Physicochemical Phenomena During the Deformation of Metallic Single Crystals

V. I. Likhtman

1. Introduction

The influence of the surrounding medium on the mechanical properties of solids was usually considered only from the standpoint of the chemical activity of the medium with respect to a given solid. It was assumed that the surrounding medium is capable of changing the mechanical properties of solids during their deformation only in those cases where, even in the absence of a stressed state, it produces quite definite irreversible changes—corrosion of the solid or its dissolution.

However, as the work of P. A. Rehbinder and his collaborators has shown, the influence of the surrounding medium in which deformation of a solid takes place is by no means exhausted by a trivial chemical action. Reversible adsorption of typical surface-active substances from the surrounding medium causes facilitation of deformation and fracture of the solid, often to a significantly greater extent than any chemical actions.

The effect of adsorption-induced facilitation of deformation, or adsorption-induced reduction of strength, discovered by P. A. Rehbinder in 1928,^1 is due to the fact that adsorbed substances, penetrating into the mouths of microcracks in the surface layers of the body being deformed, facilitate their development.

A system of defects—weak spots—even in the best-formed crystals creates nuclei on which, beginning with the very smallest deformations, microcracks develop. Their most probable dimensions, and consequently the dimensions at their mouths, continuously increase with increasing deformation; at the same time the magnitude of the adsorption effect also increases. In a state of volume stress in the body, these microcracks have a wedge-shaped cross-section and are characterized by fully opened surface regions—mouths—and blind ends, in which the crack retains an embryonic character.

Unlike Griffith’s ellipsoidal cracks, such real cracks terminate in dead ends like a sharp blade of very large curvature (Fig. 1)—with a radius of curvature of the order of the lattice constant.

The surface energy in such cracks increases rather sharply from zero to the normal value as the gap increases from the dead end to the mouth corresponding to a fully opened, i.e. external, surface of separation. When the deforming forces are removed (in the region of elastic deformations), all microcracks that have dead ends inside the body evidently close from the dead end toward the mouth under the influence of the molecular cohesive forces acting in the lattice of the solid.

Fig. 1. Scheme of the development of microcracks in a deformed solid.

When surface-active substances are introduced into the surrounding medium, adsorption of their molecules occurs freely on the outer surfaces of the body and on the fully opened portions of the surface at the mouths of the microcracks formed during deformation. The adsorbed molecules also penetrate farther into the depths of the microcracks in the process of two-dimensional migration along both of their surfaces, lowering the surface tension by an amount \(\Delta\sigma = \sigma_{0} - \sigma_{\mathrm{g}}\), which determines the two-dimensional pressure \(P_{\sigma} = \Delta\sigma\).

Such penetration occurs up to the critical gap of the microcrack (\(\beta\beta'\) in Fig. 1), corresponding to the appearance of a steric obstacle and equal to twice the diameter of the adsorbed molecules. At this place, in each microcrack, a linear boundary of propagation of the adsorption layer is formed—a kind of barrier, on each unit length of which there acts a two-dimensional pressure \((P_{\sigma} = \sigma_{0} - \sigma_{\mathrm{g}})\) in the direction of further advance of the barrier into the depth of the microcrack, thereby promoting the development of microcracks and the increase of deformation under constant external forces. This is equivalent to an increase of the external force \(F\) by an amount \(\Delta F\), expressing the mechanical action of the adsorption layers. During adsorption from a wetting liquid medium, the liquid penetrates into the mouths of the micro-

cracks under the influence of capillary pressure; however, molecules of the most surface-active component are torn away from the meniscus, migrate ahead, and cover the surfaces of the crack with a significantly greater velocity than the rate of absorption of the liquid as a whole, which experiences viscous resistance. In the part of the microcrack filled with liquid (near the mouth), a thin film of liquid may produce an additional wedging pressure, which is a measure of the lyophilicity of the solid body, of its affinity for the given liquid, and therefore may be intensified during adsorption as a result of the corresponding orientation of the adsorption layer (Fig. 2). As is known, the existence of such a wedging pressure was directly established in experiments by B. V. Deryagin and his collaborators, for example, between two plane-parallel plates with a varying gap, placed in a liquid².

However, such wedging pressure at the mouths is usually, apparently, considerably smaller than the two-dimensional pressure at the leading boundary of the adsorption layer. Solvate layers of liquid (of the pure solvent) do not have time during deformation to advance far into the interior of the deformed body along microcracks and remain only in their widest part—the mouth. The role of solvate layers of liquid increases greatly when the load is removed from the deformed body, in the process of closing of microcracks under the action of molecular forces. The wedging pressure of solvate films of liquid may strongly retard the closing of microcracks.

Fig. 2. Adsorption wedging of a microcrack by a monolayer: \(P_a\)—additional pressure due to adsorption, \(P_r\)—additional pressure at the mouth of the microcrack due to the wedging action of thin liquid films.

In addition to facilitating the development of each individual microcrack under the influence of penetration into it by adsorption layers, the effect of adsorption facilitation of deformation is also due to an increase in the number of surface microcracks developing per unit surface or, respectively, per unit length of the deformed body.

Those surface defects which, for one reason or another, do not turn into microcracks under ordinary conditions, i.e., in the absence of adsorbed substances, also develop into microcracks under the influence of adsorption.

In the region of elastic deformations, each value of the mean stress or, what is the same thing, each value of the deformation corresponds to its own equilibrium size of microcracks or, strictly speaking,

its own distribution curve of microcracks with a definite most probable size.

In the region of plastic deformations, an essential role is played by the nonuniformity in the development of microcracks corresponding to a given stress. At each given stress, a certain number of very well-developed microcracks are formed in the deforming body, considerably exceeding their most probable size. Such microcracks may prove to be “active” in the sense that the concentration of forces in their blind ends may lead to the occurrence of shear.

The number of such active microcracks is determined by the stress \(P\) applied to the body, increasing with its growth. At very small \(P\), active microcracks practically do not arise, and the deformation of a body under the action of such stresses appears to us to be “truly” elastic, fully reversible. As \(P\) increases, in connection with the displacement of the distribution curve toward larger crack sizes, beginning with some \(P = P'\), the number of active microcracks becomes sufficiently large, and the plastic shears arising on their basis can already be registered by precise instruments.

Surface-active substances contained in the medium surrounding the plastically deforming body, being adsorbed on its external surface and penetrating into the mouths of microcracks, should facilitate their development to active sizes and thereby promote the formation of plastic shears.

The practical significance of adsorption effects of this kind is extremely great. It is enough to point to their decisive role in the action of cutting and cooling fluids in all processes of working metals by cutting and pressure\(^{17}\), as well as in the influence of lubricants on wear\(^{18}\).

From the theoretical point of view, the significance of adsorption effects is not exhausted by revealing the role of microcracks that develop during the deformation of metals, or by establishing their physicomechanical properties. In many cases, consideration of the influence of surface-active substances makes it possible to draw a more complete conclusion about the mechanism of the deformation process in general and the processes accompanying it (in particular such, for example, as relaxation, elastic aftereffect, hysteresis, etc.).

Of greatest scientific interest is the study of the adsorption effect of deformation facilitation on individual crystals, and, with respect to plastic deformations, on metallic single crystals. Such studies have been carried out on single crystals of tin, lead, zinc, and aluminum. In these studies it was possible, with particular clarity, to establish the basic regularities of the influence of surface-active substances on the process of plastic flow.

II. REGULARITIES OF DEFORMATION OF METALLIC SINGLE CRYSTALS IN THE PRESENCE OF SURFACE-ACTIVE SUBSTANCES

Single crystals of tin and lead of a high degree of purity were obtained by the method of P. L. Kapitsa,^3 while aluminum crystals were obtained by the method of recrystallization after small deformations and subsequent annealing. In order to obtain a more homogeneous surface, all single crystals were preliminarily etched before the experiment.

