FRACTURE PHENOMENA IN CRYSTALLINE AND AMORPHOUS BODIES

D. B. Gogoberidze

INTRODUCTION

Until now, in all investigations of the mechanical properties of crystals and amorphous bodies, authors have especially emphasized the differences between them. Indeed, these differences are very great. In crystalline bodies we observe regular plastic deformation with definite and clearly expressed planes of deformation and with a definite geometry. In amorphous bodies, regular plastic deformation is not observed. Under the action of a force, amorphous bodies either break apart, or flow, or else enter a stressed state, noticeable from the double refraction caused by it.

However, there are phenomena in which a certain analogy is manifested between the properties of crystalline and amorphous bodies—these are fracture phenomena. Until now, it would seem that insufficient attention has been paid to such an analogy, and our task in the present article will be to discuss this interesting question.

§ 1. FRACTURE PHENOMENA IN AMORPHOUS BODIES

When an amorphous body is struck, or when a static action of sufficient magnitude is applied, its destruction occurs. As is known, amorphous bodies cannot deform plastically and, under small actions, deform elastically; then, if the action is prolonged and small in magnitude, they flow. But if the action is sufficiently large in magnitude, then brittle fracture is observed in amorphous bodies—brittle

cal cleavage. Finally, it is known that in amorphous bodies there may occur large deformations of a special kind, associated with the appearance of birefringence. These deformations may reversibly disappear when the load is removed, but they may also remain in the body.

The details of the fracture phenomenon depend very strongly on the shape and material of the specimen, on the magnitude and rate of action of the force, but the general picture remains, in all cases, similar to a certain degree. On all fracture surfaces of amorphous bodies—the so-called conchoidal fracture—we observe a smooth curved surface on which formations of two kinds are noticeable: first, systems of radial cracks, sometimes cutting through the specimen; second, a peculiar system of concentric rings. The formation of radial cracks is observed, for example, when a body with a large surface, moving at low speed but with sufficiently large kinetic energy, strikes a glass plate (Fig. 1). In this case a cone-shaped piece of glass is knocked out, which is divided by radial cracks into parts. When a body with small kinetic energy—for example, a light ball—strikes, a circular crack arises in the glass, not passing through the plate.

If the striking body has a small area but large kinetic energy—for example, a bullet—then it pierces the glass through without breaking it. In this case a cone-shaped chip is formed in the glass, with its apex directed toward the direction of motion of the bullet, sometimes without cracks. As for the cone-shaped piece of glass knocked out of the plate, it usually breaks into parts.

Finally, when a large piece of glass of irregular shape is struck, especially at its edge, fragments arise (Fig. 2) whose form is very reminiscent of a shell. Evidently, this was noticed long ago, and hence the name itself arose—conchoidal fracture.

Examining attentively the surface of such a conchoidal fracture, we notice in it, in addition to the curved fracture surface, also a peculiar system of small cracks or lines emanating from the point at which the blow was delivered and forming, as it were, a distinctive fan. We have called such a formation the “rose of fracture,” by analogy with the “wind rose.” The lines of the rose of fracture correspond to the directions of action of the force.

As has already been said, in addition to the system of radial lines, on the fracture surface we also find a peculiar system of concentric rings, which we call “fracture rings.” On each fracture surface there are formations of these two kinds—the rose of fracture and the fracture rings. In this case the relative development of these two formations (Figs. 3 and 4) will be

depends on the conditions under which the force acts, on its magnitude, on the speed of action, on the area of contact between the bodies, and on the material of the bodies. Finally, it should be noted that when, under the influence of nonuniform heating, a glass plate cracks, this crack (if there is only one) has a wave-like form, reproducing, on an enlarged scale along the ordinate axis, the pattern observed in fracture rings. With corresponding changes in the conditions of thermal action, it is possible to obtain a repetition of the same fracture rings and fracture rose as under mechanical action. In other words, sharp and nonuniform heating, which causes a noticeable expansion of the glass and the appearance of internal stresses, leads to the same consequences as local mechanical action.

