Introduction to Stress-Strain Diagrams
A Tool for Understanding Material Behavior under Load
May 6, 2009
Two of the important concepts in strength of materials calculations are stress and strain. Stress is the intensity of an applied force over a specific area. If a load of 100 pounds is applied axially to a square rod with a cross-section of one square inch, the axial stress is 100 pounds per square inch.
Strain is the representation of extension or compression of a component under load. Strain is dependent on the geometry of the part and the material properties of the part, and is defined as the change in length of the part divided by the original length.
Strain is technically a unit-less quantity, but because strains are generally very small, they are often quantified using the term micro-strain, or the strain amount multiplied by 1 million. Conventionally, parts in tension exhibit positive strain or stress, and parts in compression exhibit negative strain or stress.
What is a Stress-Strain Diagram?
A stress-strain diagram is a graph that represents how a part behaves under an increasing load, and is often used by engineers when selecting materials for specific designs. A stress-strain diagram generally contains three parts:
- Elastic Deformation – The elastic deformation portion of the stress-strain diagram is generally represented as a linear relationship between stress and strain. If the load is released while the specimen is in the elastic deformation zone, it will return to its original dimensions.
- Plastic Deformation – In the plastic deformation portion of the stress-strain diagram, the specimen begins to yield. The maximum strength of the specimen occurs in this zone, and the carried load begins to drop off as the deformation increases. The specimen endures some permanent deformation that remains after the load is released.
- Rupture – The point at which a specimen breaks into two parts
Stress-strain diagrams are generated experimentally through the performance of controlled tensile tests using precisely fabricated test specimens. The applied load and displacement are monitored during the test, and are used to calculate stress and strain, respectively.
What Properties do Stress-Strain Diagrams Illustrate?
Ductile materials will have a far longer plastic deformation zone than brittle materials, as shown in the figure below. The specimen continues to hold load because the plastically deformed material undergoes strain hardening. Ductile materials will also exhibit significant narrowing at one portion of the specimen as the length increases until rupture occurs.
A stress-strain curve can also be used to determine the yield strength of a specimen. Yield strength is defined at the stress level at which the part achieves a 0.2% permanent deformation, as shown in the figure below.
Stress-strain curves exist for a variety of materials and alloys, allowing engineers to select the right material for their particular application.
Source
Beer, F., Johnston, E.R., Mechanics of Materials, Second Edition, McGraw-Hill, 1992.
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