Unit 1.5 - Solids Under Stress Flashcards
What happens when an object is subject to tensile force (tension)?
It stretches
When does an object stretch?
When it’s subject to tensile force
Tensile force
Tension
What type of force is tension?
A tensile force
What does Hooke’s Law state?
For most objects, the degree it stretches is directly proportional to the tension (provided the force is not too large)
“For most objects, the degree it stretches is directly proportional to the tension” - which law is this?
Hooke’s law
What type of behaviour does an object exhibit under Hooke’s law?
Elastic behaviour, meaning that if it’s subject to too great a stress, the object fractures
Under which law does an object exhibit elastic behaviour?
Hooke’s law
What type of graph stops being linear before an object fractures?
Tension-extension graph
What does a tension-extension graph show before an object that follow’s Hooke’s law fractures?
It stops being linear
What type of materials enter a plastic region and what does this occur to happen?
Ductile materials, meaning they’re permanently deformed by the tension
In which region are objects permanently deformed under tension?
The plastic region
What do ductile materials do to be permanently deformed by tension?
Enter the plastic region
What would show a more stiff object on a force-extension graph?
A steeper line
What would a steeper line on a force-extension graph show?
A more stiff object
How is the force-extension graph set out? Why?
Extension on the x-axis, force on the y-axis
Tensile testing machines are usually designed to apply a specific extension and measure the tension produced
What are tensile testing machines usually designed to do?
Apply a specific extension and measure the tension produced
What type of machines measure the tension of an object?
Tensile testing machines
What does the gradient on a force-extension graph show?
The stiffness of the object (spring constant for the spring)
On what type of graph is the gradient the stiffness of the object (spring constant for the spring) ?
Force-extension
What shows the stiffness of an object (spring constant for a spring) on a force extension graph?
The gradient
Spring constant
The force per unit extension
The force per unit extension
The spring constant
Hooke’s law equation
F = kx
What is the spring constant in Hooke’s Law’s equation?
K
(F = kx)
Spring constant unit
Nm-1
How do we work out the gradient?
Change in y
——————
Change in x
What does the area underneath show on a force-extension graph?
The work done stretching the object
(For elastic materials - the elastic potential energy stored)
What shows the work done stretching the object and For elastic materials - the elastic potential energy stored) on a force-extension graph?
The area underneath the graph
The area underneath which type of graph show the work done in stretching an object (or the elastic potential energy stored in elastic materials)?
Force-extension
For what type of objects does the area underneath a force-extension graph show elastic potential energy stored?
Elastic materials
Elastic potential energy
The energy possessed by an object when it has been deformed due to forces acting on it
The energy possessed by an object when it has been deformed due to forces acting on it
Elastic potential energy
Elastic strain
Strain that disappears when the stress is removed - the specimen returns to its original size and shape
Strain that disappears when the stress is removed - the specimen returns to its original size and shape
Elastic strain
Plastic strain
When a material is permanently deformed
Atoms have been re-arranged
Mainly in ductile materials
“When a material is permanently deformed due to atoms being re-arranged” - what type of strain is this?
Plastic strain
What type of materials experience plastic strain?
Ductile materials
How does a material become deformed during plastic strain?
Atoms become re-arranged
Brittle
A material that does not deform plastically (snaps before reaching this)
What type of material does not not deform plastically and what does it do instead?
Brittle materials
Snap before reaching this
Fracture
When the material breaks
Fracture can be ductile or brittle
When a material breaks
Fracture
What are the two forms of fracture?
Ductile or brittle fractures
Ductile
The ability of a material to deform plastically
A ductile material can be drawn into wires
What type of material can be drawn into wires?
Ductile materials
The ability of a material to deform plastically
Ductility
Deform
Change in shape due to a stress
Change in shape due to a stress
Deform
Stiffness
A measure of the materials resistance to deformation
Is related to Young’s Modulus
(Higher = stiffer)
A measure of a material’s resistance to deformation
Stiffness
What does a higher Young’s modulus mean?
A stiffer material
What figure would mean a stiffer material if it was higher?
Young’s modulus
Hooke’s law
The tension in a spring or wire is proportional to its extension from its natural length, provided the extension is not too great
The tension in a spring or wire is proportional to its extension from its natural length, provided the extension is not too great
Hooke’s law
What prevents the atoms of an object being pulled apart or pushed together?
The forces between the atoms
How much does an object extend by when a force is applied?
