1.5 Solids under Stress

Question 1

Define the spring constant.

Answer 1

● The force per unit extension required to stretch a spring.
● Denoted by k.
● Inherent property of the spring.

Question 2

State Hooke’s law

Answer 2

Extension (denoted by ∆L or 𝑥) is directly proportional to force applied (F), given that the environmental conditions are kept constant.
F= k∆L, where k is the spring constant in Nm-1

Question 3

What is meant by tensile stress?

Answer 3

The force applied per unit cross-sectional area Stress, σ = F/A
Stress units: Nm-2
Force units: N
Cross-sectional area units: m2

Question 4

What is tensile strain?

Answer 4

A measure of how a material stretches. It is equal to the extension (ΔL) divided by the original length (L). Since strain is a ratio, it has no units.

Strain, ε = ΔL / L

Question 5

What is the difference between elastic and plastic deformation?

Answer 5

Elastic deformation: when the force is removed the object will return to its original shape.

Plastic deformation: after the load is removed the object will not return to its original shape. It has been stretched beyond its elastic limit.

Question 6

What is breaking stress?

Answer 6

The minimum stress needed to break a material.

Question 7

Answer 7

Question 8

What is meant when a material is described as brittle?

Answer 8

It does not extend much when a force is applied (tensile strain stays low). The material tends to break rather than stretch under a large force.

Question 9

What is the elastic limit?

Answer 9

The point after which plastic deformation occurs. It is also sometimes referred to as the ‘limit of proportionality’.

Question 10

What does the area underneath a force-extension graph represent?

Answer 10

The energy stored in the material.

Question 11

Give the equation that calculates elastic strain energy in terms of the spring constant and extension.

Answer 11

E = 1⁄2 k ΔL^2

Question 12

What is Young’s modulus?

Answer 12

Young’s modulus = tensile stress / tensile strain

Question 13

How do you find the Young’s modulus from a stress-strain graph?

Answer 13

Using the gradient of the line.

Question 14

Answer 14

Question 15

How can a force-extension graph show Hooke’s Law is being obeyed?

Answer 15

When it is a straight line through the origin – force and extension are directly proportional.

Question 16

What is the limit of proportionality and what does it look like on a force-extension graph?

Answer 16

The point after which Hooke’s law is no longer obeyed. It is shown by the line beginning to curve on a force-extension graph.

Question 17

What is meant by elastic strain?

Answer 17

Strain that disappears when a stress is removed – the material returns to its original shape.

Question 18

What is meant by plastic (or inelastic) strain?

Answer 18

Strain that decreases only slightly when stress is removed. The material does not return to its original shape.

Question 19

How is the work done to stretch or compress a material stored?

Answer 19

It is stored as elastic strain energy.

Question 20

Why are the loading and unloading lines parallel on a force-extension graph for a plastically deformed material?

Answer 20

The stiffness constant (k) has not changed - the forces between the atoms are the same when loading and
unloading.

Question 21

Why isn’t all work done stored as elastic strain energy when an object undergoes plastic deformation?

Answer 21

Work is done to move atoms apart, so energy is not stored as elastic strain energy.

Question 22

How is the dissipation of energy in plastic deformation used to design safer vehicles?

Answer 22

●Crumple zones deform plastically in a crash using the car’s kinetic energy, so less energy is transferred to the passengers.
● Seat belts stretch to convert the passenger’s kinetic energy into elastic strain energy.

Question 23

Outline the energy changes that occur when a spring fixed at the top is pulled down and released.

Answer 23

The work done in pulling the spring down (stretching it) is stored as elastic strain energy. When the spring is released, this is converted to kinetic energy, which is then converted to gravitational potential energy as the spring rises.

Question 24

Do stress-strain graphs show the behaviour of a material or a specific object?

Answer 24

Material.

Question 25

Where would you find the ultimate tensile stress on a stress-strain graph?

Answer 25

The highest point on the graph. It is the maximum stress a material can withstand.

Question 26

What is a ductile material?

Answer 26

A material that can be drawn out into a wire – plastic deformation occurs when there is enough stress.

Question 27

What is meant by ductile fracture (necking)?

Answer 27

The process of fracture in a ductile material: there is local thinning, which increases the stress (as the area decreases and stress = force / area), before the material breaks.

Question 28

What would the stress-strain graph for a ductile material look like?

Answer 28

Question 29

What is a brittle material?

Answer 29

● A material that does not plastically deform.
● Under tension, the material fractures.

Question 30

What is meant by brittle fracture?

Answer 30

● The fracture of brittle materials when they are put under tension.
● This occurs by cracks spreading throughout the material.

Question 31

What is elastic hysteresis?

Answer 31

When a material (e.g. rubber) is put under stress and then the stress is removed, the stress-strain graphs for loading and unloading do not overlap but form a loop.

Question 32

What is a crystal?

Answer 32

● A solid in which the atoms are arranged in a regular array.
● There is a long-range order, meaning that there is a pattern that repeats itself
periodically over the entire crystal.

Question 33

What is a crystalline solid?

Answer 33

● A solid made of one or many crystals (usually arranged randomly).
● In cases where it is made of many crystals, it is called a polycrystalline solid
(e.g. metals).

Question 34

What is an amorphous solid?

Answer 34

● A solid in which the atoms are arranged randomly.
● These are rare, so in practice, solids like glass or brick (that have no long-range order) are referred
to as amorphous.

Question 35

What is a polymeric solid?

Answer 35

A solid that is made up of chain-like molecules.

Question 36

What is meant by dislocations in crystals?

Answer 36

Faults in crystal structures which reduce the stress required for planes of atoms to slide (if there are not too many faults).

Question 37

What is meant by grain boundaries?

Answer 37

The boundaries between crystals (grains) in a polycrystalline material.