The Stress Strain Curve is one of the most important tools in Structural Engineering. Every solid material has it’s own unique stress-strain curve. By understanding how to interpret the curve it can provide insights into how to better design products to survive loading.
Important Stress Strain Curve Definitions
Stress in structural engineering is a measure of the amount of force applied to a cross sectional area.
Strain in structural engineering is a measure of the a materials deformation compared to it’s original length.
The proportional limit is the area under the curve before the elastic limit is reached. In this area the hooke’s law may be applied.
The elastic limit is the point at which additional stress causes permanent deformation.
Yield Strength or Stress
The yield strength or stress is the stress at which the material will retain a 0.2% permanent elongation after the stress or force is removed.
Ultimate Strength or Stress
The ultimate strength or stress is the maximum amount of stress the material can withstand. Due to strain hardening material can withstand additional stress beyond the elastic limit. At this point continued static stress will lead to further deformation and fracture.
The fracture limit is the point at which a material will fail catastrophically through fracturing.
The elastic region is where if stress is released from the material, it will return to its original state.
The plastic region is where if stress is released from the material it will retain permanent deformation and strain hardening.
Strain Hardening occurs when a material experiences plastic deformation. During this the yield point is permanently moved to the right on the stress strain curve which leads to increasing the yield stress or hardening of the material.
Necking occurs after a material hits it’s ultimate strength or stress. At this point the cross sectional area starts shrinking within the necking region. While the stress in this region is technically still increasing since the cross sectional area is shrinking, as shown by the true stress strain curve, in engineering we ignore the reduced cross sectional area due to necking leading to a decrease in stress, as shown by the engineering stress strain curve.
Interpreting the Stress Strain Curve
A materials ductility is determined by how long the plastic region tail is on the stress strain curve. This dictates how much a material will plastically deform or yield prior to failure.
One use of ductile materials such as low carbon steel is in structures to increase the safety of occupants by increasing the time a structure will deflect significantly prior to catastrophic collapse allowing occupants a greater chance to escape unharmed.
A materials total energy dissipation is determined by the total area under the curve. When a material experiences plastic deformation this area is decreased as the yield point moves to the right. A materials total energy dissipation is critical for a lot of different applications including rocket valve design, earthquake engineering and more.
While engineers typically try to design within the elastic limits of a material, for some applications make this exceedingly expensive leading to the desire to allow plastic deformation making understanding the total available energy dissipation critical to understand for repeat loading or use.
ASR is a mechanical and aerospace engineering firm that specializes in engineering design and analysis. If you are in need of engineering services then contact us today to speak to one of our experienced engineers for a free quote on your project!