Anisotropy of Plastic Deformation in Hexagonal Metals

Geometric aspects of the shear processes in hexagonal metals are analysed. They can be divided into three groups: those localized essentially between neighbouring atomic planes, occurring in narrow slabs along particular atomic planes, or covering a large crystal volume. Obviously, dislocation glide and deformation twinning are principal types of such processes. On the geometrical level, the dislocation slip as well as twin propagation are controlled by Schmid factors. Since the sample loaded by external stress can sometimes give way to fracture (cleavage) under tensile stress, it has to be also mentioned. The main aim of this work is to show only on geometrical grounds for which sample orientation which process is more likely to occur. More complex shear processes that take place during double twinning are also briefly considered. In polycrystals, the shear phenomena lead to texture formation when the processes that control the behaviour of materials may be those that act in a similar way in single crystals.

The kinetics of twinning in zinc and tin crystals

By using a high speed rotating mirror camera combined with a microscope, the rapid initial lengthening of twins and their subsequent broadening have been studied. In zinc, twins of up to 1·9 mm appeared in crystal surfaces within 1 μs and subsequently the tips of such twins were observed to move at up to 780 m/s. It is pointed out that observations of twins which simply appear in crystal surfaces do not necessarily yield information on the true twin propagation speed in the twin plane. However, such information has been derived from experiments in which the twin growth was followed from the point of twin nucleation located under a knife edge. Increasing the rate of loading applied to the knife edge by more than an order of magnitude did not significantly alter the maximum speed of growth. Therefore the maximum speed recorded in experiments using a knife edge, about 600 m/s, is thought to be close to the maximum true twin tip speed in zinc in the twin plane. It is approximately one third of the slowest sound speed in the twinning direction. Broadening of twins under a steadily increasing stress is a smooth process which, in a specimen, may occur in several twins at once and may involve the movement of either or both twin boundaries. The present investigation has shown twins to broaden at speeds of up to 35 m/s. These are one and often two orders of magnitude higher than those noted during previous investigations. By using quartz piezo-electric pressure transducers it has been possible to measure the stresses applied to crystals whilst the formation of twins in surfaces of the crystals was being recorded. Comparison with theory has shown that in one example a twin broadened at a speed more than an order of magnitude greater than that predicted on the basis of the Cottrell-Bilby mechanism. The nucleation of a twin or twins near the tip of a rapidly lengthening twin has been noted in many crystals. This nucleation occurs on a plane close to and parallel to the composition plane of the lengthening twin. A brief study of the kinetics of twinning in β-tin has shown that twins broaden at rates similar to those occurring in zinc. Detwinning of tin crystals has been observed to occur at speeds similar to those in twinning, emphasizing the reversibility of the twinning process.

Kinetics of elastic twinning in calcite

An investigation of the effect of localized transient stresses on calcite is described. It is shown that twinning may or may not occur, depending on the duration of the stress pulse, the temperature and a factor related to the length of twin which may be formed. An hypothesis is suggested to explain the results and, from it, the velocity of propagation of twin lamellae is calculated in the temperature range from 20 to 300 °C. An activation energy for twin propagation is also calculated. Direct observation of the twinning process using a high-speed camera has confirmed the above hypothesis and results and has shown that the velocity of propagation of twin lamellae in calcite is not very dependent on the applied shear stress.