Answer: the true strain in the rolling direction is approximately -0.693.
Step-by-step explanation:
To determine the true strain in the rolling direction, we can use the formula:
True Strain = ln(final thickness / initial thickness)
Given:
Initial width (W1) = 50 mm
Initial thickness (t1) = 1 mm
Final thickness (t2) = 0.5 mm
Final width (W2) = 52 mm
We can calculate the true strain as follows:
True Strain = ln(t2 / t1)
True Strain = ln(0.5 mm / 1 mm)
True Strain = ln(0.5)
Using natural logarithm (ln), we find that ln(0.5) is approximately -0.693.