Mechanical Testing and Properties
(Callister: Chapter 6)
• After completing this section, you should understand the
principles and application of the following tests used to
characterize engineering materials:
– Tensile Test
•
•
•
•
Engineering and True Stress and Strain
Shape of stress-strain curves for ductile and brittle materials
Elastic vs. plastic deformation
Young’s modulus, yield strength, UTS, ductility
– Hardness Test
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Engineering Stress and Strain
• Consider a bar of length L0 and cross-sectional area A0.
• If it is subjected to a load F, it will elongate an amount ΔL. If the
load exceeds Fy, the bar will permanently deform.
• What would you expect if:
Area
Length
Yield
Force
Elongation at
Yield Force
A0
L0
Fy
ΔLy
2A0
L0
A0
2L0
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1
Engineering Stress and Strain
• To remove the dependence of strength and elongation on the
geometry of the specimen, we introduce:
Units
• Engineering Stress:
σ=
F
A0
Force N
=
= Pa
Area m 2
1N
= 10 6 Pa = 1MPa
mm 2
• Engineering Strain:
ε=
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l − l0
l0
Length
= [−]
Length
(also ×100% )
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Engineering Stress and Strain
• Consider a bar of length L0 and cross-sectional area A0.
• If it is subjected to a load F, it will elongate an amount ΔL. If the
load exceeds Fy, the bar will permanently deform.
• What would you expect if:
Area
Length
Yield
Force
A0
L0
Fy
ΔLy
2A0
L0
2Fy
ΔLy
A0
2L0
Fy
2ΔLy
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Elongation at
Yield Stress Yield Strain
Yield Force
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2
Shear Stress and Strain
• Engineering stress and strain are normal stresses and strains.
– The force is perpendicular to the supporting cross-sectional area
• If the load is applied parallel to the supporting cross-section,
shear stresses and strains are developed.
A
F
x
y
θ
F
Shear stress : τ =
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F
A
Shear strain : γ =
x
= tan θ
y
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The Tensile Test
•
•
Testing machines can be mechanical (shown) or hydraulic. Each type
has its advantages and disadvantages.
Specimen geometry:
– Reduced gauge section ensures highest stress is away from gripping
mechanism.
– Many standard dimensions to fit various types of materials.
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3
Elastic Deformation
• All materials will elongate in response to a tensile load.
• The initial response is elastic
– i.e. if the load is removed, the material will return to its initial size
and shape.
• A plot of stress vs. strain during elastic deformation is linear.
• This linear relationship is known as Hooke’s law.
σ = Eε
E is the modulus of elasticity or Young’s Modulus.
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Modulus of Elasticity
• In reality, the elastic response of many materials is not perfectly
linear.
• The modulus of elasticity is then determined by using the
– Secant Modulus
or
– Tangent Modulus
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4
Bond Strength and Stiffness
Energy
• Just like a spring (F=kx), the
stiffness of the bond is indicated by
the slope of the force curve at F=0
r
• Young’s Modulus is the “spring
constant” for a solid.
σ = Eε
att
⎛ dF ⎞
E ∝⎜
⎟
⎝ dr ⎠ r0
Force
⎛ dF ⎞
⎜
⎟
⎝ dr ⎠ r0
r
rep
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Poisson’s Ratio
• During elastic deformation, (i.e. prior to permanent deformation)
the volume is not constant.
• The contraction in the transverse direction is given by
Poisson’s Ratio
ν=
−εx
εz
=
−εy
εz
• For most metals, ν ≈ 0.3
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5
Plastic Deformation
• On initial loading, materials deform
elastically.
• If you continue to deform the material
Hooke’s Law is no longer obeyed
• Permanent or plastic deformation
occurs.
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The Yield Strength
• For materials that deform plastically, the stress at which the curve is
no longer linear is the yield strength of the material.
• In many cases, the transition is too gradual to determine accurately.
In these cases, we define the 0.2% offset yield strength
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6
Upper and Lower Yield Point
• Some materials, the best example is
carbon steel, have an upper and
lower yield point.
• Why this happens is discussed in
Chapter 7.
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Tensile Strength
• We know from experience that plastic deformation can not go on
forever…
• If we continue to deform the material, the load (stress) reaches a
maximum and then begins to decrease.
• The point of maximum stress
is called the (Ultimate)
Tensile Strength
• It is at this point that the
specimen starts to “neck”
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Ductility
• A material is considered to be ductile if it can undergo a
significant amount of plastic deformation before fracture.
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Ductility
• Ductility is an indication of how much a material can be
plastically deformed before it fractures.
• It is commonly measured as:
•
% Elongation
% EL =
l f − l0
l0
× 100%
= ε f × 100%
•
% Reduction in Area
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% RA =
A0 − A f
A0
× 100%
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8
Stress-Strain Curve
• When a material is pulled in tension:
– it elongates in the tensile direction
– and contracts in the transverse direction(s)
• The tensile test measures the change in length. We need to be
able to determine the change in cross-section
• From the yield point to the onset of necking, we can do this by
assuming that the volume is constant:
A0 × l0 = Ai × li
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True Stress and True Strain
• In some cases, particularly when modeling deformation
processes, engineering stress and strain are not exact enough
descriptions of the material behaviour. We need to use:
• True Stress:
σ=
F
Ai
l1
• True Strain:
ε=∫
l0
dl
l
⎛l ⎞
⎛A ⎞
= ln⎜⎜ 1 ⎟⎟ = ln⎜⎜ 0 ⎟⎟
⎝ A1 ⎠
⎝ l0 ⎠
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9
Elastic Recovery
• If the load is removed from the specimen during a tensile test,
the material “springs back” elastically.
• If you continued to plot stress and strain as the load is being
removed…
• … the curve would not go
straight down,
• The unloading curve will have
a slope equal to Young’s
Modulus.
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Temperature Effects
• In general, increasing the temperature of deformation:
– decreases yield strength
– decreases tensile strength
– increases ductility
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The Hardness Test
• A measure of the materials ability to resist an indentation.
• There are a number of common hardness test methods:
– Rockwell: (based on depth of indentation)
• many scales (B&C most common)
• Fast, surface preparation not normally required
– Brinell:(based on surface area of indentation)
• Relatively large indent is made (can be detrimental)
• Limited to softer materials (indenter is steel or WC)
– Vickers:(based on projected area of indentation)
• Usually a microhardness test – very small indentation. The indenting
mechanism is incorporated into a microscope.
• Surface must be polished because the indentation is so small.
• VHN can be directly related to the strength of the material.
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The Hardness Test
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11
Hardness Tests
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