Behaviour of Three Single Crystals of Aluminium 313 test piece remains free to twist also if necessary. These conditions render this type of machine perfectly suitable for tests on single crystals. Accordingly, tests have been carried out in this machine on three single crystals of aluminium; the first was tested under reversed flexural stresses, the second under reversed torsional stresses and the third under a com bination of reversed flexural and reversed torsional stresses.
H. L. Cox and W. J. Clenshaw 314 fillets of 1 0 inch radius. Reference marks were scribed on the enlarged ends of each specimen. After machining and etching to remove the surface distortion due to machining, each specimen was X-rayed inde pendently with respect to its own axis and one of the reference marks on the enlarged ends. The results showed that the change of orientation caused by machining was in each case quite inappreciable, the only differences being constant differences in the <j/ values of the same planes in the three specimens due to the arbitrary positions of the reference marks. The spherical co-ordinates of the slip planes as obtained by correction of the original X-ray readings are given in Table I, and a stereographic diagram giving the positions of all the principal planes and directions is shown in fig. 1. The co-ordinates given in Table I refer to the reference marks scribed on the individual specimens, and the positions of these reference marks are shown in fig. 1.
Behaviour oj Three Single Crystals of Aluminium 315 The ratios of the ranges of shear stress resolved along the three possible slip directions on each of the four possible slip planes to the range of nominal maximum shear stress are shown for each of the three specimens in figs. 2a, b and c. In this figure, the diagrams have been arranged one below the other so that the central vertical (dotted) fine represents in each case the axial plane of the specimen containing the normal to the slip plane 3(1 fl). The actual positions of the planes of bending in the Reference M&rk I j CHJIEZ. | | Fig. 1—Stereographic projection of principal planes cases of the specimens CHJIE1 and CHJIE2 are shown to left and right of this common line respectively. The difference between figs. 2a and 2b should be remarked; the addition to a simple bending moment of a torsion moment sufficient to produce the same shear stress has altered the stress distribution entirely. The plane 3, which in simple flexure was the only operative slip plane, becomes under combined stresses the only slip plane not operative.
316 H. L. Cox and W. J. Clenshaw 280 290 500 510 V52a0l ue55s0 o f 5A4.0C C5H50J 1ED0 1 j 10 + 20 ^*5?0 40 50 60 70 80 90 <D H H cj 3 <D J " “ ^ T) | o “ •s s § s§ g s3 . •« ‘XO? c0tf .2 g 2 o *m-3 ^O C 120 150 150 160 170 180 Va1l3u0 es 2o00f A Z(CO HO__I_R_ ), Fig. 2—Distribution of resolved shear stress and records of slip bands observed.
Behaviour of Three Single Crystals of Aluminium 317 angle a between the plane of the applied moment and the axis of the specimen. The range of shear stress due to flexure is ± cos a and the range of shear stress due to torsion is ± sin a. The stress conditions are most easily stated in terms of q and a.
318 H. L. Cox and W. J. Clenshaw object of the preliminary run was to exhaust “ settling down ” slip; but it was intended to impose only a small number of reversals of this lower range in the hope that, if hardening under this range could be avoided, the endurances of the three specimens at the higher range would give some indication of their relative strengths. The first tests on the speci mens CHJIE2 and CHJIE3 caused so little slip that further runs at the same stress were imposed in order to be sure that slipping under this range should be exhausted. The only other departure from the general scheme was in the last test on the specimen CHJIE3. For this specimen the maximum stress factor was rather low (0 • 82) and after the specimen had endured a million reversals of the range of nominal stress that caused failure of the specimens CHJIE1 and CHJIE2, the range was increased to bring the value of the maximum resolved shear stress up to a value com parable with that which caused failure of the other two specimens.
Behaviour of Three Single Crystals of Aluminium 319 Spacing of Slip Bands—Referring again to fig. 2, it will be seen that in the specimen CHJIE1 slip was confined entirely to one plane and occurred on that plane at values of the resolved shear stress from zero (or the slip limit, if it exists) up to a maximum of ± 1*10 tons/sq inch. A panoramic photograph of the surface of this specimen from X = 270° to X = 90° was taken after the test 2a. Individual photographs taken from this panorama are shown in figs. 7, 8, Plate 6. Even these photographs suggest some correlation between value of resolved shear stress and spacing of slip bands, and from the panorama itself it is quite obvious that some correlation exists. Accordingly an attempt was made to determine the mean spacing of slip bands at intervals of 10° X and to compare the values obtained with the corresponding values of the resolved shear stress. In the first instance counts of the number of bands in the full width of the panorama (3-7 inches corresponding to about 1 mm on the specimen) were made independently by two observers.
320 H. L. Cox and W. J. Clenshaw It will be seen that, even allowing for a considerable measure of un certainty at the higher stress values, marked correlation between the value of the resolved shear stress and the spacing of slip bands is shown; moreover, the stress at which “ massed ” bands first appear is marked by a fairly well defined “ knee.” A similar comparison of slip-band spacing with range of resolved shear stress for the specimen CHJIE2 was also made; the counts were made on Number of slip bands per mm normal to slip plane Fig. 3—Slip band spacing in relation to range of resolved shear stress x CHJIE1 tested in simple flexure (plane 3) O CHJIE2 tested in combined flexure and torsion (plane 2) + CHJIE2 tested in combined flexure and torsion (plane 1) [3 CHJIE2 tested in combined flexure and torsion (plane 0) Readings enclosed in dotted circles may be in error due to the proximity of cracks reducing the effective range of resolved shear stress.
Cox and Clenshaw Proc. Roy. SocA, vol. 149, Plate 6 r- 7 On 9 x X 6 2 o 8- II - = o d 9 5 1 r< = X 5 3C E1 U I J H oo C — 6 0 Uh 1 . g i F 8 2 3 x 6 2 - 0 - = d 0 8 1 = X El I J H C — 9 . g i F (Facing p. 320).