ON THE STABILITY OF RESIDUAL STRESSES UNDER CYCLIC LOADING

D. E. ZAITSEV, G. V. TOPOROV, M. G. GOLDSHMIDT

(Presented by the scientific seminar of the Laboratory of Plastic Deformations)

In the detailed review by L. A. Glikman [1], the necessity and relevance of studying the stability of residual stresses under the action of cyclic loads are substantiated. Despite the fact that the question of the degree of stability of residual stresses under the action of cyclic loads is of great importance, it has not been investigated sufficiently broadly or in sufficient detail. In particular, the kinetics of the reduction of initial stresses in the course of cyclic action remains little studied, especially when the loading is asymmetric in character.

In the present work, the stability of residual stresses was investigated on flat specimens made of steels St. 45 and ShKh 15. Specimens of length \(l = 200\ \text{mm}\), width \(b = 10\ \text{mm}\), and thickness \(h = 4 \div 6\ \text{mm}\) were annealed in vacuum in a special fixture to prevent warping. Specimens whose lack of flatness did not exceed \(0.05\ \text{mm}\) were admitted to the experiments. The specimens were then machined on one side on a surface-grinding machine. The residual stresses induced in the surface layer as a result of grinding caused the plates to warp; from the magnitude of this warping \(\Delta\), the moment and the resultant of the residual stresses may be calculated [2]. The deflection of the specimens was measured by means of an indicator device with an accuracy of \(\pm 0.01\ \text{mm}\).

The stability of the residual stresses was investigated on a pulsator [3] at a rate of \(700\) cycles/min. In the fixture shown in Fig. 1, which makes it possible to produce deformation by pure bending, the specimen was mounted in such a way that the stresses from the external load were added to the residual stresses, and the test was carried out under conditions of an asymmetric cycle. Stepwise external loads of various magnitudes were applied to the specimen under test. The magnitudes of the applied stresses varied within the range from 5 to \(62\ \text{kg/mm}^2\).

The kinetics of the reduction of the residual stresses was recorded after \(10\), \(50\), \(10^2\), \(5 \cdot 10^2\), \(10^4\), \(2.5 \cdot 10^4\), \(5 \cdot 10^4\), and \(10^5\) cycles by measuring the decrease in the deflection of the specimen. The change in the deflection of the specimen relative to the initial value occurs as a result of irreversible phenomena (plastic deformation) taking place in the surface layer. As is known, this phenomenon occurs in the case when the sum of the residual ...

stresses in the surface layer \((\sigma_{\text{res}})\) and the stresses from the external load \((\sigma_{\text{ext}})\) exceeds the cyclic elastic limit of the material

\[ \sigma_{\text{res}} + \sigma_{\text{ext}} > \sigma_{\text{el}} . \tag{1} \]

In this series of experiments only the value of the resultant residual stresses was analyzed; therefore it was not possible to estimate numerically the magnitudes \(\sigma_{\text{res}}\) and \(\sigma_{\text{el}}\).

Fig. 1

Figure 2a presents the test results for a specimen made of steel 45, machined at a cutting speed \(V = 37\ \text{m/sec}\); the longitudinal feed was \(S_{\text{long}} = 2.2\ \text{m/min}\), and the transverse feed was \(S_{\text{trans}} = 0.10\ \text{mm/double stroke}\).

In the first series of experiments a stress \(\sigma_{\text{ext}} = 6.56\ \text{kg/mm}^2\) was applied to the specimen, and the specimen was subjected to cyclic action successively from 10 to \(10^5\) cycles. Then, in the second series of experiments, the magnitude of the applied external load was increased to \(\sigma_{\text{ext}} = 18.86\ \text{kg/mm}^2\), and the specimen was again trained over the entire range of cycles. In the subsequent series, the stress magnitude was increased stepwise, up to the complete disappearance of the residual stresses \((\Delta = 0)\).

To verify the reliability of the results obtained, a load \(\sigma_{\text{ext}} = 44.1\ \text{kg/mm}^2\) was immediately applied to a specimen having the same value of the resultant. As can be seen from Fig. 2a (dashed lines), testing of the second specimen led to the same results as testing of the specimen subjected to the action of stepwise increasing loads.

Similar experiments were carried out on specimens made of steel ShKh15 (Fig. 2b) \((V = 37\ \text{m/sec},\ S_{\text{long}} = 2.2\ \text{m/min},\ S_{\text{trans}} = 0.06\ \text{mm/double stroke})\), steel 45 (Fig. 2c) \((V = 37\ \text{m/sec},\ S_{\text{long}} = 2.2\ \text{m/min},\ S_{\text{trans}} = 0.10\ \text{mm/double stroke})\), and steel ShKh15 hardened to a hardness of \(HV\ 600\) \((V = 37\ \text{m/sec},\ S_{\text{long}} = 20\ \text{m/min},\ S_{\text{trans}} = 0.08\ \text{mm/double stroke})\).

Fig. 2

Experiments showed that the relaxation of residual stresses occurs mainly during the first stage of testing. Subsequently, a noticeable change in the residual stresses is observed only up to 100 cycles; then, up to \(10^5\) cycles, as can be seen from Fig. 2, \(\sigma_{\text{res}} = const.\)

A stepwise increase in the external load ultimately led to equalization of all the tested specimens (\(\Delta = 0\)), which indi-

Fig. 3

cates complete relaxation of the residual stresses. Attention is drawn to the fact that the magnitude of the external load at the last stage was not specially calculated; i.e., the same results apparently would have been obtained at stresses somewhat smaller than, or exceeding, those applied. This can be explained as follows.

Relaxation of residual stresses occurs when condition [1] is satisfied. In the case where \(\sigma_{\text{res}}\) is still a large quantity (in our experiments \(n > 20\ \text{kg}/\text{cm}\)), a comparatively small increase in \(\sigma_{\text{ext}}\) satisfies condition [1]. At a certain stage, complete relaxation of the residual stresses occurs, i.e., \(\sigma_{\text{res}} = 0\), and then, in order to plastically deform the specimen, it is necessary to apply to it a substantially larger external load.

Figure 3 shows the kinetics of the decrease in residual stresses under a stepwise increasing external load for specimens of steels 45 and ShKh15 having different initial values of \(n\).

The analysis of the experiments presented shows that relaxation of residual stresses under stepwise increases in external loads proceeds fairly monotonically, especially in the first steps. Specimens having a large initial value of residual stresses retain the stability of the latter at high values of external loads. Under the same external loads, residual stresses prove to be more stable in specimens made of a stronger material. This phenomenon, however, occurs only in those cases where the magnitude of the initial residual stresses is of substantial significance.

In specimens of hardened steel ShKh15 (\(HV600\)), no appreciable relaxation of residual stresses was detected in tests under loads from 5 to 72 kg/mm\(^2\).

REFERENCES

1. L. A. Glikman. Stability of residual stresses and their influence on the mechanical properties of metals and the strength of products. Surface Quality and Durability of Machine Parts. Collection No. 13. NIS—LIEI Publishing House, 1956.

2. D. E. Zaitsev, G. D. Del, M. G. Goldshmidt. On the assignment of grinding regimes for a specified tolerance for warping. Proceedings of TPI, vol. 183, Tomsk, 1968.

3. G. V. Toporov, G. V. Kozyrev. Machine for testing stability under pulsating loading. Fatigue of Metals under Impact Cyclic Loads and Investigation of Impact-Action Machines. TSU Publishing House, Tomsk, 1969.