STRENGTH ANOMALY in Cd SINGLE CRYSTALS

STRENGTH ANOMALY IN Cd SINGLE CRYSTALS

Nazim Ufar

Physics Department, Faculty of Art and Sciences Atatürk University, Erzurum, Turkey

ABSTRACT

Yield stress measurements were performed on Cd single crystals as a function of temperature, orientation and strain rate. We found that the yield stress depends not only on the test temperature and orientation, but also on the strain rate. An anomalous peak was observed because of a thermally activated cross-slip from (0001) primary slip plane to (0111) and (1011) cross-slip planes.

1. INTRODUCTION

The yield stress of crystals exhibits a temperature dependence in a certain temperature region, known as the yield stress anomaly. Accordingly, Davies and Stoloff /I/ showed that there is a corresponding peak in the yield stress vs temperature for the same alloys, and a similar behavior has been observed in a number of other LI2 ordered alloys having both single and polycrystalline form, e.g.

Ni3Ga 12,2)1, Ni3Ge /4/, Ni3Si 151. Below the peak appearance temperature, the yield stress increases with increasing temperature and the active slip systems are predominantly <110>{111}, while above the peak temperature the active slip systems are predominantly <110>{010}. This temperature dependence of the yield stress has been explained by the Kear-Wilsdorf 161 mechanism, which is a locking mechanism, and in a more sophisticated way, by the cross-slip model 111. The details of this cross-slip and how the edge dislocations continue to glide have been elucidated by Sun and Hazzledine 111, and elaborated and extended by Hirsch /8/, who also provided the first explanation of a very low strain-rate dependence of the yield stress. Moreover, the dislocation structure and the dislocations with compact cores have also been shown to be responsible for the yield stress and flow stress anomaly /9,10/. Furthermore, Umakoshi et al. /II/ showed by compressive tests on ß-CuZn single crystals that the peak temperature was also observed to be dependent on the crystal orientation.

In addition to temperature and orientation, some researches showed that the yield stress is basically insensitive at low temperatures, weakly sensitive at intermediate temperatures and strongly sensitive at high temperatures to the strain rate /12,13/. This strain-rate dependence has been explained by a deviation from the stoichiometric composition or ternary addition l\2l and by considering thermally activated locking and unlocking of dislocations /14/ or super kink motion /8/. Accordingly, on pure Be

1 Vol. 10, No. 1, 1999 Strength Anomaly in Cd Single Crystals

single crystals, a model was proposed by Regnier and Dupouy /15/ which involves alternative cross-slip events between basal and prismatic planes, leading to locking and unlocking configurations. Although the majority of experimental investigations on the yield stress anomaly using single

crystals have been carried out on compounds which possess Ll2 type structure, such as Ni3Ga /3/ and

Ni3 Al /16/, and some models have been proposed to explain the anomalous mechanical behavior, in hexagonal close packet (h.c.p.) crystals, such as Zn and Cd, some anomalies, i.e., work-hardening rate and critical resolved shear stress, were observed at intermediate temperatures. It is important to investigate the basic yield stress on Cd and Zn, since these metals show basal glide because of the large c/a ratio and they practically do not deform on secondary slip. The purpose of the present study is to investigate the orientation, temperature and strain rate of the yield stress in the temperature range from room temperature to 500K.

2. EXPERIMENTAL METHOD

Metals of 99.99 % purity were used as starting materials for this study. Single crystals of 5 mm diameter were grown in a glass tube at the rate of 15 mm/h using a modified Bridgman method. The crystals were 80 - 100 mm in length and their orientations were determined by Laue back reflection method. The orientation of all crystals was within ±4° of the required orientation. The orientations are also shown in Fig. 1 in the standard <1010 >,< 21 10 > and <0001> unit triangle. In each orientation and at each test temperature, many crystals were prepared. The crystals were pulled along their growth directions with an Instron-type machine by changing the strain rate repeatedly between 1.6 χ 10"4 - 1.3 χ 10"6 sn"1 at room temperature to 500K range. The activated slip systems, i.e., slip planes and directions, were determined in this study by the slip trace technique using an optical microscope. In this work, slip in the crystals deformed under tensile stress at room temperature occurring along < 1210 > on the basal plane only, regardless of the crystal orientation. The yield stress was determined as the intersection of the tangent line to the stress-strain curves in the easy glide region and the straight line extrapolated from the elastic region l\ll.

