Unit 1 Key Facts- Materials

•Hooke’s Law•Force extension graph•Elastic energy•Young’s Modulus•Properties of materials

Hooke’s Law

• For a spring or elastic substance:

Force applied = - k x Δx

Force ‘constant’ kIt is a property of the thing being stretched

The extension in the object= final length – original length

Hooke’s Law... For the visual learner: original length

Fixed end object of force constant k

force

Final length

Extension Δx

Force-extension Graphs

extension

Force

O

Hooke’s law applies, returns to original length when force removed

Elastic regionF proportional to ΔxUp to limit of proportionality

Elastic limit

Plastic region – here permanent deformation occurs,

Yield point: Small force results in large extension

Maximum force = upper tensile strength

Value of force at which sample fails

Elastic potential energy

When an elastic object is stretched it stores elastic potential energy

Elastic potential energy =0J

Force F

Extension Δx

Elastic potential energy = ½ FΔ x

Elastic potential energy is the area under the linear sections of a force-extension graph. Also related to k, EPE = ½ k Δ x2

Stress

• Stress (σ )is the force applied to a material per unit area

• σ = Force ÷ area (units Pa)• It can be tensile (stretching)• Or compressive (squashing)• Some materials are strong in compression but weak in tension (brick)

STRAIN

• Strain is the ration of extension to original length of a material

ε = Δ x ÷ x (no units it is a ratio)

Young’s Modulus

• Young’s modulus E is the ration of stress to strain

• E = σ ÷ ε (Units Pa same as stress)• It can be found from gradient of

stress-strain plot• Also known as the stiffness of the

material

Stress-strain plot: look familiar?

strain

stress

O

Hooke’s law applies, returns to original length when force removed

Elastic regionF proportional to ΔxUp to limit of proportionality

Elastic limit

Plastic region – here permanent deformation occurs,

Yield point: Small force results in large extension

Maximum force = upper tensile strength

Tensile strength

Gradient of this plot is Young’s Modulus = E

Examples of graphsstress

strain

Elastic Young’s modulus E

Young’s modulus 2E: this material is stiffer

stress

strain

This material is brittle after elastic limitIt just breaks

Stiff and tough

ductile

Properties of materials

Properties of materials

Properties of materials