Deformation Of Solids

This lesson covers: 

  1. Stress-strain graphs for ductile materials and their key features.
  2. Stress-strain graphs for brittle materials and how to interpret them.
  3. How to compare the strength and stiffness of different materials.
  4. Characteristics of polymeric stress-strain graphs.

Stress-strain graphs for ductile materials

Ductile materials, such as copper, are capable of being shaped or bent without breaking. The stress-strain graph for these materials typically shows a curve, reflecting their ability to stretch and deform. A notable characteristic is that these graphs do not show a sudden breaking point.

Graph showing the stress-strain relationship for ductile materials, indicating an initial straight line followed by a curve without a sudden breaking point.

Key features:

  • An initial straight line portion indicating the material's obedience to Hooke's Law.
  • Beyond the proportional region, the material experiences a large strain for small increases in stress.
  • Beyond the yield point, the material experiences noticeable deformation.

Worked example - Comparing strength and stiffness of two materials

Compare the strength and stiffness of the two materials labelled A and B.

Graph comparing the stress and strain of two materials with material A breaking at 400 MPa and material B breaking at 300 MPa.

Step 1: Assessing Strength

Strength is indicated by the stress level at which a material breaks.

  • Material A: Breaks at 400 MPa.
  • Material B: Breaks at 300 MPa.


Material A has a higher breaking stress (400 MPa) compared to Material B (300 MPa), indicating that Material A is stronger.


Step 2: Determining Stiffness

Stiffness relates to how much strain a material experiences under a given stress. A more stiff material will show less strain.

  • Material A: Strain at breaking point is 0.02.
  • Material B: Strain at breaking point is 0.03.


Since Material A undergoes a lower strain (0.02) compared to Material B (0.03) for the same stress, it is stiffer.


Conclusion:

Material A is both stronger and stiffer than Material B.

Brittle material stress-strain graphs

Graph showing the stress-strain relationship for brittle materials, with stress on the y-axis and strain on the x-axis, ending abruptly at fracture.

Brittle materials, like glass, tend to break without significant plastic deformation. Their stress-strain graphs typically:

  • Initially obey Hooke's law.
  • Abruptly end at the breaking stress, indicating a sudden failure.

Comparing material strength and stiffness

Graph showing stress versus strain for materials with different properties: stiff and strong, stiff and weak, strong and less stiff, and weak and less stiff.

Key points:

  • Stronger materials can withstand higher stresses before breaking.
  • Stiffer materials exhibit less strain for a given stress.
  • Strength and stiffness are distinct and independent properties of a material.


Polymeric stress-strain graphs

Polymers, like rubber and polythene, consist of long chain molecules, giving them unique stress-strain graph characteristics:

Graph showing stress versus strain for polymers with loading and unloading curves and energy lost as heat.

Key points:

  • Rubber typically displays elastic behaviour.
  • Polythene experiences plastic deformation.
  • Energy loss in polymers is evident in the area between the loading and unloading curves.