Quite naturally, the question arises as to the cause of the appearance of these formations.

As for the fracture rose, its lines are the lines of action of the force during fracture, and their direction characterizes the direction of the maximum shearing stresses during fracture. The situation is more complicated with fracture rings.

Indeed, in examining various glass articles, we may observe that analogous formations arise not only during fracture but also, for example, during the blowing and drawing of glass. On many windowpanes, and on the surface of glass vessels, we notice analogous formations (Fig. 5). Finally, similar formations can also be reproduced in the following way. Let us take a plate of dark glass and carefully degrease it. After this we immerse the plate in water. If its surface has been sufficiently thoroughly degreased, then it will acquire the ability to be wetted by water, and after it is removed from the water there will remain on it a thin and (if the plate is placed horizontally) uniform layer of water. If we now quickly press with a finger on a corner of this plate, we shall see a circular wave run over the surface of the water, entirely analogous to those fracture rings that are observed in glass. Of course, in the case of a water surface this wave will quickly die out and disappear, but it may be assumed with every probability that, in the fracture of amorphous bodies, the fracture rings likewise represent, as it were, the frozen trace of such a wave. In other words, one may suppose that the fracture rings formed during the drawing of glass and during the fracture of solid amorphous bodies are, as it were, the trace of that elastic wave which arose at the moment of the action of the force on the body and under whose influence the fracture occurred.

A wave running along the surface of a liquid, when some body has been thrown into it, is a completely analogous formation.

§ 2. FRACTURE IN CRYSTALLINE BODIES

As is known, fracture in crystalline bodies differs sharply from fracture in amorphous ones above all in that crystalline bodies are anisotropic and, in particular, have certain principal planes along which the separation of parts of the crystal occurs especially easily—the so-called cleavage planes—which amorphous bodies do not have. However, in addition to fracture by cleavage, conchoidal fracture is also possible in crystalline bodies. At the same time, some crystals have such poor cleavage that only conchoidal fracture is possible in them.

One should not think that conchoidal fracture in crystals is something rare or even exceptional. On the contrary, in the majority of crystals it is precisely conchoidal fracture that is the principal, and often even the only possible, type of fracture. Only in some crystals with especially perfect cleavage does fracture by cleavage play a significant role and occur frequently; but even in them it is never exclusive.

Therefore we shall first consider conchoidal fracture in crystals, and then fracture by cleavage.

§ 3. CONCHOIDAL FRACTURE IN CRYSTALS

Conchoidal fracture in crystals is entirely similar to conchoidal fracture in amorphous bodies. In crystals we encounter the same smooth curved fracture surface, covered with a system of fracture rings and lines of the fracture rose. We have happened to see fragments of quartz which, in form, were completely identical to the forms of glass splinters, so much so that without the aid of a polarizing microscope it would have been impossible to say whether the given fragment was a splinter of a crystalline or of an amorphous body.

However, not infrequently, on correctly formed crystals or on their parts one may see conchoidal fracture surfaces or portions of them. An especially clear picture of conchoidal fracture was observed by us on quartz crystals (Figs. 6, 7, and 8).

It should be noted that in mineralogy, in general, it is well known that many crystals can give conchoidal fracture. Alongside this, some scholars believe that certain crystals (for example, rock salt, calcite, etc.) are always bounded by cleavage planes when fractured. Such an assertion seems to us unfounded. Indeed, even macroscopically we can verify that conchoidal fracture is sometimes encountered in calcite crystals. As for rock-salt crystals, here the matter is more complicated.

It is very often asserted that crystals of rock salt, when crushed, always divide into parts bounded by the faces of a cube. Such an idea, for example, found expression in the well-known educational film Crystals, produced under the editorship and with the participation of the late Prof. N. I. Dobronravov, where it is shown how a large cube of rock salt, when struck with a hammer, divides into a series of rectangular parallelepipeds, and a rhombohedron of calcite into a series of other rhombohedra; phenomena connected with the occurrence of fracture along other planes and of conchoidal fracture are not shown. The same idea is taken as the basis of the theory, developed by the well-known Tomsk physicist V. D. Kuznetsov, which treats hardness as the surface energy of ionic crystals. According to V. D. Kuznetsov’s views, in the process of grinding and polishing, a number of fragments are torn away from the main crystal, having the form of rectangular parallelepipeds or cubes, which subsequently, in the course of working, undergo no further crushing. Kuznetsov believes that fracture of a rock-salt crystal along faces other than the cube face always has a stepped character, and that conchoidal fracture is altogether impossible.

