Energy and Thermodynamic Considerations Involving Electromagnetic Zero-Point Radiation (123).pdf

INTRODUCTION TO ELASTICITY
David Roylance
Department of Materials Science and Engineering
Massachusetts Institute of Technology
Cambridge, MA 02139
January 21, 2000
Introduction
This module outlines the basic mechanics of elastic response — a physical phenomenon that
materials often (but do not always) exhibit. An elastic material is one that deforms immediately
upon loading, maintains a constant deformation as long as the load is held constant, and returns
immediately to its original undeformed shape when the load is removed. This module will also
introduce two essential concepts in Mechanics of Materials: stress and strain.
Tensile strength and tensile stress
Perhaps the most natural test of a material’s mechanical properties is the tension test, in which
a strip or cylinder of the material, having length L and cross-sectional area A, is anchored at
one end and subjected to an axial load P – a load acting along the specimen’s long axis – at
the other. (See Fig. 1). As the load is increased gradually, the axial deflection δ of the loaded
end will increase also. Eventually the test specimen breaks or does something else catastrophic,
often fracturing suddenly into two or more pieces. (Materials can fail mechanically in many
different ways; for instance, recall how blackboard chalk, a piece of fresh wood, and Silly Putty
break.) As engineers, we naturally want to understand such matters as how δ is related to P ,
and what ultimate fracture load we might expect in a specimen of different size than the original
one. As materials technologists, we wish to understand how these relationships are influenced
by the constitution and microstructure of the material.
Figure 1: The tension test.
One of the pivotal historical developments in our understanding of material mechanical
properties was the realization that the strength of a uniaxially loaded specimen is related to the
1
magnitude of its cross-sectional area. This notion is reasonable whe