PRECISION ENTENSOMETER MEASURE- 775
knowledge of the properties of the crystals, together with an examin
ation of the way in ■which these properties are modified by the crystal boundaries.
The problem is approached by first studying single crystal specimens, then specimens consisting of a few crystals and their boundaries, and finally specimens consisting of many crystals of a size comparable with those met with in practice. It thus becomes possible to determine the effect of the boundaries and so to reach a more precise appreciation of the nature of the boundary region.
In order to apply this procedure, there are several desiderata to be observed in the choice of a m etal: the metal should be obtainable in a state of high purity; its grain-size should be easily controllable, and its crystals should be fairly isotropic with respect to the properties to be investigated. These conditions are satisfied by tin.
The choice of a mechanical test must also be considered; in order to satisfy the requirements stipulated above, the measurement of strain must be as sensitive as possible, while the stress must be uniform, such as tension, rather than torsion or flexure. The technique described below satisfies these conditions.
Although it is impossible from a priori considerations to decide which of the properties determined in the tensile tests are to be regarded as fundamental, a study of the results will show that a feature of great importance is the smallest stress that will cause creep to occur. I his is not necessarily the same as the limit of proportionality or the elastic limit, because completely recoverable creep can occur. Ihe smallest stress that causes creep will be referred to in this paper as the creep limit. A second fundamental stress is that which will just cause permanent extension, and will be referred to as the permanent set limit.
Such a stress cannot be measured experimentally, but its existence and value can be deduced from the experiments to be described.
The paper deals with the determination of the creep limit, and its variation with the size and arrangement of the crystals. It also describes an investigation of the effect of stresses close to the creep limit, i.e. the border line between elastic and plastic phenomena.
Pr e v i o u s Wo r k.
Although there have been several investigations of the creep pro
perties of tin, notably those of Andrade,1 Andrade and Chalmers,- and Hanson and Sandford,3 there is no previous work that is particularly applicable to the problem from the present point of view.
The investigations of Andrade, to the results of which reference will be made later, were concerned with the effects of stresses well above the
elastic limit, and with amounts of creep large enough to render high sensitivity unnecessary. The smallest extension that could be observed was of the order of 0-05 per cent. The creep was observed during the application of a stress that was maintained constant, the diminishing cross-section of the test-piece being compensated for by a reduction of tension. The experiments of Hanson and Sandford also did not require a high order of precision, since the tests were of the long period type.
In this case no provision was made for maintaining a constant stress.
Hence in neither case were the properties of the unaltered original material under investigation.
Ex p e r i m e n t a l Te c h n i q u e.
The experimental work under consideration consisted mainly of a precision investigation of changes of length of a cylindrical specimen during and after the application of tensile stresses.
The extensometer used for this purpose has previously been de
scribed,4 but a brief description may not be out of place here. The specimen S (Fig. 1) consists of a cylinder 2-5 mm. in diameter, and 7 cm.
in length, of which the central 3 cm. form the gauge-length. The appara
tus consisted of two parts, of which the functions are to apply the stress and to measure the strain. The main frame of the instrument consists of two vertical brass plates each about 25 cm. square, held parallel to each other at a distance apart of about 8 cm. by horizontal brass bars screwed to the plates. The disposition of the cross-bars is shown in section in Fig. 1 (A, F, 7 , Z).
The specimen (S, Fig. la) is fixed in chucks to the cross-bar A and to the tension rod B, so that S and B are collinear. The upper end of B is pivoted on the cross-bar C, which in turn is pivoted on the two parallel bars D. Each of these pivots consists of two gramophone needles held vertically and resting in punch holes, the result being that no couple is applied to B. The bars D are fixed together by means of cross-bars, and pivot on the points of two gramophone needles E carried by screws passing through the cross-bar F of the main frame.
A cross-bar at Or, connecting the two bars D supports a glass tube II 25 cm. long, and 6 cm. in diameter, closed at its lower end and open at the top. Water can be introduced into or removed from the tube II by means of a two-way syphon (not shown in the diagram). The stress applied depends on the water level in the tube II, the stress being zero when the weight of water in II is just sufficient to balance the counterpoise weight at J. The water level in the tube II is determined by means of a pointer which is moved vertically so as just to touch the water surface. The pointer is supported by a glass rod that moves
along a scale. The tube II is calibrated by introducing known amounts of water and observing the change in water level.
