Mechanical properties refer to how materials behave under applied forces. This document discusses key mechanical properties including stress, strain, elasticity, plasticity, strength, ductility, and toughness. It provides definitions and examples for different types of stresses and strains. The stress-strain curve is introduced and key points like the elastic limit, yield strength, tensile strength, and ductility are defined. Factors that influence properties like temperature, microstructure, and processing are covered. Comparative data on mechanical properties is provided for common metals and polymers to illustrate property variations between materials.
Em321 lesson 08b solutions ch6 - mechanical properties of metalsusna12345
This document discusses mechanical properties that can be determined from a stress-strain curve obtained via tensile testing. It defines stress and strain, explains elastic and plastic deformation, and introduces key properties like modulus of elasticity, yield strength, ultimate tensile strength, ductility, toughness, and resilience. An example stress-strain curve is analyzed to find these properties numerically. The document emphasizes that stress-strain curves are commonly used instead of force-displacement plots to characterize materials.
1. The document discusses various mechanical properties including stress, strain, elastic behavior, plastic behavior, toughness, and properties of ceramics, metals, and polymers.
2. Key mechanical properties addressed for materials include yield strength, tensile strength, elastic modulus, ductility, and hardness.
3. The mechanical behavior of different classes of materials like ceramics, metals, and polymers is compared in terms of stress-strain curves and how properties vary with temperature and loading rate.
The document discusses various mechanical properties of metals including stiffness, strength, ductility, toughness, hardness, stress and strain. It defines key terms like elastic modulus, yield strength, ultimate strength, elongation, area reduction, fracture strain. It explains concepts such as engineering stress-strain curves, Hooke's law, elastic deformation, plastic deformation, Poisson's ratio, ductile vs brittle materials, and how properties relate to microstructure. Typical testing methods and how to calculate properties from raw data are also summarized.
The document discusses mechanical properties and mechanical testing. It addresses key concepts like stress, strain, elastic behavior, plastic behavior, toughness, ductility, stress-strain curves, yield strength, tensile strength and the effects of temperature. Specifically, it explains that yield strength and tensile strength decrease with increasing temperature while ductility increases with temperature. Brittle materials have low ductility and toughness while ductile metals can absorb more energy due to plastic deformation.
The document summarizes key concepts related to mechanical properties of materials from Chapter 6 of Callister's Materials Science and Engineering text. It defines terms like elasticity, yield strength, tensile strength, ductility, resilience, toughness, and hardness. Tables provide data on these properties for various classes of materials like metals, ceramics, polymers, and composites. Equations are presented relating stress to strain for elastic deformation as well as definitions of elastic moduli.
The document summarizes key concepts related to mechanical properties of materials from a materials science and engineering textbook. It defines terms like elasticity, yield strength, tensile strength, ductility, resilience, toughness, and hardness. It provides equations to calculate properties like elastic modulus, shear modulus, and Poisson's ratio. Tables compare property values like Young's modulus, yield strength, and tensile strength for various classes of materials like metals, ceramics, polymers, and composites. Diagrams illustrate stress-strain curves and how properties are determined from tensile tests.
This document provides an overview of mechanical properties and concepts related to stress and strain. It discusses key terms like elastic behavior, plastic behavior, ductility, toughness, resilience, hardness, stress, strain, yield strength, tensile strength, elastic modulus and more. Graphs and equations are presented to define these concepts. Material property comparisons for different metals and materials are shown for properties like modulus of elasticity, yield strength and tensile strength. Methods for measuring properties like hardness are also described.
This document discusses mechanical properties and testing methods. It introduces key terms like stress, strain, tensile testing and how properties like Young's modulus, yield strength and toughness are obtained. Tensile testing provides a stress-strain curve that shows elastic and plastic deformation regions. Ceramics are more brittle so bend testing is used to determine properties like flexural strength. Hardness tests measure a material's resistance to penetration.
Em321 lesson 08b solutions ch6 - mechanical properties of metalsusna12345
This document discusses mechanical properties that can be determined from a stress-strain curve obtained via tensile testing. It defines stress and strain, explains elastic and plastic deformation, and introduces key properties like modulus of elasticity, yield strength, ultimate tensile strength, ductility, toughness, and resilience. An example stress-strain curve is analyzed to find these properties numerically. The document emphasizes that stress-strain curves are commonly used instead of force-displacement plots to characterize materials.
1. The document discusses various mechanical properties including stress, strain, elastic behavior, plastic behavior, toughness, and properties of ceramics, metals, and polymers.
