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Chapter 7
Highlights:
1.
Understand the basic concepts of engineering stress and strain, yield strength, tensile strength,
Young's(elastic) modulus, ductility, toughness, resilience, true stress and true strain, strain exponent,
and know the difference between elastic and plastic deformation.
2.
Understand what a stressstrain curve is and what information it contains about materials properties.
Be able to identify and/or calculate all the properties in #1 from a stressstrain curve, both in the
elastic and plastic (before necking) regions.
3.
Understand how the mechanical behavior of ceramics differs from that of metals.
Be able to
numerically manipulate the flexural strength and the effect of porosity on mechanical strength.
4.
Understand how the mechanical behavior of polymers differs from that of metals.
Understand and be
able to numerically manipulate the viscoelastic modulus.
5.
Understand the concept of a safety factor.
Notes:
Show Figures 7.1 to 7.4.
Define engineering stress and strain (tension and compression):
A
F
=
=
stress
g
Engineerin
0
σ
l
l
=
l
l

l
=
=
strain
g
Engineerin
0
0
0
i
Δ
ε
For shear stress,
A
F
=
stress
Shear
0
τ
=
angle)
strain
is
(
=
strain
Shear
θ
γ
tan
=
As shown in Figure 7.4, and described in Equations 7.4a and 7.4b, an applied axial force can be geometrically
decomposed into tensile and shear components.
Stressstrain test: slowly increase stress and measure strain until the material fractures (show Figures 7.2, 7.3,
7.5, 7.1012).
This is usually performed in tension.
In the linear portion of the curve, Hooke's law is obeyed,
σ
= E
ε
.
E is called the modulus of elasticity, or Young's modulus, and is a property of the material. The units
of E are psi or MPa, remembering that Pa=N/m
2
.
Typical values for E are given in Table 7.1 for metals,
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A similar relationship can be written for compressive, shear, and torsional loads.
For shear stress,
γ
τ
G
=
G is the shear modulus and is a property of the material.
On an atomic scale, lengthening (compressing) a specimen during tensile (compressive) loading results in
lengthening (shortening) of atomic bonds.
Young's modulus is a measure of the resistance to separation of
adjacent atoms.
⎟
⎠
⎞
⎜
⎝
⎛
∝
dr
dF
modulus
Youngs
r
0
Show Figure 7.7 and Table 7.1.
High E W and Ni, low E Mg, Al, Au, Ag.
Show Table 3.7.
E can be different in different directions, and this reflects the different atomic densities in
different planes and directions.
When there is not a significant linear portion of an engineering stressstrain diagram, the secant and tangent
modulus are sometimes employed.
Show Figure 7.6.
The tangent modulus is the slope of the stressstrain
curve at one particular point, while the secant modulus is the slope of a secant drawn from the origin to a
particular point on the stressstrain curve.
By common sense, tensile strain in the z direction should yield compressive strain in the x and y directions.
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This note was uploaded on 04/23/2008 for the course ES 260 taught by Professor Rasmussen during the Spring '08 term at Clarkson University .
 Spring '08
 Rasmussen

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