zinc

MICROSTRUCTUE OF FRACTURE BRITTEL ZINC MATERIAL                          

Introduction

In polycrystalline materials, propagation of a cleavage crack from grain to grain is a complex process. This is because cleavage occurs on well-defined planes and these planes in neighbouring grains do not usually meet in a line in their common grain boundary. Some additional failure mechanism must therefore be involved. In particular, the two cleavage cracks may be linked by brittle grain boundary fracture, by multiple cleavage in one or both of the grains or by localized ductile failure at the boundary. Traditionally, experimental research has suggested that these accommodation effects play only a minor role in the brittle fracture of polycrystalline materials. However, in recent years, theoretical models and computer simulations have indicated that they may be very significant. For example, in ferritic steels, the models predict that approximately 30% of brittle failure is by means of these accommodation mechanisms whereas experiments have indicated only a few per cent. One possible explanation for this discrepancy is that most of the failed grain boundaries will be oriented at a steep angle to the overall fracture surface so that microscopic examination tends to underestimate their areas. Specific experiments involving tilting the fracture surface and examining individual facets have shown that this is an important effect but can only increase the observed accommodation to 20% at the most . Thus, it appears that alternative accommodation mechanisms make a contribution to the propagation of transgranular cleavage cracks in polycrystalline materials.

The amount of accommodation failure required at each grain boundary is defined by the angle between the traces in the boundary of active cleavage planes in the adjacent grains. This angle depends crucially on the number of cleavage planes available. In ferritic steels, which have the body-centred cubic (bcc) structure, there are three {001} cleavage planes. However, in zinc, which has the hexagonal close packed (hcp) crystal structure with c/a=1.856, cleavage has been shown to occur, at least predominantly, on the unique basal (0001) plane. The authors therefore anticipated that zinc would need far more accommodation fracture than is the case for ferritic materials. Hence, in order to explore the amount of accommodation further, it was decided to model brittle fracture in zinc and to carry out detailed experiments to allow a comprehensive description of the fracture to be obtained.

Temperature dependence of the fracture mechanism

‘Matchstick’ specimens of zinc were fractured at 77, 293 and 328 K covering the brittle to the upper transition region. Fractographic examination was carried out using FIB-induced electron images and four distinct fracture mechanisms were recognized: transgranular, grain boundary, ductile and twin boundary. The relative percentage areas of these mechanisms at each temperature were estimated from the projected images. These were obtained using a grid consisting of 10×10 points placed over the image and the dominant fracture mechanism at each point of the grid was noted. Ion-induced secondary electron images for the three temperatures. As the temperature is raised, the amount of twinning decreases as slip increases. Associated with this is the removal of twin boundary fracture. In addition, cleavage cracks in either basal or prismatic planes tend to propagate through individual grains without deviation, resulting in large individual facets. Furthermore, there is an increase to 28 and 29% of brittle intergranular fracture at 293 and 328 K, to accommodate cleavage crack propagation across grain boundaries. Moreover, as the temperature is increased from 77 to 328 K, there is a progressive increase in the intervention of ductile fracture, i.e. the transition from brittle to ductile fracture is encountered.

Additional cleavage planes

It has been shown that brittle fracture in polycrystalline zinc occurs on the three variants of the {10-10} family of prismatic planes in addition to the unique (0001) basal plane. Therefore, on average, the smallest angle between the traces of cleavage planes in adjacent grains in their common grain boundary will be 11.25° rather than 45°. However, one of these planes may not be oriented favourably relative to the stress axis so that the second best angle of 33.75° will be selected. If it is assumed that the occurrence of these two cases is inversely proportional to these angles, the average angle between the traces of the two cracks will be approximately 17°. This angle can now be used, as in to estimate the percentage of grain boundary that, on average, must fail for mechanisms . The results are approximately 12.2, 9.4, 70 and 12.2%, respectively.

These figures now have to be combined with the proportions of mechanisms I–IV that occur in practice. For I and II, these are approximately 3 and 39%, as in . However, the remaining 58% for mechanism VII divides differently into its component parts, III and IV, because the angle αbetween the two traces  is now approximately 17° and not 45°. Hence, one obtains 45% for III and 13% for IV. Combining the percentages of areas and the percentages of mechanisms now gives an overall average figure of 47%. This is the average percentage area of those grain boundaries that fail partially, if cleavage cracks are to be linked together, when no other accommodation mechanism is available. As in the proportion of intergranular fracture to cleavage fracture is now given by 0.43×3×47%, i.e. approximately 61% rather than 50%, when only basal cleavage occurs. This result may seem surprising as one might expect less grain boundary failure when more cleavage planes are available. It arises owing to the higher proportion of mechanism III (45% rather than 32%) and this has a much larger amount of grain boundary failure (70%) than mechanism IV (12.2%).

It has been shown that brittle fracture in  zinc occurs on the three variants of the {10-10} family of prismatic planes in addition to the unique (0001) basal plane. Therefore, on average, the smallest angle between the traces of cleavage planes in adjacent grains in their common grain boundary will be 11.25° rather than 45°. However, one of these planes may not be oriented favourably relative to the stress axis so that the second best angle of 33.75° will be selected. If it is assumed that the occurrence of these two cases is inversely proportional to these angles, i.e. 3 : 1  the average angle between the traces of the two cracks will be approximately 17°. This angle can now be used, as in to estimate the percentage of grain boundary that, on average, must fail for mechanisms I–IV of . The results are approximately 12.2, 9.4, 70 and 12.2%, respectively.

These figures now have to be combined with the proportions of mechanisms I–IV that occur in practice. For I and II, these are approximately 3 and 39%, as in . However, the remaining 58% for mechanism VII divides differently into its component parts, III and IV, because the angle αbetween the two traces in  is now approximately 17° and not 45°. Hence, one obtains 45% for III and 13% for IV. Combining the percentages of areas and the percentages of mechanisms now gives an overall average figure of 47%. This is the average percentage area of those grain boundaries that fail partially, if cleavage cracks are to be linked together, when no other accommodation mechanism is available. As in the proportion of intergranular fracture to cleavage fracture is now given by 0.43×3×47%, i.e. approximately 61% rather than 50%, when only basal cleavage occurs. This result may seem surprising as one might expect less grain boundary failure when more cleavage planes are available. It arises owing to the higher proportion of mechanism III (45% rather than 32%) and this has a much larger amount of grain boundary failure (70%) than mechanism IV (12.2%).

8. Conclusions

The availability of three-dimensional models, albeit sometimes in a simplified form, greatly enhances our ability to simulate fracture of  materials.

1. The most effective use of such geometric models is when they are developed and employed in conjunction with related experimental work.
2. Experimental techniques that are now available enable much more detailed crystallographic information to be obtained than when earlier work on zinc was carried out in the mid-twentieth century. In particular, FIB microscopy enables a wealth of new observations to be made.
3. The experimental results on polycrystalline zinc presented here demonstrate that several phenomena, which have only been suggested tentatively in earlier work, are important mechanisms. These include prismatic cleavage, intricately stepped cleavage planes, accommodation of fracture at grain boundaries and the role of twin boundaries in the propagation of cracks.
4. The new experimental results on randomly oriented polycrystalline zinc made it necessary to extend the models to incorporate prismatic cleavage, multiple cleavage and the role of twin boundaries, and this has provided additional insights into the fracture processes.
5. The research presented is considered to provide a quantitative basis for the description of brittle crack propagation relevant to polycrystalline materials