3.4.2.2 The Young modulus Flashcards
What is the young modulus?
Tensile stress/ tensile strain
How do you find the young modulus from a graph of stress against strain?
Gradient
What does the area under a graph of stress against strain represent?
Strain energy per unit volume
What is the formula of energy per unit volume?
0.5 * stress * strain
Interpret a stress-strain graph
Before the limit of proportionality (P), the graph is a straight line through the origin, therefore obeying Hooke’s law. After P, the graph starts to bend, after which the material stops obeying Hooke’s law but would return to its original shape once the force is removed. Elastic limit (E) is the point at which the material behaves plastically, after this point, the material no longer returns to its original shape.
The Yield Point (Y) is where the material starts to stretch without any extra load. It is the stress at which a large amount of plastic deformation takes place with constant or reduced load.
How are force-extension graphs different to stress-strain graphs?
Force-extension graphs are specific for the object tested and depend on its dimensions (like its length or diameter). Stress-strain graphs describe the general behaviour of the material because stress and strain are independent of dimensions.
What is the property of the unloading line on a force-extension graph?
It is parallel to the loading line because the stiffness, k, is constant - the forces between atoms are the same as they were during the loading.
If the wire is stretched beyond its elastic limit, the unloading line does not go through the origin.
What does the area between the loading and unloading lines on a force-extension graph mean?
The work done to permanently deform the wire
What does the stress-strain graph look like for a brittle material?
Straight line through the origin.
When the line reaches a certain point, the material snaps, it doesn’t deform plastically
What does the force-extension graph look like for brittle materials?
Similar to stress-strain graphs. No plastic deformation, the line reaches a point at which the material fractures
What is the property of brittle materials?
When you apply a force to a brittle material, it won’t deform plastically, but suddenly snap when stress gets to a certain size. They can be weak if they have cracks in them
What is the structure of brittle materials like?
The arrangement in things like ceramics is crystalline or polycrystalline (where there are many grains of crystalline structure). The atoms in each grain line up in a different direction. The atoms in ceramics are bonded in a giant rigid structure, with strong bonds between atoms to make them stiff, while the rigid structure makes the brittle. When stress is applied, any tiny cracks at the material’s surface get bigger and bigger until the material breaks completely, called brittle fracture - the cracks are able to grow because these materials have a rigid structure. Non-brittle materials are not brittle because atoms in them can move to prevent cracks getting bigger.
What is the young modulus definition?
A material’s ability to withstand changes in length with an added load