The orientation of single crystals obtained by the method of P. L. Kapitsa depends on random causes (if no seed is introduced), and therefore, for tin crystals, all possible orientations of the basal plane were obtained: \(0^\circ \leqslant \chi_0 \leqslant 90^\circ\). In single crystals of lead and aluminum, where the variety of orientations of the operative octahedral slip plane is considerably smaller, the initial angle of this plane with the axis of the specimen lay within the limits from 40 to \(55^\circ\).

Complete tension–stress diagrams were measured on a Polanyi-type apparatus with a constant rate of relative elongation:

\[ V=\frac{d\varepsilon}{d\tau}=\frac{100\cdot dl}{l_0\cdot d\tau}=\mathrm{const}. \]

The tensile force was measured from the deflection of a rigid steel plate by means of a double optical lever. To avoid distorting stresses in the clamps, the specimens were sealed with Wood’s alloy (melting point \(72^\circ\text{C}\)) into special glass tubes with drawn-out ends, which were then fastened in the clamps of the apparatus. The initial length of the crystal being deformed remained a constant value in all experiments, \(l_0=10\ \mathrm{mm}\) (with the exception of special experiments on investigating the dependence of the magnitude of the adsorption effect on the external geometry of the crystals).

In earlier work on the facilitation of deformation of metallic single crystals under the influence of adsorption of surface-active substances,^4 single crystals of tin and zinc were studied by two methods: 1) under a constant regime of increasing load: a definite initial stress exceeding the yield limit, followed by an increase of the load every 15 minutes by 20 kg; and 2) at a constant deformation rate \(V=\frac{d\varepsilon}{d\tau}=\mathrm{const}\) on a Polanyi-type apparatus. The results of these investigations showed a very considerable facilitation of deformation under the action of the surface-active substance. By method (1) this was expressed in a considerable increase in the rate of flow (by 5–10 times), and by method (2) in a lowering of the yield limit by approximately a factor of two. In addition, a dependence of the magnitude of the adsorption effect on the orientation of the operative slip elements was found: reproducible values of the effect (increase of the stretching rate under a constant regime of increasing load or lowering of the tensile force at constant ...

(deformation rate) are obtained only for specimens with the same orientation of the slip planes relative to the axis of the single crystal. The maximum adsorption effect occurs at the initial orientation angles \(\chi_0 \approx 45^\circ\), corresponding to the minimum yield point. The curve of the dependence of the magnitude of the adsorption effect on the orientation (Fig. 3) is not symmetric with respect to the maximum: the decrease in the magnitude of the effect with decreasing angle is sharper than with increasing angle.\(^5\)

Fig. 3. Dependence of the magnitude of the adsorption effect on the orientation of the basal plane.

In the study of the adsorption effect on metallic single crystals, in the subsequent works only the second method of investigation was used—the method of constant deformation rate, since here the dynamics of deformation is set by the crystal itself in accordance with the slip elements. Moreover, only at a constant deformation rate is it possible to trace the principal mechanical characteristics of the crystal (yield point, hardening coefficient, breaking load) and their changes in connection with changes in the experimental conditions.

As surface-active additions to the hydrocarbon nonpolar medium, very pure preparations of oleic acid \((\mathrm{C}_{17}\mathrm{H}_{33}\mathrm{COOH})\), palmitic acid \((\mathrm{C}_{15}\mathrm{H}_{31}\mathrm{COOH})\), and cetyl alcohol \((\mathrm{C}_{16}\mathrm{H}_{33}\mathrm{OH})\) were used.

First of all, it is necessary to point out the very important circumstance that, during deformation of crystals in the presence of surface-active substances, replacement of the slip elements operating in the inactive medium by any others was never observed; but in some cases new ones are added to these elements. The latter can be observed especially often on single crystals of metals with a cubic lattice.

In the presence of surface-active substances, deformation of aluminum and lead is for the most part accompanied by the simultaneous bringing into action of two octahedral slip systems, which can be seen directly from the slip lines on the metal surface. In tin crystals the principal system of slip planes—the basal plane—remains predominant also in the presence of surface-active substances, but in this latter case it is exhausted somewhat more rapidly. The magnitude of the adsorption facilitation of deformation depends substantially on the concentration of the surface-active substance.

As a measure of the adsorption effect for tin crystals one may take the absolute magnitude of the lowering of the yield point

\[ \Delta P_m=(P_m)_0-(P_m)_A \]

or the relative lowering

\[ \frac{\Delta P_m}{(P_m)_0}\cdot 100\%= \frac{(P_m)_0-(P_m)_A}{(P_m)_0}\cdot 100\% \]

in percent (for the initial stage of deformation), and the ratio of the hardening coefficients (for the subsequent stage of plastic flow):

\[ \frac{\lambda_0}{\lambda_A}= \frac{(dP_s/da)_0}{(dP_s/da)_A}. \]

Figure 4 shows tensile diagrams of tin crystals of approximately the same initial orientation, close to the optimum \((\chi_0 \simeq 45^\circ)\), for various concentrations of oleic acid in vaseline oil. Pure vaseline oil, as control experiments showed, gives no difference in the course of the tensile curves in comparison with air.

Fig. 4. Influence of various concentrations of oleic acid in vaseline oil on the tensile diagram of tin single crystals

A relatively strongest action of the adsorbing substance is observed in the region of very small concentrations. Both the yield point and the hardening coefficient reach a minimum value at \(C=0.2\%\), and with a further increase in concentration they increase again; this, to one degree or another, is connected with aggregation of the molecules of the surface-active substance in solution—in a hydrocarbon medium—due to bonds arising between their polar groups. It is interesting to note that the concentration of the surface-active substance corresponding to the maximum effect for single crystals fully coincides with the corresponding value of the concentration for polycrystalline specimens of tin, lead, and copper in the work of P. A. Rebinder and E. K. Venstrem\(^6\), and corresponds to the equilibrium concentration of saturation of the adsorption layer, depending not on the nature of the metal, but on the nature of the surface-active substance.

substance ($C_{\max}$ in accordance with Traube’s rule decreases sharply with the lengthening of the hydrocarbon chain in the homologous series).

Figure 5 gives the hardening curves in the coordinates $P_s, a$ (where $P$ is the shear stress, $a$ is the specific displacement) for an inactive and an active medium with an optimum concentration of 0.2% oleic acid in vaseline oil. Both the critical shear stress and the hardening coefficient decrease considerably in the presence of surface-active substances.

Fig. 5. Hardening curves of tin single crystals: 1) in an inactive medium (open circles), 2) in an optimum solution of a surface-active substance (black circles).

However, the lowering of the yield point and the decrease of the hardening coefficient in the presence of surface-active substances are, in essence, secondary effects, a consequence of the basic, primary phenomenon—the action of adsorbed layers on deforming metallic crystals—which we discovered on tin single crystals.

This basic phenomenon consists in the fact that, in the process of deformation of metallic crystals in the presence of surface-active substances, a strong refinement of slip bands takes place in the active slip system. Structural change of this kind under the action of adsorbable substances was subsequently also traced on single crystals of lead and aluminum.

Fig. 6. Structural changes during deformation of single crystals under the influence of surface-active substances. Large slip bands arise in an inactive medium, fine ones in an active medium.

In Fig. 6 are given microphotographs of tin single crystals deformed in air and in an active medium.

When metallic crystals are stretched, the slip bands that form, as a rule, have different thicknesses; this, apparently, is connected with the random distribution of weak spots—defects of the crystal lattice—which initiate plastic shears. The character of the dependence of the thickness of slip bands on the rate of deformation and on temperature, namely, the thickening of bands with increasing temperature or decreasing rate of deformation, is determined by the kinetics of the formation of lattice defects into wedge-shaped microcracks, the blunt parts of which are sources of shears. For particularly pure cadmium and lead it has been shown that the thickness of slip bands varies within much narrower limits than is characteristic of ordinary-purity preparations, and proves to be almost independent of temperature and deformation rate⁷. But even for these metals, the slightest impurities immediately lead to a considerable scatter in the magnitude of the slip bands.

