10 CHAPTER 1. PROPERTIES OF MATTER
areaAiover which deformation is occurring (i.e., the neck, past the tensile point), or
‡T=F
AiA schematic comparison of engineering and true stress–strain behaviours is made in Figure
1.9. The true stress necessary to sustain increasing strain continues to rise past the tensile
pointMÕ.
Coincident with the formation of a neck is the introduction of a complex stress state
within the neck region (i.e., the existence of other stress components in addition to the
axial stress). As a consequence, the correct stress (axial) within the neck is slightly lower
than the stress computed from the applied load and neck cross- sectional area. This leads
to the “corrected” stress-strain curve as shown in Figure1.9.
DisplacementTimeStressStrainTrueCorrectedEngineeringMM’Figure 1.9: A comparison of typical tensile engineering stress–strain and true
stress–strain behaviours. Necking begins at point M on the engineering curve, which corre-
sponds to M on the true curve. The “corrected” true stress–strain curve takes into account
the complex stress state within the neck region.
1.3.2 Safety Factor
Tensile strengths may vary anywhere from 50 MPa for aluminium to as high as 3000 MPa
for the high-strength steels. Ordinarily, when the strength of a metal is cited for design
purposes, the yield strength is used. This is because by the time a stress corresponding to
the tensile strength has been applied, often a structure has experienced so much plastic
deformation that it is useless. Furthermore, fracture strengths are not normally specified
for engineering design purposes.
There will always be uncertainties in characterizing the magnitude of applied loads
and their associated stress levels for in-service applications; ordinarily load calculations
are only approximate. Furthermore, all engineering materials exhibit a variability in their
measured mechanical properties, have imperfections that were introduced during manu-
facture, and, in some instances, will have sustained damage during service. Consequently,
design approaches must be employed to protect against unanticipated failure. Therefore,
a safe stress or working stress,‡w, is used. This safe stress is based on the yield strength
of the material and is defined as the yield strength divided by a factor of safety (N),
10