Physicochemical Phenomena During the Deformation of Metals

V. I. Likhtman

1. Introduction

It has been established by the work of Soviet physicochemists[^1] that the influence of the surrounding medium on the mechanical properties of metals during their deformation is observed not only in the form of the usual chemical (corrosive) action of the medium on the metal. Adsorption (even reversible adsorption) of typical surface-active substances from the surrounding medium also causes the deformation and fracture of metals to be facilitated, and sometimes to a considerably greater extent than in the case of direct chemical transformation.

The effect of adsorption-induced facilitation of deformation, or adsorption-induced lowering of strength, is due above all to the fact that surface-active substances, by lowering the surface energy of a metal, thereby promote the initiation of plastic shears and the development of various defects at lower stresses. This constitutes the primary initiating action of adsorption[^1].

Surface defects of the structure—weak points that are always present in any solid body and even in the most well-formed crystals—are primarily subject to adsorption action. These ultramicroscopic defects, arising in a solid body in the course of its formation, apparently constitute a phenomenon just as necessary as the regularity itself of the crystal lattice of a solid body.

In the process of elastic and plastic deformation, the indicated structural defects continuously develop and, moreover, many new defects are formed, associated with plastic shears along slip planes in the metal being deformed. The character of these defects, their topography, and their distribution in the volume and on the surface have as yet been studied far from sufficiently. Most often these defects are interpreted as microscopic or even as

ultramicroscopic cracks or slits of wedge-shaped cross section, characterized at their mouths by a fully developed surface with the normal value of the specific free surface energy \(\sigma^{1,2}\). The free surface energy on the developing surfaces of such wedge-shaped microcracks \(\sigma_h=f(h)\) increases from zero in the narrowest part of the wedge, where the walls of the slit gradually come together to nothing (\(\sigma=0\) at \(h=0\)), up to the greatest normal value \(\sigma\) as the thickness of the microcracks \(h\) increases to their full opening at the mouths.

The presence of defects of this kind in the structure of solids, as is known, has a substantial effect on their mechanical properties. The influence of structural defects that develop in the process of deformation of a solid body is manifested above all in a sharp decrease in its strength in comparison with the greatest theoretical value of the strength, computed, for example, from the theory of the crystal lattice.

The role of structural defects is also revealed in the so-called scale factor, i.e., in the dependence of the strength of specimens of a given material on their dimensions. Thus, for example, a glass fiber 16 μ in diameter has a strength of \(107\ \text{kg}\cdot\text{mm}^{-2}\), a fiber of 8 μ has a strength of \(207\ \text{kg}\cdot\text{mm}^{-2}\), and a fiber of 2.5 μ has a strength of \(560\ \text{kg}\cdot\text{mm}^{-2}\)³.

Thus, structural defects—wedge-shaped microcracks, both those initially present in a solid and those arising in the process of its deformation—reduce the strength of the body and facilitate the process of deformation and fracture. At the same time, these defects play a major role in the interaction of the deforming solid with the surrounding medium, since they are the gates through which the surrounding medium and the surface-active substances contained in it can penetrate into the interior of the body.

The scientific and practical importance of physicochemical phenomena in the deformation and treatment of solids, and especially metals, determines the need for further development of this important field, which has arisen at the boundary between solid-state physics and the physicochemistry of surface phenomena under conditions of the close connection between theory and practice characteristic of Soviet science.

2. CREEP OF SINGLE CRYSTALS

Plastic flow in metallic single crystals arises at any stress, however small. This means that the true yield point (elastic limit) in these single crystals is equal to zero, and one can speak only of a certain conventional yield point \(P_m\), corresponding to the stress at which a more or less abrupt transition into the region of appreciable plastic deformations is observed. The study of the creep of tin single crystals under the action of small constant

...of stresses lying below this conventional yield limit\(^{4,5}\) led to the establishment of a dependence (Fig. 1) between the initial flow rate and the magnitude of the stress: \(P=\eta V_0\), which proved to be identical with the analogous dependence found by Newton for the viscous flow of a liquid.

Experience shows that, for any kind of testing of metals (shear, uniaxial tension or compression, torsion), the deformation stress \(P\) depends on the magnitude of the deformation \(\varepsilon\), the deformation rate \(\dot{\varepsilon}\), and the time \(\tau\). Each of these three parameters should be regarded as independent of the other two in the sense that the physical nature of the change in \(P\) with the change in each of these three parameters is essentially different.

The dependence of \(P\) on \(\varepsilon\) determines the strain hardening of the metal in the process of deformation, and it is known that hardening associated with disturbance of the regular arrangement of atoms along slip planes develops independently of the temperature \(T\), the time \(\tau\), and the deformation rate \(\dot{\varepsilon}\). However, in most cases the athermal character of hardening is masked by the phenomenon of recovery or, what is the same thing, by the change of \(P\) with time \(\tau\) (at \(T=\mathrm{const}\)) as a result of the displacement of atoms in the crystal lattice, i.e. the restoration of damaged regions at a rate noticeable only at sufficiently high temperatures.

Fig. 1. Dependence between the initial creep rate and the magnitude of the stress for tin single crystals. The stress is below the yield limit.

The dependence of \(P\) on \(\dot{\varepsilon}\) is due to the phenomenon of internal friction in the metal.

Thus,

\[ P=P(\varepsilon,\dot{\varepsilon},\tau). \tag{1} \]

The form of dependence (1) is in general unknown. Assuming, however, for the case of creep of metals, i.e. for small stresses lying below the conventional yield limit, that \(P\) is a continuous and single-valued function of \(\varepsilon\), \(\dot{\varepsilon}\), and \(\tau\), admitting expansion into a convergent power series, one may expand \(P\) in powers of \(\varepsilon\), \(\dot{\varepsilon}\), and \(\tau\) and restrict oneself to the first terms of the expansion:

\[ P=P_0+\lambda\varepsilon+\eta\dot{\varepsilon}-\chi\tau. \tag{2} \]

The physical meaning of the constant coefficients \(\lambda\), \(\eta\), and \(\chi\) is determined from equation (2):

\[ \lambda=\frac{\partial P}{\partial \varepsilon}, \qquad \eta=\frac{\partial P}{\partial \dot{\varepsilon}} \quad \text{and} \quad \chi=-\frac{\partial P}{\partial \tau}. \]

Consequently, \(\lambda\) is the coefficient of hardening, \(\eta\) the coefficient of internal friction (viscosity), \(\chi\) the coefficient of recovery, and \(P_0\) the limit of true elasticity (creep limit).

It follows from (2) that for \((\varepsilon,\tau)\to 0\), i.e., at the initial moment of loading,

\[ P=P_0+\eta\dot{\varepsilon}_0. \]

For metallic single crystals \(P_0=0\) and \(P=\eta\dot{\varepsilon}_0\), which is confirmed by experiment \(^{4,5}\).

In the general case, when \(\varepsilon\) and \(\tau\) differ from zero, from equation (2) we obtain

\[ P-(\lambda\varepsilon-\chi\tau)=\eta\dot{\varepsilon} \]

(in view of the absence of \(P_0\)). It follows from this equation that the stress \(P\) applied to a single crystal and causing its creep does not remain constant with the growth of deformation and time, but continuously decreases, being less than \(P\) by the amount \(\lambda\varepsilon-\chi\tau\). This latter quantity plays the role of the true elastic limit (creep limit), absent before deformation and arising in the course of the plastic flow of the single crystal. The appearance of a creep limit during the plastic flow of a single crystal is associated with the developing hardening, which in the initial stage of creep is incompletely compensated by recovery.