The sharpest structural changes were observed by us on tin single crystals, since at the chosen deformation rate of about \(5\%\ \mathrm{min.}^{-1}\), when stretched in air (or in pure vaseline oil), tin gives broad slip bands—on average \(50\mu\).

For a more detailed study of the characteristic surface structures arising during plastic deformation of single crystals, we, together with the photo-cinema laboratory of the Academy of Sciences of the USSR (LAFOKI), applied the method of accelerated microcinematography (64 frames per 1 sec.) in reflected light with the aid of a metallomicroscope, which made it possible to record the entire process of the onset of plastic flow of a single crystal both in an inactive and in an active medium.

This method of investigation made it possible to establish that already at the initial stages of deformation in the presence of surface-active substances a very fine structure of slip bands appears, with a thickness of the order of \(1\mu\). This is considerably less than at the same stretching rate in an inactive medium, where the thickness of the slip bands averages \(52\mu\); moreover, under conditions of considerable scatter of this quantity, very thin slip bands are altogether absent at the given magnification. Thus, the action of surface-active substances becomes visible in the direct sense of the word.

Table I (see p. 380) summarizes data on the influence of various concentrations of oleic acid in vaseline oil on the structural-mechanical properties of tin crystals stretched at a constant rate \(V = 4.8\%\ \mathrm{min.}^{-1}\) at room temperature.

Fig. 7 gives the dependence of the principal structural-mechanical characteristics of tin single crystals on the concentration of additions of oleic acid to vaseline oil. From the table and the figure it is evident,

Table I

Tin single crystals: \(d = 0.76\text{–}0.96\ \mathrm{mm}\), \(41^\circ \le \chi_0 \le 48^\circ\),
\(V = 4.8\%\ \mathrm{min}^{-1}\)

that all three effects of the action of adsorbed substances—the lowering of the yield point, the lowering of the work-hardening coefficient, and the refinement of the slip packets—display a common character of dependence on the concentration of surface-active substances, which undoubtedly indicates a single mechanism underlying these phenomena.

This mechanism consists in the fact that surface-active substances, adsorbing on the surface of the crystal, penetrate into surface microcracks that open in the process of deformation and, owing to the additional surface pressure of the adsorption layer, promote the concentration of stresses at the dead ends of the microcracks, facilitating the occurrence of slips at lower stresses.

In addition, the adsorbed layers cause to “operate” also those microcracks which, under ordinary conditions, do not attain the dimensions necessary for the occurrence of displacements in their dead-end regions, and precisely this circumstance leads to the refinement of slip packets, i.e., to the occurrence of a large number of slips. At the same time the work-hardening coefficient must inevitably decrease, since an increase in the number of active slip planes is associated with a corresponding decrease in the magnitude of the slips at a given degree of extension.

Fig. 7. Dependence of the principal physicomechanical characteristics of tin single crystals on the concentration of oleic acid in vaseline oil.

and, consequently, with less damage to the crystal lattice along the slipping planes[^8].

It is interesting to note the direct connection between the effect of refining slip packets and the previously observed phenomenon of an increase in the degree of dispersion of the products of destruction of brittle rocks in the presence of surface-active substances[^9].

III. THE INFLUENCE OF THE DEFORMATION REGIME AND TEMPERATURE ON THE MAGNITUDE OF THE ADSORPTION EFFECT

The factors influencing the process of deformation, and thereby the magnitude of the adsorption effect, include the temperature at which deformation occurs, the rate of deformation, and the character of the stressed state.

Under the influence of each of these factors, the mechanical properties of a material may vary over rather wide limits, almost to the same extent as under the influence of internal factors—the microstructure of the material and all kinds of impurities. From the point of view of the phenomena of adsorption action on the deformation process that interest us, the indicated external factors are of quite special interest as extremely powerful and, what is especially important, controllable means of influencing the kinetics of development of microcracks in the surface layer of the material being deformed.

The deformation of a solid body should be regarded as a process of internal, in a sense thixotropic, dispersion, i.e. mechanical destruction of structural bonds with their simultaneous restoration, both processes requiring time. The breaking of bonds causes the formation of a new phase in the volume and in the surface layer of the body—wedge-shaped microcracks with different mechanical properties. Such a consideration compels one, first of all, to establish the character of the stressed state under which the induced “heterogenization” of the lattice of a solid body is in general possible. The most general answer to this question will apparently be the following: any stressed state in which, in addition to normal stresses, tangential stresses also exist is capable of ensuring the required heterogenization of the system.

This circumstance was first pointed out by L. A. Schreiner in studying the adsorption effect on various rocks[^10]. However, this requirement may be fulfilled to different degrees depending on the conditions of deformation. For all phenomena of adsorption action on deformation, it is especially important to determine those deformation conditions which can, in the best possible way and to the fullest extent, ensure the development of surface microcracks and, consequently, increase the effectiveness of the action of surface-active substances. For solving this problem, merely indicating the necessary type of deformation is, of course, insufficient. As will be

as will be seen from what follows, even with a successful choice of the type of deformation, all the other external factors may nevertheless prove so unfavorable that the adsorption effect cannot be observed at all. Only with a proper choice of all external factors, with their definite correspondence to one another, is it possible to create optimal conditions for the action of surface-active substances.

1. Influence of the deformation rate and temperature on the magnitude of the adsorption lowering of the strength of single crystals

Temperature and deformation rate influence slip in metallic crystals mainly through the relaxation process, which proceeds spontaneously and depends on temperature and time[^11].

The relaxation process, like any spontaneous isothermal process, whatever its mechanism may be, is always directed toward lowering the free energy of the system, which has increased as a result of some external actions (the work of external forces on the body). Under favorable conditions the relaxation process may be so intense that the slightest increase in the free energy of the crystal during its deformation will be immediately removed in the course of the deformation itself and, consequently, the initial mechanical properties and structure of the crystal will remain unaffected by the deformation that has occurred. The other limiting case pertains to those experimental conditions under which the relaxation process proceeds with an infinitely small rate and thus cannot have any influence on the change in the free energy of the crystal during deformation. In this case the mechanical properties of the crystal undergo maximal changes as a result of the completely unhindered development of strain hardening.

Under ordinary conditions of deformation of metallic single crystals (room temperature, medium deformation rates) the relaxation process always proceeds with a finite rate, and the change in the mechanical properties of the crystal during deformation is determined by the equilibrium that arises, under the given conditions, between the rate of relaxation and the increasing strain hardening.

Whatever the atomic mechanism of hardening and relaxation may be, a certain role in these processes must be played by internal surfaces of separation, which arise during deformation of crystals and disappear under the influence of relaxation. The elastic energy of bent packets of slip and the raising of the energy level of atoms situated along the internal surfaces that bound these packets contribute their share to the overall energy balance of deformation, thereby determining a certain part of the increased free energy of the system. In the surface layer of the metal, where the internal surfaces of separation are formed into wedge-shaped microcracks with a fully developed surface,

section, the free energy of a crystal can be expressed in the form of the free surface energy of the walls of microcracks. The kinetics of the appearance and development of surface microcracks is thus inseparably connected with the “internal dispersion” of the metal in the process of deformation, with the dismemberment of an initially homogeneous crystal into separate slip packets bounded off from one another. The relaxation process, leading to the disappearance of internal separation surfaces, thereby also destroys the system of microcracks in the surface layer of the deformed crystal that had arisen on their basis.

Fig. 8. Tensile diagrams of lead single crystals under an optimal deformation regime in an inactive medium (white circles) and in an active medium (black circles).

