1. Deforming Solids

2. Stretching a spring
Strain energy
Stretching materials
Describing deformation

3. Stretching a Spring

4. 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

5. Graphs

6. Interpreting Graph
Strain Energy

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

8. Combination of Springs

9. Deformation of Rubber Band
Hysteresis

10. Deformation of Rubber Band
Hysteresis

11. 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

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

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

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

15. Testing Materials

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

18. 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

19. Materials

20. Graph

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

23. Measuring Young Modulus

24. Measuring Young Modulus

25. Measuring Young Modulus

26. Measuring Young Modulus

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

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

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

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

31. Materials