ABSTRACT
To emphasise the relationship between essentially elastic behaviour, degree of plasticity and plastic collapse, some computational studies of the load-deflection diagrams or cracked bars in bending and the corresponding spread of plasticity are shown in Fig. 2.4. Several features denoting the regimes of Fig. 2.3 are marked on this figure. Since these particular results are for a deeply notched body, plastic collapse intervenes before the fourth regime of general yield, Fig. 2.3d, can be reached and it must be recalled that the collapse load of the notched bar, Fig. 2.4, with a/W = 0·5 is roughly only one quarter of that of the unnotched bar: in fact a little more due to constraint. Clearly a rigorous application of LEF M would be restricted to a regime as marked in Fig. 2.4a, beyond which, if plotted to an enlarged extension axis, the load diagram is clearly non-linear. The positions for r pI = a/50 and a/IO according to LEFM estimates in plane strain, are marked in Fig. 2.4a. The degree of non-linearity and extent of the plastic zone up to A or B are, however, still small in comparison with the fully developed gross-yield region where plastic flow of the whole ligament may occur and a collapse-type situation develop with a limit load state reached for a non-hardening material. In short, the phrase 'extensive yielding' can be interpreted very differently when viewed in relation to the opposite extremes of LEFM or plastic collapse.
