THE ELASTIC STRENGTH OF METALS

BY FRANK CHARLES THOMPSON, M.MET., B.Sc.

( A Paper read bcfoue the F m m h y Society 011 TiiesdLiy, Mlzy 11, 1915, SIR ROBERT HADFIELD, F.R.S., PRESIDENT, in thc Choir.)

It has been recognized ever since the microscope was applied by Sorby to the study of metals that, normally, a pure metal consists of allotrimorphic crystals which meet along their boundaries. These latter would be expected at first sight to be surfaces of distinct weakness. It is a curious and rather unexpected fact, however, that when such a metal is broken in tension, frac- ture does not occur in the regions between the crystals but passes through the body of the crystal itself. In other words, the intercrystalline boun- daries are by far the strongest part of the mass.

During recent gears the idea that an amorphous intercrystalline layer occurs in normal metals between adjacent crystals has been put forward and developed by several authors, and in view of the mass of evidence which has been accumulated the theory may be accepted, at any rate as a working hypothesis. This theory is an extension of a more general one which has been developed in a long series of researches by Dr. Beilby, in which the production and continued existence of the vitreous amorphous state in plas- tically deforhed metals has been experimentally demonstrated.

Glasses and other liquids in a drastically undercooled state are in general distinctly harder than the corresponding crystdine solid, and the remarkable strength of the intercrystalline boundaries has been explained, up to the present, simply by the fact that the “cement” which exists there is itself strong. Since, however, these intercrystalline films are of extreme thinness- certainly beyond the limit of microscopic vision-this explanation necessitates the assumption of a tensile strength for the cement of an order far beyond anything of which we have experience or are justified in assuming from our knowledge of other undercooled liquids.

The extreme practical and theoretical importance of an exact knowledge of the source of the strength of these junctions, however, renders it worth while to pursue the question further, Iron, which under normal conditions has a tensile strength of perhaps 20 tons per square inch, may, when the intercrystalline cement is impaired, become so brittle as to be broken even by hand.

Since the material filling the intercrystalline space is of the nature of an undercooled liquid, evidence of the normal properties of this state should be obtainable. In this connection viscosity effects have often been observed, and in particular for the present purpose surface tension phenomena may be expected. The conception that surface tension effects are to be observed in the amorphous layer of metals is not put forward here for the first time. The idea, which was originally due to Quincke, has been used by many authors. Dr. Beilby (I), whose writings are permeated with the idea, has definitely

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THE ELASTIC STRENGTH OF METALS 105

shown that the forms assumed by the surface layers of metals during mechani- cal deformation or subsequent annealing are controlled by surface tension. Similar forces are also at work within the amorphous films formed on each plane of slip. Brillouin has used the hypothesis in order to explain the behaviour of metals in tensile tests, and the polyhedric form of the crystals of an annealed pure metal has been referred by P. Curie to surface tension in the crystal boundaries. Tanimann (2) also has considered the relationship of the surface tension to the strength in eonnection with the crystalline structure of metals during crystallization from the liquid state or after having been cold-worked. A quantitative relationship has been derived by the same author. If f is the strength of a lamina at its recrystallization temperature after cold-rolling, wire-drawing, etc., i t the number of gliding planes in it parallel to its surface, a, the tension in the gliding planes, which is always less than a, the surface tension in the free surfaces, then-

21zaI + 2a= f. Rosenhain and Ewen (3), referring to the reason for the retention of the intercrystalline metal in the amorphous condition, say, “The forces . . . may possibly be of the nature of capillarity.” The theory, however, is used in the present Paper in a novel and more dcfinite manner, and in addition a quantitative interpretation is adopted.

When two similar plates are separated by a film of a liquid which wets them, a marked attraction occurs. The intensity of the attraction is :--

‘9 dynes,

where- A is the area of the plate wet by the liquid, T is the surface tension of the liquid,

d is the thickness of the film. and-

At the crystal boundaries in a metal not dissimilar conditions obtain. Two crystalline portions are separated by a film of “ undercooled liquid.” In this case, however, the pressure must be regarded as being derived not from that of the atmosphere, but from the vectorial forces of crystallization.

