1. Mechanical Properties: Part One
Chapter 6: Mechanical Properties: Part One
Chapter 6:
Mechanical Properties:
Part One
© 2011 Cengage Learning Engineering. All Rights Reserved.`

2. © 2011 Cengage Learning Engineering. All Rights Reserved.
Chapter 6: Mechanical Properties: Part One
Learning Objectives
Technological significance
Terminology for mechanical properties
The tensile test: Use of the stress–strain diagram
Properties obtained from the tensile test
True stress and true strain
The bend test for brittle materials
Hardness of materials
Nanoindentation
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3. © 2011 Cengage Learning Engineering. All Rights Reserved.
Chapter 6: Mechanical Properties: Part One
Learning Objectives
Strain rate effects and impact behavior
Properties obtained from the impact test
Bulk metallic glasses and their mechanical behavior
Mechanical behavior at small length scales
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4. Technological Significance
Chapter 6: Mechanical Properties: Part One
Technological Significance
Biocompatible titanium alloys used in bone implants must have enough strength and toughness to survive in the human body for many years without failure.
Mechanical robustness of small devices fabricated using nanotechnology is important.
Materials processing requires a detailed understanding of the mechanical properties of materials at different temperatures and conditions of loading.
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5. Terminology for Mechanical Properties
Chapter 6: Mechanical Properties: Part One
Terminology for Mechanical Properties
Stress
Force acting per unit area over which the force is applied
Strain
Change in dimension per unit length
Elastic strain
Fully recoverable strain resulting from an applied stress
Young’s modulus or modulus of elasticity (E)
The slope of a tensile stress-strain curve in the linear regime [Figure 6-1 (b)]
Elastomers
Materials that show large elastic deformations
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6. Terminology for Mechanical Properties
Chapter 6: Mechanical Properties: Part One
Terminology for Mechanical Properties
Shear modulus (G)
Slope of the linear part of the shear stress-shear strain curve
Plastic deformation or strain
Permanent deformation of a material when a load is applied and then removed
Strain rate
Rate at which strain develops in or is applied to a material
Impact loading
Type of loading when materials are subjected to high strain rates
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7. Terminology for Mechanical Properties
Chapter 6: Mechanical Properties: Part One
Terminology for Mechanical Properties
Viscous material
One in which the strain develops over a period of time and the material does not return to its original shape after the stress is removed
Viscoelastic (or anelastic) material
A material with a response between that of a viscous material and an elastic material
Stress relaxation
Decrease in stress for a material held under constant strain as a function of time, which is observed in viscoelastic materials
Newtonian
Materials in which the shear stress and shear strain rate are linearly related
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8. Terminology for Mechanical Properties
Chapter 6: Mechanical Properties: Part One
Terminology for Mechanical Properties
Viscosity ()
Measure of the resistance to flow
Viscosity is defined by
Kinematic viscosity ()
 =  /
Non-Newtonian materials
Materials with a nonlinear relationship between shear stress and shear strain rate
Shear thinning
Materials in which the apparent viscosity decreases with increasing rate of shear
Shear thickening
Materials in which the apparent viscosity increases with increasing rate of shear
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Chapter 6: Mechanical Properties: Part One
Figure 6.1
(a) Tensile, compressive, and shear stresses. F is the applied force.
(b) Illustration showing how Young’s modulus is defined for an elastic material.
(c) For nonlinear materials, we use the slope of a tangent as a varying quantity that replaces the Young’s modulus.
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Chapter 6: Mechanical Properties: Part One
Figure 6.3
Shear stress-shear strain rate relationships for Newtonian and non-Newtonian materials.
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Chapter 6: Mechanical Properties: Part One
Figure 6.4
Apparent viscosity as a function of shear strain rate.
(b) and (c) Illustration of a Bingham plastic. Note the horizontal axis in (b) is shear strain.
Take the slope of the line obtained by joining the origin to any point on the curve, what we determine is the apparent viscosity.
Apparent viscosity(app) - Viscosity obtained by dividing shear stress by the corresponding value of the shear-strain rate for that stress.
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12. Terminology for Mechanical Properties
Chapter 6: Mechanical Properties: Part One
Terminology for Mechanical Properties
Bingham plastics
Apparent yield strength
Obtained by interpolating the shear stress-shear strain rate data to zero shear strain rate
Thixotropic behavior
Materials that show shear thinning and also an apparent viscosity that at a constant rate of shear decreases with time
Rheopectic behavior
Materials that show shear thickening and also an apparent viscosity that at a constant rate of shear increases with time
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Chapter 6: Mechanical Properties: Part One
Figure 6.5
A unidirectional force is applied to a specimen in the tensile test by means of the moveable crosshead. The crosshead movement can be performed using screws or a hydraulic mechanism.
