1. Chapter 7
Deforming Solids

2. Understand how tensile and compressive forces cause deformation
Be able to describe the behaviour of springs and understand Hooke’s law
Define and use stress, strain, and the Young modulus
Describe an experiment to measure the Young modulus
Be able to distinguish elastic and plastic deformation
Demonstrate knowledge of force-extension graph for typical ductile, brittle and polymeric materials and be able to deduce the strain energy
Objectives

3. Compressive and tensile forces
A PAIR of forces are needed to change the shape of a spring
When a spring is being squashed the forces are compressive, being pushed together
When a spring is being stretched the forces are tensile, being pulled apart.
When you bend a wire, some parts will be shorter and compressed, while others will stretched and under tension.
When a spring is hanging with a load on it, the increase in the length of the spring is called the EXTENSION.
Compressive and tensile forces

4. You plot the results of experiment by putting the extension on the horizontal axis and force on the vertical
The gradient of the straight portion becomes the quantity known as the force constant of the spring
Force constant = k = Newtons per meter
K = F/x
Spring constant = force/extention
Hooke’s Law

5. Hooke’s law and elastic limit
A stiffer spring (one that does not compress or undergo tension easily) will have a large value for the spring constant
Beyond a certain point, if a force is applied the spring will be permanently deformed, it has stretched beyond its elastic limit.
Hooke’s law – the extension produced in a material is proportional to the applied force (load). This is true of the material as long as the elastic limit is not exceeded.
Hooke’s law and elastic limit

6. Investigating springs (your lab)
Springs can be combined in different ways
End to end (series)
Side by side (parallel)
In the experiment you will predict the outcome
If the spring constant of a single spring is k, what will be the equivalent force constant of the two setups?
Investigating springs (your lab)

7. Strain is defined as the fractional increase in the original length of a wire
Strain = extension/ original legnth
Strain = x/L
The unit is a ratio (so %)
Stress is the force applied per unit cross-sectional area of a wire
Stress = force/ cross-sectional area
Stress = F/A (measured in Pa)
Stress and strain

8. The ratio of stress to strain is called the Young Modulus of the material
E = σ/ε (sigma/epsilon) stress/strain
E is measured in Pa
Young Modulus

9. Determining Young Modulus
Metals are not very elastic, most can only be stretched 0.1% of their original length
To get the Young modulus of metal certain things should be done
Use a long thin wire
Extensions must be measured in meters from millimeters (very accurate
To ensure accuracy, make sure you can do both
Get a very accurate measurement of the cross sectional area (using a micrometer screw gauge capable of +_ 0.01mm)
Determining Young Modulus

10. Determining Young Modulus
Other materials like glass and plastic are stiff and brittle, making them difficult to measure
Rubber can stretch, but their young modulus line is not straight, thus not very accurate
Determining Young Modulus

11. Describing Deformation
Glass and Cast iron
Both are brittle, they stretch slightly before they break
They have elastic behavior, before they break, they return to their original position
Copper, Gold
When these materials are stretched beyond their elastic limit, they do not return to their original length after the load is removed. Plastic Deformation
These metals are described as ductile, able to be stretched bent, shaped. Iron is as well, but cast iron is not because of added carbon.
Describing Deformation

12. Deformation continued
Polythene, Perspex
Different polymers behave differently depending on structure and temp.
Polythene (plastic bags) have plastic deformation, but eventually becomes stiff and brittle. Behavior like ductile metal
Perspex (acrylic glass) Brittle, stretches then breaks
Rubber
Rubber chords start off easy to stretch, but then becomes more difficult
When the load is released on rubber, it does not return to its original length by the same path. Elastic hysteresis
Work causes a rise in temperature, affecting the spring constant.
Deformation continued

13. Elastic – return to their original length when the force is removed.
Brittle materials break at their limit
Ductile become permanently deformed if they are stretched beyond their elastic limit, they have plastic behavior
summary

14. Strength of a material tells us about how much stress and strain is needed to break the materials.
The value of breaking stress is called the Ultimate tensile stress.
Brittle materials the UTS is the stress at the breaking point
Strength of a material

15. Elastic Potential Energy
The energy in a deformed solid, if the material has been strained elastically, the energy can be recovered
Work has been done to move atoms against each other, creating some heat.
Elastic potential energy can be determined using a force extension graph.
Elastic Potential Energy

16. Finding Elastic potential energy
Using the linear region of a graph where Hooke’s law is obey Used with the GRAPH
Method 1 E = final force/2 x extention
Method 2 = area = ½ base x height
1/2Fx
The work done in stretching and compressing a material is always equal to the area under the graph of force against extention.
Finding Elastic potential energy

17. Elastic potential energy found with spring constant
Elastic potential energy = 1/2Fx = ½ x kx x x
Elastic potenial energy = 1/2kx2
Elastic potential energy found with spring constant