TABLE OF CONTENTS With elastic deformation, a body returns to its original shape when the stress is removed and the stress and strain under elastic loading are related through Hooke s laws. Any stress will cause some strain. In contrast, no plastic deformation occurs until the stress reaches the yield strength. For ductile metals large amounts of plastic deformation can occur under continually increasing stress.
In this text experimental observations are linked with mathematical expressions. Yield criteria are mathematical descriptions of the combination of stresses necessary to cause yielding.
A yield criterion is a postulated mathematical expression of the states of stress that will cause yielding. The most general form is
For isotropic materials, this can be expressed in terms of principal stresses as
For most isotropic ductile metals the following assumptions are commonly made:
The yield strengths in tension and compression are the same. That is, any Bauschinger [*] effect is small enough so it can be ignored.
The volume remains constant during plastic deformation.
The magnitude of the mean normal stress,
does not affect yielding.
The yield criteria to be discussed involve these assumptions. Effects of temperature, prior straining, and strain rate will be discussed in later chapters.
The assumption that yielding is independent of ? m is reasonable because deformation usually occurs by slip or twining, which are shear mechanisms. Therefore the yield criteria for isotropic materials have the form
This is equivalent to stating that yielding depends only on the...