Thus, a metallic single crystal in the initial, unhardened state, with respect to its flow properties under the action of small stresses, is similar to an ideal Newtonian liquid, whose viscosity is determined by the ratio \(P/\dot{\varepsilon}_0\). However, subsequently, as plastic deformation increases, the metallic single crystal becomes a rigid-plastic body possessing a quite definite elastic limit (creep limit), and it “hardens” more and more in the sense that its elastic limit continuously increases together with the growth of deformation, up to the completion of the first stage of creep (until entry into the region of steady flow), after which the elastic limit remains constant.

In passing to polycrystalline metals it is necessary to take into account the presence of an elastic region already existing initially, characterized by a definite value of the elastic limit \(P_0\). However, this elastic limit also does not remain constant in the course of the plastic flow of the metal, but grows as a result of hardening and, in the first approximation, may be written as \(P_0+\lambda\varepsilon-\chi\tau\). Consequently, the viscosity of a polycrystalline metal, determined by analogy with colloidal structured systems as the plastic viscosity

\[ \eta=\frac{P-P_0}{\dot{\varepsilon}}, \]

does not

remains constant during the process of deformation, but changes continuously as a result of the increase in the elastic limit (yield limit) \(P_0\).

From equation (2), for \(dP\), as a total differential, we obtain

\[ dP=\lambda\,d\varepsilon+\eta\,d\dot{\varepsilon}-\chi\,d\tau. \]

But since, in investigations of the creep of metals, usually \(P=\mathrm{const}\), then \(dP=0\), and consequently,

\[ \lambda\,d\varepsilon+\eta\,d\dot{\varepsilon}-\chi\,d\tau=0. \]

Solving this differential equation under the condition that the coefficients \(\lambda\), \(\eta\), and \(\chi\) are constant, we obtain the general equation of creep:

\[ \varepsilon=\dot{\varepsilon}_m\cdot\tau+(\dot{\varepsilon}_0-\dot{\varepsilon}_m)\frac{\eta}{\lambda} \left[1-e^{-\frac{\lambda}{\eta}\tau}\right], \tag{3} \]

where \(\dot{\varepsilon}_m\) is the rate of steady-state creep. The general form of the creep curve corresponding to equation (3) agrees with experimental data (with the exception of the last stage of creep, associated with the formation of a neck).

Graphically, equation (3) is represented in Fig. 2. The general curve \(\varepsilon=\varepsilon(\tau)\) may be resolved into two components: the steady-state component, expressed by the equation \(\varepsilon_1=\dot{\varepsilon}_m\cdot\tau\), and the non-steady-state component

\[ \varepsilon_2=(\dot{\varepsilon}_0-\dot{\varepsilon}_m)\frac{\eta}{\lambda} \left[1-\exp\left(-\frac{\lambda\tau}{\eta}\right)\right], \]

whose influence at large \(\tau\) is insignificant. Such a representation of the creep curve is confirmed in many experiments with various metals.

Fig. 2. Resolution of the general creep curve \(\varepsilon=\varepsilon(\tau)\) into two components—the stationary \(\varepsilon_1=\varepsilon_1(\tau)\) and the nonstationary \(\varepsilon_2=\varepsilon_2(\tau)\):

\[ 1:\ \varepsilon=\varepsilon_1+\varepsilon_2;\qquad 2:\ \varepsilon_1=\dot{\varepsilon}_m\cdot\tau;\qquad 3:\ \varepsilon_2=(\dot{\varepsilon}_0-\dot{\varepsilon}_m)\frac{\eta}{\lambda} \left[1-\exp\left(-\frac{\lambda}{\eta}\tau\right)\right]. \]

It should be noted that, in studying the creep of colloidal structured systems, P. A. Rebinder\(^6\), proceeding from entirely different considerations based on the analysis of simple mechanical models, uses an equation formally analogous to equation (3). The difference between these equations, arising from the difference in the properties of colloidal structured systems and metals, consists in the fact that the non-steady component of creep deformation in the first case is caused by the process of elastic aftereffect, whereas for metals this component is associated with plastic flow.

The values of the constants \(\lambda\), \(\eta\), and \(\kappa\) for tin single crystals are given in Table 1.

Table 1

Values of the coefficients \(\lambda\), \(\eta\), and \(\kappa\) for tin single crystals under various stresses

The values of \(\eta\) agree well with the results of V. D. Kuznetsov’s experiments\(^{31}\) on determining the viscosity of coarse-grained tin. At first glance the values of \(\lambda\) may seem too high; however, it should be borne in mind that the magnitude of the deformation corresponding to the yield point is \(\varepsilon_m \approx 0.5\%\), and

\[ \lambda=\frac{dP}{d\varepsilon}\approx \frac{P_m}{\varepsilon_m}\approx 250/0.005, \]

whence \(\lambda \approx 50\ \mathrm{kg\cdot mm^{-2}}\), which agrees well with the calculated values.

A study of the influence of solutions of surface-active substances of different composition and structure (homologous series of fatty acids, alcohols, ethers, chloro-derivatives, etc.) on the creep of tin single crystals, carried out in our laboratory by E. K. Venstrem\(^{5}\), showed that the dependence of the effect (the magnitude of the relative deformation of the specimen in the active medium as compared with the deformation in air) on the concentration of these substances in hydrocarbon (octane) solutions is expressed by curves with a sharply pronounced maximum, after which the effect gradually decreases down to the concentration corresponding to 100% of the soluble component (Fig. 3).

The hydrocarbon solvent in this case has practically no effect on the creep of tin single crystals, thus being an inactive medium. Accordingly, the action of surface-active additives on tin is determined only by the nature of the polar-

groups of molecules, arranged according to the effect they produce (at the maximum of the curves) in the following order:

\[ (-\mathrm{COOH}) > (-\mathrm{OH}) > (-\mathrm{COOCH}_3) > (-\mathrm{Cl}). \]

From this it is evident that it is sufficient, for example, to block the carboxyl group by replacing in it the hydrogen atom with a methyl group, for the effectiveness of the additive to decrease sharply. For the same reason,

Fig. 3. Dependence of the magnitude of the adsorption effect of creep facilitation of tin single crystals on the concentration of various surface-active media in hydrocarbon (octane): 1—lauryl alcohol; 2—caprylic acid; 3—methyl laurate; 4—lauryl chloride; 5—oleic acid.

when a double (polar) bond is introduced into the hydrocarbon chain, for example in the transition from stearic acid to oleic acid, the magnitude of the effect increases from 125% to 190%.

The hydrocarbon chains of the molecules, while not affecting the magnitude of the effect, at the same time determine the concentration of the solution at which the maximum of the curve is reached. These concentrations \((C_m)\) in homologous series, as the molecular weight of the homologs increases, decrease, revealing a dependence analogous to Traube’s rule. As can be seen from Fig. 4, in the series propionic–caprylic–stearic acids these concentrations are respectively 0.640; 0.118, 0.007 mol/l (4.7; 1.7 and 0.2%), decreasing for each

the CH₂ group by 1.3–1.4 times. For stearic and oleic acids the concentrations corresponding to the maxima coincide. For weakly surface-active substances the maximum of the action is reached

Fig. 4. Shift of the maximum adsorption effect depending on the position of the surface-active substance in the homologous series: 1 — stearic acid; 2 — caprylic acid; 3 — propionic acid; 4 — oleic acid.

at very high concentrations (for methyl laurate and lauryl chloride at \(C_m\) of 35% and 48%, respectively).

The influence of the nature of the solvent is no less sharply manifested, as is seen in Fig. 5.

