Page 214 - Materials Science and Engineering An Introduction

186 • Chapter 6 / Mechanical Properties of Metals

y

120
800 Stress
–200°C
100
600
80
Stress (MPa) 400 –100°C 60 Stress (10 3 psi)

40 0.002 y Strain
25°C
200 Figure 6.15 Schematic
20 representation showing
how modulus of resilience
0 0 (corresponding to the
0 0.1 0.2 0.3 0.4 0.5
shaded area) is deter-
Strain
mined from the tensile
Figure 6.14 Engineering stress–strain behavior for iron at three tem- stress–strain behavior of a
peratures. material.

The units of resilience are the product of the units from each of the two axes of the
3
stress–strain plot. For SI units, this is joules per cubic meter (J/m , equivalent to Pa),
3
whereas with customary U.S. units it is inch-pounds force per cubic inch (in.-lb f /in. ,
equivalent to psi). Both joules and inch-pounds force are units of energy, and thus this
area under the stress–strain curve represents energy absorption per unit volume (in cubic
meters or cubic inches) of material.
Incorporation of Equation 6.5 into Equation 6.13b yields
Modulus of
resilience for linear 2
elastic behavior, U r = 1 s y P y = 1 s y a s y b = s y (6.14)
and incorporating 2 2 E 2E
Hooke’s law
Thus, resilient materials are those having high yield strengths and low moduli of elastic-
ity; such alloys are used in spring applications.

Toughness
toughness Toughness is a mechanical term that may be used in several contexts. For one, toughness
(or more specifically, fracture toughness) is a property that is indicative of a material’s
resistance to fracture when a crack (or other stress-concentrating defect) is present (as
Tutorial Video: discussed in Section 8.5). Because it is nearly impossible (as well as costly) to manufac-
Tensile Test ture materials with zero defects (or to prevent damage during service), fracture tough-
What is toughness ness is a major consideration for all structural materials.
and how do Another way of defining toughness is as the ability of a material to absorb energy and
I determine its value? plastically deform before fracturing. For dynamic (high strain rate) loading conditions and
when a notch (or point of stress concentration) is present, notch toughness is assessed by
using an impact test, as discussed in Section 8.6.