O. V. SOROKIN, Corresponding Member of the Academy of Sciences of the USSR
I. A. ODING

ON THE QUESTION OF CREEP UNDER PULSATING STRESS

1°. Modeling the high-temperature deformation of bodies by a system of two elastic and two viscous elements (Fig. 1), whose characteristics \(E_1\), \(\eta_1\), and \(\eta_2\) are functions of the stress \(\sigma\), makes it possible to give a simple graphical construction of the deformation–time curve \((\varepsilon—t)\) under pulsating stress from the creep curve obtained under stress constant in time.

Let a tensile stress be applied to the specimen, pulsating as shown in Fig. 2a, its maximum value being equal to the stress at which the initial creep curve \(O_1K\) was obtained (Fig. 2b). Let us separate from the creep curve the curve of elastic aftereffect \(O_1h\). Suppose unloading occurred at the moment \(t_1\). The total deformation accumulated by this time is determined by the point \(a_1\) of the curve \(O_1K\). The deformation of elastic aftereffect accumulated up to this moment is expressed by the segment \(b_1e_1\). The rate of recovery of the elastic-aftereffect deformation will be determined by the stress acting at the moment of unloading on the spring \(E_1\) of the system \(E_1—\eta_1\) (Fig. 1), i.e., at the moment of unloading this rate will be determined

Fig. 1

Fig. 2

by the angle of inclination of the tangent to the curve of elastic aftereffect at the point \(b'_1\) to the \(x\)-axis, with \(b'_1e'_1=b_1e_1\). The entire recovery over the time \(t_1\) will be represented by the segment \(b'_1c_1\), and the recovery deformation will be equal to \(c_1d_1\). Thus,

the curve \(c_1m_1\) repeats the segment of the elastic aftereffect curve \(b_1c'_1\), and \(c_1d_1 = c_1d'_1\). Under repeated loading by the stress \(\sigma_0\), the increase in creep deformation and elastic aftereffect will be determined by the segment \(O_2a_2\) of the curve \(O_1K\), since the rate of deformation of the system \(\eta_1—E_1\) at the instant of secondary loading will be determined by the stress \(\sigma(2t_1)=\sigma_0-e_1d''_1E_1\), where \(B_1d''_1=c_1d''_1\), \(e_1d''_1=e_1b_1-b_1d''_2\), etc.

Fig. 3

It should be noted that if the time \(t_1\) before unloading is not large, then in subsequent unloadings the rate of recovery and the magnitude of the recovery deformation may turn out to be greater than in the preceding ones, i.e. \(c_2d'_2 > c_1d'_1\).

Hence the answer is also clear to the question: how do interruptions during creep tests affect creep curves? If, for example, after unloading a specimen deformed at \(\sigma=\mathrm{const}\), it is rapidly cooled, thereby fixing the deformation of elastic aftereffect as residual, then after the next rapid heating and loading the creep curve must be restored at once, etc.

\(2^\circ\). Step loading. If at the instant \(t_1\) the stress is rapidly increased from \(\sigma_1\) to \(\sigma_2>\sigma_1\) (Fig. 3) and then the latter is maintained constant, then further deformation will proceed along the segment \(C_1B_1\) of the creep curve obtained at the constant stress \(\sigma_2\), translated parallel to the \(Ot\) axis, starting from the point \(C\), corresponding to the same value of the elastic-aftereffect deformation.

\(3^\circ\). In passing, we note that in cases of an apparent, at first glance, discrepancy in the behavior of materials under creep conditions at \(\sigma=\mathrm{const}\) and stress relaxation, one cannot yet speak of a difference in the mechanisms of deformation, and one may expect satisfactory agreement between experimental and calculated data. Let, for example, the creep curves of steels \(A\) and \(B\) for identical values of the stresses \(\sigma_1\), \(\sigma_2\), and \(\sigma_3\) be arranged as shown in Fig. 4a, respectively by solid (\(A\)) and dashed (\(B\)) lines. Then the curves expressing the dependences \(\eta_2-\sigma\) (\(\eta_1(\sigma)\) and \(E_1(\sigma)\), for simplicity, are omitted) for these steels will be arranged in accordance with Fig. 4b, and the stress-relaxation curve from the stress \(\sigma_1\) for steel \(B\) may fall lower than for steel \(A\) (Fig. 4c), although the creep deformation of steel \(B\) at this stress is smaller than that of steel \(A\).

Fig. 4

Kuibyshev Polytechnic Institute
named after V. V. Kuibyshev

Received
19 XI 1963