When octane is replaced by benzene (Fig. 5), the concentration of the solution corresponding to the maximum action of the additive—propionic acid—shifts from \(C_m = 0.64\) mole/l to \(C_m = 2.8\) mole/l, i.e., increases by a factor of 4.5, while the magnitude of the effect does not change.

In aqueous solutions, for example, of propyl alcohol, as a result of the interaction of polar groups there occurs not only a shift of the concentration \(C_m\) corresponding to the maximum from 1.62 mole/l to 4.10 mole/l, but at the same time the magnitude of the effect also drops sharply, from 120% to 50%. In this connection it should be borne in mind that in this case the effect also includes the influence of the solvent—water—which, being an active medium with respect to tin, itself gives an effect amounting to 16%.

All these results are in complete agreement with the investigations of A. B. Taubman\(^{7}\), who clarified the influence of the nature of the sol—

tor on surface activity for liquid interphase boundaries. They indicate that the basis of the effect of facilitating

Fig. 5. Influence of the nature of the solvent on the position of the maximum adsorption effect of facilitating slip in tin monocrystals:
1 — propyl alcohol in octane; 2 — propyl alcohol in water; 3 — propionic acid in octane; 4 — propionic acid in benzene.

deformations of metals by an external medium is an adsorption process with the regularities characteristic of it.

The calculation of the viscosity \(\eta\) and the hardening coefficient \(\lambda\) of tin monocrystals is given in Table II.

Table II

Values of the viscosity and hardening coefficient of tin monocrystals at \(P = 150\ \mathrm{G\ mm^{-2}}\), \(t = 20^\circ\mathrm{C}\); \(41^\circ \le \chi_0 \le 55^\circ\)

As was indicated above, the flow of an unhardened metallic single crystal at the first moment of application of the load (below the yield point) obeys Newton’s equation for a viscous liquid: \(P=\eta V_0\), where \(\eta\) is the creep viscosity and \(V_0\) is the initial relative shear rate. Assuming in this equation, in accordance with the known concepts of the dependence of viscosity on temperature, \(\eta=A\exp(U/kT)\), we shall represent the activation energy in the form \(U=U_0+S_0\sigma\), where \(S_0\sigma\) is the part of the activation energy associated with the formation of a new metal surface. Here \(\sigma\) is the free surface energy of the newly forming metal surface at the boundary with the external medium, and \(S_0\) is the “characteristic surface” of the metal (dimension \(\text{cm}^2/\text{atom}\)). Consequently,

\[ \eta=A_0\exp(S_0\sigma/kT), \quad \text{where } A_0=A\exp(U_0/kT). \]

A decrease in surface tension upon adsorption of surface-active molecules contained in the surrounding medium will entail a decrease in the viscosity of the metal \(\eta\), which, in turn, will cause an increase in the initial creep rate \(V_0\) at a given stress \(P\). Indeed, in the absence of adsorbing substances we have \(P=A_0U_0\exp(S_0\sigma_0/kT)\), while in a surface-active medium \(P=A_0U\exp(S_0\sigma/kT)\), whence \(U/U_0=\exp[S_0(\sigma_0-\sigma)/kT]\), which determines the ratio of the initial creep rates in these two cases.

A simple calculation shows that, for the initial creep rate to increase by a factor of \(e\), it is necessary for the value of \(\sigma\) to decrease by approximately \(200\ \text{ergs}/\text{cm}^2\). Such a decrease upon adsorption on metals possessing a high value of \(\sigma\) is quite possible, since even on the surface of mercury (\(\sigma \approx 470\ \text{ergs}/\text{cm}^2\)) adsorption of polar molecules causes a decrease in surface energy of up to \(200\ \text{ergs}/\text{cm}^2\).

The above scheme for calculating the adsorption effect shows that a decrease in the free surface energy on the external surface of a metal as a result of adsorption can in itself cause a significant effect, for example, an increase in the creep rate.

The influence of the surrounding medium and of the surface-active substances contained in it on the process of deformation of metals has always been considered in the works of P. A. Rebinder and his collaborators as the result of the adsorption action of surface-active substances on the metal itself and has not been connected with the presence of oxide films on the metal surface.

A number of works carried out in recent years convincingly support this point of view\(^{8,9,10}\). In recently published works by Masing and his collaborators\(^{11,12}\), in which the principal adsorption ...

effects on mono- and polycrystalline metals; the adsorption character of the observed phenomena, which take place on the surface of a metal in the absence of oxide films, is also emphasized.

At the same time, in the works of Andrade and his coworkers[^13],[^14] a different point of view is advanced on the nature of the adsorption effect. In these works the adsorption effect is associated not with the surface of the metal, but with the oxide films covering its surface. According to Andrade, surface-active substances loosen the oxide film, facilitating the plastic flow of the metal.

It is known[^15],[^16] that thin oxide films on the surface of metallic single crystals considerably raise their yield point and hinder further deformation in the main plastic region (at stresses above the yield point). The mechanism of this phenomenon remained not fully clarified. It was suggested that oxide films inhibit the nucleation of dislocations on the surface of crystals, heal existing defects and prevent the formation of new ones, and, finally, that oxide films possess high strength.

In the work of V. S. Ostrovskii in our laboratory, the influence of oxide films on the flow of cadmium single crystals was studied in detail[^17].

The oxide film on the single crystals under investigation was produced under a definite oxidation regime. The specimens were annealed in air at a temperature of \(230^\circ\) for 2 hours. Under this oxidation regime the oxide film formed had a thickness of about \(900\ \text{\AA}\). The thickness of the film was determined by the weighing method with a weighing accuracy on a microbalance of \(2 \cdot 10^{-4}\) g, which amounted to about \(5\%\) of the measured weight gain. The density of CdO was taken from tables (\(8.15\ \text{g}/\text{cm}^3\)).

Mechanical properties of Cd single crystals were investigated under conditions of a constant tensile rate \(V = 1.5\%\ \text{min}^{-1}\). The accuracy of stress measurement was about \(2\%\) of the measured value at the yield point.

Fig. 6. Typical tensile diagrams of standard oxidized (oxide-film thickness \(\sim 900\ \text{\AA}\); \(P, 1\)) and unoxidized (i.e., covered with the oxide film naturally formed in air at room temperature; \(P, 2\)) cadmium single-crystal wires of diameter \(0.5\ \text{mm}\). Also shown here is the course of the sliding stress \(P_s\) for oxidized (\(P_s, 1\)) and unoxidized (\(P_s, 2\)) specimens.

In Fig. 6 typical tensile diagrams are presented for standard oxidized (curve 1) and unoxidized (i.e., covered with an oxide film naturally formed in air at room temperature—curve 2) single-crystal cadmium wires of diameter 0.5 mm at \(\chi_0 = 55^\circ\). The yield point of the oxidized specimen proved to be 14% higher. At the same time, attention is drawn to the change in the breaking-off stress shown in the same figure. In the oxidized specimen, the breaking-off stress in the process of deformation falls rather sharply and only then, as strain hardening increases, rises. Such a decrease in the magnitude of the breaking-off stress during plastic deformation, less pronounced in specimens with a “normal” oxide film (arising during a short holding at room temperature), shows that the yield point in oxidized single crystals is higher than in the metal itself, and that before the intensified shear formation characteristic of single crystals of the hexagonal system began upon reaching the yield point, rupture of the oxide film was evidently required.

Table III gives the change in the yield point \(P_m\) and the critical breaking-off stress \(P_s\), in g/mm\(^2\), of cadmium single crystals of various orientation \(\chi_0\) and diameter \(D\), as a function of oxidation.

