Section 5.3

Stress/Strain & Elasticity

Section 5.3 Objectives

• State Hooke’s law.
• Explain Hooke’s law using graphical representation between deformation and applied force.
• Discuss the three types of deformations such as changes in length, sideways shear and changes in volume.
• Describe with examples the young’s modulus, shear modulus and bulk modulus.
• Determine the change in length given mass, length and radius.

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Terms you NEED to KNOW

• Hooke’s Law
• Shear deformation
• Stress
• Strain
• Tensile Strength
• Young’s Modulus
• Elasticity

Robert Hooke

• British Philosopher and Physicist
• Discovered the law of Elasticity

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Elasticity

• What does it mean for something to be Elastic?

Elasticity

• The ability of an object or material to resume its normal shape after being stretched or compressed.

Stress

The stress applied to a material is the force per unit area applied to the material

Strain

The ratio of extension to original length is called strain it has no units as it is a ratio of two lengths measured in meters.

Tensile Test

By pulling on something, you will determine how the material will react to forces being applied in tension. As the material is being pulled, you will find its strength along with how much it will elongate. Example applications: bridges, car frames, airplanes, etc.

The Tensile Test Specimen

Specimen after test

What is measured?

The measuring units for tensile testing are:

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• Load Newtons (N), (pounds in English)
• Extension metres (m), (inches in English)
• Stress Pascal (Pa), (PSI for English)
• Strain percentage (%) or a ratio

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Stress vs. Strain Curves

• The relationship between the stress and strain that a particular material displays is known as that particular material's stress–strain curve.

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• It is unique for each material and is found by recording the amount of deformation (strain) at distinct intervals of tensile or compressive loading (stress).

Stress-Strain Curve Terms

• Elastic Region (Hooke’s Law applies)
• Plastic Region
• Elastic Limit
• Yield Point
• Ultimate Strength or Tensile Strength
• Necking point & Necking region
• Fracture

Elastic/Plastic Region

• Elastic Region:
• Linear relationship
• Hooke’s Law Applies
• Material returns to original shape once stress is removed.

Elastic/Plastic Region

• Plastic Region:
• Relationship is no longer linear (curved)
• Hooke’s Law does NOT apply
• Material will become permanently deformed

Elastic Limit/Yield Point

• The stress at which deformation changes from elastic to plastic behaviour.
• Below the yield point unloading the specimen means that it returns to its original length
• Above the yield point permanent plastic deformation has occurred.

Ultimate Strength

Ultimate tensile strength (UTS), often shortened to tensile strength(TS) or ultimate strength, is the maximum stress that a material can withstand while being stretched or pulled before failing or breaking.

Necking

Necking, in engineering or materials science, is a mode of tensile deformation where relatively large amounts of strain localize disproportionately in a small region of the material. The resulting prominent decrease in local cross-sectional area provides the basis for the name "neck"

Fracture

This is pretty simple: the material finally breaks into 2 pieces.

Fracture

Tensile Test

https://www.youtube.com/watch?v=D8U4G5kcpcM

Quiz: Thursday, Jan. 15, 2015

Vocab to know:

• Hooke’s Law
• Elastic Region, Plastic Region
• Elastic Limit, Yield Point
• Stress & Strain
• Elasticity
• Tensile Strength
• Extensometer
• Necking

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• Ultimate Strength
• Fracture
• Gauge Length
• Tensile Test
• Load
• True Stress
• Engineering Stress

Quiz: Thursday, Jan. 15, 2015

Know SI & English Units for:

• Load
• Stress
• Original Length/Extension
• Strain

Quiz: Thursday, Jan. 15, 2015

• Know how to calculate stress given:
• Force
• diameter or area

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• Know how to calculate strain given:
• Original Length
• Extension

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Quiz: Thursday, Jan. 15, 2015

• Know how to create a Stress-Strain graph and be able to identify the various regions/points on the graph.
• Be able to describe these points and their importance.

Engineering Stress

• Engineering stress occurs when the Cross-sectional area is assumed to remain the same through the Tensile test.

Engineering Stress

But does the Cross-sectional area really remain the same throughout the test??

True Stress

The Cross-sectional area actually gets SMALLER throughout the test. So what would this do to the graph??

True vs. Engineering

Mythbusters: Duct Tape Bridge

How many rolls of duct tape will it take for the Mythbusters to create a 100 ft long bridge strong enough to support their own weight?