Fundamental Concepts of Plasticity

Fundamental Concepts of Plasticity

DOI: 10.4018/978-1-4666-6379-4.ch005


This chapter introduces some fundamental concepts of plasticity that are used in Chapter 6 to formulate the concept of plastic hinge and in Chapter 7 to describe elasto-plastic models for frames; in the present one, only the uniaxial behavior of the material is considered. In this chapter, the key concepts of perfect plasticity, yield function, and plastic hardening are introduced. The two alternative formulations for plastic hardening, isotropic and kinematic, are discussed in detail. Plasticity is presented as a way to mathematically represent the experimental behavior of ductile materials; the limits of plasticity for describing reality are also established.
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5.1 Experimental Behavior Of Ductile Materials

Consider again the example of the paper clip used in chapter 1. The loading process consists in imposed displacements that represent the actions of the paper sheets on the clip (see Figure 1). If a limited number of pages is used, the clip recovers its initial form once they are removed. If the clip is used with an excessive number of sheets, it will not recuperate its original shape. It is evident that a computer analysis that does not predict structural modifications or deterioration of the clip, no matter how many paper sheets are used, is not very useful. That would be the case if only elastic analyses of the paper clip are carried out: no permanent deformations can be predicted in that case.

Figure 1.

Paper clip as a structure

Elastic models as the ones described in chapter 3 should be used with extreme precautions and always with some elastic limit criterion at hand. If that limit is exceeded, then more sophisticated models are needed. This chapter describes a step in that direction; the elasto-plastic models differ from the elastic ones because they consider the possibility of permanent deformations, as the ones that occur when an excessive number of pages are held together.

Figure 2 shows the experimental response of a metallic specimen during a tension test with unloading: the specimen is stretched in a testing machine so that the material is subjected to the strain history shown in Figure 2a. This kind of tests is called mono-sign traction test in this book. Notice that the number and the instant of the unloadings are arbitrarily fixed by the experimenter. The behavior of metallic materials observed in these tests is summarized in table 1.

Figure 2.

Experimental behavior of a metallic specimen in a mono-sign test

Table 1.
Phenomena observed during mono-sign tests
a)Existence of a zone that can be characterized as linear elastic
b)Presence of plastic strains; i.e. strains that do not disappear after unloading if a limit in stress is reached
c)Zone of constant elasticity modulus
d)Zone of plastic hardening, which is an increase in the elastic limit with plastic strain
e)Existence of an ultimate or maximum stress
f)Zone of plastic softening or strength degradation; i.e. a decrease in the elastic limit with plastic strain
g)Zone of stiffness degradation; i.e. a decrease of the elastic modulus with plastic strain
h)Existence of a maximum or failure strain

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