Table III

It is seen from the table that the effectiveness of the action of an oxide film of a given thickness increases with decreasing specimen diameter. The increase in \(P_s\) as a result of oxidation is on the average 15% for specimens with \(D = 0.5\) mm, and 25% for specimens with \(D = 0.3\) mm. For a correct understanding of this dependence of the magnitude of the oxidation effect on the diameter of the single crystal, it should be borne in mind that the cross-sectional area of the crystal \(S_0\) in this case decreases from 0.2 to 0.07 mm\(^2\). Consequently, the load \(F = P_m \cdot S_0\), corresponding to the yield point \(P_m\), changes from 40 to 25 g. The ratio of the loads corresponding to the yield point for oxidized specimens of two

of the diameters studied, turns out to be almost exactly equal to the ratio of these diameters. This is apparently connected with the fact that the cross-sectional area of the oxide film also changes in proportion to the diameter. Indeed, the cross-sectional area of a film of thickness \(h\) is \(S=\pi Dh\), and for a given film thickness \(S_1/S_2=D_1/D_2\).

The cross-sectional area of the film for \(D=0.5\) mm is \(S_1=14\cdot10^{-5}\ \text{mm}^2\), and for \(D=0.3\) mm \(S_2=8.5\cdot10^{-5}\ \text{mm}^2\). From this one can obtain an upper limit for the strength of the oxide film (\(h=900\ \text{Å}\)), if it is assumed that at the moment of rupture of the film the entire load is applied to it. The validity of such an assumption is justified by the fact that the elastic limit of a metallic single crystal is equal to zero and, consequently, the metal under the film is involved in plastic flow and is unloaded already at the very smallest loads.

The strength of the film is \(\sigma_s=F/S=40/1.4\cdot10^{-4}\simeq3\cdot10^5\ \text{g}\cdot\text{mm}^{-2}=300\ \text{kg}\cdot\text{mm}^{-2}\). The same result is obtained for films on specimens with \(D=0.3\) mm (\(\sigma_s=25/8.5\cdot10^{-5}\simeq3\cdot10^5\ \text{g}/\text{mm}^2\)).

Fig. 7. Dependence of the magnitude of the effect of an oxide film of a given thickness (\(\sim900\ \text{Å}\)) on cadmium single crystals on the diameter of the single crystals.

Figure 7 gives the dependence of the effect of the action of the oxide film on the diameter of the Cd single crystal for one and the same initial orientation of the basal plane. The data for \(D=2.8\) mm are taken from the work of Roscoe\(^{15}\). The decrease of the effect with increasing diameter and its complete disappearance at \(D=2.8\) mm are explained by the growth of the absolute magnitude of the load applied to the single crystal. The magnitude of the load corresponding to the yield point for thick specimens considerably exceeds the strength of an oxide film about \(1000\ \text{Å}\) thick, and therefore the film’s own mechanical properties can no longer manifest themselves in the process of deformation.

The same result is obtained in studying the dependence of the magnitude of the effect of the oxide film on the angle of the initial orientation of cadmium single crystals of a definite diameter. Figure 8 shows this dependence for \(D=0.5\) mm (curve 1) and \(0.3\) mm (curve 2). As can be seen, the oxide film produces the maximum effect at \(\chi_0=45^\circ\), and the magnitude of the effect decreases on both sides of this value. The explanation for this may be seen in the dependence of the yield point of the single crystal itself on \(\chi_0\). \(P_m\) is minimal at \(\chi_0=45^\circ\) and increases both with a decrease and with an increase of this angle. Consequently, at \(\chi_0=45^\circ\) the load at the yield point will be the smallest, and the effect of the film, in accordance with this, will be the greatest.

Thus, as a result of the investigation carried out, it may be asserted that the influence of oxide films on the mechanical properties of metallic single crystals lies in the intrinsic strength properties of the oxide films.

The circumstance that this strength proves to be very considerable—about 300 kg·mm\(^{-2}\) (for CdO)—should not arouse doubt, since it is known that, with decreasing thickness, all bodies considerably increase their strength (the size factor).

Thus, for example, thin glass threads 3–5 μ thick possess a tensile strength of up to 300 kg·mm\(^{-2}\), which is already close to the theoretical value of strength\(^{3}\). It may be assumed that a CdO film about 0.1 μ thick likewise possesses a strength close to the theoretical one.

Fig. 8. Dependence of the magnitude of the effect of the action of an oxide film of a given thickness (\(\sim 900\) Å) on the angle of the initial orientation of the basal plane in cadmium single crystals of diameter 0.5 mm (curve 1) and diameter 0.3 mm (curve 2).

The effect of the action of the oxide film is manifested, as was already said, not only in an increase of the yield limit, but also in the hindrance of further deformation of the single crystal in the principal plastic region, as is also seen from Fig. 6. This phenomenon, apparently, is explained by the fact that, as plastic deformation of the oxidized specimens develops, ever new packets of slip enter into action, for the formation of which it is necessary again to tear the oxide film. Confirmation of this may be seen in the fact that oxidized cadmium single crystals form, at the beginning of slip, rather thick packets, gradually becoming thinner as the deformation develops.

The study of the influence of surface-active substances on the process of deformation of cadmium single crystals, both oxidized and deprived (completely or partially) of oxide films, was carried out in solutions of oleic acid in isooctane and of n-butyl alcohol in water at optimal concentrations\(^{5}\).

The adsorption effect of facilitating the deformation of single crystals stretched with a prescribed (constant in the present experiment) rate of elongation was evaluated by the relative decrease of the yield limit \(P_m\):

\[ \Delta P_m=\frac{P_m-(P_m)_a}{P_m}\cdot 100\%. \]

The rate of deformation was varied within the limits \(0.5\%\,\text{min}^{-1} \leq V \leq 400\%\,\text{min}^{-1}\).

It is necessary to point out that etching does not completely remove the oxide film from the surface of the specimen. A thin hydroxide film with a thickness

Fig. 9. Dependence of the magnitude of the adsorption effect during stretching of cadmium single crystals from which the standard deposited oxide film (thickness \(\sim 900\) Å) had previously been removed by etching in an HCl solution. Curve 1—in a 0.2% solution of oleic acid in isooctane; curve 2—in a 1.0% solution of \(n\)-butyl alcohol in water.

Fig. 10. Dependence of the magnitude of the adsorption effect during stretching of cadmium single crystals having a surface oxide film of thickness \(\sim 900\) Å. Curve 1—in a 0.2% solution of oleic acid in isooctane; curve 2—in a 1.0% solution of \(n\)-butyl alcohol in water.

up to 100 Å, remaining on the cadmium single crystal after etching, by itself, however, does not change its mechanical properties, as shown by control experiments.

As is seen from Fig. 9, the adsorption effect increases with increasing deformation rate and reaches a maximum at rates of \(100\text{–}200\%\ \mathrm{min}^{-1}\). In the region of low rates (about \(1\%\ \mathrm{min}^{-1}\)) the effect is practically absent. Pure solvents—isooctane and water—as shown by control experiments, are inactive on cadmium single crystals.

Figure 10 presents the dependence of the magnitude of the adsorption effect on the deformation rate for oxidized specimens

(curve 1—in a 0.2% solution of oleic acid in isooctane, curve 2—in a 1.0% solution of n-butyl alcohol in water). A significant feature of this dependence, in comparison with that which occurs for etched specimens, is the presence of an adsorption effect in the region of low rates of deformation.

