ABSTRACT
With the scientific advances of the last few decades in the field of Material Mechanics it has been realized that the classical concept of strength, understood as force per unit surface causing fracture, is in need of revision, especially in the cases where particularly large or particularly small structures are involved. The strength of the material must, that is, be compared against another characteristic, the toughness of the material, in order to define, via the dimension of the structure, the ductility or the brittleness of the structure itself. Two intrinsic characteristics of the material, plus a geometrical characteristic of the structure, are in fact the minimum basis for being able to predict the type of structural response. A foretaste of what will be dealt with in the present chapter has been provided in Section 8.11. In that section we defined the fracture energy g IC , one of the parameters capable of measuring the toughness of the material. We also described how the structural response to uniaxial tension varies as g IC and/or the length of the bar longitudinally subjected to tension varies. In that case a tendency emerged towards a ductile behaviour in the case of short lengths of the bar and, on the other hand, a tendency towards a brittle behaviour (snap-back) in the case of greater lengths of the bar. This tendency will be encountered again, in the present chapter, also in the case of two- and three-dimensional solids, in such a way as to associate ductile behaviour with relatively small solids, and brittle behaviour with relatively large solids. Just as in structures acted upon prevalently by a compressive force (Figure 17.11), there is a transition from plastic collapse to instability of elastic equilibrium as slenderness increases, so in structures acted upon prevalently by a tensile force, there is a transition from plastic collapse to brittle fracture as the size scale increases.
