4.2 - Solid Material Properties

Question 1

What’s is tension

Answer 1

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

Question 2

What does a tensile force cause

Answer 2

Causes extension

Question 3

What does a compressive force cause

Answer 3

A negative extension

Question 4

What does hookes law say bab

Answer 4

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

Question 5

What’s the elastic limit

Answer 5

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.

Question 6

What’s the mathematical version of hookes law

Answer 6

Force applied = stiffness constant x extension

Triangle F = k x triangle X

Question 7

What else is the stiffness constant referred to

Answer 7

The spring constant - either phrase refers to K in hookes law equation

Question 8

How can we investigate Hookes law - practical

Answer 8

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

Question 9

Tell me about elastic strain energy and calculating it

Answer 9

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)

Question 10

How can we calculate the work done from force-extension and force- compression graphs

Answer 10

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

Question 11

What happens if you want to calculate worm done from a force extension / compression graph but it’s non linear / curved line

Answer 11

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

Question 12

Define tension / tensile force

Answer 12

Tension is a force acting within a material in a direction that would extend the material

Question 13

Define extension

Answer 13

Is an increase in size of a material sample caused by a tension force

Question 14

Define compression

Answer 14

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

Question 15

Define the limit of proportionality

Answer 15

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

Question 16

Define the elastic limit

Answer 16

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

Question 17

Define spring constant

Answer 17

The spring constant is the hookes law constant of proportionality, k, for a spring under tension

Question 18

Define hysteresis

Answer 18

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

Question 19

Define plastic behaviour / plastic deformation

Answer 19

a permanent deformation or change in shape of a solid body without fracture under the action of a sustained force

Question 20

Define elastic behaviour/ elastic deformation

Answer 20

If the material is elastic, the object will return to its initial shape and size when these forces are removed

Question 21

Why can’t we just use F = kx/ hookes law to compare materials

Answer 21

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

Question 22

What is stress

Answer 22

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

Question 23

What is strain

Answer 23

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

Question 24

What is Young Modulus

Answer 24

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

Question 25

What’s the difference between stiffness constants k and E

Answer 25

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

Question 26

What’s the difference between elastic limit and limit of proportionality

Answer 26

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

Question 27

Define stress

Answer 27

Stress (pascals, Pa, or N/m^2) = force / cross sectional area

Sigma = F / A

Question 28

Define strain

Answer 28

Strain, (no units) = extension / original length

Epsilon = triangle x / x

Question 29

Define young modulus

Answer 29

The young modulus is the stiffness constant for a material, equal to the stress divides by its corresponding strain

Question 30

Tell me some features of a stress strain graph (stress- strain analysis)

Answer 30

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

Question 31

How can stress decrease ??

Answer 31

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.

Question 32

Describe some typical points on a stress strain graph

Answer 32

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

Question 33

What’s Ultimate tensile stress

Answer 33

It represents the highest value that stress can ever attain within this material - ultimate tensile stress or UTS or sigma subscript u

Question 34

What’s the fracture stress or breaking stress

Answer 34

It’s the value that the stress will be in the material when the sample breaks or fractures

Question 35

How can we investigate stress strain relationship for metals

Answer 35

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
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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

Question 36

Toughness is…

Answer 36

Is a measure of how much energy a material can absorb before it breaks

Question 37

Material strength is…

Answer 37

How high the line goes on a stress strain graph - higher the ultimate tensile stress, the stronger it is

Question 38

The stiffness is

Answer 38

How flexible a material is, the gradient of a stress strain graph for a material is larger for stiffer materials with higher young modulus

Question 39

Low maximum strain means

Answer 39

The material is brittle !

Question 40

Plastic deformation when stress is compressive stress means

Answer 40

The material is malleable

Question 41

Plastic deformation when stress is tensile stress…

Answer 41

Means the material is ductile