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14. The Tensile Test: Use of the Stress–Strain
Chapter 6: Mechanical Properties: Part One
The Tensile Test: Use of the Stress–Strain
Diagram
Load
The force applied to a material during testing
Strain gage or extensometer
A device used for measuring strain
Glass-transition temperature (Tg)
Temperature below which a ductile material behaves as if it is brittle
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15. The Tensile Test: Use of the Stress–Strain
Chapter 6: Mechanical Properties: Part One
The Tensile Test: Use of the Stress–Strain
Diagram
Engineering stress (S) = F Ao
Engineering strain (e) = Δl lo
where
Ao original cross-sectional area of the specimen before the test begins.
lo original length between the gage marks.
Δl change in the length after a force of F is applied
Units
Common units for stress are pounds per square inch (psi) and MegaPascals (MPa).
Units for strain include inches/inches, m/m, and cm/cm or strain may be written as unitless
Engineering stress - The applied load, or force, divided by the original area over which the load acts.
Engineering strain - Elongation per unit length calculated using the original dimensions.
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16. Properties Obtained from the Tensile Test
Chapter 6: Mechanical Properties: Part One
Properties Obtained from the Tensile Test
Yield strength
Elastic limit
The magnitude of stress at which plastic deformation commences.
Proportional limit
Level of stress above which the relationship between stress and strain is not linear.
Offset strain value
Value of strain (e.g., 0.002) used to obtain the offset yield stress value.
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17. Properties Obtained from the Tensile Test
Chapter 6: Mechanical Properties: Part One
Properties Obtained from the Tensile Test
Offset yield strength
Stress value obtained graphically that describes the stress that gives no more than a specified amount of plastic deformation (usually 0.002).
Yield point phenomenon
Abrupt transition from elastic deformation to plastic flow which occurs in some materials.
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Chapter 6: Mechanical Properties: Part One
Figure 6.8
(a) Determining the 0.2% offset yield strength in gray cast iron, and (b) upper and lower yield point behavior in a low carbon steel.
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Chapter 6: Mechanical Properties: Part One
Figure 6.9
The stress obtained at the highest applied force is the tensile strength (STS), which is the maximum stress on the engineering stress-strain curve. This value is commonly known as the ultimate tensile strength.
At some point, one region deforms more than others and a large local decrease in the cross-sectional area occurs. The locally deformed region is called a “neck” and the phenomenon is called necking.
Localized deformation of a ductile material during a tensile test produces a necked region. The micrograph shows a necked region in a fractured sample.
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20. Properties Obtained from the Tensile Test
Chapter 6: Mechanical Properties: Part One
Properties Obtained from the Tensile Test
Elastic properties
Hooke’s law
The linear-relationship between stress and strain in the elastic portion of the stress-strain curve.
It is denoted by the ratio E = S/e.
Stiffness
Measure of a material’s resistance to elastic deformation.
Stiffness of a component is directly proportional to its Young’s modulus.
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21. Properties Obtained from the Tensile Test
Chapter 6: Mechanical Properties: Part One
Properties Obtained from the Tensile Test
Poisson’s ratio ()
The negative of the ratio between the lateral and longitudinal strains in the elastic region.
Denoted by the ratio  = - elateral / elongitudinal
Modulus of resilience
The maximum elastic energy absorbed by a material when a load is applied.
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22. The Tensile Test: Use of the Stress–Strain
Chapter 6: Mechanical Properties: Part One
The Tensile Test: Use of the Stress–Strain
Diagram
Tensile toughness
Energy absorbed by a material prior to fracture.
Sometimes measured as the area under the true stress- strain curve (also known as the work of fracture).
Ductility: The ability of a material to be permanently deformed without breaking when a force is applied.
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Chapter 6: Mechanical Properties: Part One
Figure 6.13
The effect of temperature (a) on the stress-strain curve and (b) on the tensile properties of an aluminum alloy.
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24. True Stress and True Strain
Chapter 6: Mechanical Properties: Part One
True Stress and True Strain
where A instantaneous area over which the force F is applied. l instantaneous sample length. l0 initial length. After necking begins, Instantaneous area A is the cross-sectional area of the neck.
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Chapter 6: Mechanical Properties: Part One
Figure 6.14
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26. The Bend Test for Brittle Materials
Chapter 6: Mechanical Properties: Part One
The Bend Test for Brittle Materials
Flexural strength for a three-point bend test
Flexural modulus
The maximum stress or flexural stress for a four-point bend test
Flexural strength [modulus of rupture] - The stress required to fracture a specimen in a bend test.
Flexural modulus - The modulus of elasticity calculated from the results of a bend test; it is proportional to the slope of the stress-deflection curve.
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Chapter 6: Mechanical Properties: Part One
Figure 6.18
Three-point bend test setup
(b) Four-point bend test setup
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Chapter 6: Mechanical Properties: Part One
Hardness of Materials
Hardness test: Measure of resistance to penetration of
the surface of a material by a hard object.
Bulk hardness of materials measured using loads > 2N.
where
F applied load in kilograms.