This circumstance acquires special importance in connection with the fact that, in the cited works of Andrade, the adsorption effect on cadmium single crystals was studied at low rates of extension, which apparently was one of the reasons for the erroneous conclusions drawn from these works. It should also be pointed out that there was another methodological error in Andrade’s experiments, consisting in the method of removing the oxide film from the surface of the cadmium single crystal. In these experiments the oxide film was removed by heating the oxidized specimens at 250° in vacuum. However, there is evidence that under such conditions, during dissociation of cadmium oxide, the liberated oxygen penetrates in appreciable quantity into the cadmium lattice, forming a solid solution of interstitial type in the surface layer[^18]. The internal compressive stresses inevitably arising in this process sharply reduce the magnitude of the adsorption effect of deformation facilitation, as was shown by direct experiments of G. V. Karpenko[^19].

Thus, the methodological errors made by Andrade both in the preparation of the test specimens and in carrying out the experiments led to the fact that in these experiments the adsorption effect was observed only on oxidized specimens, whereas unoxidized specimens, improperly prepared and tested outside the optimal range of deformation rates, gave a negative result.

The presence of a rather considerable adsorption effect at low rates on cadmium single crystals covered with an oxide film should be explained by the influence of the oxide film itself, but not in the sense in which Andrade understands it. According to V. N. Rozhanskii[^8], the influence of the oxide film consists in the fact that its destruction during deformation of the single crystal is accompanied by the formation of cracks, in the blind ends of which a concentration of stresses arises. Previously, a positive influence of stress concentration in the surface layer on the magnitude of the adsorption effect had been established[^20].

Consequently, surface-active substances, penetrating along the cracks formed in the oxide film to the surface of the metal and being adsorbed on this surface, facilitate the deformation of the metal even at low rates of extension as a result of the nonuniform stressed state that arises during cracking of the film, with stress concentration in the blind ends of the cracks.

3. ELECTROCAPILLARY EFFECT

In a number of studies carried out by E. K. Venstrem in our laboratory[^21][^22], it was shown that, upon polarization of the surface of brittle solids possessing electronic conductivity (pyrite, graphite), as well as of metals (thallium, zinc, lead, tellurium) in aqueous electrolyte solutions, the hardness \(H\) changes as a function of the potential jump \(\varphi\) at the solid body—solution interface, analogously to the surface tension \(\sigma\) at the mercury—solution surface, in accordance with the electrocapillary curves \(\sigma=\sigma(\varphi)\) (whose general equation is \(-d\sigma/d\varphi=e_s\), where \(e_s\) is the surface charge density), with a characteristic maximum for an uncharged surface and with a decrease of \(H\) or \(\sigma\) upon charging in either direction, irrespective of the sign of the charge.

The influence of surface-active substances on this effect also proved to be entirely similar to their influence on the course of the electrocapillary curve. This influence consists in a lowering of the hardness, most strongly expressed at the maximum of the curves \(H=H(\varphi)\), and decreasing sharply upon charging of the surface.

The hardness in these experiments was measured by a modified Kuznetsov method, by damping the amplitude of oscillations of a pendulum-dispergometer. Owing to the plastic character of the deformation of metals and their comparatively low hardness, the diamond tips of the instrument were replaced by glass balls 1–2 mm in diameter, resting on the solid surface under investigation, wetted with the electrolyte solution. As electrolytes, 1.0 N and 0.1 N solutions of NaCl, \(\mathrm{Na_2SO_4}\), \(\mathrm{NaCO_3}\), and KBr were used, with alkalization on the cathodic branch of the curve to 0.01 N NaOH and with acidification on the anodic branch to 0.01 N \(\mathrm{H_2SO_4}\).

The results of measurements on metals are presented in summary Table IV.

Studies of the electrocapillary effect on metals were subsequently continued by V. K. Venstrem on the creep deformations of metallic single crystals[^5]. These investigations are of particular interest in connection with works that had appeared in the literature devoted to clarifying the question of the role of oxide films in the adsorption effect of deformation facilitation.

The study of the influence of the potential jump and of adsorbing substances on the creep of single crystals of tin and lead was carried out by recording complete extension—time diagrams \(\varepsilon=\varepsilon(t)\) at a constant stress \(P=\mathrm{const}\), lying below the yield point. The electrolyte was a 0.1 N solution of \(\mathrm{Na_2SO_4}\) (in the case of tin, with the addition of 0.01 N \(\mathrm{H_2SO_4}\)). The fresh thin oxide films present on the metal surface were reduced by strong short-term cathodic polarization (\(\varphi=3\text{–}5\ \mathrm{V}\)) in the unstressed state of the specimen, after which it was stretched.

Table IV

Potentials (in volts) of electrocapillary hardness maxima \(\varphi'_m\) (at \(\partial H/\partial \varphi = 0\)) and of surface tension, relative to the 1 N calomel electrode

\(*\) Values of \(\varphi_m\) are listed according to the data of S. Karpachev and A. Stromberg\(^{23}\) for the surface tension of molten metals at a temperature of \(420\text{–}450^\circ\) (tellurium at \(550^\circ\)) at the boundary with a salt melt, referred to the maximum of the electrocapillary curve of mercury at \(420^\circ\).

\(**\) According to A. N. Frumkin and A. B. Gorodetskaya\(^{24}\), for \(\sigma(\varphi)\) at the boundary amalgam \(41.5\%\) Tl / 1 N \(Na_2SO_4\).

An acidic medium ($pH = 2.8$) excluded the possibility of re-formation of phase oxide films on tin and eliminated the action on the metal of the alkali formed during polarization; after removal of the oxide film the medium practically did not change ($pH = 2.85$). Special experiments showed that, in the electrolyte, the magnitude of the deformation of single crystals does not change in comparison with stretching in water.

The magnitude of the effect of the active medium was estimated by the relative increase in the deformation of single crystals in this medium ($\varepsilon_a$) in comparison with the deformation ($\varepsilon_0$) in an inactive medium—an electrolyte—at a certain specified duration of stretching (5 hours), i.e., by the quantity

\[ \Delta \varepsilon \% = \frac{\varepsilon_a - \varepsilon_0}{\varepsilon_0}\cdot 100 = f(\varphi). \]

Figure 11 presents the dependence of the magnitude of the relative elongation ($\varepsilon\%$) of lead single crystals during polycreep on the value of the potential jump ($\varphi$) in an inactive medium (aqueous electrolyte solution, 0.1 N Na$_2$SO$_4$, curve 1) and in an active medium (the same electrolyte solution containing an anion-active wetting agent—sodium hexadecylbenzenesulfonate C$_{16}$H$_{33}$C$_6$H$_4$CO$_3$Na—“sulfanol” at a concentration of 0.070 mole/l, curve 2). The course of this dependence is in full agreement with the general regularity of the influence of the surface charge density of metals obtained in hardness experiments. The curves shown in Fig. 11 refer to values of $\varepsilon$ corresponding to stretching of the single crystals for 5 hours; however, similar curves can also be obtained for any other duration of the experiment.

Fig. 11. Electrocapillary curves for the facilitation of deformation by polycreep of lead single crystals (experiment duration $\tau = 5$ hours); $\varepsilon$—relative elongation in percent; $\varphi$—polarization potential in volts. Curve 1—in 0.1 N Na$_2$SO$_4$ solution; curve 2—in 0.1 N Na$_2$SO$_4$ solution + 0.07 mole/l sulfanol.

Similar curves for tin single crystals in a solution of the same electrolyte \((1.0\ \mathrm{N}\ \mathrm{Na_2SO_4} + 0.01\ \mathrm{N}\ \mathrm{H_2SO_4})\) and with the addition of \(n\)-propyl alcohol at a concentration of \(3.30\ \mathrm{mole/l}\) are shown in Fig. 12.

