3.4 Materials

Question 1

What is the elastic limit of a spring and what type of deformation occurs before and after this point?

Answer 1

• The elastic limit is the maximum a spring is able to stretch before its original length is changed.
• Before the elastic limit, the spring undergoes elastic deformation. If the tensile resultant force is removed, it will go back to its original length.
• After the elastic limit, the spring undergoes plastic deformation. If the resultant force is removed, it will no longer go back to its original length.

Question 2

What is Hooke’s law and when does it apply?

Answer 2

• The extension of the spring is directly proportional to the force applied.
• This is true before the elastic limit is reached, during elastic deformation.

Question 3

What does the force-extension graph for a spring look like?

Answer 3

• The graph is a straight line going through the origin up until the elastic limit, obeying Hooke’s law.
• After the elastic limit, the graph plateaus and does not obey Hooke’s law.

Question 4

How can you calculate the work done on a material from its force-extension or force-compression graph?

Answer 4

The work done is the area under the graph.

Question 5

What is tensile stress?

Answer 5

• The force applied per unit cross-sectional area of the wire.
• σ=F/A

Question 6

What is tensile strain?

Answer 6

• The fractional change in the original length of the wire.
• ε = x/L

Question 7

What is ultimate tensile strength?

Answer 7

• The maximum stress a material can withstand before it breaks.
• This is the highest peak on a stress-strain graph.

Question 8

What is the Young modulus?

Answer 8

• The ratio of stress to strain of a material, which is constant.
• E=σε
  = This is the gradient of a stress-strain graph.

Question 9

What does the stress-strain graph of a ductile material look like?

Answer 9

• Undergo elastic deformation up to the elastic limit, then plastic deformation.
• Can withstand large amounts of plastic deformation before breaking.

Question 10

What does the stress-strain graph of a brittle material look like?

Answer 10

• Undergoes elastic deformation until its breaking point.
• No plastic deformation.
• Loading and unloading curves are the same.

Question 11

What does the stress-strain graph of a polymeric material look like?

Answer 11

• Can endure a lot of tensile stress before breaking.
• No plastic deformation, but the loading and unloading curves are different, due to energy lost to heat.

Question 12

What is the area under a stress-strain graph?

Answer 12

Energy stored or work done per unit volume.