Materials Flashcards
Density, p =
The density of a substance is defined as its mass per unit volume i.e. Mass/volume (kg/cm^3)
Hooke’s law defined with equation and units
the force needed to stretch a spring is directly is proportional to the extension of the spring from its natural length up to the limit of proportionally i.e. Force(N), F = k∆L where k is the stiffness/spring constant(N/m) and ∆L is the extension from natural length
Elastic limit
The maximum amount that a material can be stretched by a force and still return to its original length when the force is removed (if beyond then undergoes permanent deformation)
Tensile strain = (equation)
Extension per unit length/extension divided by original length
epsilon = ∆L/L
Tensile stress = (equation)
Force per unit cross-sectional area
Sigma = (T)ension/(A)rea(cross-section)
Pascals = 1 N/m^2
Energy stored =
0.5F∆L = area under force/extension graph
Ultimate tensile stress =
Breaking stress = The point at which the wire loses its strength and extends and becomes narrower at its weakest point
Elastic strain energy =
Area under curve
Compare the use of analogue and digital meters
Analogue more accurate but harder to read
Young modulus = (graph)
linear ratio of stress to strain = tensile stress/tensile strain = FL/A∆L (gradient of stress(y) strain(x) or force(y) extension(x)) = TL/A∆L = only in straight line so when Hooke’s law is obeyed = material property
(Pa) or (Nm^-2)
Elastic potential energy stored in a stretched spring=
work done to stretch the string = area under curve = 0.5F∆L = 0.5k∆L∆L
Deformation that stretches an object is _____ whereas deformation that compresses an object is _____
tensile
compressive
Spring force extension graph
Straight line y=mx due to hookes law
Polythene strip force extension graph
Gives and stretches easily after its initial stiffness to overcome however after giving easily, it extends little and becomes difficult to stretch
Rubber band force extension graph
Extends easily when it is stretched, however it becomes fully stretched and very difficult to stretch further when it has been lengthened considerably
Describe each stage of a stress(y)strain graph for a wire
0-limit of proportionality stress is proportional to the strain
Beyond the limit of proportionality, the line curves and continues beyond the elastic limit (the point beyond which the wire is permanently stretched and suffers plastic deformation) to the yield point, which is where the wire weakens temporarily. Beyond the yield point, a small increase in the stress causes a large increase in strain as the material of the wire undergoes plastic flow. Beyond the ultimate tensile stress (breaking stress), the wire loses its strength and extends and becomes narrower at its weakest point. Increase of stress occurs due to the reduced area of cross-section at this point until the wire breaks at the breaking point.
The stiffness of different materials can be compared using
the gradient of the stress-strain line = the Young modulus
The strength of a material can be seen on a graph by its
ultimate tensile stress which is the peak of the curve i.e. distance along y axis so stress
The brittleness of a material can be seen by
whether it snaps without significant yield i.e. short curve
The ductility of a material can be seen on a graph by
distance along the x axis so its stretchiness and strain
The ductility of a material can be seen on a graph by
distance along the x axis so its stretchiness and strain
What happens when a metal wire is extended beyond its elastic limit when it is unloaded/unextended
Curve descends parallel to x axis but not to origin showing it is slightly longer showing permenant extension
For a rubber band, the change of length during unloading for a given change in tension is
greater than during loading
Describe each stage of a stress(y)strain graph for a wire
0-limit of proportionality stress is proportional to the strain
Beyond the limit of proportionality, the line curves and continues beyond the elastic limit (the point beyond which the wire is permanently stretched and suffers plastic deformation) to the yield point, which is where the wire weakens temporarily. Beyond the yield point, a small increase in the stress causes a large increase in strain as the material of the wire undergoes plastic flow. Beyond the ultimate tensile stress (breaking stress), the wire loses its strength and extends and becomes narrower at its weakest point. Increase of stress occurs due to the reduced area of cross-section at this point until the wire breaks at the breaking point.
Rubber bands have a…
low limit of proportionality
A polythene strip has a… and suffers…
low limit of proportionality and suffers plastic deformation
The brittleness of a material can be seen by
whether it snaps without significant yield i.e. short curve
The ductility of a material can be seen on a graph by
distance along the x axis so its stretchiness and strain
The work done to stretch a rubber band =
area under loading curve
The work done during unloading of rubber band =
area under unloading curve
The area between the loading and unloading curve of a rubber band represents
the difference between energy stored and useful energy recovered which is the internal energy retained by the molecules when the rubber band unstretches
The area between the loading and unloading curve of a rubber band represents
the difference between energy stored and useful energy recovered which is the internal energy retained by the molecules when the rubber band unstretches
The area between loading and unloading curves of a polythene strip represents
the work done to permenately deform the material as well as the internal energy retained by the polythene when it unstretches
Polythene is a polymer which does not regain its original length after extension however rubber is a polymer which does regain its original length after extension, why?
Rubber is also a polymer but its molecules are curled up and tangled together when it is in an unstretched state. When placed under tension its molecules are straightened out. When the tension is removed, its molecules curl up again and it regains its initial length
The work done to stretch a metal wire or spring =
0.5T∆L
The work done to stretch a rubber band =
area under loading curve = F∆L/volume
The area between loading and unloading curves of a polythene strip represents
the work done to permenately deform the material as well as the internal energy retained by the polythene when it unstretches (thermal energy)
The area between loading and unloading curves of a polythene strip represents
the work done to permanently deform the material as well as the internal energy retained by the polythene when it unstretches (thermal energy)
1) Stiff =
2) Tough =
3) Brittle =
4) Hard =
5) Ductile =
6) Dense =
7) Fractures =
8) Plastic behaviour or deformation =
9) Yield strength =
10) Elasticity =
1) high stress to strain ratio i.e. Young’s modulus
2) resists fracture= a measure of the energy needed to break a material
3) snaps without stretching or bending when subject to stress i.e. low height
4) resists dents e.g. diamond
5) readily undergoes plastic deformation e.g. gold
6) high mass to volume ratio
7) when beyond the ultimate tensile strength and reaching breaking point it fractures
8) Plastic deformation or behaviour is a permanent deformation or change in shape of a solid body without fracture under the action of a sustained force.