Such attractions may attain very considerable magnitudes, and the strength (elastic) of the junctions, and therefore also of the metal itself, is regarded as being due to these attractions between all the adjacent faces in the mass. An example of such adhesions is afforded when two blocks of ice are placed loosely together. As the excess water between the faces drains away, the remaining film draws the masses together with a force sufficient to weld them into one coherent whole. To the author this action appears analogous to the crystalline growth of a metal during annealing.

One of the most important explanations to be required from any theory of the source of the intercrystalline strength of metals is the mechanism by which the great strength of the junctions is obtained despite their extreme tenuity. As has already been shown, any explanation on the ground of the actual strength of the films themselves does not appear satisfactory. With the new theory, however, the difficulty ceases to exist. Since the attraction between the crystals is inversely proportional to the distance between them, the very thinness of the films is the source of their greatest strength, and if for any reason the width of these is increased the strength of the mass is lowered.

The greatly increased elastic strength of a fine-grained metal over a

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Id, THE ELASTIC STRENGTH OF METALS

coarser one depends, on the theory, simply on the increased area across which the attraction occurs, and thus on the grcater resolved force in any direct ion.

Ejfeds of Strain on Metals. It now becomes of interest to discover to what extent such a theory is in

accordance with the well-known facts relating to the effects of strain,on metals, and in particular with the stress-strain diagram.

Fig. I shows the curve obtained by Robertson and Cook (4) following Dalby (5 ) , which probably most accurately represents the phenomena. For strains below the elastic limit stress and strain are proportional. When this range of proportionality is passed, however, the curve bends abruptly down- wards, reaches a minimum, after which it ascends again to the maximum

Straih.

FIG. I .

stress. It is in the marked dip at the “yield point” that the diagram differs essentially from those usually obtained.

On thc present theory the elastic strength of a metal is the resultant in the direction of the application of the stress of the interface attractions. When the applied stress is less than this value comparatively little effect is produced and the strain will be small. The extension will be made up 01

the true elastic deformation of the crystalline matter itself and a!so of the slight separation of the crystals at their boundaries. Which of these factors will be the greater cannot be stated a friori. When the load is removed the extension disappears, although slight viscosity effects have been observed even within the elastic range. The true elastic deformation will be removed with great rapidity, but the rate at which the attractions will draw the crystals back to their original positions may conceivably be much less, as actual flow of the viscous amorphous material seems necessarily to accompany the

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THE ELASTIC STRENGTH OF METALS

changes. When the increasing stress applied to the specimen becomes equal to the resultant of the attractions the elastic limit is reached. A further stress, exceeding the resistance of the interface attractions, draws the crystals apart and permanent set occurs. Actual separation of the crystals is prevented by the flow of amorphous metal from more highly compressed localities. This increased thickness of the amorphous film is of the greatest importance, since the intercrystalline attraction, i.e. the resis- tance of the metal to the stress, is inversely proportional to the thickness d . The effect, therefore, of the drawing apart of the crystals just beyond the elastic limit is to lower markedly the resistance to the stress applied. During this stage of the test every increase of load, by ixicreasing the thickness of the films, produces a rapid fall in the resistance to the stress, and a period of instability-the yield point-occurs. The decided drop in the stress-strain curve when the elastic limit is passed is thus explained.

Up to this stage the demands of the theory seem to be in complete accord with experience, but much further it is impossible to go. Once the elastic limit is passed, slipping occurs on numbers of cleavage plaiics within each crystal. At each slip amorphous material is formed, across which further attractions, which cannot be allowed for, act. The metal is stiffened up and the curve rises again, but at an indeterminate rate.

Having seen how eininently satisfactory is the qualitative agreement between the demands of the theory and the experimentally determined diagram, it becomes of interest to determine what quantitative significance the foriiiula possesses. In the first place the thickness d of the intercrystalline cement is not known, though it is probably nearly within the range of microscopic vision. The second source of uncertainty arises from the lack of knowledge of the surface tension of these films. It has been shown, however, that the surface tension of an undercooled liquid iz quite unaffected by the freezing-point (6), the curve expressing the relationship of this quantity to the temperature being a straight line without inflection, till in the neighbourhood of the critical temperature the tension becomes zero. Thus, if the critical temperature and the surface tension of the molten metal at any definite temperature are known, the surface tension of the amorphous material at room temperatures can be calculated. The critical temperatures for practically all metals are unknown, but a rough approximation may be arrived at from the use of the formula of Thorpe and Rucker :-

At the outset two difficulties present themselves.

where- DI = density of liquid metal at temperature P A , DO = ,, 9 , J , 273*A,

aiid- T,"A = critical temperature.