2. Key mechanical properties addressed for materials include yield strength, tensile strength, elastic modulus, ductility, and hardness.
3. The mechanical behavior of different classes of materials like ceramics, metals, and polymers is compared in terms of stress-strain curves and how properties vary with temperature and loading rate.
The document discusses various mechanical properties of metals including stiffness, strength, ductility, toughness, hardness, stress and strain. It defines key terms like elastic modulus, yield strength, ultimate strength, elongation, area reduction, fracture strain. It explains concepts such as engineering stress-strain curves, Hooke's law, elastic deformation, plastic deformation, Poisson's ratio, ductile vs brittle materials, and how properties relate to microstructure. Typical testing methods and how to calculate properties from raw data are also summarized.
The document discusses mechanical properties and mechanical testing. It addresses key concepts like stress, strain, elastic behavior, plastic behavior, toughness, ductility, stress-strain curves, yield strength, tensile strength and the effects of temperature. Specifically, it explains that yield strength and tensile strength decrease with increasing temperature while ductility increases with temperature. Brittle materials have low ductility and toughness while ductile metals can absorb more energy due to plastic deformation.
The document summarizes key concepts related to mechanical properties of materials from Chapter 6 of Callister's Materials Science and Engineering text. It defines terms like elasticity, yield strength, tensile strength, ductility, resilience, toughness, and hardness. Tables provide data on these properties for various classes of materials like metals, ceramics, polymers, and composites. Equations are presented relating stress to strain for elastic deformation as well as definitions of elastic moduli.
The document summarizes key concepts related to mechanical properties of materials from a materials science and engineering textbook. It defines terms like elasticity, yield strength, tensile strength, ductility, resilience, toughness, and hardness. It provides equations to calculate properties like elastic modulus, shear modulus, and Poisson's ratio. Tables compare property values like Young's modulus, yield strength, and tensile strength for various classes of materials like metals, ceramics, polymers, and composites. Diagrams illustrate stress-strain curves and how properties are determined from tensile tests.
This document provides an overview of mechanical properties and concepts related to stress and strain. It discusses key terms like elastic behavior, plastic behavior, ductility, toughness, resilience, hardness, stress, strain, yield strength, tensile strength, elastic modulus and more. Graphs and equations are presented to define these concepts. Material property comparisons for different metals and materials are shown for properties like modulus of elasticity, yield strength and tensile strength. Methods for measuring properties like hardness are also described.
This document discusses mechanical properties and testing methods. It introduces key terms like stress, strain, tensile testing and how properties like Young's modulus, yield strength and toughness are obtained. Tensile testing provides a stress-strain curve that shows elastic and plastic deformation regions. Ceramics are more brittle so bend testing is used to determine properties like flexural strength. Hardness tests measure a material's resistance to penetration.
Terminology for Mechanical Properties The Tensile Test: Stress-Strain Diagram...manohar3970
Terminology for Mechanical Properties
The Tensile Test: Stress-Strain Diagram
Properties Obtained from a Tensile Test
True Stress and True Strain
The Bend Test for Brittle Materials
Hardness of Materials
This document discusses mechanical properties and tensile testing. It introduces key terms like stress, strain, elastic deformation, plastic deformation, yield strength, tensile strength, and ductility. It explains how mechanical properties like Young's modulus, yield strength, and tensile strength are determined from a stress-strain curve generated through uniaxial tensile testing. It also discusses plastic deformation through dislocation motion, strain hardening, necking, and factors that influence properties like processing methods. True stress and true strain are introduced as alternatives to engineering stress and strain for accounting for changes in cross-sectional area during deformation.
The document discusses tensile testing to determine material properties. Tensile testing involves applying a load to a test specimen and measuring the resulting elongation. This provides load-deformation data that can be converted to stress-strain data using the specimen's original dimensions. The stress-strain curve indicates material properties like elastic modulus, yield strength, and ductile vs. brittle behavior.
This document provides an overview of mechanical properties and behavior of engineering materials. It defines concepts such as stress, strain, elastic deformation, plastic deformation, yield strength, tensile strength, ductility and more. Examples and calculations are provided to illustrate these concepts. Learning outcomes are stated, and issues to address in the topic are outlined. Comparative data on properties of various materials is also presented.
Mechanical properties of materials (lecture+2).pdfHeshamBakr3
The document discusses the mechanical properties of materials when subjected to different types of loading like axial, lateral, and torsional loads. It defines concepts like stress, strain, elastic and plastic deformation. It explains stress-strain diagrams and how they are used to determine properties like modulus of elasticity, yield strength, tensile strength, ductility, toughness, and resilience. Typical stress-strain behaviors of ductile and brittle materials are compared. Examples of determining properties from stress-strain curves are also provided.
