a tensile stress is developed in the former. Consequently the centre is subjected to compression. As the temper ature gradient between the surface and the centre increases, both the surface and central portions are subjected to
plastic flow with an elastic region in between. However at later stages during the quench the rate of cooling at the surface decreases, and unloading of the tensile
stresses occurs at this point in the specimen, this is followed by a stress reversal. Simultaneously unloading and subsequent reversal of the compressive stresses is produced at the centre. Shortly afterwards the surface
begins to transform into martensite, which is associated with an expansion of that part of the specimen. This
causes a marked increase in the compressive stress, which is not curtailed by the onset of plastic flow, on account of increase in flow stress associated with the formation of martensite. The centre, which is still untransformed and at a higher temperature is subjected simultaneously to tensile plastic flow. The compressive stresses
produced at the surface begin to unload as the transform ation front travels into the interior regions of the plate, and the tensile plastic flow at the centre is terminated as the martensitic transformation begins at the centre. Unloading and subsequent reversal of the tensile stresses now occurs towards the centre of. the plate. The model used gives a better understanding of the stress generation process in quenched steels, but the absence of any
consideration of the time-dependent viscous processes is a serious omission, especially in the case of the least severe quenchants, such as oil. The significance of the viscous processes is further supported by the poor level of agreement found between the predicted and experimental residual stress distributions in the case of an oil
quenched plate (figure 25b). The experimental results show a tensile residual stress at the surface and
compressive stress at the centre, while the predicted results show the opposite stress distribution. However
situation where there is much less time for viscous processes to occur (figure 25a). Therefore it is
considered necessary to incorporate the viscous process into the existing model, and to observe its effect on the stress generation process during the quenching operation. (ii) The effect of viscous processes on the characteristic
stages of the stress generation process:
The introduction of stress relaxation and creep into the mathematical model discussed above has been found to be significant, particularly when the least severe
quenchants-.are used. The extent to which viscous processes affect the stress generation process depends in a complex fashion on the temperature, the magnitude of the stress and the time available for viscous flow. Thus during any time interval the stress increment prior to the use of the yield criterion consists of two parts, viz:
a) that which is directly due to the elastic strain b) that which is due to the inelastic processes, when
a tensile stress produces a negative stress increment and vice versa.
The relative size of these two factors varies during the course of the quench. When the second is predominant a marked departure from the elastic Hooke’s Law relation ship is obtained and in extreme cases the slope of the stress-strain curve may even become negative. The viscous processes are most prominent when the rate of cooling is relatively small and the temperature is relatively high e.g. in the later stages of the vapour blanket stage in
an oil quench (see figure 57) or when the level of internal stress is high e.g. during the martensitic transformation. This is discussed in detail below.
6.2 Representation of Viscous Processes in the Stress Generation Model
(i) Use of the experimental stress relaxation and creep data obtained: under isothermal condition^
The relationships between stress, strain and time at high temperatures is predicted by the use of mechanical models made up from a combination of springs arid dashpots, in which the latter represents the time dependent and the former the time independent processes. The selection of the most appropriate model is made by a comparison of the experimental stress relaxation curves obtained at different temperatures, with the corresponding data predicted by the various models. It is found that the standard linear
solid which generates the following equation — = (1 - A) exp(-B.t) + A
o°
gives a satisfactory description of the experimentally
derived results. The establishment of this good correlation under all combinations of time and temperature is aided by the use of two physical parameters n and <f> that are dependent on the material under consideration. The
parameters A and B in the equation includes these material parameters in the following combinations.
_ 2 (J) ri (1+v) E