D diameter of the indenter in millimeters.
Di diameter of the impression in millimeters.
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29. Figure 6.19 - Indenters for the Brinell and Rockwell Hardness Tests
Chapter 6: Mechanical Properties: Part One
Figure Indenters for the Brinell and
Rockwell Hardness Tests
In the Brinell hardness test, a hard steel sphere (usually 10 mm in diameter) is forced into the surface of the material.
The Rockwell hardness test uses a small-diameter steel ball for soft materials and a diamond cone, or Brale, for harder materials.
E.g.: Brinell hardness is related to the tensile strength of steel by approximation
Tensile strength (psi) = 500HB
where HB has units of kg/mm2 and 1 psi =  103 Pa.
The Knoop hardness (HK) test is a microhardness test, forming small indentations that a microscope is required to obtain the measurement.
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30. © 2011 Cengage Learning Engineering. All Rights Reserved.
Chapter 6: Mechanical Properties: Part One
Nanoindentation
Nanoindention is hardness testing performed at the nanometer length scale.
The reduced elastic modulus Er is related to the unloading stiffness S according to
where  is a constant for the shape of the indenter ( = for a Berkovich indenter)
where
E elastic modulus of the material being indented
 Poisson’s ratio of the material being indented
Ei elastic modulus of the indenter
i Poisson’s ratio of the indenter
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31. Figure 6.20 - Indentation in a Bulk Metallic Glass
Chapter 6: Mechanical Properties: Part One
Figure Indentation in a Bulk Metallic Glass
An indentation in a Zr41.2Ti13.8Cu12.5Ni10.0Be22.5 bulk metallic glass made using a Berkovich tip in a nanoindenter.
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Chapter 6: Mechanical Properties: Part One
Figure 6.21
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Chapter 6: Mechanical Properties: Part One
Figure 6.23
The impact test: (a) the Charpy and Izod tests, and (b) dimensions of typical specimens.
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34. Strain Rate Effects and Impact Behavior
Chapter 6: Mechanical Properties: Part One
Strain Rate Effects and Impact Behavior
Impact test
Measures the ability of a material to absorb the sudden application of a load without breaking
Impact energy
Energy required to fracture a standard specimen when the load is applied suddenly
Impact toughness
Ability of a material to withstand an impact blow
Tensile toughness
Energy absorbed by a material subjected to tension prior to fracture
Fracture toughness
Resistance of a material to failure in the presence of a flaw
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35. Properties Obtained from the Impact Test
Chapter 6: Mechanical Properties: Part One
Properties Obtained from the Impact Test
Ductile to brittle transition temperature (DBTT)
Temperature below which a material behaves in a brittle manner in an impact test.
Notch sensitivity
Evaluated by comparing the absorbed energies of notched versus unnotched specimens.
Use of impact properties
Absorbed energy and the DBTT are very sensitive to loading conditions.
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Chapter 6: Mechanical Properties: Part One
Figure 6.26
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Chapter 6: Mechanical Properties: Part One
Figure 6.27
A schematic diagram of the compressive stress-strain behavior of various engineering materials including metallic glasses. Serrated flow is observed in the plastic region.
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Chapter 6: Mechanical Properties: Part One
Figure 6.29
A schematic diagram of a thin film on a substrate. The grains have diameters on the order of the film thickness. Note that thin films typically have thicknesses about 1/500th of the substrate thickness (some are far thinner), and so, this diagram is not drawn to scale.
(b) Stress versus temperature for thermal cycling of a 0.5 m polycrystalline aluminum thin film on an oxidized silicon substrate during a wafer curvature experiment.
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Chapter 6: Mechanical Properties: Part One
Key Terms
Stress
Strain
Elastic strain
Young’s modulus or modulus of elasticity (E)
Shear modulus (G)
Plastic deformation
Plastic strain
Strain rate
Impact loading
Viscoelastic
Stress relaxation
Shear thinning
Apparent viscosity
Bingham plastics
Yield strength
Thixotropic behavior
Rheopectic behavior
Load
Glass-transition temperature
Engineering stress
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40. © 2011 Cengage Learning Engineering. All Rights Reserved.
Chapter 6: Mechanical Properties: Part One
Key Terms
Engineering strain
Elastic limit
Proportional limit
Offset strain value
Offset yield strength
Yield strength
Plastic strain
Yield point phenomenon
Tensile strength
Ultimate tensile strength
Necking
Hooke’s law
Poisson’s ratio
Modulus of resilience
Tensile toughness or Work of fracture
Ductility
Percent elongation
Percent reduction in area
True stress
True strain
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Chapter 6: Mechanical Properties: Part One
Key Terms
Bend test
Elastic limit
Flexural strength or Modulus of rupture
Flexural modulus
Hardness test
Macrohardness
Impact energy
Impact toughness
Tensile toughness
Fracture toughness
Ductile to brittle transition temperature
Notch sensitivity
Modulus of resilience
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