The document discusses various mechanical properties of materials important for manufacturing including modulus, yield strength, tensile strength, stress-strain relationships, ductility, toughness, hardness, and fatigue. It explains how properties like modulus, strength, and stress-strain behavior are evaluated using tensile tests, and how properties like ductility, toughness, and hardness are measured and related to a material's suitability for manufacturing processes. Comparative data on the mechanical properties of common materials like metals, ceramics, polymers is also presented.
Theory of Plasticity is a very important topic in solid mechanics & Strength of Materials. It is very very useful for Mechanical & Civil Engineering students.
The document discusses plastic deformation in crystalline materials. It describes how plastic deformation occurs primarily through slip mediated by dislocation motion. Other mechanisms like twinning and creep can also contribute to plastic deformation under certain conditions. The uniaxial tension test is discussed as a common experimental technique to evaluate plastic deformation behavior. True stress-strain curves are preferred over engineering stress-strain curves for quantitative analysis since they account for changes in cross-sectional area during deformation. Key regions of the stress-strain curve are also outlined, including the elastic portion, yield point, strain hardening region, and necking/fracture points.
The document discusses plastic deformation in crystalline materials. It describes how plastic deformation occurs primarily through slip mediated by dislocation motion. Other mechanisms like twinning and creep can also contribute to plastic deformation under certain conditions. The uniaxial tension test is discussed as a common experimental technique to evaluate plastic deformation behavior. True stress-strain curves are preferred over engineering stress-strain as they account for changes in cross-sectional area during deformation. Key regions of the stress-strain curve are described including the elastic portion, yield point, strain hardening region, necking onset, and fracture.
The document discusses fatigue failure and fatigue analysis. It begins by explaining that fatigue failure starts with a crack, usually at a stress concentration, which then propagates until sudden fracture. It then provides examples of fatigue failures and discusses different fatigue analysis methods. The key points are:
- Fatigue failure results from repeated or fluctuating stresses that are lower than the material's ultimate strength.
- It can be analyzed using stress-life, strain-life, or fracture mechanics methods, with stress-life most common for high-cycle fatigue.
- The stress-life approach estimates fatigue strength (Sf) based on stress levels and uses modifying factors to account for real-world differences from test specimens.
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This document discusses stress-strain relationships in materials subjected to axial loads. It covers key concepts such as elastic and plastic deformation, ductile and brittle behavior, stress-strain diagrams, and the effects of temperature, strain rate, and time-dependent behavior like creep and stress relaxation. Measurement techniques for strain like strain gages and extensometers are also described. Various stress-strain models are presented, including Hooke's law, the Ramberg-Osgood equation, and idealized perfectly plastic, elastic-plastic, and strain hardening models. The relationships between stress, strain, elastic modulus, yield strength, and other mechanical properties are examined through diagrams and equations.
This document discusses the mechanical properties of solids. It covers topics such as elasticity, stress and strain, mechanical testing techniques for properties like hardness, ductility, deformation mechanisms, fracture, and fatigue. Elasticity is divided into elastic deformation, where the material returns to its original shape, and plastic deformation, where the shape is permanently changed. Stress is defined as force over cross-sectional area while strain is the change in length over original length. Various mechanical tests are used to characterize properties like hardness, toughness, and ductility. Deformation, fracture, and fatigue failure mechanisms are also examined.
This document discusses various concepts related to stress and strain. It begins by explaining the three main types of loads - tension, compression, and shear. It then provides diagrams demonstrating these different types of loads. The document goes on to define engineering stress and strain and discuss their units. Several mechanical properties are also defined, including yield strength, ultimate tensile strength, and elongation. Finally, the document discusses various tests used to determine mechanical properties, including tensile, compression, hardness, and impact tests.
This document discusses mechanical properties that can be determined from tensile and shear tests. It defines key terms like stress, strain, elastic modulus, yield strength, and tensile strength. A typical stress-strain curve is shown and each region is explained. The elastic portion is linear up to the yield point, then the plastic region involves necking and strain hardening until ultimate failure. True stress and strain account for changes in cross-sectional area during deformation. The document also compares properties like ductility and toughness between different materials.