In contrast to the electrocapillary curves obtained earlier for the decrease in the hardness of metals, which had a maximum, here the effect of facilitating deformation is expressed by an increase in the rate of plastic flow of the metal, and therefore the curves are characterized by the presence of a minimum. As is seen from Figs. 11 and 12, the positions of the minima of the curves \(\varepsilon(\varphi)\), corresponding to the uncharged surface

Fig. 12. Electrocapillary curves for the facilitation of creep deformation of tin single crystals (longitudinal orientation of the experiment, \(\tau = 5\) hours): \(\varepsilon\) — relative elongation in percent; \(\varphi\) — polarization potential in volts. Curve 1 — in a \(0.1\ \mathrm{N}\) solution of \(\mathrm{Na_2SO_4} + 0.01\ \mathrm{N}\ \mathrm{H_2SO_4}\); curve 2 — in a \(0.1\ \mathrm{N}\) solution of \(\mathrm{Na_2SO_4} + 0.01\ \mathrm{N}\ \mathrm{H_2SO_4} + 3.3\ \mathrm{mole/l}\ \mathrm{C_3H_7OH}\).

of the metals, correspond to the values of \(\varphi\): for tin \(\varphi = -0.52\ \mathrm{V}\) and for lead \(\varphi = -0.88\ \mathrm{V}\) (relative to the normal calomel electrode). This latter value agrees well with the value of the potential that was obtained earlier for the maximum hardness of lead \((\varphi = -0.84\ \mathrm{V})\).

As might have been expected, for the metals studied it is possible to obtain only the cathodic branches of the curves, since in the anodic region the formation of surface oxides occurs, although for lead the curve can be extended somewhat to the left of the minimum (by \(\sim 0.2\ \mathrm{V}\)). The effect of the influence of surface-active substances, expressed in facilitating the flow of metals, again, as expected, proved to be most sharply expressed at the minimum of the curves, in the region close to the zero-charge points of the metals. As the magni-

values of polarization, independently of the sign of the charge, to the right and to the left of the minimum, the effect gradually decreases and becomes practically zero at sufficiently large potentials. To this characteristic dependence of the influence, on the adsorption of surface-active substances, of the electric field of ions displacing organic molecules from the metal—solution interface correspond curves 2 in Figs. 11 and 12, which in the region of the minimum give a section with an almost rectilinear segment and then merge with the principal curves (at \(\varphi=-1.8\ \text{V}\) for tin and \(\varphi=-2.0\ \text{V}\) for lead). In Fig. 13 the corresponding dependence of the magnitude of the adsorption effect on polarization, \(\Delta \varepsilon=f(\tau)\), is presented for both metals.

Fig. 13. Dependence of the magnitude of the adsorption effect on the polarization potential for single crystals of lead (curve 1) and tin (curve 2).

The presence of an adsorption effect on cadmium single crystals, with complete removal of phase oxide films from its surface, was discovered by V. S. Ostrovskii under conditions of cathodic polarization of specimens in an electrolyte solution\(^9\). The results of these experiments are presented in Fig. 14. The electrolyte was a 1 N solution of KCl, slightly acidified with hydrochloric acid.

The stationary potential of cadmium under these conditions proved to be equal to \(-0.5\ \text{V}\). As is seen from Fig. 14, the yield point of a cadmium single crystal is maximal at the point of zero charge (curve 1) and decreases both when the potential is increased and when it is lowered (the point of zero charge in these experiments was near a potential of \(-0.7\ \text{V}\) relative to the normal hydrogen electrode).

In the presence of surface-active substances (a 1% solution of n-butyl alcohol, curve 2), a flattening of the electro-

capillary curve in complete agreement with the general theory of electrocapillary phenomena. The maximum adsorption effect is observed at the point of zero charge and decreases when the potential changes, as a result of a decrease in adsorption when the surface is charged.

All these results clearly illustrate the adsorption character of the phenomena observed.

In connection with the study of the electrocapillary effect on metals, it is necessary to point out the interesting work of Pfotzenreiter and Mazing[^11], which appeared above all in connection with the works of E. K. Venstrem considered here, and also in connection with the works of Andrade on the mechanism of the adsorption effect.

Fig. 14. Electrocapillary curves of deformation softening of cadmium single crystals; \(P_m\) is the value of the yield limit in \(G/mm^2\); \(\varphi\) is the polarization potential in volts. Curve 1 is in a 1.0% solution of KCl, slightly acidified with hydrochloric acid; curve 2 is in the same solution + 1.0% butyl alcohol.

In the work of the authors mentioned, the electrocapillary effect was studied on certain polycrystalline metals (lead, zinc, silver, gold, platinum), of which the noble metals are of special interest, since under ordinary conditions they do not have phase oxide films on their surface.

The experiments were carried out very carefully, and the results obtained are in complete agreement with our data.

Table V gives the results of the experiments of Pfotzenreiter and Mazing.

The conclusions that follow directly from the work of E. K. Venstrem, and also from the work of Pfotzenreiter and Mazing, are in complete contradiction with the conclusion of Andrade and other authors that the principal role in the adsorption effect of softening the deformation of metals belongs to surface (oxide) films, which, under the action of surface-active substances, are destroyed to one degree or another, thereby facilitating the flow of the metal.

The following facts described above contradict this:

1. The deformation of single crystals in the work of E. K. Venstrem was carried out under conditions of prolonged cathodic polarization, which excludes the possibility of preserving phase oxide films on the surface of the metal.

Table V

oxide films. Typical electrocapillary curves can be obtained only under conditions in which oxide films are absent.

1. The influence of polarization, like the influence of surface-active substances, is manifested in a change in the rate of deformation of single crystals immediately after a change in the magnitude of the potential jump or in the concentration of the adsorbing additive.

2. The electrocapillary effect is observed independently of the sign of polarization, both in the cathodic and in the anodic regions, as was established in the work of Pfotzenreuter and Masing on gold and platinum.

Therefore, the data obtained in the study of the electrocapillary effect and of the effect of adsorption-induced facilitation of deformation of metals allow one to conclude that both of these effects are localized on the surface of the metal itself and are not connected with the presence of oxide films on its surface, although there is no doubt that the presence and thickness of oxide films can cause significant changes in the magnitude of the adsorption effect ^8, ^10.

In the latest work of G. Masing and his collaborators ^12, devoted to the adsorption effect on metals, the untenability of the viewpoint of Andrade and other English investigators on the nature of the interaction of a deformable metal with an ambient medium containing surface-active substances was once again convincingly shown.

In this work the influence of solutions of typical surface-active substances in vaseline oil on the creep of zinc and cadmium single crystals, as well as of polycrystalline wires of zinc, tin, and gold, was investigated.

The authors reproduced all the basic regularities of the influence of surface-active substances on the plastic flow of mono- and polycrystalline metals previously discovered by P. A. Rebinder and his collaborators; they showed the presence of a considerable effect on gold, where, as is known, there is no phase oxide film, and, as a result of carefully conducted investigations, they joined the explanation of these effects given by P. A. Rebinder.

4. THE INFLUENCE OF THE MEDIUM ON THE MECHANICAL PROPERTIES OF POLYCRYSTALLINE METALS

The mechanical properties of polycrystalline metals are determined to a considerable extent by their microstructure, i.e., by the average size of the grains composing the metal. It is known that metals with a fine-crystalline structure possess high resistance to external deforming forces, whereas single crystals are the most plastic. In the works of T. A. Amfiteatrova and B. Ya. Yampolsky, the influence of the microstructure of a polycrystalline metal on the magnitude of the adsorption effect was established ^23.

