Solids under Stress Flashcards
What is tension?
The magnitude of the force that a stretched object exerts on whatever its end are attached to.
This is equal to magnitude of the force which is applied to the ends of an object to keep it stretched
What is extension?
The increase in the length of an object when put under tension
When is a material elastic?
If it returns to its original shape and size if the tension is removed
What is the elastic limit?
The point at which the deformation ceases to be elastic
What is Hooke’s law?
Provided the elastic limit is not exceeded, the extension of a spring is directly proportional to the tension
F=kx
What is the spring constant?
The force per unit extension of the spring, the stiffness of the spring
What is stress?
The tension per unit cross-sectional area
What is strain?
The tension per unit length due to the applied stress
What is the Young modulus?
E - the ratio of stress to strain for a material in the Hooke’s law region - usually in the value of around 10-200 GPa
How do you calculate the work done in stretching out a spring?
F=0.5kx^2
Area under a tension-extension graph
Define crystalline
consisting of crystals;regular array of particles (usually ions)
What is a crystalline material?
long range, regular (unit cell repeated)
Solid with a long range order
particles in a regular arrangement called a lattice
Define polycrystalline
consisting of a large number of interlocking crystals
What are polycrystalline metals?
Most frequent crystalline engineering materials
Lattice particles in metals are spherical metal ions arranged hexagonally in the lattice planes
Why are particles arranged hexagonally?
This gives maximum possible number of near neighbours so the potential energy of the hexagonal lattice is the lowest possible
This is the same as the plane below, so each ion is in contact with 12 near neighbours (maximum possible)
Why do crystal planes in a metal have random orientations?
A piece of metal is made up of lots of crystals which all started to form seperately from molten state
What is a metal?
A condensed material (solid or liquid) in which the atoms have lost one or more electrons to become positive ions, which are held together by the released ‘delocalised’ electrons
What are amorphous materials?
short range, irregular
Materials with no long range order, because when they were cooled they didn’t have time to assume a crystal arrangement before they lost the ability to move
What are ceramics?
Not usually formed from molten state
Partly crystalline with an amorphous matrix
Consist of molecules of metals and non-metals, with either covalently or ionically bonded
What is a polymer?
A material comprising large molecules which consist of many repeat units
What is a monomer?
A molecule which can combine with other molecules to form a polymer
Has one or more double bonds
A material is plastic if…
when the stress is removed the material is permanently deformed
What is a ductile material?
A material which can be drawn into a wire
What is the elastic limit?
The stress at which the deformation ceases to be elastic
What is the yield point?
The point on a stress-strain graph at which a large increase in strain occurs for little or no increase in stress
Yield stress
The stress at the yield point
What might you need to label on a stress-strain graph?
Limit of proportionality Elastic limit Yield point Yield stress Breaking stress Breaking point
What is an edge dislocation?
an additional part-plane of ions in a crystal
if a large enough force is applied (stress exceeds yield stress) the dislocation will move irreversibly and the crystal will suffer permanent deformation
Easy ductile metal to draw a stress-strain graph for
Steel
How can edge dislocations form large deformations?
Large stresses can cause a crystal plane to snap at a point of weakness (missing ion) producing two edge dislocations, which migrate in opposite directions, making the crystals elongate in the direction of the stress
What can strengthen and stiffen a material?
Foreign (impurity) atoms, grain boundaries and other dislocations impede the movement of edge dislocations
What is ductile fracture?
Breaking that occurs when a ductile material is stressed to a breaking point. Involves plastic deformation and necking
As the stress reaches the breaking stress, more edge dislocations are generated and migrate, causing the elongation. A decreases so stress increases, causing more dislocations in a runaway process
Are brittle materials elastic?
YES
What are reasons for brittle materials having no mobile edge dislocations?
They are amorphous (no regular lattice) eg glass
They are ionically or covalently bonded eg ceramics
They are metallic but have very small crystals with large numbers of impurities eg cast iron
Why are materials brittle under tension?
They have microscopic cracks in the surface and no mobile edge dislocations to relieve the stress
How are brittle materials used in engineering?
Propagation of cracks must be avoided
In concrete and brick structures the brittle material is always under compression so the cracks do not open up
How is pre-stressed concrete made?
Pouring concrete around steel rods under tension, and the rods are slackened off when the concrete has cured, putting the concrete under compression
How is pre-stressed glass manufactured?
A rapid cooling of the surface and a later cooling of the core puts the surface under compression, so a tension can be applied without the crack-bearing surface being put under tension.
What is elastic hysteresis?
When a material such as rubber is put under stress and then relaxed, the stress-strain graphs for increasing and decreasing stress do not coincide but form a loop
In a hysteresis loop what does the area between the graphs represent?
Energy dissipated in moving - manifests itself as random vibrational energy of rubber molecules
What happens in elastic hysteresis?
First it straightens out the molecules - no bonds are stretched. Then it stretches the bonds. When it’s relaxed, natural vibrations of molecules tangles up the long chains again
What is vulcanisation?
Introducing cross-linkage between molecules or different parts of the same molecule
Polymeric
long chain molecules (no order between, only
within molecules)