Visible labels in the diagram: \(\rho\,[\mathrm{g/mm}^{-2}]\), \(\varepsilon\%\), Pb, \(t=20^\circ\), \(v=240\%\,\mathrm{min}^{-1}\), points \(O\), \(A\).

Fig. 9. Tensile diagrams of lead single crystals under a non-optimal deformation regime.

Visible labels in the diagram: \(\rho\,[\mathrm{g/mm}^{-2}]\), \(\varepsilon\%\), “Vaseline oil,” “Vaseline oil + 0.2% oleic acid,” Pb, \(t=20^\circ\), \(v=150\%\,\mathrm{min}^{-1}\).

“Self-healing” of the crystal takes place: the closing of microcracks under the action of considerable molecular forces arising at the crack tips within the metal and gradually, as the crack closes, shifting from the tip toward the mouth.

Thus, the effectiveness of the influence of surface-active substances on the plastic flow of single crystals must depend substantially on temperature and on the rate of deformation as factors determining the intensity of the relaxation process.

L. P. Yanova, in our laboratory, carried out an investigation of the dependence of the magnitude of the adsorption-induced decrease in strength on temperature and deformation rate in tin and lead single crystals. The tin single crystals in these experiments were selected only with an optimal orientation of the slip planes \((\chi_0 \approx 45^\circ)\).

For lead single crystals, the orientation of the active octahedral slip plane, owing to the presence of several crystal—

logarithmically equidistant octahedral planes always lies in the region of optimum orientations.

Figure 8 presents typical tensile curves for lead crystals in inactive and active media. The entire process of stretching a single crystal in an active medium takes place at considerably smaller tensile forces, and the difference in breaking stresses, \(\Delta P\), taken as a measure of the adsorption effect of the reduction in strength, reaches almost \(30\%\).

However, under another tensile regime the magnitude of the adsorption effect decreases, as is seen from Fig. 9, which presents a tensile diagram of a lead crystal at a different rate of deformation.

Figure 10 presents the dependence of the magnitude of the adsorption effect on lead crystals on the rate of deformation at different temperatures. Here the absolute reduction of the maximum breaking stress is taken as the measure of the adsorption effect. At room temperature the adsorption effect of reduction in strength becomes appreciable only in a definite interval of deformation rates, approximately from 100 to \(400\%\ \mathrm{min}^{-1}\); the maximum of the adsorption effect lies in the interval of rates from 200 to \(250\%\ \mathrm{min}^{-1}\), and both toward lower rates and toward higher rates the influence of surface-active substances becomes less and less noticeable, until finally it disappears completely.

Fig. 10. Dependence of the magnitude of the adsorption effect on lead single crystals on the rate of deformation and temperature.

Visible labels in the figure: ordinate \(\Delta P\ \mathrm{g/mm^2}\); abscissa \(v\ \%\ \mathrm{min}^{-1}\); “oleic acid”; “palmitic acid”; “cetyl alcohol”; \(20^\circ\mathrm{C}\); \(100^\circ\mathrm{C}\), “oleic acid.”

With an increase in temperature to \(100^\circ\mathrm{C}\), the whole curve of the dependence of the magnitude of the adsorption effect on the rate of deformation is displaced toward higher rates, and the maximum of the curve lies within the range from 800 to \(900\%\ \mathrm{min}^{-1}\). At a rate of \(1500\%\ \mathrm{min}^{-1}\) the adsorption effect decreases and, apparently, at very high rates becomes zero. A very important result was obtained in comparing the adsorption action on lead crystals of three surface-active substances: oleic acid, palmitic acid, and cetyl alcohol. All these surface-active substances give a maximum of the adsorption effect at the same deformation rates, which indicates a single mechanism of their action. Since, of these three substances, cetyl alcohol certainly does not give chemical adsorption on the metal, while oleic and palmitic—

new acid can enter into chemical bonding with the metal (forming lead oleate and palmitate), then the result obtained can be interpreted only in such a way that the influence of surface-active substances is effected by physical, not chemical, adsorption. During deformation, some portion of the fatty-acid molecules adsorbed on lead is chemically fixed and does not participate in the adsorption effect on deformation. The wedging apart of surface microcracks, and thereby the facilitation of deformation of the crystal, is accomplished by that portion of the adsorbed molecules which has retained its mobility and its ability to migrate over the metal surface. These same considerations make it possible to explain

Fig. 11. Dependences of the magnitude of the adsorption effect on tin single crystals on the rate of deformation and temperature.

a certain decrease in the magnitude of the adsorption effect with increasing temperature. It is evidently connected with a change in the character of adsorption toward a transition to activated (chemical) adsorption and with a decrease in the mobility of the adsorbed molecules.

For tin crystals at \(20^\circ\mathrm{C}\), the maximum adsorption effect lies at a deformation rate of about \(V = 5\%\ \mathrm{min}^{-1}\). When the deformation rate is decreased to \(0.05\%\ \mathrm{min}^{-1}\), the adsorption effect practically disappears and is no longer observed upon further slowing of deformation. On the other side of the maximum, when the deformation rate is increased, the adsorption effect practically disappears at \(V\) of about \(100\%\ \mathrm{min}^{-1}\). At elevated temperature \((100^\circ\mathrm{C})\), the maximum of the adsorption effect shifts to considerably higher rates—about \(240\%\ \mathrm{min}^{-1}\), practically disappearing when \(V\) is lowered to \(10\text{–}15\%\ \mathrm{min}^{-1}\) and when it is raised to a value on the order of \(1000\%\ \mathrm{min}^{-1}\). Figure 11 gives the dependence of the magnitude

of the adsorption effect, expressed as the difference between the yield limits

\[ \Delta P_m=(P_m)_0-(P_m)_A \]

of tin single crystals, on the rate of deformation. The magnitude of the critical shear stress

\[ P_s=P_m\cdot \sin \chi_0\cdot \cos \lambda_0, \]

corresponding to the yield limit, also shows a dependence on the rate of deformation. With an increase in the rate of deformation, the critical shear stress of the single crystal increases monotonically, which also occurs at \(100^\circ\mathrm{C}\). In the presence of surface-active substances this dependence has a clearly expressed minimum, corresponding to the optimal rates of deformation.

An increase in the rate of deformation in all cases leads to stronger strain hardening and to an increase in the yield limit and the critical shear stress. These phenomena, caused by the simultaneous action of several slip planes during rapid tension, are especially clearly expressed in tin, since in cubic crystals, even at insignificant rates of tension, several slip systems begin to operate already at comparatively small deformations.

The results obtained indicate the exceptionally important role of the process of recovery in the plastic deformation of a metallic crystal under conditions of adsorption action.

Significant effects of adsorption facilitation of deformation arise only on the condition that the metal, in the course of the deformation itself, has been prepared for the most active action of the adsorbed layers. A necessary and sufficient condition for this kind of preparation is ensuring the maximum development, during deformation, of a network of surface microcracks penetrating to a sufficient depth into the metal. In the process of tension of a single crystal, this condition is satisfied only by that region of deformation rates at which recovery no longer influences the course of deformation, but at the same time the shear mechanism of deformation in the principal slip system has not yet been disturbed. If the rate of deformation is commensurate with the rate of recovery, then the self-healing of microcracks that arises in the process of deformation squeezes the adsorbed layers out onto the external surface of the metal and thereby eliminates the action of the adsorbed layers.

The adsorption effect on the dynamics of plastic deformation is realized in full measure in the absence of the retarding influence of recovery, i.e. at such deformation rates at which recovery during the time of deformation may be neglected. If, however, the deformation rate becomes so considerable that the shear mechanism of slip along the principal system of slip planes is thereby disturbed, then several slip systems immediately come into operation and the process of twinning develops intensively, which is connected with insufficient and improper development of surface microcracks. Moreover, the development of microcracks is already inhibited at small depths of their penetration into the crystal owing to the predominant development

only some of them, deformation by which ends in rupture. The newly formed surface in these cracks does not have time to become covered with an adsorption layer, which leads to a sharp decrease or even disappearance of the adsorption effect.