9) stress at which a material starts to yield
10) the ability to regain its shape after it has been deformed
Young’ s modulus is the gradient of the straight line not the
curve
Spring’s transfer of energy throughout movement
Top = gravitational energy Bottom = elastic potential energy Middle = Gravitational, elastic and kinetic energy
The greater the value of k
the stiffer the spring
Young’s modulus is the gradient of the straight line not the
curve
Polythene -
low limit of proportionality
suffers plastic deformation
does not return to original length
work done in unstretching is therefore less than the work done in stretching
Stress-strain for a
Force-extension for a
material
object
What happens after the elastic limit
Beyond elastic limit means metal suffers permanent extension but still obeys Hooke’s law as it unstretches.
Stress-strain for a
Force-extension for a
material
object
As long as elastic limit is not reached…
all the stored elastic energy can be recovered
As long as elastic limit is not reached…
all the stored elastic energy can be recovered
Distance between origin and final point on unloading curve =
permanent extension
How to know if curve ductile or brittle
If permanently stretched, undergoes plastic deformation or does not break then ductile not brittle
How to know if curve ductile or brittle
If permanently stretched, undergoes plastic deformation or does not break then ductile not brittle
A student is asked to measure the mass of a rock sample using a steel spring, standard masses and a metre rule. She measured the un-stretched length of the spring and then set up the arrangement shown in the diagram below. Describe how you would use this arrangement to measure the mass of the rock sample. State the measurements you would make and explain how you would use the measurements to find the mass of the rock sample.
State and explain one modification you could make to the arrangement in the diagram above to make it more stable
Measure length of spring with metre ruler when it supports a known mass and the rock sample (repeat for different known masses). Plot a graph of mass against extension, read off mass corresponding to extension due to rock sample. To improve accuracy use multiple masses and use a set squire to measure the position of the lower end of the spring against the vertical ruler.
Use a clamp to fix the base of the stand to the table (clamp provides an anticlockwise moment about the edge of the stand greater than the moment of the object on the strong) to counterbalance the load.
Describe how to obtain, accurately by experiment, the data to determine the Young modulus of a metal wire
A long, uniform wire is suspended vertically and a weight, sufficient to make the wire taut, is fixed to the free end (the length is then measured with a ruler). Then increase the load gradually by adding known weights. As each weight is added, the extension of the wire is measured accurately with a ruler. Then measure the diameter of the wire with a micrometer and calculate the cross-sectional area using π (D/2)^2
• extension = extension length /original length (needed for six marks)
Vary mass, repeat readings, measure diameter in several places, use large length of wire to improve accuracy
Plot force against extension and draw the line
Measure gradient = EA/L
Divide by cross-sectional area and multiply by the original length to find the Young’s Modulus
A student is asked to measure the mass of a rock sample using a steel spring, standard masses and a metre rule. She measured the unstretched length of the spring and then set up the arrangement shown in the diagram below. Describe how you would use this arrangement to measure the mass of the rock sample. State the measurements you would make and explain how you would use the measurements to find the mass of the rock sample.
State and explain one modification you could make to the arrangement in the diagram above to make it more stable
Measure length of spring with metre ruler when it supports a known mass and the rock sample (repeat for different known masses). Plot a graph of mass against extension, read off mass corresponding to extension due to rock sample. To improve accuracy use multiple masses and use a set squire to measure the position of the lower end of the spring against the vertical ruler.
Use a clamp to fix the base of the stand to the table (clamp provides an anticlockwise moment about the edge of the stand greater than the moment of the object on the strong) to counterbalance the load.
A metallic wire is stretched. The curve looks like / that then bends narrower so it looks like a rigid letter r. Explain each point
Curve increases proportionally as wire obeys Hooke’s law up to the limit of proportionality. A bit further up it reaches its elastic limit and then it becomes narrower as it shows plastic behaviour (ductile). After the elastic limit when it increases at a lower gradient it will not regain its original length. Beyond this point it will reach the breaking point and the wire breaks
Gradient of stress-strain graph =
Young’s modulus = E
Gradient of force-extension graph =
E * A/L
Explain a brittle material on a force-extension graph and what it looks like and why
Material A: high force, high gradient, small extension - Brittle e.g. cast iron, glass, a brittle material deforms under load and breaks without significant deformation (often suddenly)
Explain a ductile material on a force-extension graph and what it looks like and why
Material B, Hooke’s law, elastic limit, plastic deformation, break point - ductile e.g. steel/copper, a ductile material is easily stretched without breaking or lowering in strength, ductile materials can also often withstand large forces, ductile materials have defined areas of plastic deformation, highly ductile materials can be drawn into long thin wires without breaking
Explain a polymeric material on a force-extension graph and what it looks like and why
Material C: Small force, large extension, small gradient - polymeric e.g. rubber, no linear region on force-extension graph, do not obey Hooke’s law
How graph shows material obeys Hooke’s law
Straight line
Through origin
