3.4 Materials Flashcards
How the force constant, k, be found from a force extension graph?
It is equal to the gradient. For rubber bands it varies and is indicated by the gradient of a tangent to the stretching curve.
State Hooke’s law.
The extension of a spring is directly proportional to the force exerted on it, as long as the limit of proportionality is not exceeded
What is the formula for Hooke’s law?
F = kx
State the formula to find the combined force constant, k꜀, for springs combined in parallel.
k꜀ = k₁ + k₂ + …
State the formula to find the combined force constant, k꜀, for springs combined in series.
1 / k꜀ = 1/ k₁ + 1/ k₂ + …
When two springs are placed in parallel, how does the force constant change?
It doubles.
When two springs are placed in series, how does the force constant change?
It halves.
On a force-extension graph, what does the area beneath the loading line represent?
The energy stored in the material as it is deformed
On a force-extension graph, what does the area beneath the unloading line represent?
The energy transferred back out of the material into external stores as the load is removed.
If a material obeys Hooke’s law, how would this be represented on a force-extension graph?
There will be a straight line through the origin.
What is the unit of stress?
The pascal (Pa)
What is the unit of strain?
It does not have a unit - it is a ratio.
What is the unit of Young’s modulus?
The pascal (Pa)
What is a material that behaves elastically?
A material that deforms when a force is applied, but returns to its original shape when the force is removed.
What is a material that has plastic behaviour?
A material that deforms when a force is applied, and stays in its deformed shape when the force is removed.
What is a brittle material?
A material which breaks through cracks / fracture with little plastic deformation.
What are tensile forces?
Forces which stretch / pull an object
What are compressive forces?
Forces that compress an object
What is a ductile material?
A material which undergoes large plastic deformation under tensile forces.
What is a malleable material?
A material which undergoes plastic deformation under compressive forces.
What is a tough material?
A material that can withstand large dynamic loads without breaking.
What is a hard material?
A material which is resistant to scratching. The harder a material is, the more difficult it is to dislodge atoms from its surface
What is a stiff material?
A material which requires a lot of force for only little deformation.
What is a strong material?
A material which can widthstand large static loads without breaking.
What is a polymeric material?
A material made from long chain molecules.
What is the difference between static and dynamic loads?
Static loads are applied gradually and don’t change in magnitude, while dynamic loads can change rapidly and exert more force.
Define the elastic limit of an object or material.
The point beyond which it becomes permanently deformed and will not return to its original length or shape once any forces are removed.
How can the Young’s modulus of a material be found from its stress-strain graph?
From the gradient of the initial straight-line section of its stress-strain graph.
What does the area under the straight line section of a material’s stress-strain graph represent?
The energy stored in the material per unit volume.
Define the Ultimate Tensile Stress (UTS) of a material. What does a higher UTS indicate?
The maximum stress the material experiences. This means it is a measure of the material’s strength; a higher UTS indicates a stronger material.
What type of material has a high Young modulus?
A stiff material.
What type of material has a high UTS and breaking point?
A strong material.
Describe a stress-strain graph for a typical ductile material.
After the limit of proportionality, There is a curve in the line before the elastic limit (from which the material starts to behave plastically).
Describe a stress-strain graph for a typical brittle material.
- The graph is linear with a steep slope, indicating that the material obeys Hooke’s Law up to its breaking point.
- There is little to no plastic deformation, and the material fractures suddenly after a small amount of strain.
Describe a stress-strain graph for rubber, a typical polymeric material.
The loading and unloading curves for rubber are different - the energy released when the rubber is unloaded is less than the work done to stretch the rubber. This is because some of the elastic potential energy in the rubber is converted to heat.
If a material obeys Hooke’s law, how would this be represented on a stress-strain graph?
It will have a straight line through the origin.