The document describes the process and results of a tension test, which is used to determine the mechanical properties of materials. In a tension test, standardized specimen grips are pulled apart in a testing machine while measuring the applied force and deformation. The data collected - stress, strain, ultimate strength, and ductility - are used to analyze a material's elasticity, plasticity, hardness, and failure point. Tension tests provide information about a material's behavior and suitability for engineering applications.
Mechanics of Materials
Materials Characterization
The American Society for Testing and Materials (ASTM) specifies test procedures for determining the various properties of a material.
These descriptions are guidelines used by experimentalists to obtain reproducible results for material properties.
This document discusses various mechanical properties that are important for selecting materials for structural components. It describes different types of mechanical tests like tension, compression, torsion, bending, impact and fatigue tests that are conducted on metal specimens to determine properties like strength, ductility and toughness. Specifically, it outlines the process for a uniaxial tension test including the equipment used, steps to conduct the test, and how to analyze the stress-strain diagram produced. It also discusses factors that influence mechanical properties like temperature, notches, grain size and hardness tests.
The document discusses various mechanical properties of metals including resilience, toughness, true stress and strain, hardening, fatigue failure, creep, and factor of safety.
Resilience is the ability of a material to absorb energy elastically. Toughness is the total energy absorbed before fracture. True stress and strain account for changes in cross-sectional area during deformation. Hardening occurs as yield strength increases with plastic deformation. Fatigue failure results from initiation and propagation of cracks under cyclic stresses. Creep is permanent deformation over time at high temperatures and stresses. Factor of safety determines a system's load-carrying capacity beyond the actual load.
This document summarizes the mechanical properties of materials through stress-strain diagrams. It discusses the differences between stress-strain diagrams for ductile versus brittle materials. For ductile materials, the diagram shows elastic behavior, yielding, strain hardening, necking, and true stress-strain. Brittle materials exhibit no yielding and rupture occurs at a much smaller strain. The document also discusses Hooke's law, Poisson's ratio, axial loading of materials, and provides examples of calculating deformation based on applied loads and material properties.
Mechanical failures can occur due to improper material selection, inadequate design, or misuse. The document discusses various failure mechanisms including ductile and brittle fracture, fatigue, and creep. It emphasizes that sharp corners and flaws act as stress concentrators that can lead to premature failure at stresses lower than theoretical values. The type of failure depends on the temperature and applied stress conditions.
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Terminology for Mechanical Properties
The Tensile Test: Stress-Strain Diagram
Properties Obtained from a Tensile Test
True Stress and True Strain
The Bend Test for Brittle Materials
Hardness of Materials
This document discusses mechanical properties and tensile testing. It introduces key terms like stress, strain, elastic deformation, plastic deformation, yield strength, tensile strength, and ductility. It explains how mechanical properties like Young's modulus, yield strength, and tensile strength are determined from a stress-strain curve generated through uniaxial tensile testing. It also discusses plastic deformation through dislocation motion, strain hardening, necking, and factors that influence properties like processing methods. True stress and true strain are introduced as alternatives to engineering stress and strain for accounting for changes in cross-sectional area during deformation.
The document discusses tensile testing to determine material properties. Tensile testing involves applying a load to a test specimen and measuring the resulting elongation. This provides load-deformation data that can be converted to stress-strain data using the specimen's original dimensions. The stress-strain curve indicates material properties like elastic modulus, yield strength, and ductile vs. brittle behavior.
This document provides an overview of mechanical properties and behavior of engineering materials. It defines concepts such as stress, strain, elastic deformation, plastic deformation, yield strength, tensile strength, ductility and more. Examples and calculations are provided to illustrate these concepts. Learning outcomes are stated, and issues to address in the topic are outlined. Comparative data on properties of various materials is also presented.
Mechanical properties of materials (lecture+2).pdfHeshamBakr3
The document discusses the mechanical properties of materials when subjected to different types of loading like axial, lateral, and torsional loads. It defines concepts like stress, strain, elastic and plastic deformation. It explains stress-strain diagrams and how they are used to determine properties like modulus of elasticity, yield strength, tensile strength, ductility, toughness, and resilience. Typical stress-strain behaviors of ductile and brittle materials are compared. Examples of determining properties from stress-strain curves are also provided.
The document discusses various mechanical properties of materials important for manufacturing including modulus, yield strength, tensile strength, stress-strain relationships, ductility, toughness, hardness, and fatigue. It explains how properties like modulus, strength, and stress-strain behavior are evaluated using tensile tests, and how properties like ductility, toughness, and hardness are measured and related to a material's suitability for manufacturing processes. Comparative data on the mechanical properties of common materials like metals, ceramics, polymers is also presented.