In these works the influence of surface-active substances on the mechanical properties of metals was studied by the method of uniaxial tension under the action of small constant stresses (creep). Copper and aluminum were chosen as the objects of investigation. The experiments were carried out with specimens of copper wire of diameter 0.5 and 2.0 mm made of electrolytic copper containing 99.98% Cu, and with specimens of aluminum wire of diameter 1.0 and 1.3 mm containing 99.95% Al. By appropriate heat treatment, polycrystalline specimens with different dispersity of the microstructural elements were obtained, so that the mean grain size varied in different copper specimens from 0.2 to 0.005 mm, and in aluminum from 0.22 to 0.06 mm. Before the creep test the specimens were subjected to preliminary stretching (by 3% of the initial length) in order to give them a uniform initial strain hardening. Experience showed that this achieved satisfactory reproducibility of the results.

The creep diagrams were recorded at various stresses, but stresses constant for a given experiment. However, the magnitude of the stress in all experiments remained considerably below the yield point of the metals being deformed. In Fig. 15 the dependence of the initial rate of plastic flow of copper on the magnitude of the applied stress is presented. The rectilinear course of this dependence indicates that in polycrystalline metals, too, there exists a certain initial region of plasticity, characterized by the presence of direct proportionality between the initial flow rate \(V_0\) and the stress \(P\). However, in contrast to a similar regularity for single-crystal metals, in polycrystals extrapolation of the straight line \(V_0=f(P)\) to the value \(V_0=0\) does not lead to the origin of coordinates, which would correspond to the absence of a creep limit \(P_0\), but cuts off on the stress axis a quite definite segment, which should be regarded as the creep limit under the given experimental conditions. As is seen from Fig. 15, in the presence of surface-active substances the creep limit shifts toward lower stresses.

Fig. 15. Dependence of the initial creep rate of copper on the magnitude of the applied stress. Curve 1—creep in air; curve 2—creep in a surface-active medium.

Special experiments established the optimum concentrations of surface-active substances producing the greatest adsorption effect. For butyl alcohol the optimum concentration in nonpolar kerosene (mole/l) proved to be 2.25; for hexyl alcohol, 0.75; for octyl alcohol, 0.30; for cetyl alcohol, 0.02; for oleic acid, 0.02; and for sodium dioctyl sulfosuccinate, 0.01.

As a measure of the adsorption effect, the relative increase in the rate of flow of specimens under tension in an active medium was adopted, in comparison with an inactive medium. The dependence of the relative rates of metal flow in active \((v_a)\) and inactive \((v_0)\) media on the magnitude of the deformation \((\varepsilon)\), namely the dependence \(\ln(v_a/v_0)=f(\varepsilon)\), is shown for copper specimens in Fig. 16. An analogous dependence also occurs for aluminum.

Fig. 16. Change in the relative rate of flow of copper wires in active and inactive media as a function of the magnitude of deformation.

The existence of direct proportionality between the initial rate of deformation and stress, found at small stresses on polycrystalline specimens of copper and aluminum, enabled T. A. Amfiteatrova and B. Ya. Yampolsky to apply to the initial portion of the creep curve a general physical scheme \({}^{32}\) of this process and to calculate the viscosity and the hardening coefficient. These values are given in Table VI.

As is evident from the data of this table, deformation in an active medium is accompanied by a lowering of the yield limit, a decrease in the viscosity of the metal, and some decrease in the hardening coefficient.

Experiments with specimens possessing different dispersion of the microstructure showed that the magnitude of the adsorption-induced facilitation of plastic flow of both copper and aluminum depends substantially on the size of the grains composing the polycrystalline specimen. The effect becomes appreciable when the average grain size is about 20% of the specimen diameter, remaining constant with further growth of the grain. Figure 17 presents the dependence of the magnitude of the adsorption effect for copper on the dimensionless parameter \(\delta=d/D\), where \(d\) is the average grain size and \(D\) is the specimen diameter.

Table VI

Copper \((P = 9.15\ \mathrm{kg}\cdot \mathrm{mm}^{-2},\ t = 20^\circ)\)

Surface-active substances, adsorbing on the outer surface of the metal, act mainly on the grains located in the surface layer. The higher the dispersion of the grains, i.e., the smaller the relative volume accounted for by the crystals located in the surface layer of the metal, the less sensitive the metal as a whole proves to be to the action of surface-active substances during the creep process.

The adsorption effect of facilitating deformation acquires important significance in the problem of fatigue strength. It could be assumed that, under certain conditions, the structure of a metal under the influence of alternating stresses “loosens” considerably faster in adsorption-active media, and that certain phenomena of corrosion fatigue are associated with this effect.

Fig. 17. Change in the magnitude of the adsorption effect as a function of relative grain size.

The influence of surface-active substances on the fatigue strength of steel was first investigated by Sh. Ya. Korovskii \(^{26}\). The investigation was carried out by comparing endurance under identical regimes

loading of specimens located in a nonpolar solvent (vaseline oil, purified by distillation in vacuum) and in a solution of a surface-active substance (0.2% oleic acid in vaseline oil).

Table VII presents the endurance of specimens of normalized steel 40Kh, tested in symmetrical torsion on a Schenck machine at a loading frequency of 1450 cycles per minute. The working diameter of the specimens was 14 mm. The tests were carried out at a stress of 24.2 kg·mm\(^{-2}\), slightly exceeding the endurance limit.

Table VII

Endurance (in millions of cycles)

In the work of Sh. Ya. Korovskii it was also shown that the presence of residual compressive stresses in the surface layer of the metal sharply reduces the magnitude of the adsorption decrease in fatigue strength. Compressive stresses were produced in specimens of normalized steel 18KhNMA by two methods: a) work-hardening as a result of blasting with metallic shot and b) nitriding. In both cases the adsorption effect was practically absent.

Subsequently, investigations on the adsorption fatigue of steels were continued and considerably broadened by G. V. Karpenko \(^{27,28,29}\). In these works chromium steel 20Kh (of pearlite–ferrite structure), steel 40Kh in the hardened and tempered state (martensitic, troostitic, and sorbitic structures for hardened steels and pearlite–ferrite structure for tempered steel), and also ball-bearing steel ShKh-15 in the hardened state (cryptocrystalline martensite + carbides) were investigated. Table VIII gives the results of fatigue tests of steel 40Kh in various media.

From the data of Table VIII it is evident that media of group II significantly reduce the endurance of steel 40Kh, and this reduction clearly depends on the heat treatment of the steel; for example, the reduction for a martensitic structure reaches 83%, while for a pearlite–ferrite structure it is only 34%. All media of group III also produced a fairly considerable reduction in the endurance of steel 40Kh, although

Table VIII

Values of the fatigue limit and of the cyclic-strength coefficient in a given medium \(\beta\) (in %) for heat-treated 40Kh steel in various media*)

*) The fatigue limit was determined: for air at \(N=5\cdot10^6\) loading cycles, for hydrocarbon media at \(N=10^7\); for media of group II, and also for an isoamyl-alcohol solution at \(N=2\cdot10^7\). Frequency \(n=3000\) cycles/min.

and less than the corrosive medium. Similar results were also obtained for steels 20Kh and ShKh-15.

In the works of G. V. Karpenko, the influence of various factors—the structure of the steel, the frequency of cyclic-load changes, the scale factor, etc.—on the adsorption and corrosion fatigue of steels was studied in detail.

