Mechanics of Materials - M1-Tensile Response of Materials - 4. Stress-Strain Curves.pdf

STRESS-STRAIN CURVES
David Roylance
Department of Materials Science and Engineering
Massachusetts Institute of Technology
Cambridge, MA 02139
August 23, 2001
Introduction
Stress-strain curves are an extremely important graphical measure of a material’s mechanical
properties, and all students of Mechanics of Materials will encounter them often. However, they
are not without some subtlety, especially in the case of ductile materials that can undergo sub-
stantial geometrical change during testing. This module will provide an introductory discussion
of several points needed to interpret these curves, and in doing so will also provide a preliminary
overview of several aspects of a material’s mechanical properties. However, this module will
not attempt to survey the broad range of stress-strain curves exhibited by modern engineering
materials (the atlas by Boyer cited in the References section can be consulted for this). Several
of the topics mentioned here — especially yield and fracture — will appear with more detail in
later modules.
“Engineering” Stress-Strain Curves
Perhaps the most important test of a material’s mechanical response is the tensile test1,inwhich
one end of a rod or wire specimen is clamped in a loading frame and the other subjected to
a controlled displacement δ(see Fig. 1). A transducer connected in series with the specimen
provides an electronic reading of the load P (δ) corresponding to the displacement. Alternatively,
modern servo-controlled testing machines permit using load rather than displacement as the
controlled variable, in which case the displacement δ(P ) would be monitored as a function of
load.
The engineering measures of stress and strain, denoted in this module as σe and e respec-
tively, are determined from the measured the load and deflection using the original specimen
cross-sectional area A0 and length L0 as
P δ
σe = ,e = (1)
A0 L0
When the stress σe is plotted against the strain e,anengi