With increasing temperature, relaxation becomes more intense, its rate increases, which entails an acceleration of the processes associated with the disappearance of internal separation surfaces and with the closure of microcracks developing on their basis.

If, at room temperature, such a deformation rate is chosen at which relaxation does not have time to occur noticeably and, consequently, does not affect the deformation process, then with increasing temperature such a ratio between the rates of deformation and relaxation will be disturbed, and in order to attain the former ratio again it will be necessary correspondingly to increase the deformation rate. From this point of view one can explain the influence of temperature on the dependence of the magnitude of the adsorption effect on the deformation rate. The optimum deformation regime, corresponding to the maximum adsorption effect, with increasing temperature will shift more and more toward higher rates, i.e., in order to maintain the same ratio between the deformation rate and the relaxation rate that gave the maximum adsorption effect at room temperature, higher values of the deformation rate will now be required at the higher temperature.

The results obtained show that the magnitude of the adsorption effect—the facilitation of deformation (reduction of strength) of crystals—is determined by the deformation regime, i.e., by the rate at which it proceeds and by temperature, and can be observed in a certain, though rather broad, region of some intermediate optimum deformation rates. The position of this region is determined by the temperature of the crystal*)¹².

2. Influence of the dimensions of metallic crystals on the form of the tensile diagram and on the magnitude of the adsorption effect of strength reduction

As is known, ordinary deformation diagrams represent only averaged values of forces and deformations at different points of the body being deformed and give no idea of the true distribution of stresses and deformations inside the body. In the case of tension of cylindrical specimens, the linear-stress state with uniform—

) Everything set forth in this section convincingly shows that, in tension of crystals at a constant rate, the deformation regime has a decisive influence on the magnitude of the adsorption effect. Insufficient attention to this important circumstance may lead to misunderstandings similar to that which occurred in a recent communication by Kimsley in Nature* (March 1949).

a uniform distribution of stresses over the cross section occurs only in the middle part of the specimen, sufficiently far removed from the grips. In the zones directly adjoining the grips, a triaxial stressed state arises, with a nonuniform distribution of stresses over the cross section. In these zones there occurs a concentration of stresses in a narrow surface layer of the specimen, which may exceed the mean value of the stress in the cross section many times over. The degree of stress concentration depends essentially on the geometry of the transition part of the specimen, and the sharper the transition from the grips to the working part, the higher the stress concentration.

As the distance from the grips increases, the nonuniformity in the distribution of stresses over the cross section decreases, and at distances of \(1.5\)—\(2\) diameters of the specimen it disappears completely.

Thus, in tension of metallic rods of a given diameter, an essential role in the pattern of stress distribution over the cross section must be played by the parameter \(\gamma=\dfrac{l}{d}\), where \(l\) is the length of the specimen between the grips in the absence of a transition part and \(d\) is the diameter of the specimen. For sufficiently large \(\gamma\), of the order of 10 and higher, the significance of the zones with a nonuniform stress distribution is relatively small, since in the main part of the specimen the stresses are distributed uniformly. With decreasing \(\gamma\), i.e., with decreasing specimen length, the role of these zones increases, and, finally, at \(\gamma\) equal to 3—4, the entire specimen proves to be in a triaxial stressed state with a nonuniform distribution of tensile stresses over its cross section. In this case an intensified formation of microcracks should be observed in the surface layer owing to the concentration of stresses in it. Thereby very favorable conditions are created for the adsorption effect of the surrounding medium on the process of plastic deformation. Since the diameter of the glass grip mentioned above is about \(1\ \mathrm{cm}\), then at small \(\gamma\), i.e., at a small ratio \(\dfrac{l}{d}\), the grip—crystal system may be regarded as a smooth cylindrical specimen of large diameter, provided with a deep annular groove.

The results obtained by E. K. Venstrem for single-crystal tin specimens of diameter \(1\ \mathrm{mm}\) at different values of the ratio \(\dfrac{l}{d}=\gamma\) are presented in Fig. 12.

At small \(\gamma\), in all the specimens tested, two characteristic phenomena are clearly manifested: an increase in the yield point and an increase in the plastic deformation corresponding to the yield point. As is known, the yield point of a single crystal by no means indicates the beginning of plastic flow; it begins much earlier, at very small stresses, but is accompanied by a high coefficient of strain hardening. The increase in plastic deform-

mation corresponding to the yield point (at small \(\gamma\)), and, moreover, a much more considerable one than the increase in the yield point itself, leads to a lowering of the coefficient of hardening in the initial region of deformation, i.e. to a facilitation of plastic deformation in this region. From Fig. 12 it is seen that the same force which at \(\gamma=10\) imparted to the crystal an elongation of \(1\)—\(1.5\%\), at \(\gamma=1.5\) imparts to the same crystal an elongation of \(18\)—\(20\%\). Such a facilitation of the flow of a single crystal may be explained, as it seems to us, by enhanced shear formation caused by the presence of many microcracks in the surface layer, by analogy with the well-known experiments of A. V. Stepanov[^13], who observed, in the stretching of rock salt, preferential formation of shears at the bases of artificially made scratches on the surface of the crystal. However, the presence of a state of volumetric stress hinders entry into the plastic region lying beyond the yield point, which also leads to an increase in the yield point. It is interesting to note that after the yield point has been passed, further deformation of the crystal proceeds with the same coefficient of hardening as at large \(\gamma\), but nevertheless the whole tensile diagram at small \(\gamma\) lies, as a rule, higher than at large \(\gamma\). This circumstance indicates a considerable weakening of the influence of the nonuniform distribution of stresses beyond the yield point, but not the complete disappearance of this influence. The same phenomenon also occurs for single crystals of other diameters. In all cases without exception, a decrease in \(\gamma\) entails an increase in the adsorption action of surface-active substances (oleic acid at a concentration of \(0.2\%\) in pure vaseline oil was used as the surface-active substance), and the plasticity of single crystals at small \(\gamma\) increases considerably. In addition, in the presence of surface-active substances there completely disappears the increase of the yield point characteristic of the state of volumetric stress. The concentration of stresses in the surface layer at small \(\gamma\) creates much more favorable conditions for the development of microcracks and thereby promotes a more substantial action of the adsorbed substances on the dynamics of deformation, beginning with the very smallest

Fig. 2. Tensile diagrams of tin single crystals at different \(\gamma\) (different \(l\) for a given \(d\)).

external forces. It is precisely for this reason that such high plasticity of tin single crystals occurs under very small external stresses. The same circumstance also explains why the yield point does not increase in the presence of surface-active substances. The point is that surface-active substances, by expanding and deepening microcracks at the expense of monomolecular surface pressure, promote the most rapid equalization of stresses over the entire cross section of the crystal and, in essence, remove the volume-stressed state, replacing it by the usual linearly stressed one. The internal wedging pressure of adsorption layers in the surface layer of the metal may in this case be regarded as compensation for those compressive stresses which are inevitably produced when stresses are concentrated in the surface layer[^19].

IV. THE INFLUENCE OF SURFACE-ACTIVE SUBSTANCES ON SMALL DEFORMATIONS OF METALLIC CRYSTALS. ELASTIC-KINETIC PHENOMENA IN SINGLE CRYSTALS

1. The influence of surface-active substances in the initial plastic region of deformation of single crystals

As is known, the yield point of metallic single crystals does not by itself determine the onset of plastic deformation. Irreversible plastic shifts along slip planes take place already at the very smallest external stresses, very far from the yield point, and the mechanism of these shifts is apparently exactly the same as beyond the yield point. Thus, the plastic flow of metallic crystals may be regarded as consisting of two plastic regions, the physical boundary between which is the critical shear stress: the first, or initial, plastic region and the second, or principal, one.