Theory of Plasticity is a very important topic in solid mechanics & Strength of Materials. It is very very useful for Mechanical & Civil Engineering students.
The document discusses plastic deformation in crystalline materials. It describes how plastic deformation occurs primarily through slip mediated by dislocation motion. Other mechanisms like twinning and creep can also contribute to plastic deformation under certain conditions. The uniaxial tension test is discussed as a common experimental technique to evaluate plastic deformation behavior. True stress-strain curves are preferred over engineering stress-strain curves for quantitative analysis since they account for changes in cross-sectional area during deformation. Key regions of the stress-strain curve are also outlined, including the elastic portion, yield point, strain hardening region, and necking/fracture points.
The document discusses plastic deformation in crystalline materials. It describes how plastic deformation occurs primarily through slip mediated by dislocation motion. Other mechanisms like twinning and creep can also contribute to plastic deformation under certain conditions. The uniaxial tension test is discussed as a common experimental technique to evaluate plastic deformation behavior. True stress-strain curves are preferred over engineering stress-strain as they account for changes in cross-sectional area during deformation. Key regions of the stress-strain curve are described including the elastic portion, yield point, strain hardening region, necking onset, and fracture.
The document discusses fatigue failure and fatigue analysis. It begins by explaining that fatigue failure starts with a crack, usually at a stress concentration, which then propagates until sudden fracture. It then provides examples of fatigue failures and discusses different fatigue analysis methods. The key points are:
- Fatigue failure results from repeated or fluctuating stresses that are lower than the material's ultimate strength.
- It can be analyzed using stress-life, strain-life, or fracture mechanics methods, with stress-life most common for high-cycle fatigue.
- The stress-life approach estimates fatigue strength (Sf) based on stress levels and uses modifying factors to account for real-world differences from test specimens.
Chapter 2: Axial Strains and Deformation in BarsMonark Sutariya
This document discusses stress-strain relationships in materials subjected to axial loads. It covers key concepts such as elastic and plastic deformation, ductile and brittle behavior, stress-strain diagrams, and the effects of temperature, strain rate, and time-dependent behavior like creep and stress relaxation. Measurement techniques for strain like strain gages and extensometers are also described. Various stress-strain models are presented, including Hooke's law, the Ramberg-Osgood equation, and idealized perfectly plastic, elastic-plastic, and strain hardening models. The relationships between stress, strain, elastic modulus, yield strength, and other mechanical properties are examined through diagrams and equations.
This document discusses the mechanical properties of solids. It covers topics such as elasticity, stress and strain, mechanical testing techniques for properties like hardness, ductility, deformation mechanisms, fracture, and fatigue. Elasticity is divided into elastic deformation, where the material returns to its original shape, and plastic deformation, where the shape is permanently changed. Stress is defined as force over cross-sectional area while strain is the change in length over original length. Various mechanical tests are used to characterize properties like hardness, toughness, and ductility. Deformation, fracture, and fatigue failure mechanisms are also examined.
This document discusses various concepts related to stress and strain. It begins by explaining the three main types of loads - tension, compression, and shear. It then provides diagrams demonstrating these different types of loads. The document goes on to define engineering stress and strain and discuss their units. Several mechanical properties are also defined, including yield strength, ultimate tensile strength, and elongation. Finally, the document discusses various tests used to determine mechanical properties, including tensile, compression, hardness, and impact tests.
This document discusses mechanical properties that can be determined from tensile and shear tests. It defines key terms like stress, strain, elastic modulus, yield strength, and tensile strength. A typical stress-strain curve is shown and each region is explained. The elastic portion is linear up to the yield point, then the plastic region involves necking and strain hardening until ultimate failure. True stress and strain account for changes in cross-sectional area during deformation. The document also compares properties like ductility and toughness between different materials.
The document describes the process and results of a tension test, which is used to determine the mechanical properties of materials. In a tension test, standardized specimen grips are pulled apart in a testing machine while measuring the applied force and deformation. The data collected - stress, strain, ultimate strength, and ductility - are used to analyze a material's elasticity, plasticity, hardness, and failure point. Tension tests provide information about a material's behavior and suitability for engineering applications.
Mechanics of Materials
Materials Characterization
The American Society for Testing and Materials (ASTM) specifies test procedures for determining the various properties of a material.
These descriptions are guidelines used by experimentalists to obtain reproducible results for material properties.
