1.1. To understand the keywords associated with To understand the keywords associated with the deformation of different types of solidsthe deformation of different types of solids

2.2. To be able to calculate stress, strain and To be able to calculate stress, strain and hence Young’s modulushence Young’s modulus

3.3. To be able to describe and compare stress To be able to describe and compare stress strain graphsstrain graphs

Book Reference : Pages 167-169Book Reference : Pages 167-169

Elasticity: Elasticity: The ability of a solid to regain its shape The ability of a solid to regain its shape after it has been deformed or distortedafter it has been deformed or distorted

TensileTensile : Deformation due to stretching : Deformation due to stretching

Compressive Deformation: Compressive Deformation: deformation due to deformation due to compressioncompression

Ductile: Ductile: The ability to be drawn into a wire The ability to be drawn into a wire (Copper is a good example)(Copper is a good example)

Brittle: Brittle: Material breaks without any “give”. Material breaks without any “give”. Cannot be permanently stretchedCannot be permanently stretched

Tensile StressTensile StressThis is the force per unit area of cross section when This is the force per unit area of cross section when

a material is stretcheda material is stretched

For a wire of length L and cross section AFor a wire of length L and cross section A

Tensile Stress = Tension / AreaTensile Stress = Tension / Area = F/A= F/A

Units : Derived N/mUnits : Derived N/m22, named Pascals (Pa), named Pascals (Pa)Area is often for a wire with a circular cross section. So Area is often for a wire with a circular cross section. So

rr22, but ¼, but ¼dd22 is more convenient since we is more convenient since we measure diameter with a micrometer rather than measure diameter with a micrometer rather than radiusradius

Tensile StrainTensile StrainThis is the ratio of change in length (This is the ratio of change in length (ΔΔL) to L) to

original length (L)original length (L)

For a wire of length LFor a wire of length L

Tensile Stress = Extension / Original Tensile Stress = Extension / Original LengthLength

= = L/LL/L

Units : None! It is a ratio (units cancel out)Units : None! It is a ratio (units cancel out)

Graphs of Stress against Strain are useful. Graphs of Stress against Strain are useful. They provide a method of comparing They provide a method of comparing materials of different thicknesses and materials of different thicknesses and original lengthsoriginal lengths

1.1. Linear region where Linear region where Hooke’s law is obeyedHooke’s law is obeyed

2.2. The limit of proportionalityThe limit of proportionality

3.3. Elastic Limit – point where Elastic Limit – point where the material stops the material stops returning to its original returning to its original length length

4.4. Yield point(s) where the Yield point(s) where the material ‘necks’material ‘necks’

5.5. Ultimate Tensile Stress Ultimate Tensile Stress (U.T.S.)(U.T.S.)

6.6. B. breaking pointB. breaking point

Elastic Limit: Elastic Limit: The maximum amount a material can The maximum amount a material can be stretched by a force and still return to its original be stretched by a force and still return to its original shape and size. The material has no permanent shape and size. The material has no permanent change in shape or sizechange in shape or size

Yield Point: Yield Point: Beyond the elastic limit, a point is Beyond the elastic limit, a point is reached at which there is a noticeably larger reached at which there is a noticeably larger permanent change in length. This results in plastic permanent change in length. This results in plastic behaviourbehaviour

Ultimate Tensile Strength: Ultimate Tensile Strength: The maximum stress The maximum stress that can be applied without breakingthat can be applied without breaking

Plasticity: Plasticity: A plastic material does not return to its A plastic material does not return to its original size and shape when the force is removed. original size and shape when the force is removed. There is a permanent stretching and change of There is a permanent stretching and change of shapeshape

Stiffness: Stiffness: A measure of how difficult it is to change A measure of how difficult it is to change the size or shape of a material.the size or shape of a material.

•Thick steel wire is stiffer than thin steel wire of the Thick steel wire is stiffer than thin steel wire of the same length.same length.•Short steel wire is stiffer than longer steel wire of the Short steel wire is stiffer than longer steel wire of the same diameter.same diameter.•Steel is stiffer than copper of the same diameter and Steel is stiffer than copper of the same diameter and length, because copper extends more per unit forcelength, because copper extends more per unit force

Young’s =Young’s = Tensile StressTensile StressModulus Modulus Tensile StrainTensile Strain

Expands toExpands to E = E = // = F/A = F/A L/LL/L

Units simply come from the tensile stress N/mUnits simply come from the tensile stress N/m22 or Pa or Pa

The linear region where The linear region where Hooke’s law is obeyed is of Hooke’s law is obeyed is of interest and allows us to interest and allows us to compare materials.compare materials.

This is known as Young’s This is known as Young’s modulusmodulus

E = F/A E = F/A L/LL/L Can be rearranged as Can be rearranged as

E = F/E = F/L x L/AL x L/A (invert the divisor ÷2 (invert the divisor ÷2 x x ½)½)

Why is this helpful?Why is this helpful?

F/F/L can be foundL can be foundExperimentallyExperimentally

Gradient of graph!Gradient of graph!

F

L

L (m)

Comparing stress/strain graphs of brittle and Comparing stress/strain graphs of brittle and ductile materials for example glass and copperductile materials for example glass and copper

DuctileDuctile materials have a very materials have a very large plastic region. Just before large plastic region. Just before it fails the material necksit fails the material necks

Cross sectional reduces, and as stress = F/A the neck sees Cross sectional reduces, and as stress = F/A the neck sees an increase in tensile stress. an increase in tensile stress.

BrittleBrittle materials show little plastic deformation. Failure is materials show little plastic deformation. Failure is sudden and ‘catastrophic’. Better under compressionsudden and ‘catastrophic’. Better under compression