For purposes of calculation of the critical temperature Do is taken as the density of the ordinary metal itself-if known in the work-hardened state- since changes of density when a metal is converted into the amorphous con- dition by cold work are not great. The values of the critical temperature arrived at in this way are certain to deviate markedly from the truth, but since the temperature is in all cases very high compared with that at which the surface tension of the molten metal has been determined-usually the freezing-point-the increase in the experimentally determined figure for

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108 THE ELASTIC STRENGTH OF METALS

the surface tension will be slight, whence the latter will be known for the amorphous films within fairly narrow limits.

The total attraction per C.C. is according to the formula-

2AT - d ' - --

where A is the total intercrystalline area per unit volume. The resultant attraction therefore in any one direction is-

, 2AT 3 . -. d

Now, considering the crystals as perfectly regular rhombic dodecahedra, and remembering that A is one-half of the total crystalline surface, the

resuitant in any direction, i.e. the elastic limit, will be I - z ~ ~ z - , where n is the

number of crystals per cm. Since, however, the crystals never are uniform dodecahedra, the area will be greater, and probably-

T d

T E (the elastic limit) = 1 * 5 n ~ . . . . . expresses the attraction as nearly as it is possible to do so. The foregoing is by no means a rigid proof, but the equation appears to correspond with the experimental results with a reasonable degree of exactness.

For pure metals only has the surface tension bcen accurately determined, and these alone, therefore, are available for the experimental verification of the expression. The values of the surface tensions used are those given by Smith (7) with the exception of the values for cadmium, which is Quincke's, and for iron, which is not known at all well, and where 1,350 is taken as being as near as possible.

The values of the densities are taken from the tables of Landolt and Bornstein, supplemented where possible by the valuable determinations of Pascal and Journiaux (8).

Copper, zinc, antimony, silver, lead, tin, nickel, and very pure iron were selected for examination. All, with the exception of the nickel, were prac- tically free from any impurity. The tatter metal, however, contained 0.79 per cent. of manganese, the remains of 1'5 per cent. thermit manganese which had been added to the molten metal to remove oxygen taken up during melting. The copper, zinc, antimony, silver, lead, and tin were cast in bars 12 in. long and I in. diameter, from which the tensile test pieces were pre- pared with 2 in. turned accurately to a diameter of 0.564 in. The iron and nickel were cast as 2-in. square ingots and rolled to I-in. round bars. To investigate the influence of alterations of crystal size in the same metal, test pieces were prepared of the iron, after several different thermal treatments, viz. :-

(I) As received from the rolls. (2) Normalized, i.e. heated to p o o C. and cooled in air. (3) Quenched from 0000 C. and then tempered at 6500 C. (4) Heated to 9000 C. and cooled over 12 hours. (5) Heated to 900" C., kept at the temperature for about 15 hours, and

cooled over another 40 hours.

By these treatments the number of crystals per im. was varied from 6 p in sample (3) to 10 in sample (5).

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THE ELASTIC STRENGTH OF METALS I09

The analysis of the iron was :- C. Si. Mn. S. P. Al. E'e (by difference).

'049 '04 -03 -02 -016 trace 99'87 Figs. 4-7 are micrographs taken at 100 diameters of the structure of

The test pieces were broken on the 10-ton centre of a Buckton testing- machine. The elastic limit was determined in the cases of the silver, copper, nickel, and iron with the aid of a Metzger extensometer reading to '0001 in. In the other tests it was somewhat less exactly determined as that stress at which permanent elongation could first be observed with dividers (i.e. an elongation of -01 in. on a gauge length of 2 in. or 0'5 per cent.). The bars of zinc and antimony broke without any observed deformation, the elastic limits coinciding in these cases with the maximum stresses. Since annealed copper is practically without any true elastic range, great care was taken with the test of this metal in the cast state, and up to 1-52 tons per square inch perfect proportionality between stress and strain was observed. The elastic limit is taken as the limit of proportionality of stress and strain.

2, 3, 4, and 5.

Table I records the experimental results.

TABLE I.

Material.

