Page 232 - Materials Science and Engineering An Introduction

204 • Chapter 6 / Mechanical Properties of Metals

• Yield and tensile strengths and ductility are sensitive to any prior deformation, the
presence of impurities, and/or any heat treatment. Modulus of elasticity is relatively
insensitive to these conditions.
• With increasing temperature, values of elastic modulus and tensile and yield strengths
decrease, whereas the ductility increases.
• Modulus of resilience is the strain energy per unit volume of material required to
stress a material to the point of yielding—or the area under the elastic portion of the
engineering stress–strain curve. For a metal that displays linear-elastic behavior, its
value may be determined using Equation 6.14.
• A measure of toughness is the energy absorbed during the fracture of a material, as
measured by the area under the entire engineering stress–strain curve. Ductile metals
are normally tougher than brittle ones.

True Stress and • True stress (s T ) is defined as the instantaneous applied load divided by the instantane-
Strain ous cross-sectional area (Equation 6.15).
• True strain (P T ) is equal to the natural logarithm of the ratio of instantaneous and
original specimen lengths per Equation 6.16.
• For some metals, from the onset of plastic deformation to the onset of necking, true
stress and true strain are related by Equation 6.19.

Elastic Recovery after • For a specimen that has been plastically deformed, elastic strain recovery occurs
Plastic Deformation if the load is released. This phenomenon is illustrated by the stress–strain plot of
Figure 6.17.

Hardness • Hardness is a measure of a material’s resistance to localized plastic deformation.
• The two most common hardness testing techniques are the Rockwell and Brinell
tests.
Several scales are available for the Rockwell test; for the Brinell test, there is a single
scale.
Brinell hardness is determined from indentation size; the Rockwell test is
based on the difference in indentation depth from the imposition of minor
and major loads.
• The two microindentation hardness testing techniques are the Knoop and Vickers
tests. Small indenters and relatively light loads are employed for these two tech-
niques. They are used to measure the hardnesses of brittle materials (such as ceram-
ics) and also of very small specimen regions.
• For some metals, a plot of hardness versus tensile strength is linear—that is, these two
parameters are proportional to one another.

Variability of • Five factors that can lead to scatter in measured material properties are the following:
Material Properties test method, variations in specimen fabrication procedure, operator bias, apparatus
calibration, and inhomogeneities and/or compositional variations from sample to
sample.
• A typical material property is often specified in terms of an average value (x),
whereas magnitude of scatter may be expressed as a standard deviation (s). Equations
6.21 and 6.22, respectively, are used to calculate values for these parameters.

Design/Safety • As a result of uncertainties in both measured mechanical properties and in-service
Factors applied stresses, design or safe stresses are normally utilized for design purposes. For
ductile materials, safe (or working) stress s w is dependent on yield strength and factor
of safety as described in Equation 6.24.