Lack of Yield Plateau
Based on load-deflection diagrams, one may distinguish two basic types of structural failure: plastic and brittle. The typical characteristic of plastic failure is that the structure develops a single-degrce-of – freedom mechanism such that the failure in various parts of the structure proceeds simultaneously, in proportion to a single parameter. Such failures are manifested by the existence of a long yield plateau on the load-deflection diagram (Fig. 1.2.3a). If the load-deilection diagram lacks such a plateau, the failure is not plastic but brittle (Fig. 1.2.3b) . When there are nosignificant geometric elfects (such as the P-Д effect in buckling), the absence of a plateau implies the existence of softening in the material due to fracture, cracking, or other damage. This further implies that the failure process cannot develop a single-degree-of-freedom mechanism but consists of propagation of the failure zones throughout the structure. The failure is nonsimultaneous and propagating.
To illustrate such behavior, consider the punching shear failure of a slab (Fig. 1.2.4). The typical (approximate) distributions of tensile stress a along the failure surface are drawn in the figure. If the material is plastic, the cross-section gradually plasticizes until all its points are at the yield limit (Fig. 1.2.4b). However, if the material exhibits strain softening, then the stress peak moves across the failure z. one, leaving a reduced stress (strain softening) in its wake (Fig. 1.2.4c, d). The stress reduction in the wake is mild if the structure is small, in which case the plastic limit analysis is not too far off (Fig. 1,2.4c). If the structure is large, however, the stress profile develops a steep stress drop behind the peak-stress point, and then the limit analysis solutions grossly overestimate the failure load (Fig. 1.2.4d).