PART XI – November 1967 - Papers - The Effect of Specimen Diameter on the Flow Stress of Aluminum

The effect of the specimen diameter, d, on the flow stress, cra of polycrystalline aluminunz (99.997) was studied. The increase in the flow stress could be accountedfor by the increase in the surface layer stress, with decreasing specimen diameter. Both , and a, were found to be proportional to For the smaller-dianzeter specimen (< 0.033 in.) at strains less than aboul 0.1, the work hardening of the surface layer was greater than that associated with the bulk of the specimen. At higher strains the work hardening due to the bulk appears to be independent of the specimen diameter. THE increase in the strength of metals with decreasing diameter is well-known; however, an adequate explanation for the cause of the size effect is still lacking. The earliest systematic investigation of size effect appears to be that of Onol who reported that for aluminum monocrystals the resistance to slip at low strains increased as the specimen diameter decreased. A change in the stress-strain curve beyond 0.001 strain was not found. However, Suzuki et a1 .&apos; reported for monocrystals of a brass and copper having diameters in the range of 2 to 0.12 mm that the entire stress-strain curve was raised as the specimen diameter was decreased. The effect of size was most apparent when the diameter of the specimen was less than 0.5 mm. In the discussion of this paper Honey-combe reported a size effect in copper crystals as large as % in. diam. These results are in agreement with those of paterson3 and Garstone et al.4 While the majority of the investigations on size effects was conducted in terms of the variation in the diameter of the specimen, several investigators studied the influence of the specimen geometry. For example, Wu and smoluchowski 5 reported that in aluminum monocrystals the slip system was a function of the specimen dimension in the slip direction. King-man and Green 6 studied the influence of size on the compressive stress-strain relationship of aluminum monocrystals when the ratio of length to diameter was constant. Their specimen diameters ranged from to & in. For specimens oriented for single slip the critical resolved shear stress for the smaller-size specimens increased with decreasing diameter. No effect was observed in the large-size specimens. Specimens having an orientation near the corners of the stereographic triangle did not exhibit a size effect. Apparently, the increase in strength with decrease in the diameter of the specimen is a general phenomenon and has been observed in a brass |T and cadmium as well as in aluminum and copper.&apos; In a series of investigations (for example Ref. lo), it was shown that during deformation a surface layer was formed which imposes a back stress, a,, on the moving dislocations. It is reasonable to predict that this surface layer stress, as, should be a function of the specimen diameter and could possibly account for the flow stress size effect. In fact, experimental evidence will be presented to show that this is the case; i.e., the increase in flow stress with decreasing size is equal to the increase in the surface layer stress, as, with size. In addition, data will be presented on the variation with size of and a* where is the back stress associated with the generation of dislocation obstacles in the bulk of the specimen and a* is the net effective stress acting on the mobile dislocations. A limited investigation was carried out on gold specimens to determine the influence of an oxide film. EXPERIMENTAL PROCEDURE The aluminum specimens were prepared from -in. bar stock (99.997 pct purity). The 0.350- and 0.150-in.-diam specimens were machined directly from the bars while the specimens having a diameter of 0.033, 0.020, and 0.015 in. were prepared by swaging and drawing to 0.04 in. and electropolishing almost to final size. The specimens were prepared with a 2-in. gage length. The specimens were annealed in vacuum (-10-4 Torr) at 350°C for 8 hr. The grain diameter of the specimens in the various specimen diameter groups was 0.08 ± 0.02 mm. Gold specimens of two diameters, 0.14 and 0.03 in., were prepared in a similar way and annealed at 650°C for 8 hr. The grain diameter of the gold specimens was 0.2 mm. After annealing the specimens were electrochemically polished to the final size and tested in an Instron tensile machine at a strain rate, E&apos;, of 10- 3 per min. While it was possible to determine the surface layer stress, a,, in the larger-size specimens by measuring the difference, Aa, between the stress before unloading the specimens and the initial flow stress after removal of the surface layer as outlined in detail in Ref. 10, this method is not applicable for small wires because of the difficulty in obtaining a sufficiently accurate measure of the diameter. The values at the various strains were therefore determined by measuring after the specimen had been annealed at 35°C for 4 hr. It has previously been shown" that the two methods give the same results for a provided that the annealing temperature is low enough to affect only the surface layer and not the dislocation barriers in the bulk of the specimen. For the gold specimens a treatment at 150°C for 16 hr was found to be satisfactory for the determination of by the low-temperature annealing method. EXPERIMENTAL RESULTS Determination of a,, and a,. The stress-strain curves for the various diameter aluminum specimens, plotted in terms of the logarithms of the true stress, and true strain, are given in Fig. 1. These curves represent the average data taken from at least ten specimens at each size. Over the range of strains investigated the curves follow the empirical equation