This document discusses various mechanical properties that are important for selecting materials for structural components. It describes different types of mechanical tests like tension, compression, torsion, bending, impact and fatigue tests that are conducted on metal specimens to determine properties like strength, ductility and toughness. Specifically, it outlines the process for a uniaxial tension test including the equipment used, steps to conduct the test, and how to analyze the stress-strain diagram produced. It also discusses factors that influence mechanical properties like temperature, notches, grain size and hardness tests.
The document discusses various mechanical properties of metals including resilience, toughness, true stress and strain, hardening, fatigue failure, creep, and factor of safety.
Resilience is the ability of a material to absorb energy elastically. Toughness is the total energy absorbed before fracture. True stress and strain account for changes in cross-sectional area during deformation. Hardening occurs as yield strength increases with plastic deformation. Fatigue failure results from initiation and propagation of cracks under cyclic stresses. Creep is permanent deformation over time at high temperatures and stresses. Factor of safety determines a system's load-carrying capacity beyond the actual load.
This document summarizes the mechanical properties of materials through stress-strain diagrams. It discusses the differences between stress-strain diagrams for ductile versus brittle materials. For ductile materials, the diagram shows elastic behavior, yielding, strain hardening, necking, and true stress-strain. Brittle materials exhibit no yielding and rupture occurs at a much smaller strain. The document also discusses Hooke's law, Poisson's ratio, axial loading of materials, and provides examples of calculating deformation based on applied loads and material properties.
Mechanical failures can occur due to improper material selection, inadequate design, or misuse. The document discusses various failure mechanisms including ductile and brittle fracture, fatigue, and creep. It emphasizes that sharp corners and flaws act as stress concentrators that can lead to premature failure at stresses lower than theoretical values. The type of failure depends on the temperature and applied stress conditions.
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ACEP Magazine edition 4th launched on 05.06.2024Rahul
This document provides information about the third edition of the magazine "Sthapatya" published by the Association of Civil Engineers (Practicing) Aurangabad. It includes messages from current and past presidents of ACEP, memories and photos from past ACEP events, information on life time achievement awards given by ACEP, and a technical article on concrete maintenance, repairs and strengthening. The document highlights activities of ACEP and provides a technical educational article for members.
2. • Mechanical Properties refers to the behavior of
material when
• external forces are applied
• Stress and strain ⇒ fracture
• For engineering point of view: allows to predict the
ability of a component or a structure to withstand the
forces applied to it
2
For science point of view: what makes
materials strong →helps us to design a
better new one
3. 3
Elastic means reversible!
Elastic Deformation
2. Small load
F
d
bonds
stretch
1. Initial 3. Unload
return to
initial
F
d
Linear-
elastic
Non-Linear-
elastic
Grey iron, concrete,
polymers)
4. 4
Plastic means permanent!
Plastic Deformation (Metals)
F
d
linear
elastic
linear
elastic
dplastic
1. Initial 2. Small load 3. Unload
planes
still
sheared
F
d elastic + plastic
bonds
stretch
& planes
shear
d plastic
5. Direct Stress Examples
Load, P
P
Area
Ao
Lo
L/2
L/2
Direct Stress - Tension
Load, P
P
Area
Ao
Lo
L/2
L/2
Direct Stress - Compression
S
P
Ao
e
L
Lo
Engineering Stress
Engineering Strain
5
6. 6
Stress has units:
N/m2 or lbf /in2
Engineering Stress
• Shear stress, t:
Area, Ao
Ft
Ft
Fs
F
F
Fs
t =
Fs
Ao
• Tensile stress, s:
original area
before loading
s =
Ft
Ao
2
f
2
m
N
or
in
lb
=
Area, Ao
Ft
Ft
7. 7
• Simple tension: cable
Note: t = M/AcR here.
Common States of Stress
o
s
F
A
o
t
Fs
A
s
s
M
M Ao
2R
Fs
Ac
• Torsion (a form of shear): drive shaft Ski lift (photo courtesy
P.M. Anderson)
Ao = cross sectional
area (when unloaded)
F
F
8. 8
(photo courtesy P.M. Anderson)
Canyon Bridge, Los Alamos, NM
o
s
F
A
• Simple compression:
Note: compressive
structure member
(s < 0 here).
(photo courtesy P.M. Anderson)
OTHER COMMON STRESS STATES (i)
Ao
Balanced Rock, Arches
National Park
9. 9
• Bi-axial tension: • Hydrostatic compression:
Pressurized tank
s < 0
h
(photo courtesy
P.M. Anderson)
(photo courtesy
P.M. Anderson)
OTHER COMMON STRESS STATES (ii)
Fish under water
s z > 0
s
q
> 0
10. 10
• Tensile strain: • Lateral strain:
Strain is always
dimensionless.