The strain is measured by determining the changes in the distance between two points on the specimen. This measurement is made by an optical interference method as follows. Two screws K, 4 cm. apart as measured along the bars Z,Z, each carry a gramophone needle, point upward. On these points rests a brass frame L, the bearing surface being of hard steel. A flat piece of glass M is rigidly attached to L. The
W
Fig. 1.—Diagram of Extensometer.
device by which the motion of the specimen is communicated to the frame L is shown in Fig. lb, and consists of two similar brass plates, between which are held two razor-blades of the three-hole type. The positions of the razor blades, which lie in a horizontal plane, are shown by dotted lines in Fig. 16. The razor blades are set just to cut the surface of the specimen when it is inserted.
The second frame P of the interferometer holds a second glass plate Q and a second device It similar to that shown in Fig. 16. The frame P is supported on L at two points by means of two screws T, the actual points of support again being gramophone needles projecting downwards
from the screws and resting 0 11 a piece of steel. The distance and angle between the glass plates Q and M can be adjusted by means of the screws T.
The frames L and P are each counterbalanced by adjustable weights at U and V so that no stress is applied to S through R or N. The interferometer is illuminated from above by means of light from a mercury arc passing through a water, cell and a mono-chromatic green filter, and reflected downwards from the glass slip X . The fringes produced by the interference between the light reflected upwards from the lower surface of Q and from the upper surface of M are viewed through a microscope at W. The direction and spacing of the fringes, which are lines of equal separation of M and Q, can be adjusted by means of the screws T. This adjustment is made so that the fringes form a series of parallel lines whose direction is parallel to the axis about which the interferometer unit turns. When the distance RN alters, the fringes move in a direction perpendicular to their length. Good fringes are obtained with no silvering on Q or M , which were pieces of good plate glass.
The apparatus was supported in a thermostatic water-bath of which the temperature variations were less than 0-05° C. Vibration was obviated by placing the whole apparatus on apier with a foundation inde
pendent of the rest of the building, a heavy slate top being supported on the pier by 12 rubber-sponge balls. No vibration that could be detected was transmitted through this arrangement, although the pier itself underwent considerable vibration.
The syphon apparatus, the device for measuring the water level, the stirring motor and the mercury are were supported on a second bench to avoid any disturbance originating from them.
The length of the specimen between R and N was about 3 cm.
and the change of this length which will cause a displacement of the fringe system by one fringe space is 3-68 x lO-5 cm., so that AI/I, the extension per unit length per fringe is 1-23 X 10"5, approximately.
The microscope used for observing the fringes contained an eye-piece scale. By adjusting the fringes to be about ten scale divisions apart, and reading the positions of the fringes to one-tenth of a scale division, movements of the fringes could be determined to 0-01 fringe. This represents a value of Al/l of 1-23 x lO '7. The accuracy of reading the water level was comparable, a change of water level of 0-1 mm.
corresponding roughly to a change of length of 10~7.
When observations of tsljl are made to an accuracy of the order of lO-7 cm./em., the temperature of the specimen assumes considerable importance. The coeflicient of expansion of tin is about 2 x IO- 5/ 0 C.,
so an increase of length of 10-7 cm./cm. is produced by an increase of temperature of about 0-005° C. The thermostat fluctuated within 0-05° C., giving periodic changes of length of the order of 10~s cm./cm.
which were corrected for in the results.
Pr e p a r a t i o n o p t h e Sp e c i m e n s.
The specimens consisted of cylinders about 3 mm. in diameter and 7 cm. long, and were prepared by casting in glass tubes. The material used in all these experiments except where otherwise specified was Chempur tin (tin 99-987, copper 0-00132, antimony 0-00118, lead 0-00585, iron 0-00055, bismuth 0-00352, arsenic 0-00005, nickel 0-00003, silver 0-00018 per cent., zinc, cobalt and sulphur nil).
The method of preparing the single crystal specimens was as previously described,5 and was that of gradually raising a glass tube filled with tin by suction from a crucible of molten tin.
The crystal size could be reduced by increasing the rate of with
drawal of the glass tube, giving quite satisfactory control of the grain- size.
Ex a m i n a t i o n o f t h e Sp e c i m e n s.