Δl
If a bar has its cross-sectional area increased to 2A, how much is the total F that needs to be applied for the same Δl?
2F
Which ratio must be kept the same if two bars of the same composition and length will be stretched by the same amount?
F/A ratio
What is “two bars of the same composition with the same length will be stretched by the same amount if the ratio F/A is the same” the definition for?
Tensile stress
What’s the symbol for tensile stress?
σ
What’s σ the symbol for?
Tensile stress
Tensile stress definition
The force per unit area applied when equal forces act on a body
The force per unit area applied
Tensile stress
Stress equation
Stress (σ) = force
———
Cross sectional area (m^2)
What’s F/A the equation for?
Stress
Unit of stress
Pa
What’s the total extension if two bars are welded end to end and why?
2Δl, as tension has the same value (F) in each half, so each half extends by Δl
Which ratio is the same for two bars of the same composition, same cross-sectional area and same tension?
Δl
—
l
Under which conditions is the Δl/l ratio the same?
With two bars of the same composition, the same cross-sectional area and the same tension
What is the Δl/l quantity known as?
Tensile strain
Tensile strain symbol
ε
ε meaning
Tensile strain
Strain equation
Strain (ε) = extension (Δl)
———————
Original length (l)
What’s extension (Δl). the equation for?
———————
Original length (l)
Strain
Units of strain
No units (remember to make this clear)
What’s proportional in the elastic region?
Force is proportional to extension
(Stress is proportional to strain)
In which region is force proportional to extension (stress proportional to strain)?
The elastic region
Young’s modulus in simple terms
How stiff a material is
Young’s modulus symbol
E
E symbol meaning
Young’s modulus
What does a higher Young’s modulus value mean for a material?
More stiff = less elastic deformation
What would show that a material is more stiff and what would this lead to?
A higher Young’s modulus value
Less elastic deformation
What type of material experiences less elastic deformation?
A stiff material
Young’s modulus equation (in data book)?
E = σ
—
ε
What’s E = σ the equation for calculating?
—
ε
Young’s modulus
How do we actually work out Young’s modulus?
E = Fl
—
AΔl
Units of Young’s modulus
Nm-2 or Pa
Which type of material has the highest Young’s modulus value?
Ceramics
Which material has a medium Young’s modulus?
Metals
Which type of material has the lowest Young’s modulus?
Polymers
Which two types of materials have the highest Young’s modulus values and why?
Ceramics and metals
Interatomic bonds (strong)
Which type of material has the lowest Young’s modulus value and why?
Polymers
Intermolecular bonds = weak
Which are the strongest - interatomic bonds or intermolecular bonds?
Interatomic bonds
How do we calculate elastic potential energy? Why?
Tensile force x extension
As work = force applied x distance in that direction
What’s the area underneath a force-extension graph?
Energy stored in the material
What shows the energy stored in the material in an extension-force graph?
Area underneath
The area underneath which type of graph shows the energy stored in the material?
Extension-force
What’s the equation for calculating the energy stored in a material/work done by it?
1/2fx OR 1/2kx^2
What are 1/2fx and 1/2kx^2 used for calculating?
The energy stored in a material
Which elements go across each axis on an extension-force graph?
Extension - x-axis
Force - y-axis
What do we do if the extension and force are along the wrong axes on an extension-force graph?
The spring constant is calculated as 1/gradient
When is spring constant calculated as 1/gradient
When the extension and force are along the wrong axis on an extension-force graph
What type of samples do we use for stress-strain curves?
Samples of uniform cross-sectional area
What do stress-strain curves analyse?
Te strength of solids under tension
What does the precise shape of the stress-strain curve vary with?
-type of material
-history of the material (e.g - heat or working treatment)
Draw and label a typical stress-strain curve
(Check notes)
What comes first on a stress-strain curve - the elastic limit or the limit of proportionality?
The limit of proportionality
Where on a stress-strain curve would the gradient be the Young’s modulus of the material?
On the limit of proportionality
What does the limit of proportionality show for a material and how on a stress-strain curve?
The gradient is the Young’s modulus of the material
How do we find out the Young’s modulus of a material on a stress-strain curve?
At the limit of proportionality
The gradient of which part of a stress-strain curve shows the Young’s modulus of the material?
The limit of proportionality
In which region on a stress-strain curve is the strain directly proportional to the stress and can deformation be reversed?
Elastic region
What is the relationship between stress and strain in the elastic region?
Directly proportional
What can occur to a material in the elastic region alone?
Deformation can be reversed