1. Describing deformation
Deforming Solids
Stretching a spring
Stretching materials
Describing deformation
Strain energy

2. Stretching a Spring
A pair of forces are needed to change the shape of the spring
Compressive
Tensile
Stiffness of the spring
Load
Extension
Hooke’s Law

3. Hooke’s Law Slope = force/extension Slope = spring constant k= F/x
F = k x

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. Elastic Limit

6. Elastic versus Plastic
Elastic Behaviour
Material has the ability to go back to its original shape when the force is removed

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

8. Stretching Materials Stress
Measure of force required to cause a particular deformation
Stress =
load (or force) / cross-sectional area

9. Stretching Materials Stress Stress (solids) = Pressure (fluids)
Units: N/m2 ̴ Pascal, Pa
Tensile stress
= Tensile Force/ Cross-sectional Area

10. Stretching Materials Strain Resulting deformation Tensile Strain =
extension/original length
Dimensionless quantity

11. Stretching Materials

12. Stretching Materials Young Modulus, Y
Ratio of tensile stress to tensile strain
Y = stress/strain
Units: Nm-2 ≈Pa

13. Young Modulus

14. Materials

15. 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

16. Stress-Strain curve
1. Ultimate strength 2. Yield strength 3. Rupture 4. Strain hardening region 5. Necking region.

17. Measuring Young Modulus

18. Measuring Young Modulus

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

20. Describing Deformation
Curve B is a strong material which is not ductile.
Brittle but deforms before breaking
Example is steel

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

22. Describing Deformation
Curve D is a plastic material.
Example is polyethylene

23. Stiffness vs. strength
Stiffness tells us about the elastic behavior of the material.
Strength tells us about how much stress is needed to break the material

24. Ultimate Tensile Stress

25. Materials

26. Materials

27. Materials

28. Strain Energy

29. Strain Energy