4.2 - Solid Material Properties Flashcards
What’s is tension
Whenever a force acts on a material sample, the sample will be deformed to a different to a different size or shape - if the new shape is longer, the force is referred to as tension
The extra length is known as extension
What does a tensile force cause
Causes extension
What does a compressive force cause
A negative extension
What does hookes law say bab
Hookes law states that the force needed to extend a spring is proportional to the extension of the spring, a material only obeys hookes law if it has not passed what is called the limit of proportionally
The line must go through the origin and be directly proportional
What’s the elastic limit
OKUUURRRrrrrh
If an object is subject to only a small force, it will deform elastically - when the force is removed, it returns to its original size and shape, providing the elastic limit was not passed.
What’s the mathematical version of hookes law
Force applied = stiffness constant x extension
Triangle F = k x triangle X
What else is the stiffness constant referred to
The spring constant - either phrase refers to K in hookes law equation
How can we investigate Hookes law - practical
You can perform a single experiment to measure the stiffness constant for a spring
By hanging various masses on a spring and measuring the corresponding extensions, you can gather a set of results for triangle F and triangle X
In each case you could calculate the spring constant from a pair of readings, but you will get more accurate results / final answer for K if you plot a graph and find its gradient which will be equal to K - but only gradient up to the elastic limit
Tell me about elastic strain energy and calculating it
The work done (energy transferred) in deforming a material sample before it reaches its elastic limit will be stored within the material as elastic strain energy
Work done can be calculated by force x distance in direction of force - this is still true in deforming materials, but hookes law means that the force value varies with differnt extensions
If we plot the extension against increasing force on a graph, the graph will follow hookes law - to find the work done to extend the spring a certain amount, we must calculate it using the average force over distance of extension
Therefore, elastic strain energy / work done = 0.5 x F x triangle X ( or area under the graph)
How can we calculate the work done from force-extension and force- compression graphs
The work done in deforming materials is calculate by multiplying the extension or compression by an appropriate average force value
If the force is varying in a non linear way, which is common for some materials, finding the average force may not be a straight forward process
The area between the line on a force-extension graph and the extension axis will represent the work done
If it’s a linear relationship then area is just formula for triangle
Elastic strain / work = 0.5 x K x X
You can add up different sections to get total energy for a given extension
What happens if you want to calculate worm done from a force extension / compression graph but it’s non linear / curved line
Finding the area may involve estimating or counting the squares on the graph paper under the line
In this case, will also need to multiply the number of squares by the elastic strain energy value ( f x X) for each individual square
Define tension / tensile force
Tension is a force acting within a material in a direction that would extend the material
Define extension
Is an increase in size of a material sample caused by a tension force
Define compression
Compression is a force acting within a material in a direction that would squash the material. Also, the decrease in size of a material sample under a compressive force
Define the limit of proportionality
The limit of proportionality is the maximum extension (or strain) that an object (or sample) can exhibit, which is still proportional to the load (or stress) applied
Define the elastic limit
A materials elastic limit is the maximum extension or compression that material can undergo and still return to its original dimensions when the force is removed
Define spring constant
The spring constant is the hookes law constant of proportionality, k, for a spring under tension
Define hysteresis
For the extension of a material sample, hysteresis is where the extension under a certain load will be different depending on its history of past loads and extensions
Define plastic behaviour / plastic deformation
a permanent deformation or change in shape of a solid body without fracture under the action of a sustained force
Define elastic behaviour/ elastic deformation
If the material is elastic, the object will return to its initial shape and size when these forces are removed
Why can’t we just use F = kx/ hookes law to compare materials
It doesn’t consider the forces in context of there dimensions
And doesn’t consider properties of materials themselves
Eg. A thin metal wire will extend with less force compared to a thicc block
What is stress
Tensile (or compressive) stress is a measure of the force within a material sample, but it takes account of the cross sectional area across the sample, this allows force comparisons to be made between samples of different sizes, so that they can be measured under comparable conditions
Stress (sigma symbol)(in Pa or N/m^2) = force / cross sectional area
Sigma symbol = F/A
What is strain
Tensile (or compressive) strain is a measure of the extension (or compression) of a material sample, but it takes account of the original length of the sample. This allows extension comparisons to be made between samples of different sizes, so that they are measured under comparable conditions
Strain (no units) = extension / original length
^^ units cancel out as strain is a ratio, often expressed as a percentage by multiplying ratio by 100
Curly E (elipson) = triangle x / x
What is Young Modulus
If a material is deformed elastically, stress will be proportional to strain, with a constant of proportionality that is a measure of the STIFFNESS of the material - how much it deforms under certain stress
The stiffness constant is called the young modulus so thus, young modulus is a measure of the stiffness of a material, which takes account of the shape and size of the sample, so that different samples of the same material will all have the same value for young modulus.