Copper . . . . . . Zinc . . . . . . Antimony ... Nickel . . . . . . Lead . . . . . . Tin . . . . . . Silver . . . . . . Iron (annealed) ... Iron (normalized) Iron (quenched

tempered)

... ... ... ... ... ...

... ... ... and

Elastic Limit. Tons per sq. in.

1-52 2-64 0-69 0.60

I '40 9 6 I

I 1.5

I '20

12'0 14.0

No. of Crystals

per sq. cm. Metal.

Lead . . . . . . Antimony . . . . . . Tin . . . . . . Silver . . . . . . Copper . . . . . . Zinc . . . . . . Nickel . . . . . . Iron (annealed) ... Iron (normalized) Iron (quenched

and tempered)

Max. Stress. Tons per sq. in.

9'0 2-64

0.98 2-40 8.0

2 1.8 23.2

0.69 36'71

21'1

TABLE 11.

T.

Elongation per cent. on 2 in.

~~

22'0 0'0 0'0

66.4 54'5 36'5 60.0 47'0 47'5 46.0

2-66 x 103

3'2 x 103 4'45 x I@ 8.6 x I@ 1.62 x 104

1'72 x 1 0 4 5'2 x I& 5.6 x 105 6.9 x I&

13'9 x 1 0 5

E.L. x I O - ~ Dynes

per sq. cm.

0'93 I '04 1-86 2-17 2'35 4.08

I 7.8 148 18.6 21'6

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I I 0 THE ELASTIC STRENGTH OF METALS

In Table I1 the number of crystals per cni.n, the calculated surface tension of the amorphous film (T), r'51zT and the elastic limit E in dynes per sq. cm. are recorded. With the cxception of a slight alteration in thc position of the nickel-readily explicable since it alone deviates appreciably from absolute purity-the orders of the metals in the last two columns are identical, and it is impossible to believe that such agreement could be found did not the theory of the elastic strength of metals at present under consideration contain distinct elements of truth.

The three tests made on the pure iron give rise to a point of coiisiderable interest. In a ductile metal such as this, it has been conclusively proved that fracture in tension occurs within the crystals themselves and not in the intercrystalline boundaries. Now, there is no reason to suppose that the heat treatments applied would appreciably alter the state of the crystalline matter. Hence, beyond a certain small stiffening-up, due to the greater amount of the amorphous cement, one would not expect the maximum stresses in the three cases appreciably to differ. This is shown to be the case, since the increase in the maximum stress from least to greatest is oiily 10 per cent. On the

6 12 15 18 21 24 3

FIG. 2.-Elastic limit x 10-' (dynes per sq. cm.).

other hand, according to the theory here advanced, the magnitude of the elastic limit is intimately connected with the boundaries between the crystals, and the change in this quantity in the cases under consideration is no less than 46 per cent. To the author this seems striking evidence that the conditions governing the elastic limit are, as his theory demands, essentially different from those governing the maximum stress.

Probably, however, the most striking proof of the truth of this is supplied by figures published by Professor Arnold (9) of tests made on a steel casting, as cast and after drastic annealing.

Elastic Limits. Maximum Stress. Tons pet- sq. in. Tons per sq. in.

As cast . . . . . . . . . . . . 16 2.5'5 Annealed . . . . . . . . . 4 24'3

In Fig. 2 the last two columns of Table I1 are plotted against each other, and it will be seen that to a first approximation, which is all that can be expected, the relationship is a linear one.

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THE ELASTIC STRENGTH OF METALS 111

If- T E = 1*5n -, d

then

the thickness of the amorphous intercrystalline film. From Fig. 2 d = 3-7 x 10-1 cm. This value will be discussed later. There is, of course, no reason why the

thickness of the film should not vary markedly from metal to metal, but the results of Table I1 and Fig. 2 suggest that in all the metals examined the thickness of the intercrystalline cement is of the same order.

During a consideration of the possibility of extending the application of the equation of Van der Waals to the solid state, Traube (10) arrived at the con- clusion that the hardness of a metal is determined by its " intrinsic pressure." That this is not a complete expression of the facts is evident from the well- founded experience-confirmed by results on iron contained in the present Paper-that the hardness of a metal is largely determined by the size of the component crystals, increasing as these decrease. Thus, in any mathematical expression of the hardness of a metal a term, depending on the grain size, must be introduced. For a single crystal it may well be that Traube's hypothesis holds, but such isolated crystals of metals are merely curiosities. As has been already noted, how- ever, the maximum stress of a pure metal is dependent chiefly on the crys- talline material itself, and only to a smaller extent on the crystal boundaries. Hence this measure of the hardness of a metal will probably bear an intimate relation to the intrinsic pressure.

