A Consideration on Thermal Fatigue Strength of Metals

Abstract

Studies were made of thermal fatigue strength of metals with reference to the relation between the plastic strain range ε_p and a number of cycles to fracture _N. The relation was first presented by S.S. Manson in the from ε_pNα=C, and the values of the constants α and C were given by L.F. Coffin as α=1/2 and C=1/2 ln{1/(1-φ)}, where φ was the reduction of area. In the first part of this paper, these values of the constants are examined experimentally by means of several results of thermal fatigue tests on various metals presented by N. Kato, R.W. Swindeman & D.A. Douglas and others. It is found that in most cases α=0.5∼0.6 and the value of C is smaller than the value given by Coffin's equation and is much affected by thermal cycle conditions, such as upper temperature and mean temperature of the cycle. As the upper temperature T_max and mean temperature T_m of the thermal cycle become high, the value of C decreases rapidly, and the life up to fracture is much reduced, so that Coffin's equation might give a thermal fatigue life on unsafe side.
In order to examine the effect of thermal cycle conditions on the value of C, the authors carried out a series of thermal fatigue tests on 12-Cr steel in the condition that during each series of test the upper and lower temperatures were kept constant and a variable mechanical strain was combined to a constant thermal strain, so that a different resultant strain could be imposed on each specimen under the same thermal cycle condition. The result was that the value of α was not much varied from the mean value α=0.55 by variation of thermal cycle condition, but the value of C decreased as T_max and T_m became high, and was far lower than Coffin's value. From the test results the authors reduced an experimental equation, which expressed the relation between plastic strain range ε_p and the life N, encluding the effect of thermal cycle condition, i.e.
ε_pN^α=K·exp(Q₁/T_m+Q₂/T_max) (1)
In the second part of the paper, the relation is reexamined from another standpoint by the aid of dislocation theory. The proposed model for the mechanism of thermal fatigue is that during the thermal cycling the density of supersaturated vacancies, which are produced by repeated plastic strain, increases gradually and reaches the critical value, then a number of voids are created suddenly by segregation of vacancies, and the density of supersaturated vacancies decreases to a stable state. Thenceforth, the surfaces of the created voids act as absorption saurces of vacancies, that is, the most part of the supersaturated vacancies produced by the subsequent repeated plastic strain is absorbed into the voids. Thus with repetition of cycles, the voids grow and reach a dimention that the adjacent voids touch together, then the voids expand suddenly and microcracks are created and extended to macro-cracks.
By means of this model, some theoretical calculations were carried out, and the relation of the form of eq. (1) was again obtained. The value of the constant α was estimated to be 0.5∼0.6 by the theory, so that it agreed with the above experimental values quite well.