The size and disposition of the crystallites which formed the surface of a specimen could bo examined visually after etching in ferric chloride solution. When the crystal size was such that there were a number of crystals in the cross-section, the method described below, analogous to the method used by Desch 8 with brass, allowed a fuller examination to be made.
When a specimen of tin is dipped in mercury, the grain boundaries are rapidly softened by the diffusion of mercury along them, and it becomes possible after a few minutes to pull the specimen to pieces, each piece being one crystal. Thus, when the crystal size is not too small for easy manipulation, it can be readily studied. It may be mentioned in this connection that such softening by diffusion does not take place along twin boundaries prepared by a method described else
where.5
With single and large crystal specimens, a knowledge of the orienta
tion of the crystal axes relatively to the length of the specimens becomes desirable, and for this purpose the optical reflection method ' was used.
Ex p e r i m e n t a l Re s u l t s.
In the experiments under discussion, the crystal size was varied from that in which one crystal occupied the whole gauge-length of the specimen to that in which the number of crystals in the cross-section
was about 20. Of tbese experiments, tbose on single crystals have already been described,8 but for completeness the conclusions will be briefly recapitulated here and included with the other results.
In the experiments on any given specimen, results may be obtained for; (a) the extent to which Iloohe’s Law is obeyed; (b) the elastic modulus; (c) the limit of proportionality; (d) the variation of initial rate of creep with stress ; (e) the creep limit ; ( /) the form of creep and recovery curves; (g) the relation between recovery and creep; and (h) the permanent set point. It may be remarked here that corrections have been made, where necessary in the present work, for the spurious
“ thermal ” creep and recovery effect, considered in detail elsewhere.8 The observations show that the experiments form three distinct
R A TE O F CREEP X lO ^CM ./C M /M IN .
Fid. 2.-—Stress-Initial Creep Rate Curve for Single Crystals.
groups : (a) the single crystals, (b) the large crystals, and (c) the small crystals; these three groups will first be considered separately.
(a) Single Crystals.
The general result for single crystals is that there is no creep limit, and that the initial rate of creep plotted against stress is as shown in Fig. 2. The curve consists of a region of micro-creep AB and of macro- crcep CD. In the micro-creep range of stresses, the rate of creep under constant stress decreases exponentially, while in the macro-creep region it is constant. In both cases the recovery on removal of the stress is too small to be detected.
(b) Specimens Consisting o f a Few Crystals with Longitudinal Boundaries.
With specimens of this type the stress-strain curve was straight or nearly so, up to the creep limit, which coincides with the limit of
proportionality. The initial and final creep rates varied with stress in the manner shown in Fig. 3, giving a fairly well defined creep limit for any one specimen.
R A TE O F CREEP X I0-*CM,/CM./ M IN .
FiO. 3,—Stress-Crecp Rate Curves for Large Crystal and Small Crystal Specimens.
This creep limit varied over a very wide range of stress, i.e. from 112 to 264 grm./mm.2. For a series of typical specimens the number of crystals was counted and the total area of crystal boundaries within the gauge-length was estimated; Table I shows that there is no relation between the area of the crystal boundary and the creep limit.
Ta b l e I.
Creep Limit,
Grin./mni.1. Kumber oi Crystals.
Area of
BoimUaries-A 264 3 2 cm.*
B 238 5 6 cm.2
C 124 5 4 cm.2
D 112 4 3 cm.2
E 120 3 2 cm.2
An examination of the orientations of the crystallites was made by the optical reflection method, with the large crystal specimens. In some cases the arrangement of the reflection spots did not differ greatly
from that of a single crystal; in other cases the reflections from one of the crystallites was very different from tlie arrangement to be anticipated if the crystallite concerned shared the orientation of the remainder. In the former cases the differences of orientations of the crystals were small, and those were the specimens with low creep limits, e.g. specimens C, D, and E ; the specimens with large differences of orientation were the ones which showed a high creep limit such as A and B.
The conclusion is that the creep limit is influenced to a far greater extent by the differences in orientation of the crystals than by the extent of the boundaries.
TIM E, M IN U TE5
Fio. 4.— Creep and Recovery Curves for Large Crystal Specimens.
It may be noted that the creep-stress curves obtained from single crystals do not vary appreciably with the orientation.
The forms of the creep and recovery curves obtained with such specimens are shown in Fig. 4, in which two pairs of curves are given.