I n view of the close relationship between the surface tension and intrinsic pressure of a substance, it is to be expected that, if the author's theory is true, a certain degree of proportionality will be found between the elastic strength of a metal and its intrinsic pressure.

Such a term equation (I) does contain.

TABLE 111.

Metal.

Lead ... Tin,.. ... Zinc ... Antimony ... Silver ... Copper ... Iron ... Nickel ...

Intrinsic Pressure.

Megabars.

Clastic Limit Tons

per sq. cm.

0.60

2-64

I '40 1-52 9.6 I

1'20

0.69

12'0

1 I . j I 4.0

Max. Stress. Tons

per sq. cm.

0.98 2-40 2-64 0.69 8-00 9.00

21'1

22'2 21.8

36-71

Brinell Hardness (500 kilos).

Too soft to measure Do. but harder than lead

2 9 7 Crushed

45 70 83

10s 109

-

Table I11 gives for the metals used in the present research the intrinsic pressure (Traube's results), the elastic limit, maximum stress, rind Brinell hardness. Though a certain correspondence between the intrinsic pressure and the elastic limit is evident, the agreement is far less perfect than when

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I I 2 THE ELASTIC STRENGTH OF METALS

the equation (I) is utilized. The maximum stress results checked by the Brine11 hardness, however, strikingly confirm Traube’s theory, with the exception of the values for antimony.

Two further details pointing in the same direction may here be noted. Hanriot (I I ) has recently shown that a cube of metal subjected on every face to considerable hydraulic pressure was appreciably hardened, although no dis- tortion of the crystals could be detected rnicroseopically. Cleavage slipping, therefore, presumably did not occur, so that the hardening was not due to an increase in the quantity of the amorphous modification. The result admits of a simple explanation in view of the theory under consideration. Pressure from all sides would tend to produce closer contact between adjacent crystals, so that d in equation (I) would be decreased and E in proportion increased.

The second point arises from the discovery of Schottky (12) that the strength of gold leaf begins to decrease when the thickness is reduced below a certain value. The extra reduction would produce, if possible, more amorphous material than before, and so should, according to present concep- tions, give a still harder material. Such a result, however, would follow necessarily from the surface-tension theory of strength. As the amount of the amorphous variety increases, more and more surfaces. over which the attractions could be exerted would at first be formed, and hence an increase of strength result. After a very great amount of cold work has been put upon the metal, the crystalline phase will have decreased to such an extent, however, that the area across which attraction occurs will have decreased also, and a corresponding loss of strength occurs.

Efect of Temperature on iiie Mechanical Properties of Metals.

As has already been emphasized, the normal fracture of a ductile metal at room temperatures passes through the body of the crystals. At the same time the crystals are pulled out, and slipping along cleavage planes occurs. Above a certain temperature, however-720’ C. in the case of copper-the fracture changes entirely in type, and now passes through the intercrystalline regions. The crystalline matter i s not appreciably deformed, the metal having become typically brittle. This remarkable change is the result of the gradual loss of strength of the intercrystalline junctions. So long as these are stronger than the crystals, so long is the low-temperature type of fracture found. When the conditions are reversed, intergranular weakness results, and the fracture passes between the crystals.

This loss of strength of the cement has been explained in a perfectly satisfactory manner (13) by the reversion of the extremely viscous under- cooled liquid to a more mobile-and hence weaker-state. The present hypothesis, however, still affords a simple and rational explanation of these facts. The surface tension falls off as the temperature rises, the crystals grow in size at the same time, i.e. n in equation (I) decreases, and Van der Waals has shown that surface films may increase in thickness as the temperature is raised, i.e. d increases. Thus every term in the equation-

