Materials Flashcards
Define Hooke’s Law:
The extension of a spring is directly proportional to the force applied up to the limit of proportionality.
Define elastic deformation:
When a material returns to its original length when a load is removed.
Define plastic deformation:
When a material has a permanent change in length/shape when the load is removed.
Define the elastic limit:
The maximum amount a material can be stretched and still return to its original length. Beyond this limit the deformation will no longer be elastic but plastic.
This point is always after the limit of proportionality.
How to calculate the force from springs in series?
The force acting through each spring is the same:
F = F = F
How to calculate the force from springs in parallel?
The force is split between the springs:
Total F = F1 + F2
For the number of identical springs, n, in parallel, how do you calculate the spring constant for the system?
In parallel, the spring constant for the system is nk
What is the spring constant of a system for a number, n, of identical springs in series?
In series, the spring constant for the system is k/n
Definition of stress:
Stress (Nm^-2) = Force applied / Cross sectional area
Sigma = F/A
Definition of strain:
Strain (no units) = extension/original length
E=x/L
Definition of Young’s Modulus:
Young’s Modulus (Nm^-2) = Stress/Strain
Definition of a ductile material:
A material that can be stretched into a wire or hammered into sheets and will both elastically and plastically deform.
Definition of a Polymeric material:
Never obeys Hooke’s law yet elastically deforms and can stretch a great deal before fracture; consists of long molecular chains.
Definition of a brittle material:
Brittle materials such as glass, obeys Hooke’s law, only elastically deforms before the material breaks.
Limit of Proportionality:
The maximum stress for a linear stress-strain relationship Beyond this point, Hooke’s law is no longer true i.e. the extension is no longer proportional to the applied force.
Ultimate Tensile Strength:
The maximum stress that a material can withstand before fracture
Breaking stress/breaking strength
The stress the material experiences before it fracture.
Yield point
The stress level at which a material transitions from elastic to plastic deformation.
Define elastic potential energy:
Elastic potential energy = 1/2Fx
Elastic potential energy = 1/2kx^2
How do you write cross sectional area of a circle in terms of diameter not radius?
A = (pid)^2/4
Compare a stress-strain graph for a stiff and less-stiff material:
Stiff material has a higher gradient
On which axes should stress and strain be plotted for the gradient of the line to give the Young modulus?
Stress on y-axis, strain on x axis
What property does the force constant describe?
Stiffness (higher force constant = stiffer)
Give the force constant for two springs in parallel in terms of their individual force constants?
k = k1 + k2
What is represented by the area enclosed by the loading and unloading lines for a force-extension graph for a polymer?
Energy transferred to the thermal energy store of the polymer and surroundings.
Give the force constant for two springs in series in terms of their individual force constants:
1/k = 1/k1 + 1/k2
What do the gradient and area under the line represent on a stress-strain graph?
Gradient is Young modulus, area under line is energy stored per unit volume.
Compare a stress-strain graph for a strong and weak material:
Breaking point for a strong material has higher stress.