We have already indicated that such a mechanism of these phenomena appears to us to be incorrect. Cracks arising in crystals of rock salt under the action of a concentrated load, both under impact and under static indentation, are more readily formed along the planes of the rhombic dodecahedron. When a cube face is struck, a system of cracks first arises that run approximately along the planes of the rhombic dodecahedron, and only afterward a system of cracks running exactly along the cube faces; the latter are less clearly expressed and, at small deformations, i.e. at small loads, may be entirely absent. Thus, under conditions of the action of a localized load, fracture along the rhombic dodecahedron may proceed more easily than along the cube, i.e. than along the cleavage plane.

It must be noted, however, that cracks along the rhombic dodecahedron do not run exactly in the crystallographic direction; they may deviate noticeably from it (as V. D. Kuznetsov has already pointed out) and even curve, whereas cracks along the cube, narrower and less clearly expressed, run exactly along the cube face.

Further, thanks to V. D. Kuznetsov’s investigations it is known that the plane of free oscillations of a pendulum with a single support (an edge or a ball) tends to set itself in such a way as to coincide with the direction of least strength of the material on which the pendulum rests. In other words, a pendulum with a single support, when this support is placed on an anisotropic body, turns until the plane of its oscillations coincides with the direction of least strength in this body. In particular, as was found from V. D. Kuznetsov’s observations, in a crystal

of rock salt the direction of free oscillations of such a pendulum coincides with the plane of the rhombic dodecahedron. This is understandable, since the support of the pendulum, when oscillating, presses out a depression of elliptical cross-section and, according to the principle of least work, the pendulum must be oriented so that the direction of the major axis of this ellipse coincides with the direction of least strength on the given face.

Thus, we again arrive at the conclusion that under certain conditions the plane of the rhombic dodecahedron in crystals of rock salt is indeed the plane of least strength.

When grinding and sawing crystals of rock salt, triangular fragments often break off, bounded by two faces close to the rhombic dodecahedron (the short sides of the triangle, meeting at an obtuse angle) and by one (the long side) cube face. This is very clearly seen in Fig. 9. Such fragments occur most often in comparison with other forms. Alongside such, the most frequently encountered fragments of comparatively regular form, in the grinding and cutting of rock salt there are also fragments of completely irregular form, bounded, apparently, only by surfaces of conchoidal fracture. A microphotograph of such a fragment is shown in Fig. 10.

Thus, we arrive at the conclusion that even in crystals with very perfect cleavage, for example rock salt and calcite, conchoidal parting is observed, with all its characteristic features noted in the case of amorphous bodies and crystals with poorly expressed cleavage. On the surface of the fracture we find the same fracture rose and fracture rings as on the surface of amorphous bodies.

§ 4. FRACTURE ALONG CLEAVAGE

In addition to conchoidal fracture, in some crystals we encounter fracture along cleavage, and this cleavage may be of varying degrees of perfection. The considerations given below relate to the fracture and cleavage of crystals with very perfect cleavage, for example rock salt, calcite, barite, etc. In these crystals the cleavage plane obtained upon splitting is an almost ideal, mirror-smooth surface. Only comparatively negligible irregularities are noticeable on it. This has led to the fact that it is usually considered that the surface of cleavage splitting in crystals with very perfect cleavage is indeed a very smooth surface. Meanwhile, this is not at all so. Examining the surface of cleavage splitting in reflected light at a small angle, we noticed characteristic irregularities on it. These irregularities acquire an especially simple form in the case when the splitting is carried out

with the aid of a very sharp blade and if this blade is oriented in a definite way relative to the crystal.

