3 Deformation of Solids

elastic behaviour

the material will return to its original shape when the stress is removed

energy involved in elastic behaviour

all the work done to stretch the spring is stored as EPE

plastic behaviour

will not return to its original shape after deforming forces are removed

energy involved in plastic behaviour

work is done to move atoms apart so energy is not only stored as EPE but also dissipated as heat

fracture

caused by a strain placed on an object such that it deforms beyond its elastic limit and breaks

tension

a pulling force trying to extend (and then possibly break) a material

compression

a pushing force trying to squeeze/compress a material

elastic

the material will return to its original shape after the deforming forces have been removed (the part of the graph before the elastic limit)

plastic

when the load is removed the object will NOT return to its original shape (graph: after the elastic limit)

brittle

how soon after the yield point a material fractures. Failure will be through the propagation of cracks. A brittle material cannot absorb much energy before breaking.

ductile

can be easily drawn into a wire through necking and being put under tension (graph: ductile materials will have a large plastic region)

malleable

a measure of plastic behaviour under compression. It gives an indication of how easily a material can be worked (graph: malleable materials will have a large plastic region)

hardness

Hardness is a measure of a materials ability to resist impact or scratching.

stiffness

measures how much a material resists deformation. A measure of stiffness is the Young Modulus

strong

max force/stress that a material can withstand (UTS)

toughness

a measure of the ability of a material to resist failure through crack propagation. It is the opposite of brittleness. A tough material is able to absorb a lot of energy without breaking. energy is calculated by finding the area under the graph.

strength

often measured as the maximum stress a material can withstand before permanent deformation. This is known as the yield stress.

dislocation

additional 1/2 plane present in a crystalline structure

opposite of toughness

brittleness

examples of crystalline and polycrystalline materials

metals, ceramics diamond

examples of polymeric materials

rubber

examples of amorphous materials

glass

examples of composite materials

wood

crystalline materials

- large regular lattice
- long and short range order
- metals are regular lattices of ions with a sea of delocalised electrons
- interatomic bonds ionic or covalent

polycrystalline materials

have different crystals - grains - bound together at their boundaries

polymers

- long tangled up chains of molecules
- short range order, no long range order
- interatomic bonds are covalent, between strands there are weak van der waal bonds

amorphous materials

- no regular structure
- no long/short range order
- disordered weak covalent bonds
- tend to be brittle

edge dislocation

extra half plane of atoms inserted in a crystal structure

crystal slip

when a force is applied to an edge dislocation, the edge dislocation will make/break bonds and eventually move to the end of the row of atoms. plastic deformation due to the dislocation motion.

when does necking occur?

between the UTS and breaking point

metal structure

- positive ions in a sea of delocalised electrons
- during elastic deformation, spaces between ions get larger and smaller
- during plastic deformation planes of ions slip past one another
- movement of dislocations enables plastic deformation

three ways of hardening a metal

- quenching
- work hardening
- introduction of impurities

quenching

Heating a metal to a moderate temperature and then cooling it rapidly to make it harder and more brittle by making the grains smaller (since they don't have enough time to form). therefore there will be more boundaries and this will decrease the length an edge dislocation can travel.

introduction of impurities/alloying

- the addition of alloying atoms can pin a dislocation in place
- the metal is therefore no longer able to deform by dislocation movement.
- the material has greater yield stress and is less ductile

work hardening

- as a metal is deformed, the dislocations move through the structure
- the dislocations will reach the grain-boundaries or other dislocations which will inhibit their movement
- the metal becomes less ductile and more brittle

annealing

will increase ductility and decrease hardness.
- heat a metal above recrystallisation point, maintain a high temperature for a long time then cool slowly.
- reduction of edge dislocations.

polymer structure

- long chain molecules weakly held together by intermolecular forces
- initial force applied, difficult to move the polymer chains
- as the chains unravel they straighten out by bond rotation, relatively little force for a large increase in strain

stretching rubber

- initial high YM related to breaking weak VDW between strands
- lower YM relates to unfolding chains
- higher YM related to separating molecules

Elastic hysteresis

- area between the two curves is the energy transferred to internal energy, due to which the rubber band becomes warmer

tensile strain

Extension per unit original length

tensile stress

The force per unit cross-sectional area, measured in Pa

spring constant

force per unit of extension of a material during its proportional phase of deformation. The spring constant is often used as a measure of stiffness of an object