The yield stresses of several samples of a steel containing 0.12% carbon with different grain sizes were measured. The data are shown here.
Grain-Size Inverse
Sample d^(-1/2) [mm^(-1/2)] Yield Stress (MPa)
A 24 500
B 19 420
A 12 320
A 10 250
A 6 190
(a) calculate the grain size of each steel sample in micrometers.
(b) Which sample has the grain size of 27.7 micrometers?
(c) Fit these data to a straight line and calculate the constants sigma_0 and K for the Hall-Petch equation
(d) What is the grain size of the sample that has the highest yield strength?
(e) A sample of this steel with a 15 micrometer grain size is produced. What will be the yield stress of this sample?