In particular, in the case of a rock-salt crystal the blade should be oriented in the plane of the cube along which the split is to be produced, and moreover in such a way that it forms angles of \(45^\circ\) with the cube planes perpendicular to the plane along which we wish to split the crystal. In other words, the blade must be perpendicular to that edge of the cube which, in turn, is perpendicular to the plane along which it is desired to produce the split, and at the same time must form equal angles with both planes that intersect in this edge.

If a non-mosaic rock-salt crystal is split in this manner, then on the surface of the cleavage fracture we shall see formations of two kinds. On the one hand, there is a series of lines diverging fanwise from the point where the blade was located at the moment of splitting. This fan of lines is completely analogous to the fracture rosette that arises on the fracture surface of amorphous bodies. In the case of the cleavage fracture of a crystal the lines are smaller and finer. On carefully examining the surface of such a crystal, we easily become convinced that the lines of the fracture rosette on its surface constitute a series of very small steps, i.e. that the cleavage split has a slightly stepped character (Fig. 11). In some cases, if the number of these steps is small, their height may be considerable (of the order of \(0.1\) mm); if there are many of them, then they are much lower.

Along with this, besides the lines forming the fracture rosette, lines of another kind are also observed. These lines form, as it were, a series of concentric rings. They are entirely analogous to the fracture rings described above, only in the case of a crystal they are much smaller than in amorphous bodies. In profile these rings differ greatly from the lines of the fracture rosette. Whereas the former are steps, the latter are elevations having a wavy character (Figs. 12 and 13). We believe that they do indeed constitute fracture rings, the same as in the case of amorphous bodies or of conchoidal fracture. It should be noted that, in addition to rock-salt crystals, we have also happened to observe fracture rings and a fracture rosette on the cleavage fracture of barite crystals.

The relative development of the fracture rings and the fracture rosette on cleavage-fracture surfaces is not always the same. Depending on the conditions during splitting, on the degree of perfection of the crystal, and on how accurately the razor blade was oriented during the split, either the fracture rings or the fracture rosette are more clearly expressed. The presence of imperfections in the crystal, for example leading to the appearance of ledges on the splitting plane, necessarily leads to the occurrence near this ledge of especially

of a dense system of cleavage rings. This is quite similar to the especially dense system of surf waves at a breakwater in the sea.

Thus, we see that in the case of cleavage splitting we encounter the same formations—the cleavage rosette and cleavage rings—whose presence we have already noted in the case of amorphous bodies.

In conclusion, the author would like to note that some of the photographs in the present article were made by Tsarikovskaya. The author expresses sincere gratitude to Docent V. A. Frank-Kamenetsky for providing a number of crystals.

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b

Fig. 1. Effect of a localized force on a square glass plate.

Fig. 2. A glass fragment with a conchoidal fracture; in shape it truly very much resembles a shell.

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Fig. 3. Fracture rings on a large piece of glass.

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Fig. 4. Fracture rings and a fracture rosette in rosin.

Fig. 5. Rings on the surface of a glass funnel.

Fig. 6. Fracture rings on a quartz crystal.

Fig. 7. Fracture rosette and fracture rings on the surface of a crystal.

Fig. 8. Conchoidal fracture on quartz. Fragment.

Fig. 9. A triangular fragment of typical shape for a rock-salt crystal, obtained at the initial stage of grinding. The long side is the edge of the cube; the short sides are close to a rhombic dodecahedron. Surfaces of conchoidal fracture are also visible. Microphotograph. Magnified 20 times.

Fig. 10. A fragment of a rock-salt crystal, obtained during grinding and bounded by surfaces of conchoidal fracture. Microphotograph. Magnified 20 times.

Fig. 11. Lines of a rose of fracture on a cleavage chip of a rock-salt crystal.

Fig. 12. A very perfect cleavage fracture of rock salt. The finest rosette lines of fracture and their bends, forming fracture rings.

Fig. 13. Fracture rings on the surface of a cleavage fracture at a step on the surface.