The following data were obtained for a carbon steel and an aluminum alloy. Aluminum Alloy d...

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The following data were obtained for a carbon steel and an aluminum alloy. Aluminum Alloy d (um) 42 16 11 8.5 5 3.1 Carbon Steel d (um) 406 106 75 43 30 16 Oy (MPa) 93 129 145 158 189 233 Oy (MPa) 223 225 225 226 231 238 a) Show that the yield strengths of this steel and aluminum alloy obey the Hall-Petch Relationship (graph them). 1 y = + kd Determine and ky for each material. b) Certain microalloyed steels contain small additions of vanadium or niobium that permit the grain size to be reduced to about 2 m if the processing of the steel is carefully controlled. Similarly, advanced aluminum alloys containing special types of particles can be processed to yield a grain size of about 2 m. Suppose we reduce the grain size of steel and aluminum from 150 to 2 m by such processing. Would you expect a substantial increase in the strength of these materials as a result? Comment on your answer (use your fits from part a to guide your thinking.) The following data were obtained for a carbon steel and an aluminum alloy. Aluminum Alloy d (um) 42 16 11 8.5 5 3.1 Carbon Steel d (um) 406 106 75 43 30 16 Oy (MPa) 93 129 145 158 189 233 Oy (MPa) 223 225 225 226 231 238 a) Show that the yield strengths of this steel and aluminum alloy obey the Hall-Petch Relationship (graph them). 1 y = + kd Determine and ky for each material. b) Certain microalloyed steels contain small additions of vanadium or niobium that permit the grain size to be reduced to about 2 m if the processing of the steel is carefully controlled. Similarly, advanced aluminum alloys containing special types of particles can be processed to yield a grain size of about 2 m. Suppose we reduce the grain size of steel and aluminum from 150 to 2 m by such processing. Would you expect a substantial increase in the strength of these materials as a result? Comment on your answer (use your fits from part a to guide your thinking.)