Solutions for Plasticity

6.1. Introduction

There is no mean to determine the plastic behaviour of a material, unless through experiments. Similarly, structural design that considers material plasticity involves complex calculations and iterations as the gradient of curve (yields the amount of stress required to produce a unit of strain) varies from one point to another. Engineers usually adopt linear plastic curve, which is easy to implement yet conservative enough to be safe.

By considering plastic behaviour, an element is expected to carry more stress before the plastic hinge formed (fracture). In this way, element design from elastic design can be optimised. In structural engineering, plasticity is allowed in structural steel design, due to the property of steel where strain hardening will occur at some point beyond its elastic limit. This is a favourable situation that enable steel to carry load without failing drastically, and safe enough for an engineer to allow plastic behaviour in steel. In Eurocode 3, plasticity is allowed only for class l and 2 section, where local buckling will not occur within the member and causes premature loss of sectional resistance.

For plasticity analysis, yield point is important: it is the point where the material changes from having linear stress-strain relationship (elastic) to non-linear (plastic). To ease the analysis, mathematical models are developed alongside simplification of a stress-strain diagram. Fig. 6.1 below shows such effort for perfect plastic and plastic with linear work hardening behaviours.

Yields criteria

For material scientists and engineers, the amount of stress a material can sustain before it exhibits plastic behaviour is concerned. Given the stress-strain diagram for the material, different yield criteria can be applied depending on the actual situation. Despite the differences, the concepts of those criteria are similar: if the stress developed within a body exceeds its yield strength, then the body is expected to exhibit plastic behaviour. To date, yield criterion always assumes the material to be isotropic. For other types of material, the plastic behaviour will be too difficult and complicated to predict.