C6 (Materials) Flashcards
Equation for young modulus
E = stress / strain = Fx/a change in x
N/m^2
Equation for stress
Units
Force/ area
N/m^2
Strain equation
Change x / x
(Change in length/ o.g length)
Unit less
In stress-strain graphs the steeper (higher) the gradient the greater the…
Greater the young modulus
In a stress-strain graph what does the ‘P’ stand for?
P is the limit of proportionality, where the linear relationship between stress and strain ends
In a stress-strain graph what does the ‘E’ stand for?
Elastic limit
Below the elastic limit the wire would have returned to its original shape
In a stress-strain graph what does the ‘Y’ stand for?
Yield point
Where plastic deformation begins. A large increase in strain is seen for a small increase in stress
In a stress-strain graph what does the ‘UTS’ stand for?
Ultimate tensile stress
The materials maximum resistance to fracture
In a stress-strain graph what does the ‘S’ stand for?
The point where the wire snaps (called breaking stress).
Tensile forces
Forces that produce extension
Compressive forces
Those that shorten an object
When do helical springs undergo tensile deformation
When tensile forces are exerted on it
When does a helical spring undergo compressive deformation
When compressive forces are exerted
How does the force extension graph look like
A straight like from the origin up to the elastic limit (directly proportional). The linear region where the spring is undergoing elastic deformation (meaning that it will return to its original length). Beyond this point the spring begins to undergo plastic deformation (permanent structural changes).
When does Hookes law apply
For forces less than the elastic limit of the spring
Hookes law states:
The extension of the spring is directly proportional to the force applied. Only true if the elastic limit isn’t exceeded.
For a spring obeying Hookes law, the applied force F is directly proportional to
The extension, x
F directly proportional to x
F=kx
In Hookes law what does the constant k stand for
The spring constant
This is the measure of the stiffness of a spring.
What else can you use the equation F=kx for
For a compressible spring (x then represents the compression of the spring).
In a force-extension how can you find the value of the spring constant, k
The gradient of the linear region
Hooke’s law can be applied to almost any object that…
Can be elastically squashed or extended
When a material is compressed or extended without going beyond elastic limit, what can happen to the work done on the object
It can be fully recovered
If the material has gone through plastic deformation, then what happens to the work done?
So of the work done on the material has gone into moving it’s atoms to new permanent positions, this energy is not recoverable.
The work done equation by a force in extending the spring
Work done = force x change in x
What is the area underneath a force-extension graph equal to?
Work done
What’s the equation for elastic potential energy
E= half Fx
You can also interpret the equation as work done = average force x final extension
What’s another equation for elastic potential energy (after substituting hookes law)
E= half kx^2
For a given spring E is directly proportional to extension squared. So doubling the extension does what to the extension stored?
Quadruples it
Metal wire (loading and unloading graph)
Loading graph follows hookes law until the elastic limit. Unloading graph will be identical for forces less then the elastic limit. However beyond the limit its parallel to the loading graph but not identical.
Rubber bands (loading and unloading graph)
Rubber bands do not obey Hookes law. The rubber band will return to its original length after the force is removed (elastic deformation), but the loading and unloading graphs are both covered in a different.
Polythene (loading and unloading graph)
A polythene strips don’t obey Hooke’s law. Thin strips of polythene very easy to stretch and they suffer plastic deformation under relatively little force, they do not return to their original size after being stretched.
Brittle
Material that fractures with plastic deformation first (just snaps)
Strong
Resists both deformation and failure (withstands a lot of force).
Ductile
Deforms before it breaks
Hard
Resists dents, scratches and other permanent changes under compressive force
Weak
Low UTS (opposite to strong)
Tough
Can take lots of Kinetic force
Soft
Easily dented/ scratched
Malleable
Can easily change shape