The fatigue strength of steels in the presence of surface-active substances is reduced by 15–25%, and on the curves of the dependence of the number of cycles on the load the fatigue limit is clearly expressed, in contrast to curves of the same kind obtained in corrosive media, where this limit is absent. The dependence, discovered by G. V. Karpenko, of the magnitude of the adsorption effect on the frequency of cyclic loading has fundamentally the same character as the dependence of this magnitude on the rate of deforma-

tion, established earlier on metallic single crystals^30. Both at very low and at very high (\(\sim 10\,000\ \mathrm{min}^{-1}\)) frequencies, surface-active substances practically cease to act, and the maximum of the adsorption effect is observed in a certain region of medium loading frequencies \((1500—3000\ \mathrm{min}^{-1})\).

It is necessary to point out one of the principal results of the work of G. V. Karpenko, closely connected with the general mechanism of the action of the surrounding medium on a metal being deformed. In numerous and carefully arranged experiments Karpenko showed that the lowering of the fatigue limit in a corrosion-active medium can always be divided into two components. The first of them, manifested in the early stages of fatigue, is connected with the purely adsorption action of the medium on the metal. It can be separated from the total effect of adsorption and corrosion action by the method of coating or of inhibitor protection. The second component is connected only with the corrosive action of the medium, and its principal characteristic feature is that the magnitude of this component grows continuously with the time during which the metal remains in the corrosive medium.

The known limitations of existing theories of corrosion fatigue, even the most advanced ones, are connected with the extremely essential circumstance that all these theories completely ignore adsorption phenomena, which undoubtedly occur also in corrosion processes, and explain corrosion fatigue only by purely chemical and electrochemical phenomena. Such an approach to the solution of the problem of corrosion fatigue at the present time, when there is already sufficiently extensive experimental material indicating the important role of adsorption phenomena in the reduction of the fatigue strength of metals, is one-sided and cannot claim to solve the indicated problem.

The correct approach to the solution of this problem must take into account both corrosion phenomena and adsorption phenomena, which also occur in corrosion-active media.

No corrosion process proceeding on the surface of a metal can take place without a preceding process of adsorption. Every corrosive medium is, first of all, a surface-active medium in the sense of adsorption action on the mechanical properties of the metal. Consequently, at the first stage of the action of a corrosive medium on the fatigue strength of a metal, the adsorption effect of this action is realized, consisting in a lowering of the fatigue limit as a result of an increase in the number of slip bands, a lowering of the yield point, and facilitation of the formation of fatigue microcracks. And only at the subsequent stages, when the corrosive medium penetrates into these microcracks and accumulates corrosion products in them, the volume

which, as a rule, exceeds the volume of the metal, adsorption phenomena give way to purely corrosion phenomena.

Corrosion, by producing additional stresses inside cracks as a result of the wedging action of corrosion products, promotes the further development of fatigue cracks. The amount of corrosion products increases with time and depends on the aggressiveness of the medium, on the one hand, and on the corrosion resistance of the metal, on the other. The intensity of the corrosion process inside cracks decreases with time, i.e., the intensity of the growth of corrosion stresses decreases, and with it also the intensity of the decrease in endurance.

Corrosion stresses are precisely the factor in the reduction of endurance in a corrosive medium that depends on the time for which a cyclically loaded part remains in this medium.

Adsorption-fatigue phenomena always prepare the ground for the occurrence of the corrosion process. The corrosion process takes place either in cracks formed by adsorption fatigue, or in ultramicrocracks that open under the influence of adsorption-fatigue phenomena in strain-hardened regions of the metal. Thus, corrosion fatigue is an electrochemical process occurring under cyclic loading of a metal whose structure has already been loosened by an adsorption-fatigue process.

Thus, in corrosion fatigue two processes always take place: the primary one—consisting in the adsorption-induced facilitation of the formation of microcracks under the influence of cyclic loading—and the secondary one—the corrosion process proper (electrochemical corrosion) inside already formed cracks, which promotes their further growth. In this connection, the mechanism of corrosion fatigue set forth here may be called adsorption-electrochemical.

The adsorption lowering of fatigue strength is a universal effect characteristic of all surface-active media, including corrosive ones. In the case where the medium is not corrosion-active, only the adsorption effect of reducing fatigue strength is observed, not associated with any chemical or electrochemical action of the medium on the deforming metal. In the opposite case, alongside the adsorption action there also appears, and with the passage of time increases more and more, a corrosion action, which in sufficiently long tests may substantially exceed the magnitude of the adsorption effect.

Such an understanding of corrosion-fatigue phenomena, apparently, may also be extended to other kinds of stressed state arising in a metal during its deformation.

in corrosion-active media. At the same time, such a point of view brings together two previously unconnected areas of phenomena associated with the adsorption and corrosion effects of the surrounding medium on the metal being deformed.

References

1. P. A. Rebinder, Zeits. Phys. 72, 91 (1931).
2. P. A. Rebinder, Anniversary Collection of the Academy of Sciences of the USSR 1, 137 (1947).
3. A. P. Aleksandrov, S. N. Zhurkov, Phenomena of Brittle Fracture, GTTI, 1933.
4. E. Chalmers, Proc. Roy. Soc. 156, 427 (1936).
5. V. I. Likhtman, P. A. Rebinder, Izv. AN SSSR, Ser. Phys. 17, 3 (1953).
6. P. A. Rebinder, in: New Methods of Physicochemical Research, Publishing House of the Academy of Sciences of the USSR, 1950.
7. A. B. Taubman, ZhFKh 10 (1934).
8. V. N. Rozhanskii, P. A. Rebinder, DAN 91, 1 (1953).
9. V. S. Ostrovskii, V. I. Likhtman, DAN 96, 2 (1954).
10. L. A. Kochanova, B. Ya. Yampol’skii, DAN 91, 3 (1953).
11. A. Pfützenreuter, G. Masing, Zeits. Metallkunde 42, 361 (1951).
12. W. Klinkenberg, K. Lucke, G. Masing, Zeits. Metallkunde 44, 362 (1953).
13. E. Andrade, Nature 164, 563 (1949).
14. E. Andrade, R. Randall, Nature 164, 1127 (1950).
15. R. Roscoe, Phil. Mag. 21, 399 (1936).
16. R. King, Nature 169, 543 (1952).
17. V. I. Likhtman, V. S. Ostrovskii, DAN 93, 1 (1953).
18. Smekal, Handb. d. Phys. u. Techn. Mech. 4/2, 116 (1931).
19. G. V. Karpenko, DAN 73, 5 (1950).
20. V. I. Likhtman, E. K. Venstrem, DAN 66, 5 (1949).
21. E. K. Venstrem, P. A. Rebinder, ZhFKh 19, 1 (1945).
22. E. K. Venstrem, P. A. Rebinder, ZhFKh 12 (1952).
23. S. Karpenchev, A. Stromberg, Acta physicoch. URSS 12 (1940).
24. A. N. Frumkin, A. B. Gorodetskaya, Zeits. Phys. Chem. 136 (1928).
25. T. A. Amfiteatrova, B. Ya. Yampol’skii, DAN 82, 5 (1952).
26. Sh. Ya. Korovskii, DAN 59, 8 (1948).
27. G. V. Karpenko, DAN 77, 5 (1951).
28. G. V. Karpenko, DAN 74, 1 (1950).
29. G. V. Karpenko, DAN 73, 6 (1950).
30. V. I. Likhtman, P. A. Rebinder, L. P. Yanova, DAN 56, 8 (1947).
31. K. D. Kuznetsov, Physics of the Solid State, vol. 4, Tomsk, 1947.
32. V. I. Likhtman, DAN 72, 6 (1950).