1010

2110

Fig. 1: Tensile axis of Cd single crystals.

2 Nazim Ucar Journal of the Mechanical Behavior of Materials

3. EXPERIMENTAL RESULTS

The traditional metallurgical description of the yield stress in metals is based on the stress-strain diagram in a tensile test. Fig. 2 and Fig. 3 show some typical examples of stress-strain curves obtained from orientation A and the temperature dependence of the yield stress of Cd single crystals for all orientations at a strain rate 1.6 χ 10"4, respectively. It can be seen in Fig. 3 that the yield stress increases

with increasing temperature at low temperatures, exhibiting a peak in the range 0.65 Tm - 0.75 T,„ (Tm

Fig. 2: Typical stress-strain curves of Cd single crystals with orientation A deformed at various temperatures and measured at a strain rate of 1.6 χ 10"4 s"1.

300 500 Temperature (K)

Fig. 3: Temperature and orientation dependence of the yield stress in Cd single crystals.

3 Vol. 10, No. 1, 1999 Strength Anomaly in Cd Single Crystals

is melting point) depending on the crystal orientation, and then a rapid decrease in yield stress follows at high temperatures. The level of the yield stress was much higher than in orientation A at the peak temperature than those of the other orientations. In this respect, Umakoshi et al. /11/ have shown by compressive tests on single crystals that the peak temperature, at which yield stress shows a peak, depends on the crystal orientation. This orientation dependence has been explained by the Schmid factor and asymmetry of dislocations of crystals deformed in the twinning and anti-twinning sense /18/. The strain rate dependence of the yield stress of Cd single crystals for orientation C has been plotted in Fig. 4. Below the peak temperature, the yield stress was found to be independent of the strain rate although it changed temporarily when strain rate changed. Meanwhile, the peak temperature and yield stress value at the peak temperature tended to increase with increasing strain rate. The results observed for the other orientations are similar to that of orientation C.

300 500 Temperature (K)

Fig. 4: Strain-rate dependence of the yield stress of Cd single crystals with orientation C.

4. DISCUSSION

Yield stress anomaly can be defined as a positive stress response to an increase in temperature at a constant imposed strain rate. Different mechanisms have been proposed to explain this stress anomaly. Ardley and Cottrell /19/ attributed it to the maximum in the shear modulus in the slip direction occurring around the peak temperature. Brown /20/ explained it in terms of the difference in long-range order between the antiphase boundary produced by glide. Umakoshi et al. /11/ invoked the cross-slip of super lattice dislocations on the slip systems. But there is a consensus on stress anomaly that mobile dislocations cross-slip owing to thermal activation and are immobilized where the Kear-Wilsdorf locks

4 Nazim Ucar Journal of the Mechanical Behavior of Materials

form. This is a characteristic of deformation of single crystals and the cause of yield stress anomaly. In this study, we found a temperature dependence of the yield stress regardless of crystal orientation. The yield stress increased with increasing temperature up to peak temperature, then decreased for all orientations. This phenomenon, which is called positive temperature dependence of

yield stress, is similar to that in alloys with the LI2 structure. Above the peak temperature, there was an increasing tendency for slip to occur predominantly on (0111) and (1011) non-basal planes. This case shows that a dissociated screw dislocation, lying along < 1210 > which normally glides in the basal plane, moves in the other slip plane because of restricted glide on the basal plane by obstacles or a favorable stress field. Therefore, a cross-slip takes place from (0001) to (0111) and (1011) planes at around peak temperature. In fact, this transition, cross-slip, was confirmed by slip trace observations in this study. Once a screw dislocation shows cross-slip and becomes sessile, it forms a barrier called by Kear-Wilsdorf a lock to new dislocation from the same source. The formation of the barriers would result in a relatively high yield stress. This suggestion has been supported by TEM studies, indicating cross-slip events between the basal and non-basal planes of h.c.p. metals, leading to the locking and unlocking configurations /21/. The transition in the slip planes can also be explained by the separation of super-partial dislocations which considerably increase with increasing temperature because of the decrease in the degree of long-range order, so that at the defined temperature the movement of super- partial pairs is confined to the lowest antiphase boundary energy plane. A different approach, based on the lattice vacancies at high temperature and dislocation loops, explaining the relationship between the slip plane and the temperature, has been developed by Kuhlman-Wilsdorf 1221. Meanwhile, slip line

observations showed that <21 10>and<21 13> dislocations dominate above Tp. Thus, it is reasonable to conclude that multiple slip, presumably consisting of <21 10>and<21 13 > slips,

takes place above Tp. Above the peak temperature, Burgers vectors are changed from <1210> to < 2l 10 >and< 2113 >. It seems that cross-slip of dislocations on (0001) planes is an important factor controlling the anomaly yield stress behavior of Cd single crystals.