The initial plastic region, which occurs at shear stresses smaller than the critical one, is characterized by a high value of the modulus \(\frac{P}{\varepsilon}\) (more precisely \(\frac{dP}{d\varepsilon}\)), which may be called the “modulus of plasticity,” or the hardening coefficient in this plastic region, and by a very small total residual deformation \(\varepsilon_m\).

The principal plastic region begins when the external stress reaches the critical value, and is distinguished by a considerable total deformation of the crystal (up to \(1000\%\) of the initial length) with a comparatively low hardening coefficient.

Metallic single crystals with one principal axis (hexagonal, tetragonal) exhibit a very abrupt transition from the first-

plastic region into the second, whereas cubic crystals, owing to the variety of active slip elements, do not possess a clearly expressed yield point. However, even for these crystals, in each given octahedral slip system the critical shearing stress has an equally definite physical meaning.

In discussing the causes of the occurrence of the initial plastic region in metallic crystals, it is necessary to bear in mind two very essential circumstances. The first of them is that the plastic shears in the region under consideration have a clearly expressed local character, as can be verified by direct examination of the surface of a deformed crystal under a microscope; the second circumstance is connected with the kinetics of deformation and consists in an increase or decrease of the yield point with an increase or decrease in the rate of deformation, which indicates the role of time in establishing the upper stress boundary for the region of initial plasticity.

Above, general ideas were set forth concerning the role of defects—weak places in the structure of a crystal—in the process of deformation. From this point of view, the occurrence of the initial plastic region is explained by the nonuniform development of microcracks corresponding to a given external stress.

The distribution curve of microcracks by size, corresponding to a definite elastic stress, in view of the completely random arrangement of the initial structural defects, must apparently correspond to the Gaussian distribution. The maximum of the distribution curve indicates the most probable size of the microcracks, i.e. that size possessed by the majority of microcracks. With increasing external stresses, the maximum of the distribution curve shifts toward larger microcrack sizes. If by \(X\) we denote the size of a crack at its mouth (in the widest part of the crack), and by \(X_0=f(P)\) the most probable size corresponding to the given stress, then the relative number of microcracks \(\frac{dn}{n_0}\) falling within the interval \(dX\), enclosed between \(X\) and \(X+dX\), will be

\[ \frac{1}{n_0}\,dn=\frac{1}{J}\cdot e^{-\alpha(X-X_0)^2}\,dX, \]

where

\[ J=\int_{0}^{\infty} e^{-\alpha(X-X_0)^2}\,dX \]

by the normalization condition.

Thus, at each given stress in the crystal being deformed there is formed a certain number of highly developed microcracks, considerably exceeding in their dimensions the most probable

size \(X_0\). These larger microcells turn out to be “active” in the sense that the concentration of stresses in their dead-end parts leads to the appearance of displacement, and subsequently of slip. If the minimum size of an active microcell is denoted by \(X_m\), then the number of such active cells will be

\[ n_1=\frac{n_0}{J}\cdot\int_{X_m}^{\infty} e^{-\alpha (X-X_0)^2}\cdot dX . \]

The minimum size of an active microcell is a characteristic of the deformable body and, consequently, independently of the stress \(P\) always remains equal to \(X_m\). This means that the number of active cells will be determined by the stress \(P\), increasing with its increase. At very small \(P\), active microcells may not arise at all, i.e. the distribution curve of microcells practically merges with the abscissa axis without reaching the value \(X\) equal to \(X_m\). In this case there will occur “truly elastic” deformation, completely reversible at any moment of time. With increasing load, in connection with the displacement of the distribution curve toward larger cell sizes, beginning from some \(P=P'\), the value \(X_m\) on the abscissa axis will be reached by the distribution curve. This load value \(P=P'\) may be regarded as the “true” elastic limit, since a further increase of \(P\) will entail the appearance of active microcells and, consequently, will be accompanied by plastic slips.

It is evident from this that the “true” elastic limit cannot be regarded as a strictly determined quantity, but of necessity will always depend on the accuracy of recording small residual deformations.

At all stresses \(P>P'\) there always arises some number of active microcells, the greater the higher \(P\) is in comparison with \(P'\), which also ensures the possibility of plastic slips under small loads, i.e. under those loads which satisfy the condition \(P'\leq P\leq P_s\), where \(P_s\) is the critical shear stress.

It is necessary to point out two possible processes of plastic flow of metallic single crystals under the action of small stresses \(P\) \((P'\leq P\leq P_s)\), depending on the conditions of the experiment. If the experiment is arranged in such a way that the stress remains constant, then the “active” microcells that have arisen will cause the formation of plastic slips. However, the hardening that arises in this process will slow the rate of deformation, and, finally, there will be established a certain constant, minimal under the given conditions, rate of plastic flow, the magnitude of which will be determined by the attained state of equilibrium between the process of recovery of the crystal and the process of hardening. Such plastic flow of the crystal represents

constitutes “creep”—the plasticity of a metal under the action of small constant forces. The creep rate remains constant for a long time only under the condition of constancy of the stress, but not of the constancy of the load on the specimen.

If, however, the experiment is arranged in such a way that the deformation remains constant (under the same condition for \(P\)), then the plastic slips caused by the active microcracks will lead to a partial removal of the stressed state and, consequently, to a shift of the entire distribution curve of microcracks toward smaller crack sizes.

The number of active microcracks thus decreases irreversibly, which must lead to a gradual decrease in the rate of plastic flow down to zero, when the elastic stress of the crystal becomes equal to \(P'\)—the elastic limit. The decrease of the elastic stresses must be proportional to the number of active microcracks capable of producing slip, i.e.,

\[ -\frac{d(P-P')}{d\tau}=k'\cdot n_1; \]

but, on the other hand, the number of active microcracks \(n_1\) is itself proportional to the excess of the given stress over the “true” elastic stress, i.e., \(n_1=k''(P-P')\). Consequently,

\[ -\frac{d(P-P')}{d\tau}=k(P-P'). \]

Such plastic flow of a crystal represents a relaxation of elastic stresses with time, the law of which in the indicated form was first given by Shvedov\(^{14}\).

This law becomes Maxwell’s relaxation law—

\[ -\frac{dP}{d\tau}=k\cdot P \]

in the absence in the system of “true” elastic stresses that do not depend on time.

Surface-active substances contained in the medium surrounding the deformed crystal, in accordance with the above scheme of development of the initial plastic region, must under these conditions also exert an effect on the deformation of the crystal owing to their activating influence on the development of microcracks. That such an effect actually takes place is evident at least from the fact that the yield point of a single crystal in the presence of surface-active substances is lowered almost by a factor of two. But since this effect is already the result of the action of adsorbing substances in the region of plastic deformations up to the yield point, then, using only these data, it is impossible to determine the regularities of the adsorption effect in this plastic region.

A more detailed study of this influence was carried out by E. P. Zakoshchikova in our laboratory in the following way.

A specimen of single-crystal tin, 1 mm in diameter and 2–3 cm long, was fixed with Wood’s alloy in the clamps of Polanyi’s apparatus. An “instantaneous” load on the crystal was applied by bending it.

steel dynamometric plate on which the prism of the upper clamp of the instrument rested. The magnitude of the initial load was chosen with the intention that the stress \(P\) arising in this way should remain considerably smaller than the yield limit corresponding to the given orientation of the base plane. The plastic deformation arising under the action of such loads usually does not exceed a few tenths of a percent and lies entirely in the initial plastic region. As the residual deformations in the single crystal increase, the elastic bending of the dynamometric plate decreases, i.e., the stress applied to the crystal decreases.