It may be observed that the recovery depends on the creep; the curves refer only to gradual changes of length, the much larger instantaneous changes not being represented in the diagram.
(c) Specimens Consisting o f Small Crystals.
There were no marked differences in behaviour between the various specimens of this type, although the crystal size varied from about 60 to about 1000 to the cubic centimeter.
Except in the conditions described below, the stress-stiain line showed no deviation from linearity until the creep limit was reached.
If correction for creep is made the stress-strain line retains its linearity well beyond the creep limit.
The initial creep-stress curve follows its usual form (Fig. 3), giving a fairly well marked creep limit which is rather below the stress at the bend of the corresponding curve for single crystals. The creep curves (Fig. 5) show several features of interest, the creep either becoming linear or ceasing after a fairly short time, corresponding to the (3 and
Fig. 5.— Grecp and Recovery Curvea for Small Crystal Specimens.
y stages of Andrade.1 It is found that the recovery follows a curve identical with the ¡3 curve of the creep, whether the y part has a finite or a zero slope.
If the stress-strain data are taken when the recovery from previous strains is complete, it is linear; if, however, the readings are taken before the recovery is complete, the curve is not linear near the origin, but- takes the form shown in Fig. 6, BCD, the point A of the intercept of the straight line part of the curve corresponding to a shorter length than the length B of the material when under zero stress by the amount of recovery that has not yet taken place.
The distance AB is a measure of the residual recoverable strain of
the material, and decreases with time until the curve finally becomes linear.
Di s c u s s i o n.
The advantages o£ the present technique over those more often used for tensile tests will first be discussed. The necessity for thermo
static temperature control has already been indicated, and this in turn
0 10 20 30 40 50
STRESS. GRM./MM.2
Fig. 6 .—Strcss-Strain Curves for Partially Recovered Polycrystalline Specimens.
demands a small specimen; a small specimen requires the detection and measurement of a very small absolute extension, for which purpose the interference method is the most convenient, and, since it requires no calibration, probably the most accurate.
In an investigation such as the present one, in which control of crystal size and shape are of importance, the small size of the specimen is also advantageous, as such control can be more easily applied to a small specimen. Further, if a particularly pure material is to be used,
VOL. L X I. H
as is the tendency in fundamental investigations, the small quantity of material required is another advantage. Another consideration is that the value of the stress applied is independent of the strain which results, in which particular the instrument is superior to instruments in which the stress decreases as the strain increases.
The maximum elongation that can be measured without resetting the extensometer is 10~3 cm./cm., i.e. one thousandth; hence the stress under a given force can be regarded as sensibly constant without the application of a constant stress device such as those to which reference has been m ade.*• 2
A further advantage of the present method of experiment is that it is possible to detect very small total amounts of creep and recovery, as well as very small rates of change of length; the latter can be measured with equal or greater accuracy by using a longer time unit (e.g. day instead of minute) if the creep continues long enough; otherwise it may remain undetected by the long period methods. The results show that there is often a type of creep which is complete within a short time of the application of the stress (the p creep), and it is by a study of creep of this kind that the creep limit can be investigated.
In considering the results described above, two features in particular yield new information, i.e. the experiments on specimens consisting of a few crystals, and those on the fully polycrystalline material. The interpretation of the former results depends on the data obtained with single crystals; as mentioned previously, the behaviour of single crystals of tin is nearly independent of orientation (owing to the large variety of possible slip directions) and consists of micro-creep up to a fairly definite stress between 100 and 140 grm./mm.2, above which macro-creep occurs.
In the specimens now under consideration, several such crystals side by side form the specimen, the crystals being joined by boundaries parallel to the direction of application of the stress. The effect of the boundaries on the property which determines the creep limit is consider
able. In the first place, such boundaries always inhibit micro-creep, and secondly the lower limit of creep varies from 110 to 264 grm./mm.2.
Thus the effect of the boundaries varies considerably from specimen to specimen, and, as shown above, is related to the difference of orientation between the crystals. This fact presents new evidence as to the nature of the crystal boundary, and it will first be shown that it is inconsistent with an amorphous cement theory.
If the intercrystalline material were truly amorphous, it would have an atomic arrangement independent of the structure or orientation of its surroundings, and so would always be the same in a given material;