Historical review: strength of materials and fracture mechanics

Abstract

Plasticity criteria. The mechanical behavior of most engineering materials under uniaxial tension consists of four stages as shown in Figure 1.1. They are linear elastic, strain-hardening, perfectly plastic and strain-softening. The strain-hardening and softening stage may be linearized in order to make the computations easier, Figure 1.1. Such an approximation does not lead to any serious loss in solution accuracy. The contribution of the individual stages, however, can vary over a wide range. For example, when a steel specimen is subjected to uniaxial tension, the linear elastic range is usually followed by perfect plasticity and then by strain-hardening. The strain-softening behavior is not significant and is represented by a nearly vertical drop in the stress-strain diagram, Figure 1.2(a). For a concrete specimen, the linear elastic range is immediately followed by strain-softening while the intermediate stages do not appear, Figure 1.2(b). Note that the elastic modulus for concrete is much lower than that for steel as well as the strain-softening modulus. These observations exhibit that the energy absorption* properties of steel and concrete vary at different stages. The former during the plastic and hardening stages, the latter during the softening stage.