Engineering Strain
• Shear strain:
q
90º
90º - q
y
x
q
g = x/y = tan
e d
Lo
Adapted from Fig. 6.1(a) and (c), Callister & Rethwisch 8e.
d /2
Lo
wo
-d
eL L
wo
d
L/2
𝛿 = 𝐿-𝐿°
11. 11
Stress-Strain Testing
• Typical tensile test
machine
Adapted from Fig. 6.3, Callister & Rethwisch 8e. (Fig. 6.3 is taken from H.W.
Hayden, W.G. Moffatt, and J. Wulff, The Structure and Properties of Materials,
Vol. III, Mechanical Behavior, p. 2, John Wiley and Sons, New York, 1965.)
specimen
extensometer
• Typical tensile
specimen
Adapted from
Fig. 6.2,
Callister &
Rethwisch 8e.
gauge
length
15. 15
Linear Elastic Properties
• Modulus of Elasticity, E:
(also known as Young's modulus)
• Hooke's Law:
s = E e
s
Linear-
elastic
E
e
F
F
simple
tension
test
• Elastic deformation is not permanent; it means that when the load is
removed, the part returns to its original shape and dimensions.
• For most metals, the elastic region is linear. For some materials, including
metals such as cast iron, polymers, and concrete, the elastic region is
non-linear.
17. The elastic modulus is proportional to the slope of the
interatomic force-separation curve at the equilibrium spacing
The
magnitude of
modulus of
elasticity is a
measure of
the resistance
to separation
of adjacent
atoms, that is
interatomic
17
18. Modulus of elasticity- Temperature
18
Values of the modulus of elasticity for
ceramic materials are about the same
as for metals; for polymers they are
lower. These differences are a direct
consequence of the different types of
atomic bonding in the three materials
types.
Furthermore, with increasing
temperature, the modulus of elasticity
diminishes, as
is shown for several metals in Figure.
21. Elastic Properties of Materials
• Poisson’s ratio: When a metal is strained in one
direction, there are corresponding strains in all other
directions.
• For a uniaxial tension strain, the lateral strains
are constrictive.
• Conversely, for a uniaxial compressive strain,
the lateral strains are expansive.
• i.e.; the lateral strains are opposite in sign to
the axial strain.
• The ratio of lateral to axial strains is known as
Poisson’s ratio, n.
21
22. 22
Poisson's ratio, n
• Poisson's ratio, n:
Units:
E: [GPa] or [psi]
n: dimensionless
n > 0.50 density increases
n < 0.50 density decreases
(voids form)
eL
e
-n
e
n - L
e
metals: n ~ 0.33
ceramics: n ~ 0.25
polymers: n ~ 0.40
Ratio of
lateral
and
axial
strains
23. Poisson’s Ratio, n
n -
ex
ez
-
ey
ez
For most metals,
0.25 < n < 0.35
in the elastic range
Furthermore:
)
1
(
2 n
G
E
23
24. 24
• Elastic Shear
modulus, G:
t
G
g
t = G g
Other Elastic Properties
simple
torsion
test
M
M
• Special relations for isotropic materials:
2(1 n)
E
G 3(1 - 2n)
E
K
• Elastic Bulk
modulus, K:
pressure
test: Init.
vol =Vo.
Vol chg.
= V
P
P P
P = -K
V
Vo
P
V
K
Vo
25. 25
(at lower temperatures, i.e. T < Tmelt/3)
Plastic (Permanent) Deformation
• Simple tension test:
engineering stress, s
engineering strain, e
Elastic+Plastic
at larger stress
ep
plastic strain
Elastic
initially
Adapted from Fig. 6.10(a),
Callister & Rethwisch 8e.
permanent (plastic)
after load is removed
27. 27
• Stress at which noticeable plastic deformation has
occurred.
when ep = 0.002
Yield Strength, sy
sy = yield strength
Note: for 2 inch sample
e = 0.002 = l/l
z = 0.004 in
Adapted from Fig. 6.10(a),
Callister & Rethwisch 8e.
tensile stress, s
engineering strain, e
sy
ep = 0.002
28. 28
Room temperature
values
Based on data in Table B.4,
Callister & Rethwisch 8e.
a = annealed
hr = hot rolled
ag = aged
cd = cold drawn
cw = cold worked
qt = quenched & tempered
Yield Strength : Comparison
Graphite/
Ceramics/
Semicond
Metals/
Alloys
Composites/
fibers
Polymers
Yield
strength,
s
y
(MPa)
PVC
Hard
to
measure
,
since
in
tension,
fracture
usually
occurs
before
yield.