On the other hand, the yield stress was found to be independent of strain rate at low temperatures and dependent on the strain rate at intermediate and high temperatures (Fig. 4). This effect can be explained by increasing mobile dislocation density. When the strain rate is increased, the mobile dislocation density must increase in order to compensate for the increase in the strain rate. This requires an extra stress causing an increase in the yield stress. Meanwhile, peak temperature changes with strain rate. The strain-rate dependence has been explained by a pinning mechanism due to a thermal activation process, which is essentially time-dependent, and a change in the amount of Kear-Wilsdorf locks or stacking faults /23/. In conclusion, although body-centred cubic (b.c.c.) metals usually have a much larger temperature dependence on the yield stress than h.c.p. metals, we have shown that the yield stress is highly sensitive to temperature, orientation and strain rate. Also, it is concluded that the anomalous strength peak observed in Cd single crystals at high temperatures is to be attributed to a transition of the slip direction

5 Vol. 10, No. 1, 1999 Strength Anomaly in Cd Single Crystals

and a cross-slip from basal plane to non-basal planes. This is in good agreement with results of early deformation studies on other single crystals.

REFERENCES

1. R.G. Davies and N.S. Stoloff, Trans. T.M.S.-A.l.M.I., 233, 714 (1965). 2. S. Takeuchi and E. Kuramoto, J. Phys. Soc. Jpn.,3\, 1282 (1971). 3. S. Takeuchi and E. Kuramoto, Acta Metall., 21, 415 (1973). 4. H R. Pak, Τ. Saburi and S. Nenno, Trans. Jpn. Inst. Metals, 18, 617 (1977). 5. P.H. Thornton and R.G. Davies, Metall. Trans., 1 A, 549 (1970). 6. B.H. Kear and H.G.F. Wilsdorf, Trans. MS AIME, 224, 382 (1962). 7. Y.Q. Sun and P.M. Hazzledine, Phil. Mag. A, 58, 603 (1988). 8. P.B. Hirsch, Phil. Mag. A, 65, 569 (1992). 9. K.H. Hemker, B. Viguier and M.J. Mills, Mater. Sei. Eng., A164, 391 (1993). 10. B. Viguier, K.J. Hemker, J. Bonneville, F. Louchet and J.L. Martin, Phil. Mag. A, 71, 1295 (1995). 11. Y. Umakoshi, M. Yamagushi, M. Namba and Y. Murakami, Acta Metall., 24, 89 (1976). 12. Τ. Takasugi and O. Izumi, J. Mater. Sei., 23, 1265 (1988). 13. Τ. Takasugi, Μ. Yoshida and O. Izumi, J. Mater. Sei., 26, 1941 (1991). 14. Y. Sodani and V. Vitek, in: Proceedings of International Symposium on Intermetallic Compounds, O. Izumi (Ed.), 1991; p. 27. 15. R. Regnier and J.M. Dupouy, Phys. stat. sol., 39, 79 (1990). 16. P.H. Thornton, R.G. Davies and T.L. Johnton, Met. Trans., 1, 207 (1970). 17. K. Kojima and I. Okida, Phil. Mag. A, 61, 607 (1990). 18. A. Matsumoto and H. Saka, Phil. Mag. A, 67, 217 (1993). 19. G.W. Ardley and A.H. Cottrell, Proc. Roy. Soc. A, 219, 328 (1953). 20. N. Brown, Phil. Mag., 3, 693 (1959). 21. A. Couret and D. Caillard, Phil. Mag. A, 59, 738 (1989). 22. D. Kuhlman-Wilsdorf, Phil. Mag. A, 4, 72 (1959). 23. T. Kawabata, T. Kanai and O. Izumi, Phil. Mag. A, 63, 1291 (1991).