As a result of this, the rate of plastic flow of the single crystal gradually decreases and after some time practically becomes zero at \(P=P_m\), i.e., even before the complete straightening of the elastic dynamometer, which is associated with the strain hardening of the single crystal. A secondary “instantaneous” loading of the single crystal up to the initial stress \(P_0\) again causes the development of plastic deformation, but with a lower initial rate, and the equilibrium state will be reached at a smaller absolute value of the plastic deformation, i.e., at a higher stress of the elastic dynamometer \(P'_m>P_m\). Further loading cycles with subsequent plastic flow of the crystal lead to an ever greater displacement of the equilibrium state in the direction of increasing \(P_m\). In each separate cycle the magnitude of the strain-hardening coefficient

\[ \lambda = k \frac{P_m}{P_0 - P_m}, \]

where \(k\) is the elastic modulus of the dynamometric plate. Hence it is seen that the strain-hardening coefficient of the crystal increases as the number of cycles increases, since \(P_m \to P_0\).

If the crystal and the elastic dynamometer are regarded as a single system subjected to deformation, then the decrease, observed during one cycle, of the elastic part of the deformation of the dynamometer \((\varepsilon_1)\) at the expense of the plastic deformation of the crystal \((\varepsilon)\) is, in essence, a process of relaxation of elastic stresses in this system under the condition that the total deformation is constant: \(\varepsilon_0=\varepsilon_1+\varepsilon=\mathrm{const.}\); at \(\tau=0\), \(\varepsilon_1=\varepsilon_0\), at \(\tau=\infty\;(\gg\theta)\), \(P=P_m\), \(\varepsilon=\varepsilon_m=\dfrac{P_m}{\lambda}\). Here \(\varepsilon=\dfrac{\Delta l}{l_0}\) is the plastic elongation of the single crystal; \(\Delta l\) does not exceed \(200\,\mu\), and the magnitudes \(\varepsilon_1\) and \(\varepsilon_0\) amount to no more than \(1\%\) of \(l_0\). Thus, the process of spontaneous decrease of the stress with time, \(P=f(\tau)\), can indeed be regarded as relaxation.

The relaxation process in such a system is carried out according to Shvedov’s scheme[^14]

\[ P - P_m = (P_0 - P_m)\cdot l^{-\frac{\tau}{\theta}}, \]

where \(\tau\) is time, and \(\theta\) is the relaxation period.

In Fig. 13 a typical graph \(P(\tau)\) is given for tin single crystals in air (white circles) and in a \(0.2\%\) solution of oleic acid in vaseline oil (black circles). As can be seen, the rate

Fig. 13. Creep curves of tin single crystals in an inactive medium (white circles) and in an active medium (black circles).

Fig. 14. Variation of the hardening coefficient as a function of the number of loading cycles. White circles—in an inactive medium. Black circles—in an active medium.

of plastic flow of a crystal deformed in a surface-active medium increases by a factor of 3–5, while the equilibrium state, characterized by the remaining elastic stress of the dynamometer \(P_m\), is shifted considerably toward a decrease in the remaining stresses. Figure 14 shows the course of the hardening coefficient \(\lambda\) with increasing number of cycles in air and in an active medium.

The second series of experiments consisted in the fact that one and the same tin single crystal was first subjected to deformation in air, and then, after 2–3 cycles of increasing load, was placed in an active medium, where its further deformation continued. As can be seen from Fig. 15, the “inclusion” of a surface-active substance in the process radically changes the deformation pattern. The creep curves, instead of rising ever higher with increasing number of cycles, as always occurs in an inactive medium, now under the influ-

Fig. 15. Creep curves of tin single crystals in an inactive medium (white circles) and creep curves after immersing the same specimen in an active medium (black circles).

...by adsorption in microcracks begin to descend and after 3–4 cycles of increasing the load in the surface-active medium pass even below the flow curve corresponding to the first cycle.

Consequently, substances adsorbed upon acting on an already hardened crystal are capable, during subsequent deformation, of lowering the hardening coefficient almost to the value corresponding to the unhardened metal. In addition, in the presence of surface-active substances the external stress \(P_0\), applied to the crystal and decreasing with the growth of plastic deformation, causes a greater plastic deformation in the crystal. Consequently, the final state of equilibrium between the magnitude of the plastic deformation and the remaining elastic stress in the crystal is shifted toward a decrease of the remaining elastic stresses. Thus, the relaxation of elastic stresses in a crystal in the presence of surface-active substances proceeds more completely, and the magnitude of the remaining, nonrelaxing elastic stresses is smaller than in an inactive medium \(^{20}\).

2. Elastic aftereffect in deformed tin single crystals

The study of the elastic properties of metallic single crystals has shown that the magnitude of the elastic shear in them is vanishingly small. Thus, in a first approximation an undeformed single crystal may be regarded as an ideally plastic body in the sense that the yield point corresponds to deformations (elongations) that are very small in comparison with their possible values in the principal region of plastic flow. This region begins when the shearing stress reaches a certain critical value in the operative slip system.

As plastic deformation develops, and with it the splitting of an initially homogeneous crystal into separate blocks with the formation of internal separation surfaces as a result of rotations and bending of slip packets, one may expect a considerable development of the elastic region, by analogy with the way in which an increase in dispersion—grain refinement—expands the region of elastic deformations in polycrystals.

However, it is necessary at once to point out the fundamental difference between these phenomena for single crystals and for polycrystalline aggregates.

In polycrystalline metals the disordered orientation of the grains leads to their differing stability with respect to external deforming forces. Grains favorably oriented relative to the direction of these forces may undergo plastic deformation, whereas unfavorably oriented grains will still remain in the region of purely elastic deformation. Therefore at the grain boundaries

PHYSICOCHEMICAL PHENOMENA DURING DEFORMATION

volume-stressed regions are created, hindering the further development of plastic deformation and contributing to the expansion of the elastic zone.

With an increase in the dispersity of a polycrystalline aggregate, i.e., in the transition to fine-grained structures, the significance of volume-stressed regions at grain boundaries increases in the overall system of internal stresses in each grain and in the specimen as a whole, which causes the development of elastic properties. In single crystals, in this sense nothing hinders the free slipping of individual blocks of the lattice—slip packets—and in this process they retain a common crystallographic orientation. The improvement of elastic properties during deformation is associated here with an increase in the excess free energy of the crystal in the course of deformation, chiefly due to the increase in surface energy along the slip planes during the formation and development of wedge-shaped microcracks, and also due to the elastic bending of slip packets. The first factor is especially important for the influence of adsorption from the external medium on the processes of elastic and plastic deformation of single crystals, since it is precisely the internal separation surfaces, arising and developing during deformation, that are the conductors of this influence.

A considerable development of the elastic region in deformed single crystals was discovered in studying the process of “recovery” of previously stretched single crystals of tin of a high degree of purity after removal of the load. Single crystals in the form of wire about 1 mm in diameter were subjected to tension at a constant rate of elongation \(V = 5\% \ \mathrm{min}^{-1}\). The experiments were carried out in an inactive medium—pure vaseline oil—and in vaseline oil with the addition to it of 0.2% oleic acid as a surface-active substance. During stretching, in addition to recording the complete deformation diagram \(P = f(\varepsilon)\), the electrical conductivity of the specimen was also recorded after every 10% elongation by means of a differential circuit of a Thomson double bridge.

After the specified degree of stretching had been reached—about 200%—the specimen was unloaded by reverse rotation of the counterweight to the zero position of the optical dynamometer. From this moment, for a fairly long time, while the first stage of the recovery process lasted (about 1.5 hours), a gradual shortening of the specimen was observed, expressed in the appearance of a force acting on the optical dynamometer of the instrument; to remove it, further rotation of the counterweight was required.

