Final answer:
Engineering stress is calculated using the initial cross-sectional area, while true stress is calculated using the actual reduced area after deformation. Engineering strain is the ratio of the change in length to original length, and true strain is the natural logarithm of the ratio of final to original length.
Step-by-step explanation:
Engineering Stress vs. True Stress
Engineering stress, also known as nominal stress, is the applied load divided by the initial cross-sectional area of the specimen. In the case of the low carbon steel, this would be calculated as the load applied (17,000 lb) divided by the area of the original cross-section. The area can be obtained using the diameter provided (0.500 in) by converting it into radius (0.500 in / 2) and applying the area formula for a circle (A = πr²).
On the other hand, true stress accounts for the decrease in cross-sectional area as the specimen is deformed. This would require us to recalculate the cross-sectional area using the reduced diameter under load (0.472 in) and use this new area to determine the true stress with the same load of 17,000 lb.
Engineering Strain vs. True Strain
Engineering strain is defined as the change in length divided by the original length. If the specimen undergoes some deformation, the change in length is the difference between the final and initial lengths. True strain, however, is the natural logarithm of the ratio of the final length to the original length, taking into account the continuous deformation of the material.
Calculating Stress and Strain
To find the engineering stress, use the formula:
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- Stress = Force / Initial Area
To find the true stress, the formula gets modified due to the changing area:
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- True Stress = Force / Actual Area under Load
For strain, the processes are similar:
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- Engineering Strain = Change in Length / Original Length
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- True Strain = ln(Final Length / Original Length)