Nylon 6,6
LDPE
70
20
40
60
50
100
10
30
200
300
400
500
600
700
1000
2000
Tin (pure)
Al (6061) a
Al (6061) ag
Cu (71500) hr
Ta (pure)
Ti (pure) a
Steel (1020) hr
Steel (1020) cd
Steel (4140) a
Steel (4140) qt
Ti (5Al-2.5Sn) a
W (pure)
Mo (pure)
Cu (71500) cw
Hard
to
measure,
in
ceramic
matrix
and
epoxy
matrix
composites,
since
in
tension,
fracture
usually
occurs
before
yield.
HDPE
PP
humid
dry
PC
PET
¨
29. 29
Tensile Strength, TS
• Metals: occurs when noticeable necking starts.
• Polymers: occurs when polymer backbone chains are
aligned and about to break.
Adapted from Fig. 6.11,
Callister & Rethwisch 8e.
sy
strain
Typical response of a metal
F = fracture or
ultimate
strength
Neck – acts
as stress
concentrator
engineering
TS
stress
engineering strain
• Maximum stress on engineering stress-strain curve.
30. 30
Tensile Strength: Comparison
Si crystal
<100>
Graphite/
Ceramics/
Semicond
Metals/
Alloys
Composites/
fibers
Polymers
Tensile
strength,
TS
(MPa)
PVC
Nylon 6,6
10
100
200
300
1000
Al (6061) a
Al (6061) ag
Cu (71500) hr
Ta (pure)
Ti (pure) a
Steel (1020)
Steel (4140) a
Steel (4140) qt
Ti (5Al-2.5Sn) a
W (pure)
Cu (71500) cw
LDPE
PP
PC PET
20
30
40
2000
3000
5000
Graphite
Al oxide
Concrete
Diamond
Glass-soda
Si nitride
HDPE
wood ( fiber)
wood(|| fiber)
1
GFRE(|| fiber)
GFRE( fiber)
CFRE(|| fiber)
CFRE( fiber)
AFRE(|| fiber)
AFRE( fiber)
E-glass fib
C fibers
Aramid fib
Based on data in Table B.4,
Callister & Rethwisch 8e.
a = annealed
hr = hot rolled
ag = aged
cd = cold drawn
cw = cold worked
qt = quenched & tempered
AFRE, GFRE, & CFRE =
aramid, glass, & carbon
fiber-reinforced epoxy
composites, with 60 vol%
fibers.
Room temperature
values
31. Microstructural Origins of Plasticity
• Slip, Climb and Slide of atoms in the crystal
structure.
• Slip and Climb occur at Dislocations and Slide
occurs at Grain Boundaries.
t
t
31
32. 32
• Plastic tensile strain at failure:
Ductility
• Another ductility measure:
100
x
A
A
A
RA
%
o
f
o
-
=
x 100
L
L
L
EL
%
o
o
f
-
Lf
Ao
Af
Lo
Adapted from Fig. 6.13,
Callister & Rethwisch 8e.
Engineering tensile strain, e
Engineering
tensile
stress, s
smaller %EL
larger %EL
, ductility is defined by the degree to which a material can
sustain plastic deformation under tensile stress before failure.
33. Ductile Vs Brittle Materials
• Only Ductile materials will exhibit necking.
• Ductile if EL%>8% (approximately)
• Brittle if EL% < 5% (approximately)
Engineering
Stress
Engineering Strain
33
35. 35
Summary
• Stress and strain: These are size-independent
measures of load and displacement, respectively.
• Elastic behavior: This reversible behavior often
shows a linear relation between stress and strain.
To minimize deformation, select a material with a
large elastic modulus (E or G).
• Toughness: The energy needed to break a unit
volume of material.
• Ductility: The plastic strain at failure.
• Plastic behavior: This permanent deformation
behavior occurs when the tensile (or compressive)
uniaxial stress reaches sy.
38. Problems
38
A cylindrical metal specimen having an original diameter of
12.8 mm (0.505 in.) and gauge length of 50.80 mm (2.000 in.)
is pulled in tension until fracture occurs. The diameter at the
point of fracture is 8.13 mm (0.320 in.), and the fractured
gauge length is 74.17 mm(2.920 in.). Calculate the ductility in
terms of percent reduction in area and percent elongation.