Microscopic aspect of fracture: Cleavage and ductile rupture

Abstract

In Chapter I, the theoretical cohesive stress of the material on the scale of the crystalline lattice, i.e., on the scale of nm, has been estimated from the theoretical surface energy. This energy for some metals is given in Table 5.1. The value is ofthe order of 10-5 da J . cm-2 . In Chapters 2 and 3, it was emphasised that the fracture theories based only on this theoretical stress and on purely elastic behaviour were insufficient and in fault, because for microcracks and cracks, a plastic deformation that appears around the crack normally for physical reasons is to be taken into account. This plastic behaviour will have to particularly explain why energies of the order of G tC = O.5daJ . cm-2 (with Ktc = 100M Pa.,;m for a steel) are associated with fracture.In fact, as it is experimentally observed, plasticity is necessary to trigger a fracture nucleation, which will lead to the whole fracture of the cracked or uncracked body. This aspect is illustrated in Figure 5.1, first with a tensile test of a plain specimen, i.e., without flaw, with a dimension of the order of cm, of an ideal totally homogeneous material, which breaks in an ideal manner after a total plastic deformation when the stress reduced to the current section and the area of this section go simultaneously to zero. But more in agreement with experience, some inhomogeneity appears during the plastic deformation and at the scale ofthe specimen, fracture occurs at various levels of deformation, (Fig. 5.1): for low values of deformation, fracture is said to be brittle; it requires low strain deformation energy and the preceding deformation does not allow the detection of its occurrence. For high values of deformation and generally beyond the necking, fracture is said to be ductile: it needs high energy and its occurrence can be predicted a long time before. As for necking, this corresponds to a geometrical instability and not to a fracture mechanism. (Exercise 5.1).When the preceding fractures are observed and analysed on their fracture surfaces and on axial metallographic sections, at a midway scale between the inter-atomic spacing, the nm, and the dimension of the specimen, the cm, i.e., at the scale of the inclusion, the /J-m, or at the scale of the grain, 10 /J-m, these fractures can be classified in a decreasing order of brittleness ( Figures 5.2 and 5.3) as • brittle or semi-brittle intergranular fracture, D. P. Miannay, Fracture Mechanics