By C. N. Reid
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Additional info for Deformation Geometry for Materials Scientists
4* 44 DEFORMATION GEOMETRY FOR MATERIALS SCIENTISTS THE L Ü D E R S BAND—A SELF-ARRESTING T E N S I L E INSTABILITY Certain materials have stress-strain curves that are concave upwards, such as that in Fig. 4(b). When such materials begin to deform, eqn. 9 is not satisfied and a neck forms. However, as deformation continues the slope of the stress-strain curve increases and eqn. 9 becomes satisfied. The neck is then stable and this self-arresting necking spreads to the adjacent elements of undeformed material, forming a Lüders band.
1. In three dimensions, stress and strain are each specified by no less than six components; Hooke's law speaks of a linear relation between stress and strain, but this begs the question : which component of stress is related to which component of strain? It is empirically justifiable to write the linear relation between stress and elastic strain in three dimensions in one of two ways. Either we express each component of stress as a linear function of every com ponent of strain or, conversely, we write each strain component as a linear equation in all of the stress components.
This behaviour is called viscoelastic, and it is illustrated by Fig. 5. FEATURES OF THE TENSILE TEST All of these tests involve interaction between a specimen and a testing machine, and the results are determined by the properties of both the specimen material and the testing machine. It is most important for us to appreciate that some aspects of behaviour, such as necking, are artifacts of the tensile test, and that other aspects, such as yield points, are very sensitive to the properties of the testing apparatus.