The __area under__ a force-extension (or compression) graph gives the __work done.__ This is transferred to __elastic potential__ __energy__ within the material.

Elastic potential energy is given by:

__Tensile stress__ is defined as the force applied per unit cross sectional area of the wire. The unit of stress is __pascals.__

__Tensile strain__ is the fractional change in the original length of the wire. Strain is a ratio so has no units.

Within the limit of proportionality, stress is directly proportional to strain, The ratio of stress to strain for a particular material is constant and is known as the __Young modulus, E.__

The unit of Young modulus is the same as stress, __Pa__ or Nm^{-2}. It is equivalent to the __gradient__ of the linear region of the stress-strain graph and a __property of a material__, not an object.

__Stress-strain graph features:__

__Limit of proportionality, P:__the point up to which the material obeys Hooke’s Law (the graph is linear).__Elastic limit, E:__the point up to which the stress can be increased before the onset of permanent, plastic deformation,__Yield points, Y1 and Y2:__points where the material extends rapidly.__Ultimate tensile strength, UTS:__the maximum stress a material can withstand when being stretched before breaking. Beyond this point, the material may become longer and thinner at its weakest point (necking) before eventually snapping.__Breaking point, B:__the point at which the material snaps.__Breaking strength:__the stress vale at the point of fracture.

__Characteristics of matter:__

__Strong:__a strong material that has a high UTS.__Stiff:__a material with a large Young’s modulus (and large force constant). Large gradient on stress-strain graph.__Brittle:__shows elastic behaviour up to its breaking point, without plastic deformation. Breaks when linear region ends.

Break due to spreading of cracks.

__Ductile:__can be drawn into a wire, so shows plastic deformation. Linear region ends quickly.__Polymeric:__consists of long molecular chains. Behave differently depending on structure and temperature. Can stretch a great deal before breaking, but may show elastic or plastic behaviour.__Tough:__deforms plastically to reduce the spread of cracks. Requires a large amount of work (area under forceextension graph) to break.__Hard:__resistance to scratching and surface indentation.

__Types of deformation:__

__Elastic:__returns to original length when force causing deformation is removed.

__Plastic:__ permanent deformation/extension. Doesn’t return to original length when force is removed. Flow, slip or slide internally before breaking.