True stress, which measures the actual force acting on a material’s cross-sectional area, and engineering stress, which divides the applied force by the original cross-sectional area, provide critical insights into material behavior. These concepts, along with strain and the true plastic strain, enable a comprehensive understanding of material deformation and failure. True stress and engineering stress differ because true stress accounts for the change in cross-sectional area during deformation, while engineering stress does not.
Engineering Stress vs. True Stress
The terms “engineering stress” and “true stress” are often used interchangeably, but they are actually two different concepts. Engineering stress is the force applied to a material divided by the original cross-sectional area of the material. True stress is the force applied to a material divided by the actual cross-sectional area of the material at the point where the force is applied.
The difference between engineering stress and true stress is important because it can affect the way that a material behaves. For example, a material that elongates under stress will have a lower true stress than a material that does not elongate. This is because the actual cross-sectional area of the material that is elongating is decreasing, which means that the force is being applied to a smaller area.
The following table summarizes the key differences between engineering stress and true stress:
| Property | Engineering Stress | True Stress |
|---|---|---|
| Definition | Force applied to a material divided by the original cross-sectional area | Force applied to a material divided by the actual cross-sectional area |
| Units | Pascals (Pa) or pounds per square inch (psi) | Pascals (Pa) or pounds per square inch (psi) |
| Effect of elongation | Decreases with elongation | Increases with elongation |
In general, engineering stress is used for calculations that involve the original cross-sectional area of a material, such as yield strength and ultimate tensile strength. True stress is used for calculations that involve the actual cross-sectional area of a material, such as stress-strain curves and fracture toughness.
Example
Consider a round bar of steel with a diameter of 10 mm. The bar is subjected to a tensile load of 10,000 N.
The engineering stress is calculated as follows:
Engineering stress = Force / Original cross-sectional area
Engineering stress = 10,000 N / (π * (5 mm)^2)
Engineering stress = 636.6 MPa
The true stress is calculated as follows:
True stress = Force / Actual cross-sectional area
True stress = 10,000 N / (π * (4.9 mm)^2)
True stress = 674.5 MPa
As you can see, the true stress is slightly higher than the engineering stress. This is because the actual cross-sectional area of the bar decreases as it elongates under load.
Question 1:
How do true stress and engineering stress differ in their calculation?
Answer:
True stress is calculated using the current cross-sectional area of the specimen, while engineering stress uses the original cross-sectional area.
Question 2:
What is the significance of the difference in calculation between true and engineering stress?
Answer:
True stress provides a more accurate representation of the actual stress on the material, as it accounts for the changes in cross-sectional area due to plastic deformation.
Question 3:
In what situations is it appropriate to use true stress instead of engineering stress?
Answer:
True stress is more suitable for situations where large plastic deformation occurs, such as in the analysis of ductile materials and in the design of components subjected to significant plastic strain.
And there you have it, folks! Whether you’re designing a skyscraper or just taking a leisurely stroll, true stress and engineering stress are essential concepts to understand. They give us a deeper appreciation for the forces at play around us. Thanks for joining me on this stress-filled adventure. I’ll be here waiting whenever you need a refresher or want to dive further into the world of stress and mechanics. Until then, keep exploring and stay curious!