Final answer:
True strain is calculated using the formula B) ln(d/D), where d is the final diameter and D is the original diameter. This uses the natural logarithm to express the relative change in diameter due to deformation. Therefore, the correct answer is option B) ln(d/D)
Step-by-step explanation:
In engineering and specifically in the context of material science, true strain is calculated using the natural logarithm (ln) when considering changes in the diameter of a material under deformation.
The formula for true strain using natural log when considering an original diameter, D, and a final diameter, d, is B) ln(d/D). This is because strain is defined as the natural logarithm of the ratio of the current dimension to the original dimension. In this case, the dimension we are concerned with is the diameter.
So, when a material undergoes deformation, we are interested in how the diameter changes, which can be expressed in terms of natural logarithm as ln(d/D), where d is the final diameter and D is the original diameter.
According to the properties of logarithms, the logarithm of the number resulting from the division of two numbers is the difference between the logarithms of the two numbers, hence ln(d) - ln(D) simplifies to ln(d/D).
Therefore, the correct answer is option B) ln(d/D)