The total magnitude of this peculiar elastic aftereffect of unloading in an inactive medium—air or pure vaseline oil—reached 10–15 μ, or about 0.03% of the specimen length, and its completion required about 1.5 hours. In the presence of surface-active additions to the hydrocarbon medium, the magnitude of the elastic aftereffect increased to 40–50 μ, or to-

0.1–0.15%, and the time for completion of this phenomenon increased to 6–7 hours.

Simultaneously with the development of elastic after-effect there occurs a certain increase in the electrical conductivity of deformed single crystals, reaching 2–3% in an inactive medium and 15–20% in an active medium; moreover, the final value of the electrical conductivity at the same degree of elongation is considerably lower than in an inactive medium[^4].

Fig. 16. Growth of elastic after-effect in deformed tin single crystals (white circles) and change of electrical resistance in this process (black circles).

In Fig. 16 the curve of elastic after-effect is compared with the curve of the fall of electrical resistance with time.

In the work of E. Schmid and his collaborators, who studied the recovery process of preliminarily deformed metallic single crystals after removal of the load, it was established that complete restoration of the initial mechanical properties (estimated by the value of the yield point) at room temperature occurs for tin in approximately the course of a day and depends on the temperature and the degree of hardening. Thus, the observed phenomenon of elastic after-effect, being a component part of the recovery of the deformed crystal, does not exhaust this process completely.

The entire recovery process may be divided into three main stages. The first, the shortest in time, is completed already upon removal of the load (at the speed of sound) and is connected with the partial disappearance of the “true” elastic stresses in the crystal. The second, more prolonged stage consists in the gradual disappearance of internal separation surfaces, arising in the process of deformation along the slip planes, and in the closing of wedge-shaped microcracks formed on their basis in the surface layer.

Finally, the last, most prolonged, third stage includes the further gradual decrease of the free surface energy at the sites of the “damaged lattice,” connected with the restoration of interatomic bonds disrupted during deformation and with their partial rearrangement—a kind of recrystallization.

The elastic after-effect of unloading is connected mainly with the second stage of the recovery process, being the result of the action of molecular cohesion forces at the tips of microcracks, which cause their closing.

The significance of adsorption in this phenomenon apparently reduces to the development of the role of the second—slow—stage at the expense of the first—rapid—stage in the overall relaxation process, and also at the expense of a shortening of the third stage as a result of lesser damage to the lattice during deformation in the presence of surface-active substances.

Indeed, as we have shown, the adsorption action of surface-active substances leads to a considerable reduction in the work-hardening of a deforming single crystal and, consequently, to relatively slight damage to the lattice. In addition, the adsorption layers, by causing a significant increase in the number of active slip bands and penetrating into the metal, reduce the true elastic stresses in the crystal, converting part of the elastic energy of the deforming crystal into the free surface energy of the developing microcracks. This makes understandable the increase in the magnitude of the elastic aftereffect in the presence of surface-active substances. The aftereffect is associated here with the closure of much deeper microcracks. The adsorption layers covering the walls of the microcracks must be forced outward, which slows the closure process; this can also be traced from the increase in the electrical conductivity of the single crystal during relaxation.

We have already indicated the considerable role of surface microcracks during relaxation occurring in the very process of plastic deformation. The phenomenon of elastic aftereffect upon unloading of deformed single crystals shows that the role of surface microcracks is no less great in the process of relaxation after unloading^15^.

V. CONCLUSION

According to P. A. Rehbinder’s theory, the mechanism by which deformation is facilitated and the strength of a deforming body is reduced under the influence of the penetration of adsorption layers of molecules from the surrounding liquid into developing microcracks is based on three most important actions of these layers.

1. Facilitation of the formation of microcracks in the surface layer under the influence of adsorption of surface-active molecules, owing to a decrease in the uncompensated molecular forces acting on the surface particles of the solid body. The diversion of molecular forces to adsorption expands the system of defects—weak points that permeate all solid bodies and even well-formed crystals—and thereby promotes the formation of nuclei on which, beginning with the smallest deformations, microcracks develop.

2. The active wedging action of the adsorption monomolecular films themselves in all those narrowest portions of wedge-shaped microcracks into which only these films can penetrate. Such a wedging force is created by a tangential force equal to the product of the two-dimensional pressure by the length of the linear boundary of the adsorp-

tion layer, where a deeper penetration of the adsorbed molecules becomes impossible in accordance with their dimensions. The magnitude of the two-dimensional pressure is determined by the decrease of the free surface energy upon adsorption.

In the wider parts of microcracks, nearer to their mouth, the entire gap of the crack may prove to be filled with a transitional solvate layer of the liquid medium. In these sections of the cracks, the active spreading action of the interlayer, directed normally to the surfaces of the crack and tending to increase its thickness, may, following B. V. Deryagin, be regarded as a wedging pressure. Becoming noticeable beginning with a thickness of about \(0.2\mu\), the wedging pressure then increases sharply with decreasing thickness of the wetting film and, at sufficiently small thicknesses, becomes very considerable.

1. Difficulty or, in any case, retardation of the closing of embryonic sections of microcracks under the influence of adsorption layers after removal of the load. This effect acquires special significance in all elastic-kinetic phenomena accompanying the deformation of solids, and above all in the phenomena of elastic aftereffect and hysteresis. The role of solvate liquid layers in this effect may prove considerable, especially in the region of small deformations.

In general it is necessary to bear in mind that, in order to obtain significant effects of facilitating the deformation of solids, the penetration into microcracks of the thinnest monomolecular adsorption layers is sufficient.

The possible cases of interaction of a solid with substances adsorbed from the external medium are, according to P. A. Rehbinder, divided into two groups\(^{16}\), if one uses the following simplest scheme: let \(C\) be the work of the cohesive forces in the crystal, or the binding energy of the particles of the solid; \(A\) the work of the adsorption forces, or the binding energy of the adsorbed molecules with the surface of the body; and \(E\) the work of external forces in deforming the solid, calculated for the given microcrack. Then two cases are possible:

1) \(A > C\) and 2) \(A < C\).

In the first case the adsorption forces exceed the cohesive forces in the solid at least in some regions, which corresponds to the phenomena of swelling and colloidal dissolution—peptization—of bodies that are comparatively soft and heterogeneous in structure and composition. More interesting is the second case, when the cohesive forces in the body certainly exceed the adsorption forces: \(C > A\). In this case penetration of adsorbing molecules into an undeformed body will not take place, as was shown on crystals of mica, quartz, and metals by P. A. Rehbinder and his collaborators. However, such penetration even of large molecules of surface-active organic substances may occur, as experience shows, into the mouths of microcracks during deformation, when the work of deformation \(E\) together with the work of the adsorption forces \(A\) exceeds the cohesion energy: \(A + E > C\), i.e.

provided that \(E > C - A\). It follows from this that after the body is unloaded (\(E = 0\), i.e., \(A < C\)), spontaneous closing of microcracks must occur, beginning at the blind, embryonic end of the crack, with displacement of the adsorption layers.

It must be pointed out that the mechanism we have described for the adsorption effect on the strength of solids is a purely physicochemical surface process, not connected with any chemical reactions.

The study of the influence of adsorption layers on processes associated with the deformation of solids also contributes to a deeper penetration into the essence of the process of deformation in the absence of surface-active substances. But at the same time—and this is especially important—the laws governing the deformation of solids in the presence of surface-active substances are so essential, both theoretically, for understanding any processes occurring in a real solid under the action of external forces, and practically, for various processes of treating solids, that these laws can already now be singled out as a special field of the physicochemical mechanics of solids.

REFERENCES

1. P. A. Rebinder, VI Congress of Russian Physicists, Moscow, 1928; P. Rehbinder, Zeits. f. Phys. 72, 91 (1931).
2. B. V. Deryagin, M. M. Kusakov, Izv. OMEN AN SSSR, chemical series, 5, 771 (1936).
3. P. Kapitza, Proc. Roy. Soc. 119, 358 (1928).
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