1’ n I!: = 1’512

changes so as to reduce the value of the elastic limit. When the crystalline part has become stronger than the junctions, the stress sufficient to overcome these will be sufficient to smash the specimen. Hence the maximum stress

coincides with the elastic limit. Since I*jnT is a measure of the strength of n

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"HE ELASTIC STRENGTH OF METALS 1 I3

the crystal junctions, it represents above the temperature at which the order of the relative strengths of these and the crystals changes the maximum stress. Below that temperature it is a measure of the elastic limit, thus in the curve tensile-strength-temperature an abrupt change should occur. This is in entire accord with the results obtained by Bengough and Hanson (14) with copper. Fig. 3 shows the typical curve which these investigators obtained. The interesting corollary arises from these considerations that the elastic- limit curve below the temperature of change should be a continuation of the maximum-stress curve above. The paper quoted does not contain the values of the elastic limits, but if the curve above P be continued back the value of the limit at room temperature for annealed copper broken in air is 3 tons per sq. in., and for hard-rolled copper 6 toils per sq. in., results of approximately the right order of magnitude.

When such a temperature is attained that the crystalline growth has an appreciable velocity, the term IZ of equation ( I ) starts to decrease rapidly, and with it the elastic

For a pure metal, however, the curve will not be straight.

Temperature.

FIG. 3.

limit. This curve in the diagram will therefore bend downwards. The values of the elastic limit of copper just obtained by simple extrapolation will err notably on the high side. The curve showing the relationship of the elastic limit of copper to temperature has, however, been obtained by Huntington (IS), and is exactly of this type.

Electrical Conductivity.

One calculation of the order of thickness of the intercrystalline medium has already been obtained, viz. 3 . 7 ' ~ 104, and it is also possible to obtain the same value using determinations of the elecirical resistivity.

When an electrical current is passed through a normal metal the opposed resistance may be considered as the sum of two factors, one for the actual crystalline material, the second depending on the resistance of the crystalline junctions. Since the actual thickness of these latter will always

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* 14 THE ELASTIC STRENGTH OF METALS

Observed.

be small, the length of the crystalline material to be traversed will remain sensibly constant, so that the crystalline factor will itself bc,a constant. The total resistance of the boundaries will depend on the number of these to be traversed, so that

where- pI =p,+ wR. . . . . . . . . . (2) <:

p, = specific resistance of the sample. pa = specific resistance of the crystalline material. n = number of crystals per cm.

R = the boundary resistance. and-

For the experimental testing of this equation the samples of heat-treated iron were used. The specific resistances were measured by comparing the p.d. between the ends of the bars 8 in. long and I cm. diameter with that in a standard low resistance when traversed by the same current. The results are found in Table IV.

Calculated.

TABLE IV.

Treat men t.

I 1 Sp. Resist. in microhms per C.C.

I No. of I

l- Annealed drastically Annealed . . . . . . 1:: 1 Normalized . . . . . . . . . Quenched and tempered ... As received . . . . . .

7'152 7'25 I 7.513 7'563 7'986

- 7'307 7'422 7'564 8.019

Difference, Observed- Calculated.

- - -056 + '09' - '033 - '001

Without a single exception the increased size of grain is accompanied by a corresponding decrease in the specific resistance. To I per cent., which is as near as the mean crystal size can be determined, the equation (2) holds good.

The value 7.56 microhms per C.C. for the iron as received from the rolls is in excellent agreement with that (7.6) arrived at by Benedicks (16) from his study of thc specitic resistance of steels.

The number of crystals per cm. in the drastically annealed sample could not be determined, as the structure was most curiously and to the author in-

* Since writing this, the attention of the author has been drawn to a paper by von Weimarn (Zntc.rnatiotta1 Jouriznl of Iclc&Clography, iii., 2, p. 65) in which a very similar relationship has been given. Reasoning from the known properties of colloidal solutions, it is found that the measured resistance of a metal p is the sum of two values pv and ps, of which the first depends of the volume of the sample, the second on the surface energy. Thus-

p = pv + PS.

In addition ps is dependent on the number of crystal grains per cc. The close relationship of this expression to the equation of the author will be

readily seen. No attempt, however, was made to supply any experimental evidence in support of the idea.

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THE ELASTIC STRENGTH O F METALS

explicably uneven. About seven-eighths of the microsection consisted of crystals so large as to be visible to the naked eye, while the remainder con- sisted of crystals almost as fine as those in the annealed sample (Fig. 7).

From the values obtained the true specific resistance of the crystalline material p. and the boundary resistance R could be calculated. Substituting the mean values of these in equation ( 2 ) it becomes for iron-

H = 6-83 + 1-72n x 1 0 3 microhms per C.C.