Thus, we can compare materials !
Young modulus, E = stress / strain
Measured in pascal
E = sigma/ epsilon
Definition also includes the fact that the material must be undergoing elastic deformation. Beyond the limit of proportionality, this equation will no longer work to calculate the stiffness of a material
What’s the difference between stiffness constants k and E
The stiffness constant, k, from hookes law relates to a particular object, such as a spring.
For a material, young modulus E, Is the stiffness constant for the material in general, regardless of sample size
What’s the difference between elastic limit and limit of proportionality
elastic limit is strain below which the material can regain its original shape if the forces are released, doesn’t matter if the stress-strain relation is linear or not! A material can have reached the elastic limit but is still acting elastically
Whereas, proportional limit is strain below which the stress is proportional to strain i.e. linear relation between the two
Define stress
Stress (pascals, Pa, or N/m^2) = force / cross sectional area
Sigma = F / A
Define strain
Strain, (no units) = extension / original length
Epsilon = triangle x / x
Define young modulus
The young modulus is the stiffness constant for a material, equal to the stress divides by its corresponding strain
Tell me some features of a stress strain graph (stress- strain analysis)
Stress on y axis
Strain on x axis
From the definition of the young modulus, the stress should be proportional to the strain if a material is undergoing elastic deformation, so we should get a straight line graph if we plot stress against strain, in practice we do find a straight line relationship for small stresses.
Once the limit of proportionality is passed, the internal structure of the metal starts to behave differently, and this means the graph starts to curve.
Depending on the material under test, the graph will go through various phases as the molecular substructure of the specific material determines its response to increasing stress.
Eventually the stress will become too great, and material will fracture and line on graph must end
How can stress decrease ??
The stress can go down if there is a change in the arrangement of the atomic structure of the material,using engineering stress - there can be a drop in stress
However with true stress, there is no drop as CSA will increase when above elastic limit and so increase stress
When using engineering stress and the CSA decreases so much that the force necessary to keep deforming the force decreases and we keep using the same CSA(when in reality it’s changed) , as a result engineering stress decreases.
Describe some typical points on a stress strain graph
In the straight line portion - metal extends elastically, and will return to its original size and shape when force is removed - gradient equal to young modulus
beyond the straight line portion, is the limit of proportionality- slightly beyond this, the metal may still behave elastically, but it cannot be relied upon to increase strain in proportion to the stress
The elastic limit occurs after, beyond this point the material is permanently deformed and will not return to its original shape and size when the deforming force is released
After is the YIELD POINT, beyond which the material undergoes a sudden increase in extension as its atomic substructure is significantly reorganised, the realignment / slip of the metals atoms reduces the internal stresses causing a large jump in strain - the material is behaving plastically
Ultimate tensile stress and fracture stress are after
OFTEN the limit of proportionality, elastic limit and yield point are the same
What’s Ultimate tensile stress
It represents the highest value that stress can ever attain within this material - ultimate tensile stress or UTS or sigma subscript u
What’s the fracture stress or breaking stress
It’s the value that the stress will be in the material when the sample breaks or fractures
How can we investigate stress strain relationship for metals
You can preform a simple experiment to measure the stiffness constant - young modulus - for a metal by stretching a thin wire. The original length and diameter of the wire must be measured first. Then, using increasing forces as the independent variable, you will need to take measurements of the extension corresponding to each force - there will be some regions which increase uniformly. Beyond the elastic limit, it will increase with greater extensions with each increase in the load force until eventually fracture stress will be reached and wire will snap
WEAR SAFETY GOGGLES
plot a graph of stress on y axis against strain on x axis so gradient is young modulus - In normal practice you plot independent variable on x axis but it’s easier to call calculate gradient with stress (independent) on y axis
Toughness is…
Is a measure of how much energy a material can absorb before it breaks
Material strength is…
How high the line goes on a stress strain graph - higher the ultimate tensile stress, the stronger it is
The stiffness is
How flexible a material is, the gradient of a stress strain graph for a material is larger for stiffer materials with higher young modulus
Low maximum strain means
The material is brittle !
Plastic deformation when stress is compressive stress means
The material is malleable
Plastic deformation when stress is tensile stress…
Means the material is ductile
