# Deforming Solids.

## Presentation on theme: "Deforming Solids."— Presentation transcript:

Deforming Solids

Stretching a spring Strain energy Stretching materials Describing deformation

Stretching a Spring

Hooke’s Law states that
The extension is proportional to the force The spring will go back to its original length when the force is removed So long as we do not exceed the elastic limit

Graphs

Interpreting Graph Strain Energy

Strain Energy Stored ability to do work due to stretching or compression or displacement 𝑬 𝒔 = 𝟏 𝟐 𝐤 𝒙 𝟐

Combination of Springs

Deformation of Rubber Band
Hysteresis

Deformation of Rubber Band
Hysteresis

Elastic versus Plastic
Elastic Behaviour Material has the ability to go back to its original shape Elastic Limit A point where beyond it the material is permanently deformed

Elastic versus Plastic
Plastic Behaviour Material has been permanently deformed but not broken

Describing Deformation
Stress Measure of force required to cause a particular deformation Force per unit area Pressure Units: Nm2 Pascal 𝑺𝒕𝒓𝒆𝒔𝒔= 𝑭 𝑨

Describing Deformation
Strain Resulting deformation Extension divided by original length Dimensionless quantity 𝑺𝒕𝒓𝒂𝒊𝒏= ∆𝑳 𝑳 𝒐

Testing Materials

Describing Deformation
Young Modulus, Y Ratio of tensile stress to tensile strain Units: Nm-2 Pascal 𝒀= 𝑺𝒕𝒓𝒆𝒔𝒔 𝑺𝒕𝒓𝒂𝒊𝒏 𝒀= 𝑭𝑳 𝒐 𝑨∆𝑳

Some interesting values of Young Modulus
DNA                                       ~ 108  Pa spaghetti (dry)                    ~ 109  Pa cotton thread                  ~ 1010 Pa plant cell walls                    ~ 1011 Pa carbon fullerene nanotubes  ~ 1012 Pa

Materials

Graph

Interpreting Graph Slope = Young Modulus Ultimate Tensile Stress
Maximum stress a material can withstand before breaking Slope = Young Modulus

Measuring Young Modulus

Measuring Young Modulus

Measuring Young Modulus

Measuring Young Modulus

Describing Deformation
Curve A shows a brittle material. Strong The fracture of a brittle material is sudden and catastrophic Example: cast iron

Describing Deformation
Curve B is quite brittle and slightly ductile Brittle but deforms before breaking Example: steel

Describing Deformation
Curve C is a ductile material Deforms permanently Drawn into thin wires Examples are copper and gold

Describing Deformation
Curve D is a plastic material. Deforms permanently Deformation is not proportional to stress applied Example is polyethylene

Materials