Chapter 3 Flashcards
What is the equation and symbol of stress?
> Stress = Force / Cross-sectional area
> Symbol: σ
What is the equation for strain?
Strain = Change in length / original length
What is Hookes law?
Force ∝ Extension
What is young’s modulus? (Not equation)
Stretching forces
What is the equation for youngs modulus? What is the symbol for young modulus?
Youngs Modulus = Stress/strain
Symbol: E
What is a better equation for stress?
σ = dF/dA
What is tensile stress?
This is stress that produces extension
What is uniaxial stress?
This is when the stress acts in a single direction
What is plane stress?
This is when the stress acts in a single plane (2 directions)
e.g. x & y or y & z or x & z
What is the poisson ratio?
> For compressive or tensile forces in a single plane which causes deformation to the volume of the object
Symbol v
What is the equation for poisson ratio for square objects? Explain it
> ν = - Lateral Strain / Direct Strain
Lateral strain is the change in the width (W) of the material
Direct strain is the change in the length (L) of the material
What are the units for the poisson ratio?
There are none
During uniaxial stress, what happens to the stress forces on the other sides of the object?
The other sides experience a compressive stress towards the centre of the object
What are the equations for strain in the direction of the axes of a square object experiencing uniaxial stress? (The stress applies in the x-axis direction)
Direct strain: εx= σx / E
Lateral strain: εy= -σxv/E and εz= -σxv/E
E = Youngs modulus
v = Poisson ratio
What are the equations for strain in the direction of the axes of a square object experiencing plane stress? (The stress applies to the x and y axes)
> Strain in X = σx/E - (v × σy)/E
Strain in Y = σy/E - (v × σx)/E
Strain in Z = - (v × σy)/E - (v × σx)/E
What are the equations for strain in the direction of the axes of a square object experiencing triaxial strain?
> Strain in X = σx/E - (vσy)/E - (vσz)/E
Strain in Y = σy/E - (vσx)/E - (vσz)/E
Strain in Z = σz/E - (vσy)/E - (vσx)/E
What is sheer stress?
This is when a force is acting on a tangent to the plane.
What is the symbol and equation for sheer stress?
> Symbol: τ
> Equation: τ = F/A and τ = dF/dA
What is sheer strain? What is the symbol and units?
> This is the deformation of an object due to a force acting perpendicularly.
Symbol: γ (Gamma)
Units: radians
How is sheer strain calculated for a square OACB?
> The angle AOB is calculated
After the sheer stress is applied the angle AOB is calculated again to give you A’OB’
Use the equation: γ = ∠AOB- ∠A’OB’
What is volumetric strain? What is the symbol?
> This is the change in the objects volume when a force is applied to it.
Symbol: e
What is the equation for volumetric strain?
e = (volume change)/(original volume) = (∆x×∆y×∆z)/xyz
How can volumetric strain be calculated from direct strain?
e= εx+εy+εz
What is thermal strain?
> This is produced when there is a restriction to the free change in the size of the material due to a temperature change.
What is the symbol for thermal strain?
𝛿
What is the equation for thermal strain?
𝛿 = αL(T-T0) > α = constant for linear thermal expansion > L = Original Length > T = Temperature > T0 = Original temperature
What is plane strain? How does this occur?
> This is when one dimensions length stays the same.
> The side that remains constant must have a force acting on it
What is poissons ratio for cylinders? Describe also how all the elements of the equation are found
v = εradial / εaxial εradial = ∆d/d > Where d is diameter εaxial = ∆L/L > Where L is length
What are the equations for strain in the radial direction of a cylindrical object experiencing axial strain?
εradial = -v × σaxial/R
What happens when the direct stress on a cube is compressive not tensile?
The strain on the other sides of the cube is negative (tensile)
What is the shear modulus? What is its symbol?
This is the relationship between shear stress and shear strain.
Symbol: G
What is the equation to calculate shear modulus?
G = τ/γ G = Shear stress / Shear strain
What is engineering stress?
True stress requires remeasuring the correctional area as the force changes. This is not possible to measure in real life so we use engineering stress.
We usually use materials in the elastic region where dimensional changes in the material are small and can be ignored. All we care about is the initial dimensions measured.
What is the equation for engineering stress?
σ = F/A0
What is Engineering strain?
The change in length of the an object experiencing stress might not be the same at all times, it might go up and down. True strain is the integration of δL/L so accounts for all changes in the length of an object.
Engineering strain is just the final change in length of an object divided by the initial object length.
What is the equation for engineering strain?
ε =δL/L
What is the unit for youngs modulus?
Nm^-2
Pa
What is viscoelasticity?
> This is for non-perfect elastic materials and is when a material loses energy when a load is removed.
Also called dampening
What is creep?
This is when the applied stress is greater than you back stress so the material deforms
What is back stress?
> This is what causes the material to return to its original shape.
This is the internal stress caused by the rearrangement of polymer fibres in the material
Using polymers as an example, explain the action of back stress
When a tensile load is applied to a polymer, it causes the polymer chain molecules to move around and rearrange. This is hard to do and causes a back stress within the material preventing it from stretching. When the load is removed, the back stress within the material brings the material back to its original shape.
What is material resilience?
This is the ability of a material to absorb energy when deforming elastically and return it when unloaded.
What is the symbol and unit for resilience?
Symbol: U0
Unit: Jm^-3
What is the equation to calculate resilience?
U0 = 0.5σε
What is compressibility? What is its symbol and unit?
This is a measure of how easily a material can be compressed.
Symbol: C
Unit: m^2N^-1 (m^2/N) (inverse of pascals)
What is the equation to calculate compressability?
C = Volumetric strain / Stress C = (δV/V) / (F/A)
When does compressibility occur?
When a force is applied to all sides of an object
What is bulk modulus?
The inverse of compressibility and is related to material density.
What is the symbol and unit for bulk modulus?
Symbol: K
Unit: Nm^2
What is the equations to calculate bulk modulus? (2)
K = 1/C K = (F/A)(∆V/V)
What happens to bulk modulus as δV ⇒ 0?
K ⇒ ∞
What does a bolt in single shear mean?
The most simple use of a bolt. Two plates connected together by a bolt.
What is the equation for single shear stress?
τ = Total bearing force (P) / ((πd^2) / 4)
Total bearing force = The force applied by the plates
What does a bolt in double shear mean?
This is when there are 3 plates connected to the bolt in an alternating pattern. The two on the outside are connected together and take a single force. The other plate in the middle takes an equal but opposite force.
What is the equation for double shear stress?
τ = 0.5 × Total bearing force (P) / ((πd^2) / 4)
What is bearing stress?
This is the force on the area of pin that a plate surrounds.
What is the equation for bearing stress?
σ = Total bearing force (P) / (Plate thickness × Bolt diameter)