The value 6.83 microhms per C.C. is the only logical value for the specific resistance of iron. The great variation in the specific resistance as the grain size alters (7*15-7*9) seems to explain the wide divergence of the values ob- tained by different investigators for this “constant,” even where pure materials have been used. In view of these results no determination is complete which does not also give the crystal size and sufficient data for the calculation of p? and R.

If equations ( I ) and (2) are combined-

From which, with the values already determined, d can be calculated.

Material. I ncm. --____-

Annealed iron . . . . . . . . . . . . I 3’4 x 10-4 Normalized iron . . . . . . . . . . . . 4’3 X 10-4 Quenched and tempered . . . . . .

Mean . . . . . . . . .

This value is in very close agreement with that already obtained, 3’7 x 10-4 cm.

It is at once evident, however, when considering the result, that 4 x 10-4 cm. is an impossible figure for the thickness of the films. Films of such thickness would be readily seen even at a magnification of no more than 500 diameters. The result, however, far from being useless, throws a flood of light on the question of the origin of the amorphous material.

Two explanations of the manner in which this is produced have been put forward. The idea of Rosenhain and Ewen involves the assumption of “ crystal units” of definite size. Between adjacent crystals, spaces exist less than the crystal unit, in which therefore crystallization is impossible.

Humfrey’s (17) explanation, which has always appeared. more probable to the author, is as follows : ..... When two crystals are gradually growing towards one another each will endeavour to marshal the . . . molecules surrounding it to its own orientation, and it would seem . . . that there would be formed between the two crystals a layer of matter in which the molecules are so arranged as to pass by gradual small displacements from the orientation of one crystal to that of the other.” In such a case of gradual change from one “substance” to another the surface tension is greatly rcduced. Thus T in equations (T) and (3) is not that calculated, but a dis- tinctly smaller value. In each case d is proportional to T , with the result that the thicknesses of the amorphous film thus calculated should be

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116 THE ELASTIC STRENGTH OF METALS

decidedly high. The results obtained thus lend strong support to this theory of the formation of the film.

So far as the actual values of the thickness are concerned, nothing more definite can be said than that they are probably nearly within the range of microscopic vision, i.e. of the order of 10-5 cm.

The author's sincerest thanks are due to Professor J. 0. Arnold, D.Met., F.R.S., for his valuable interest and advice.

BIBLIOGRAPHY.

(I) BEILBY : Phil. Mug., 1904, p. 258. The May Lecture, 1911, of the Inst.

(2) TAMhfANN : Lehrbuch tler Metallographie, pp. 20-23 and 75-78. (3) ROSENHAIN and EWEN : g. Znst. Mctals, 1912 (2 ) , vol. viii. (4) ROBERTSON and COOK : Proc. Roy. SOC., 88, A, p. 462. (5) DALBY : Proc. Roy. Soc., 86, A, 1912, and 88, A, 1913. (6) HOOK : Akad. Wiss. Wien Sitz, 6, 108, 2, A, p. 1516, 1899. (7) SMITH : g. I d . Mefuls, 1914 (2 ) , vol. xii. (8) PASCGL and JOURNIAUX : Comptes Rendus, 158, p. 414. (9) ARNOLD : Trans. Zrtsf. Naval Architects, 1908, p. 5.

(10) TRAUBE : Zeit. Anorg. Chem., 34, p. 413 (11) HANIUOT : Cornftes Rendus, 155, p p . 713 and 1502. (12) SCHOTTKY : Nachrichten der Kgl. Gesellschaft der Wiss. Gottiiigen,

(13) ROSENHAIN : Eizgiiteering, October 17, 1913, p. 539. (14) BENGOUGH and HANSON : 7. Insf . Met.. 1914 (2), vol. xii. (15) HUNTINGTON : J. Znst. Met., 1912 (2), viii., p. 126. (16) BENEDICKS : Doctorate Thesis, Upsala, IW. (17) HUMFREY : J. Zron and Steel Z i z s f . , Carnegie, vol. 5, p. 86.

of Metals is a rksumd of Dr. Beilby's work.

Math.-Physik. Klasse, 1912.

THE METALLURGICAL DEPARTMENT, SHEFFIELD UNIVERSITY.

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